WO2017204750A1

WO2017204750A1 - Method of assessing a performance of an electrochemical cell, and apparatus thereof

Info

Publication number: WO2017204750A1
Application number: PCT/SG2017/050274
Authority: WO
Inventors: Rachid Yazami
Original assignee: Nanyang Technological University
Priority date: 2016-05-27
Filing date: 2017-05-29
Publication date: 2017-11-30

Abstract

There is provided a method of assessing a performance of an electrochemical cell including a cathode and an anode. The method includes: obtaining a full-cell thermodynamic data on the electrochemical cell; obtaining a cathode half-cell thermodynamic data and an anode half-cell thermodynamic data on the cathode and the anode, respectively; determining at least one relationship between a state of charge of at least one of the cathode and the anode in the electrochemical cell and a state of charge of the electrochemical cell based on the obtained full-cell thermodynamic data, the obtained cathode half-cell thermodynamic data, and the obtained anode half-cell thermodynamic data; and assessing the performance of the electrochemical cell based on the at least one relationship. There is also provided a corresponding apparatus for assessing a performance of an electrochemical cell, and a method of electrochemical cell regeneration based on the performance of the electrochemical cell determined.

Description

METHOD OF ASSESSING A PERFORMANCE OF AN ELECTROCHEMICAL CELL, AND APPARATUS THEREOF

[0001] This application claims the benefit of priority of Singapore Patent Application No. 10201604303T, filed 27 May 2016, the contents of which being hereby incorporated by reference in its entirety for all purposes.

TECHNICAL FIELD

[0002] The present invention generally relates to a method of assessing a performance of an electrochemical cell and an apparatus thereof.

BACKGROUND

[0003] Electrochemical cells, such as rechargeable batteries, are a fast growing area of research and development worldwide. Typical rechargeable batteries may include alkaline batteries, acid batteries, and lithium ion batteries (LIBs). Alkaline batteries may include Ni-Cd and Ni-MH (nickel-metal hydride) batteries. Acid batteries may include lead acid batteries. LIBs may now be the most commonly used batteries for a wide variety of applications, including portable electronics, electric mobility and energy storage. For example, LIB comprises a positive electrode (cathode) and a negative electrode (anode), which store and release lithium ion during battery charge and discharge operations. To operate at their maximum energy storage capability, both anode and cathode should store and release maximum amounts of lithium.

[0004] As an example based on LIB, one of the LIB performance indicators may be energy density (Wd)- Wd may be expressed in mass and volume by the following equations, respectively:

_W m ₌ QU_ _{(Wh kg})_; (Equation 1) m

and w_d =— (WM), (Equation 2) v where Q is the discharge capacity (Ah), U is the average discharge voltage (V), m is the total mass of the LIB (kg), and v is the total volume of the LIB (litre). In existing conventional LIB, W™ may range between about 100 to 250 Wh/kg and W™ may range between 300 and 700 Wh/1, depending on chemistry and cell engineering.

[0005] Accordingly, to increase Q, both the anode and cathode should operate at their maximum lithium storage capability. However, for example, there appears to be no existing practical and reliable method to determine whether the anode and cathode are operating at their maximum storage capabilities in a LIB cell. For example, there may exist methods used to assess the LIB's state of health, which relate to performance including energy density and power density. However, such existing methods do not assess whether the anode and cathode are operating at their maximum storage capabilities, such as assessing the amounts or percentages of anode and cathode that are actually being used in the LIB (i.e., utilization rate).

[0006] Although the above problems have been described based on LIB, similar or corresponding problem(s) also exist on other types of electrochemical cells, such as alkaline batteries, and acid batteries.

[0007] A need therefore exists to provide a method of assessing performance of an electrochemical cell and an apparatus thereof that seek to overcome, or at least ameliorate, one or more of the deficiencies of conventional methods or apparatuses. It is against this background that the present invention has been developed.

SUMMARY

[0008] According to a first aspect of the present invention, there is provided a method of assessing a performance of an electrochemical cell comprising a cathode and an anode, the method comprising:

obtaining a full-cell thermodynamic data on the electrochemical cell; obtaining a cathode half-cell thermodynamic data and an anode half-cell thermodynamic data on the cathode and the anode, respectively;

determining at least one relationship between a state of charge of at least one of the cathode and the anode in the electrochemical cell and a state of charge of the electrochemical cell based on the obtained full-cell thermodynamic data, the obtained cathode half-cell thermodynamic data, and the obtained anode half- cell thermodynamic data; and

assessing the performance of the electrochemical cell based on the at least one relationship.

[0009] In various embodiments, the at least one relationship is dependent on at least one parameter, and said determining at least one relationship comprises determining the at least one parameter based on a deviation between the obtained full-cell thermodynamic data and a computed full-cell thermodynamic data, the computed full-cell thermodynamic data being computed based on the obtained cathode half-cell thermodynamic data and the obtained anode half-cell thermodynamic data.

[0010] In various embodiments, the computed full-cell thermodynamic data is computed based on a difference between the obtained cathode half -cell thermodynamic data and the obtained anode half-cell thermodynamic data.

[0011] In various embodiments, the above-mentioned determining the at least one parameter comprises determining the at least one parameter through optimization such that the obtained cathode half-cell thermodynamic data and the obtained anode half-cell thermodynamic data when adjusted based on the determined at least one parameter minimize the deviation.

[0012] In various embodiments, each of the obtained full-cell thermodynamic data, the obtained cathode half-cell thermodynamic data, and the obtained anode half-cell thermodynamic data comprises a plurality of types of thermodynamic data.

[0013] In various embodiments, the plurality of types of thermodynamic data is selected from a group consisting of an open circuit potential data over a range of state of charge, an entropy data over a range of state of charge, and an enthalpy data over a range of state of charge, an entropy data over a range of open circuit potential, and an enthalpy data over a range of open circuit potential.

[0014] In various embodiments, the deviation comprises a plurality of deviations associated with the plurality of types of thermodynamic data, respectively, wherein the deviation associated with a type of the plurality of types of thermodynamic data is between the obtained full-cell thermodynamic data of the type and the computed full-cell thermodynamic data of the type, and the at least one parameter is determined based on the plurality of deviations associated with the plurality of types of thermodynamic data.

[0015] In various embodiments, the at least one parameter comprises a plurality of parameters, and the plurality of parameters are determined collectively based on the plurality of deviations associated with the plurality of types of thermodynamic data.

[0016] In various embodiments, the at least one relationship comprises a first relationship between the state of charge of the cathode in the electrochemical cell and the state of charge of the electrochemical cell, and a second relationship between the state of charge of the anode in the electrochemical cell and the state of charge of the electrochemical cell, and wherein the at least one parameter comprises a first parameter and a second parameter, the first relationship is dependent on at least the first parameter, and the second relationship is dependent on at least the second parameter.

[0017] In various embodiments, the first and second relationships are based on first and second linear functions, respectively, the first linear function being dependent on the first parameter and a third parameter, and the second linear function being dependent on the second parameter and a fourth parameter, and wherein the first, second, third, and fourth parameters are determined collectively based on the plurality of deviations associated with the plurality of types of thermodynamic data.

[0018] In various embodiments, the above-mentioned assessing a performance of the electrochemical cell comprises determining a utilization rate of the cathode in the electrochemical cell based on the first relationship, and/or determining a utilization rate of the anode in the electrochemical cell based on the second relationship.

[0019] In various embodiments, the above-mentioned assessing a performance of the electrochemical cell further comprises determining a composition range of an active chemical element in the cathode in the electrochemical cell based on the determined utilization rate of the cathode and/or determining a composition range of an active chemical element in the anode in the electrochemical cell based the determined utilization rate of the anode.

[0020] In various embodiments, the active chemical element in the cathode and/or the active chemical element in the anode is lithium. [0021] In various embodiments, the obtained full-cell thermodynamic data is based on a measurement of a full-cell open circuit potential on the electrochemical cell over a range of state of charge of the electrochemical cell, the obtained cathode half-cell thermodynamic data is based on a measurement of a half-cell open circuit potential on the cathode over a range of state of charge of the cathode, and the obtained anode half-cell thermodynamic data is based on a measurement of a half-cell open circuit potential on the anode over a range of state of charge of the anode.

[0022] According to a second aspect of the present invention, there is provided an apparatus configured for assessing a performance of an electrochemical cell comprising a cathode and an anode, the apparatus comprising:

a memory; and

at least one processor coupled to the memory and configured to:

obtain a full-cell thermodynamic data on the electrochemical cell; obtain a cathode half-cell thermodynamic data and an anode half- cell thermodynamic data on the cathode and the anode, respectively;

determine at least one relationship between a state of charge of at least one of the cathode and the anode in the electrochemical cell and a state of charge of the electrochemical cell based on the obtained full-cell thermodynamic data, the obtained cathode half-cell thermodynamic data, and the obtained anode half-cell thermodynamic data; and

assess the performance of the electrochemical cell based on the at least one relationship.

[0023] In various embodiments, the at least one relationship is dependent on at least one parameter, and said determine at least one relationship comprises determining the at least one parameter based on a deviation between the obtained full-cell thermodynamic data and a computed full-cell thermodynamic data, the computed full-cell thermodynamic data being computed based on the obtained cathode half-cell thermodynamic data and the obtained anode half-cell thermodynamic data.

[0024] In various embodiments, the computed full-cell thermodynamic data is computed based on a difference between the obtained cathode half -cell thermodynamic data and the obtained anode half-cell thermodynamic data. [0025] In various embodiments, the above-mentioned determining the at least one parameter comprises determining the at least one parameter through optimization such that the obtained cathode half-cell thermodynamic data and the obtained anode half-cell thermodynamic data when adjusted based on the determined at least one parameter minimize the deviation.

[0026] In various embodiments, each of the obtained full-cell thermodynamic data, the obtained cathode half-cell thermodynamic data, and the obtained anode half-cell thermodynamic data comprises a plurality of types of thermodynamic data.

[0027] In various embodiments, the plurality of types of thermodynamic data is selected from a group consisting of an open circuit potential data over a range of state of charge, an entropy data over a range of stage of charge, and an enthalpy data over a range of state of charge, an entropy data over a range of open circuit potential, and an enthalpy data over a range of open circuit potential.

[0028] In various embodiments, the deviation comprises a plurality of deviations associated with the plurality of types of thermodynamic data, respectively, wherein the deviation associated with a type of the plurality of types of thermodynamic data is between the obtained full-cell thermodynamic data of the type and the computed full-cell thermodynamic data of the type, and the at least one parameter is determined based on the plurality of deviations associated with the plurality of types of thermodynamic data.

[0029] In various embodiments, the at least one parameter comprises a plurality of parameters, and the plurality of parameters are determined collectively based on the plurality of deviations associated with the plurality of types of thermodynamic data.

[0030] In various embodiments, the at least one relationship comprises a first relationship between the state of charge of the cathode in the electrochemical cell and the state of charge of the electrochemical cell, and a second relationship between the state of charge of the anode in the electrochemical cell and the state of charge of the electrochemical cell, and wherein the at least one parameter comprises a first parameter and a second parameter, the first relationship is dependent on at least the first parameter, and the second relationship is dependent on at least the second parameter.

[0031] In various embodiments, the first and second relationships are based on first and second linear functions, respectively, the first linear function being dependent on the first parameter and a third parameter, and the second linear function being dependent on the second parameter and a fourth parameter, and wherein the first, second, third, and fourth parameters are determined collectively based on the plurality of deviations associated with the plurality of types of thermodynamic data.

[0032] In various embodiments, the above-mentioned assess a performance of the electrochemical cell comprises determining a utilization rate of the cathode in the electrochemical cell based on the first relationship, and/or determining a utilization rate of the anode in the electrochemical cell based on the second relationship.

[0033] In various embodiments, the above-mentioned assess a performance of the electrochemical cell further comprises determining a composition range of an active chemical element in the cathode in the electrochemical cell based on the determined utilization rate of the cathode and/or determining a composition range of an active chemical element in the anode in the electrochemical cell based the determined utilization rate of the anode.

[0034] In various embodiments, the active chemical element in the cathode and/or the active chemical element in the anode is lithium.

[0035] In various embodiments, the obtained full-cell thermodynamic data is based on a measurement of a full-cell open circuit potential on the electrochemical cell over a range of state of charge of the electrochemical cell, the obtained cathode half-cell thermodynamic data is based on a measurement of a half-cell open circuit potential on the cathode over a range of state of charge of the cathode, and the obtained anode half-cell thermodynamic data is based on a measurement of a half-cell open circuit potential on the anode over a range of state of charge of the anode.

[0036] According to a third aspect of the present invention, there is provided a computer program product, embodied in one or more computer-readable storage mediums, comprising instructions executable by at least one processor to perform the method of assessing a performance of an electrochemical cell described according to the first aspect of the present invention.

[0037] According to a fourth aspect of the present invention, there is provided a method of electrochemical cell regeneration, the method comprising: assessing a performance of an electrochemical cell comprising a cathode and an anode according to the method described according to the first aspect of the present invention; and

regenerating the anode and the cathode based on the performance of the electrochemical cell determined.

[0038] In various embodiments, the above-mentioned regenerating the anode and the cathode comprises:

determining a residual amount of an active chemical element in the anode based on the performance of the electrochemical cell determined;

transferring the residual amount of the active chemical element from the anode to an auxiliary electrode; and

transferring the residual amount of the active chemical element from the auxiliary electrode to the cathode.

BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Embodiments of the present invention will be better understood and readily apparent to one of ordinary skill in the art from the following written description, by way of example only, and in conjunction with the drawings, in which:

FIG. 1 depicts a schematic flow diagram of a method of assessing performance of an electrochemical cell according to various embodiments of the present invention;

FIG. 2 depicts a schematic drawing of an apparatus 200 configured for assessing performance of an electrochemical cell;

FIG. 3 depicts a schematic drawing of an exemplary computer system;

FIGs. 4A and 4B depict X-Ray diffraction (XRD) patterns of an anode and a cathode, respectively, according to various example embodiments of the present invention;

FIG. 4C depict an energy-dispersive X-ray spectroscopy results of the cathode of FIG. 4B, which shows an atomic ratio of about 1: 1 : 1: of Mn:Co:Ni; FIGs. 5A, 5B, and 5C depict representative voltage profiles of a full-cell, a cathode half-cell, and an anode half-cell, respectively, according to various example embodiments of the present invention;

FIGs. 6A, 6B, and 6C depict graphs of thermodynamic data of open circuit potential (OCP) vs state of charge (SOC), entropy vs SOC, and enthalpy vs SOC, respectively, of the full-cell during discharge, according to various example embodiments of the present invention;;

FIGs. 7A, 7B, and 7C depict graphs of thermodynamic data of OCP vs SOC, entropy vs SOC, and enthalpy vs SOC, respectively, of the cathode half-cell during discharge (reduction), according to various example embodiments of the present invention;

FIGs. 8A, 8B, and 8C depict graphs of thermodynamic data of OCP vs SOC, entropy vs SOC, and enthalpy vs SOC, respectively, of the anode half -cell during charge (oxidation), according to various example embodiments of the present invention;

FIGs. 9A, 9B, and 9C depict graphs of thermodynamic data of OCP vs SOC, entropy vs SOC, and enthalpy vs SOC, respectively, for both the measured full-cell thermodynamic data (labelled "full cell") and the computed full-cell thermodynamic data (labelled "cathode-anode") computed by subtracting the cathode half-cell thermodynamic data with the anode half-cell thermodynamic data, according to various example embodiments of the present invention;

FIGs. 9D and 9E depict graphs of thermodynamic data of entropy vs OCP and enthalpy vs OCP, respectively, for the measured full-cell thermodynamic data (labelled "full cell") and the computed full-cell thermodynamic data (labelled "cathode-anode") computed by subtracting the cathode half-cell thermodynamic data with the anode half- cell thermodynamic data, according to various example embodiments of the present invention;

FIGs. 10A, 10B, and IOC depict graphs of thermodynamic data of OCP vs SOC, entropy vs SOC, and enthalpy vs SOC, respectively, for the measured full-cell thermodynamic data (labelled "full cell"), the computed full-cell thermodynamic data (labelled "cathode-anode") computed by subtracting the cathode half-cell thermodynamic data with the anode half-cell thermodynamic data, and the adjusted full-cell thermodynamic data (labelled "adjusted") by shifting and stretching along SOC, according to various example embodiments of the present invention;

FIGs. 10D and 10E depict graphs of thermodynamic data of entropy vs OCP and enthalpy vs OCP, respectively, for the measured full-cell thermodynamic data (labelled "full cell"), the computed full-cell thermodynamic data (labelled "cathode-anode") computed by subtracting the cathode half -cell thermodynamic data with the anode half- cell thermodynamic data, and the adjusted full-cell thermodynamic data (labelled "adjusted") by shifting and stretching along SOC, according to various example embodiments of the present invention;

FIGs. 11A and 11B depict graphs of thermodynamic data of entropy vs SOC and enthalpy vs SOC, respectively, for the measured full-cell thermodynamic data (labelled "full cell"), the measured cathode half-cell thermodynamic data, and the measured anode half-cell thermodynamic data, according to various example embodiments of the present invention;

FIGs. 12A, 12B, and 12C depict graphs of thermodynamic data of OCP vs SOC, entropy vs SOC, and enthalpy vs SOC, respectively, for the measured full-cell thermodynamic data (labelled "full cell"), the computed full-cell thermodynamic data (labelled "cathode-anode") computed by subtracting the cathode half-cell thermodynamic data with the anode half-cell thermodynamic data, and the adjusted full-cell thermodynamic data (labelled "adjusted") by shifting and stretching along SOC, with respect to the full-cell and cathode and anode half-cells aged at 55 °C for 100 cycles, according to various example embodiments of the present invention;

FIGs. 12D and 12E depict graphs of thermodynamic data of entropy vs OCP and enthalpy vs OCP, respectively, for the measured full-cell thermodynamic data (labelled "full cell"), the computed full-cell thermodynamic data (labelled "cathode-anode") computed by subtracting the cathode half -cell thermodynamic data with the anode half- cell thermodynamic data, and the adjusted full-cell thermodynamic data (labelled "adjusted") by shifting and stretching along SOC, with respect to the full-cell and cathode and anode half-cells aged at 55 °C for 100 cycles, according to various example embodiments of the present invention; FIGs. 13A, 13B, and 13C depict graphs of thermodynamic data of OCP vs SOC, entropy vs SOC, and enthalpy vs SOC, respectively, for the measured full-cell thermodynamic data (labelled "full cell"), the computed full-cell thermodynamic data (labelled "cathode-anode") computed by subtracting the cathode half-cell thermodynamic data with the anode half-cell thermodynamic data, and the adjusted full-cell thermodynamic data (labelled "adjusted") by shifting and stretching along SOC, with respect to the full-cell and cathode and anode half-cells aged at 55 °C for 200 cycles, according to various example embodiments of the present invention;

FIGs. 13D and 13E depict graphs of thermodynamic data of entropy vs OCP and enthalpy vs OCP, respectively, for the measured full-cell thermodynamic data (labelled "full cell"), the computed full-cell thermodynamic data (labelled "cathode-anode") computed by subtracting the cathode half -cell thermodynamic data with the anode half- cell thermodynamic data, and the adjusted full-cell thermodynamic data (labelled "adjusted") by shifting and stretching along SOC, with respect to the full-cell and cathode and anode half-cells aged at 55 °C for 200 cycles, according to various example embodiments of the present invention;

FIGs. 14A, 14B, and 14C depict graphs of thermodynamic data of OCP vs SOC, entropy vs SOC, and enthalpy vs SOC, respectively, for the measured full-cell thermodynamic data (labelled "full cell"), the computed full-cell thermodynamic data (labelled "cathode-anode") computed by subtracting the cathode half-cell thermodynamic data with the anode half-cell thermodynamic data, and the adjusted full-cell thermodynamic data (labelled "adjusted") by shifting and stretching along SOC, with respect to the full-cell and cathode and anode half-cells aged at 55 °C for 300 cycles, according to various example embodiments of the present invention;

FIGs. 14D and 14E depict graphs of thermodynamic data of entropy vs OCP and enthalpy vs OCP, respectively, for the measured full-cell thermodynamic data (labelled "full cell"), the computed full-cell thermodynamic data (labelled "cathode-anode") computed by subtracting the cathode half -cell thermodynamic data with the anode half- cell thermodynamic data, and the adjusted full-cell thermodynamic data (labelled "adjusted") by shifting and stretching along SOC, with respect to the full-cell and cathode and anode half-cells aged at 55 °C for 300 cycles, according to various example embodiments of the present invention;

FIGs. 15A, 15B, and 15C depict graphs of thermodynamic data of OCP vs SOC, entropy vs SOC, and enthalpy vs SOC, respectively, for the measured full-cell thermodynamic data (labelled "full cell"), the computed full-cell thermodynamic data (labelled "cathode-anode") computed by subtracting the cathode half-cell thermodynamic data with the anode half-cell thermodynamic data, and the adjusted full-cell thermodynamic data (labelled "adjusted") by shifting and stretching along SOC, with respect to the full-cell and cathode and anode half-cells aged at 25 °C for 200 cycles, according to various example embodiments of the present invention;

FIGs. 15D and 15E depict graphs of thermodynamic data of entropy vs OCP and enthalpy vs OCP, respectively, for the measured full-cell thermodynamic data (labelled "full cell"), the computed full-cell thermodynamic data (labelled "cathode-anode") computed by subtracting the cathode half -cell thermodynamic data with the anode half- cell thermodynamic data, and the adjusted full-cell thermodynamic data (labelled "adjusted") by shifting and stretching along SOC, with respect to the full-cell and cathode and anode half-cells aged at 25 °C for 200 cycles, according to various example embodiments of the present invention;

FIGs. 16A, 16B, and 16C depict graphs of thermodynamic data of OCP vs SOC, entropy vs SOC, and enthalpy vs SOC, respectively, for the measured full-cell thermodynamic data (labelled "full cell"), the computed full-cell thermodynamic data (labelled "cathode-anode") computed by subtracting the cathode half-cell thermodynamic data with the anode half-cell thermodynamic data, and the adjusted full-cell thermodynamic data (labelled "adjusted") by shifting and stretching along SOC, with respect to the full-cell and cathode and anode half-cells aged at 25 °C for 300 cycles, according to various example embodiments of the present invention;

FIGs. 16D and 16E depict graphs of thermodynamic data of entropy vs OCP and enthalpy vs OCP, respectively, for the measured full-cell thermodynamic data (labelled "full cell"), the computed full-cell thermodynamic data (labelled "cathode-anode") computed by subtracting the cathode half -cell thermodynamic data with the anode half- cell thermodynamic data, and the adjusted full-cell thermodynamic data (labelled "adjusted") by shifting and stretching along SOC, with respect to the full-cell and cathode and anode half-cells aged at 25 °C for 300 cycles, according to various example embodiments of the present invention;

FIGs. 17A, 17B, and 17C depict graphs of thermodynamic data of OCP vs SOC, entropy vs SOC, and enthalpy vs SOC, respectively, for the measured full-cell thermodynamic data (labelled "full cell"), the computed full-cell thermodynamic data (labelled "cathode-anode") computed by subtracting the cathode half-cell thermodynamic data with the anode half-cell thermodynamic data, and the adjusted full-cell thermodynamic data (labelled "adjusted") by shifting and stretching along SOC, with respect to the full-cell and cathode and anode half-cells aged at 25 °C for 500 cycles, according to various example embodiments of the present invention;

FIGs. 17D and 17E depict graphs of thermodynamic data of entropy vs OCP and enthalpy vs OCP, respectively, for the measured full-cell thermodynamic data (labelled "full cell"), the computed full-cell thermodynamic data (labelled "cathode-anode") computed by subtracting the cathode half -cell thermodynamic data with the anode half- cell thermodynamic data, and the adjusted full-cell thermodynamic data (labelled "adjusted") by shifting and stretching along SOC, with respect to the full-cell and cathode and anode half-cells aged at 25 °C for 500 cycles, according to various example embodiments of the present invention;

FIGs. 18A and 18B depict graphs showing the upper and lower limits of x in

Li_xM0₂ and y in Li_yC₆ of a fresh cell and cells (HT100, HT200, and HT300) aged at 55 °C and aged at 25 °C, respectively, according to various example embodiments of the present invention;

FIGs. 18C and 18D depict graphs showing the utilization ratio of cathode and anode capacities of fresh cell and cells aged at 55 °C and aged at 25 °C, respectively. The values are calculated assuming the working compositional range for fresh anode in half- cell is 0 to 0.74 (275 mAh/g) and fresh cathode in half-cell is 0.47 to 0.92 (150 mAh/g);

FIG. 19 depicts a table showing computed parameters for various different cells, according to various example embodiments of the present invention; FIG. 20 depicts a flow diagram illustrating a method of improving or optimizing the performance of an electrochemical cell, such as a LIB cell, according to various example embodiments of the present invention;

FIG. 21 depicts a flow diagram illustrating another method of improving or optimizing the performance of an electrochemical cell, such as a LIB cell according to various example embodiments of the present invention;

FIG. 22 depicts a schematic drawing of an electrochemical cell according to various example embodiments of the present invention;

FIG. 23 depicts a flow chart illustrating a method of regenerating an electrochemical cell according to various example embodiments of the present invention;

FIGs. 24 and 25 depict schematic drawings illustrating electrochemical cell regeneration involving one buffer (auxiliary) electrode according to various example embodiments of the present invention;

FIG. 26 depicts a schematic drawing of an electrochemical cell comprising three electrodes, namely, a cathode, an anode, and an auxiliary electrode according to various example embodiments of the present invention;

FIG. 27 illustrates measurement results obtained in an experiment performed in relation to electrochemical cell regeneration according to various example embodiments of the present invention; and

FIG. 28 depicts a schematic drawing of a method of electrochemical cell regeneration according to various embodiments of the present invention.

DETAILED DESCRIPTION

[0040] Various embodiments of the present invention provide a method of assessing a performance of an electrochemical cell comprising a cathode and an anode, such as, but not limited to, an alkaline battery cell, an acid battery cell, and a lithium ion battery (LIB) cell. In various embodiments, the performance of an electrochemical cell may relate to the utilization rate of the cathode and/or anode in the electrochemical cell during operation, or in other words, the amount or percentage of the cathode's and/or anode's capability or capacity (e.g., maximum capacity) that is actually being used or utilized in operation. Accordingly, in various embodiments, assessing a performance of an electrochemical cell may interchangeably refer to assessing a condition or state of the electrochemical cell.

[0041] In various embodiments, an electrochemical cell refers to a device comprising of three major active materials/components, namely, anode, cathode, and electrolyte.

[0042] Anode is typically the electrode where an oxidation takes place. Oxidation is a loss of electron and can be schematized as: R_a→ O_a + n_ae, where R_a is the reduced form and O_a is the oxidized form of a chemical specie or used for the anode material. The anode may comprise a neutral or positively charged (cation) or negatively charged (anion), and n_a is the number of electron moles exchanged in the anode reaction per R_a mole. The anode is the negative pole of the cell during discharge.

[0043] Cathode is typically the electrode where a reduction (electron gain) takes place. The reaction is the reverse of oxidation, i.e., O_c + n_ce→ R_c, wherein O_c is the oxidized form and R_c is the reduced form of a chemical specie or used for the cathode material. The cathode may comprises a neutral or positively charged (cation) or negatively charged (anion), and n_c is the number of electron moles exchanged in the anode reaction per O_c mole. The cathode is the positive pole of the cell during discharge.

[0044] Electrolyte is an ionically conductive material, which functions to provide anions and cations needed for the electrode reactions to be achieved. The electrolyte usually comprises a solvent medium and a solute material such as a salt, an acid or a base. In some cases, the electrolyte changes composition as a result of the cell's charge and discharge, such as in lead-acid batteries where sulfuric acid is consumed during discharge: Pb + Pb0₂ + 2H₂S0₄→ 2PbS0₄ + 2H₂0.

[0045] Referring to LIBs as an example only and without limitation, LIBs are currently the main power source in a wide range of applications, including mobile electronics, electric vehicles and in stationary energy storage. During charge and discharge operations, lithium ions are shuttled between the anode and the cathode in the LIB cell through the electrolyte owing to, e.g., lithium intercalation/de-intercalation and/or alloying/de-alloying electrode processes among various electrode processes. Accordingly, lithium composition in anode and cathode varies with the LIB cell's state of charge (SOC). In an ideal cell design, the SOC of the full-cell and the SOCs of the anode and the cathode in the full-cell should be equal to the maximize energy storage performances. In practice, however, according to various embodiments of the present invention, it has been identified that the SOC of the full-cell does not match the SOCs of the anode and the cathode in the full-cell for various reasons, such as, but not limited to: 1) electrode processes causing irreversible active lithium losses, such as formation (and reformation) of a solid-electrolyte interphase (SEI) on the surfaces of anode and following thermal ageing, trapped lithium, and active material electrical disconnection, and 2) unbalanced anode and cathode active masses in cell starting from inception. Irreversible lithium losses cause the full-cell, hence anode and cathode in the full-cell to become lithium deficient. Therefore, according to various embodiments of the present invention, it has been identified that lithium composition ranges in the anode and cathode in the full-cell depart from the lithium composition ranges achieved or measured in the anode and cathode half-cells.

[0046] Lithium half-cells may contain excess metallic lithium so as to fully charge and discharge the working electrode (anode or cathode). Excess lithium may also compensate for lithium losses during cycling and ageing. In half-cells, the SOC of the working electrode may be determined by Coulomb counting and voltage measurements, with a lithium element (e.g., a lithium metal foil) being used as a counter and reference electrode. A full-cell (e.g., commercial full-cell), however, includes two-electrode cells whereby the voltage of the full-cell is the difference between the cathode and anode voltages. However, the voltage reading of the full-cell does not indicate or provide information on individual electrode voltages, and therefore, not on their compositions. In this regard, even if a reference electrode is used, the voltage composition relationship is not unequivocal (e.g., does not accurately or unambiguously indicate the composition based on the voltage reading) since, for example, electrodes such as a graphite anode or a lithium iron phosphate cathode possesses voltage plateaus over a wide range of lithium composition.

[0047] Various embodiments of the present invention provide a method of assessing a performance of an electrochemical cell comprising a cathode and an anode that seek to overcome, or at least ameliorate, one or more of the problems mentioned above. For example and without limitation, various embodiments of the present invention enable the utilization rate of the cathode and/or the anode in the electrochemical cell to be determined, based on which the performance of the electrochemical cell may be assessed (or identified or determined). In this regard, for example, a high utilization rate may indicate that the electrochemical cell has a good or corresponding high performance in operation. On the other hand, a low utilization rate may indicate that the electrochemical cell has a poor or corresponding low performance in operation. Various further embodiments of the present invention may also enable the composition range of an active chemical element (e.g., lithium) in the cathode and/or anode in the electrochemical cell (i.e., in the full-cell) during operation to be determined. In this regard, a composition range of the active chemical element determined to be smaller than expected (e.g., ideal or theoretical composition range, such as achieved on the anode and cathode half-cells) may indicate a reduced performance of the electrochemical cell (e.g., for a full-cell discharge, an amount of the active chemical element may still be retained in the anode, and the cathode is thus deficient of the amount of the active chemical element). On the other hand, a composition range of the active chemical element determined to be as expected (or substantially as expected) may indicate an optimal or near optimal performance of the electrochemical cell (e.g., operable at or near maximum capability or capacity).

[0048] Electrochemical thermodynamic measurement (ETM) techniques have been disclosed and have since been used as investigation method for electrode materials and full-cells. For example, ETM techniques have been disclosed in the following references, the contents of which being hereby incorporated by reference in their entirety for all purposes: Reynier et al., "Evolution of lithiation thermodynamics with the graphitization of carbons", J. Power Sources, 2006, 165(2), pages 552-558; Reynier et al, "Entropy of Li intercalation in LixCo02", Phys. Rev. 2004, B 70, pages 174304; Maher et al., "A thermodynamic and crystal structure study of thermally aged lithium ion cells", J. Power Sources, 2014, 261(0), pages 389-400; and Maher et al, "A study of lithium ion batteries cycle aging by thermodynamics techniques", J. Power Sources, 2014, 247, pages 527- 533. In ETM, temperature may be used as an additional parameter enabling entropy and enthalpy profiles to be obtained or achieved.

[0049] FIG. 1 depicts a schematic flow diagram of a method 100 of assessing a performance of an electrochemical cell comprising a cathode and an anode according to various embodiments of the present invention. The method 100 comprises a step 102 of obtaining a full-cell thermodynamic data on the electrochemical cell, a step 104 of obtaining a cathode half-cell thermodynamic data and an anode half-cell thermodynamic data on the cathode and the anode (i.e., as cathode and anode half-cells), respectively, a step 106 of determining at least one relationship between a state of charge (SOC) of at least one of the cathode and the anode in the electrochemical cell and a SOC of the electrochemical cell based on the obtained full-cell thermodynamic data, the obtained cathode half-cell thermodynamic data, and the obtained anode half-cell thermodynamic data, and a step 108 of assessing performance of the electrochemical cell based on the at least one relationship.

[0050] In various embodiments, the state of charge (SOC) of an electrochemical cell may refer the amount which the electrochemical cell is charged based on its maximum capacity. For example, the amount may be expressed as a percentage whereby a SOC of 0% may indicate that the electrochemical cell is fully discharged, a SOC of 100% may indicate that the electrochemical cell is fully charged, and a SOC of an amount therebetween may indicate that the percentage which the electrochemical cell is charged based on its maximum capacity. Therefore, the SOC of the electrochemical cell may be based on a ratio of a first value to a second value. In an example embodiment, the first value is a net amount of charge remaining in the electrochemical cell and the second value is a rated charge capacity of the electrochemical cell or a theoretical charge capacity of the electrochemical cell. In another example embodiment, the first value is a net amount of charge required to charge the electrochemical cell to a rated charge capacity of the electrochemical cell or to a theoretical charge capacity of the electrochemical cell and the second value is the rated charge capacity of the electrochemical cell or the theoretical charge capacity of the electrochemical cell.

[0051] In various embodiments, the SOC of the cathode and/or the SOC of the anode in the electrochemical cell (i.e., in full-cell) may refer to those determined based on the at least one relationship with the SOC of the electrochemical cell.

[0052] In various embodiments, thermodynamic data (or thermodynamic parameter(s)) may refer to the measurement data captured from an ETM technique, such as any one of the ETM techniques disclosed in the references mentioned hereinbefore. For example, the thermodynamic data may comprise one or more types of thermodynamic data obtained on the full-cell and/or cathode and anode half-cells, such as but not limited to, an open circuit potential (OCP) data, an entropy data, and an enthalpy data. In various embodiments, the types of thermodynamic data may be selected from a group consisting of an open circuit potential data over a range of SOC, an entropy data over a range of SOC, an enthalpy data over a range of SOC, an entropy data over a range of open circuit potential, and an enthalpy data over a range of open circuit potential.

[0053] Accordingly, various embodiments of the present invention advantageously determine at least one relationship between a SOC of at least one of the cathode and the anode in the electrochemical cell and a SOC of the electrochemical cell, and thus, the performance of the electrochemical cell may be assessed based on the at least one relationship determined. Determining such a relationship advantageously addresses, or at least mitigates, the problem(s) or issue(s) associated with the deviation or discrepancy between the full-cell thermodynamic data obtained based on measurement on the electrochemical cell (e.g., may herein be referred to as "measured full-cell thermodynamic data" or "obtained full-cell thermodynamic data") and the computed full- cell thermodynamic data computed based on (e.g., a difference between) the cathode half-cell thermodynamic data and the anode half-cell thermodynamic data obtained (e.g„ may herein be referred to as "computed full-cell thermodynamic data"). In this regard, the cathode half-cell thermodynamic data and the anode half-cell thermodynamic data are obtained based on measurements on the cathode and anode half-cells, respectively.

[0054] In theory or in an ideal situation, the measured full-cell thermodynamic data should be the same as the computed full-cell thermodynamic data. However, for various factors such as those as mentioned hereinbefore, according to various embodiments of the present invention, it has been identified that misfits or deviations exist between the measured and computed full-cell thermodynamic data. Therefore, in various embodiments, it has been found that such misfits or deviations indicate that the anode and cathode in the electrochemical cell (i.e., in the full-cell) have lower performance (e.g., less utilization rate or smaller composition range of the active chemical element) than that achieved on the anode and cathode half-cells. Accordingly, the at least one relationship between a SOC of at least one of the cathode and the anode in the electrochemical cell and a SOC of the electrochemical cell determined advantageously enables the degree of misfits or deviations to be taken into account, and moreover, utilized advantageously to provide an indication of or information on the actual performance of the anode and cathode in the electrochemical cell, and thus the actual performance of the electrochemical cell.

[0055] In various embodiments, the at least one relationship is dependent on at least one parameter (or comprises at least parameter), and the step 106 of determining at least one relationship comprises determining the at least one parameter based on a deviation between the obtained full-cell thermodynamic data (e.g., corresponding to the "measured full-cell thermodynamic data" described hereinbefore) and a computed full-cell thermodynamic data (e.g., corresponding to the "computed full-cell thermodynamic data" described hereinbefore), the computed full-cell thermodynamic data being computed based on the obtained cathode half-cell thermodynamic data and the obtained anode half- cell thermodynamic data. In various embodiments, the computed full-cell thermodynamic data is computed based on a difference (e.g., an arithmetic difference) between the obtained cathode half-cell thermodynamic data and the obtained anode half-cell thermodynamic data.

[0056] In various embodiments, the at least one relationship comprises a first relationship between the SOC of the cathode (in the electrochemical cell) and the SOC of the electrochemical cell, and a second relationship between the SOC of the anode (in the electrochemical cell) and the SOC of the electrochemical cell. In this regard, the at least one parameter comprises a first parameter and a second parameter, and the first relationship is dependent on at least the first parameter (or comprises at least the first parameter), and the second relationship is dependent on at least the second parameter (or comprises at least the second parameter).

[0057] In various embodiments, the first and second relationships are based on first and second linear functions, respectively. In other words, the first and second relationships may be expressed as first and second linear functions or equations, respectively. In this regard, the first linear function may be dependent on the first parameter and a third parameter (or comprises the first parameter and a third parameter), and the second linear function is dependent on the second parameter and a fourth parameter (or comprises the second parameter and a fourth parameter). By way of example only and without limitation, the first and second linear functions may be expressed respectively as follows:

xca = tt_Ca^X fc + ea (Equation 3) X_m = a_mX_fc + _m (Equation 4) where X_c is the SOC of the electrochemical cell, X_ca is the SOC of the cathode in the electrochemical cell (determined based on the first relationship), a_ca is the first parameter, βεα is the third parameter, X_m is the SOC of the anode in the electrochemical cell (determined based on the second relationship), _an is the second parameter, and β_αη is the fourth parameter.

[0058] In various embodiments, the at least one parameter is determined through optimization such that the obtained cathode half-cell thermodynamic data and the obtained anode half-cell thermodynamic data when adjusted (or modified) based on the determined at least one parameter minimize the above-mentioned deviation (preferably optimally minimizes the above-mentioned deviation through the optimization process). Various optimization algorithms or techniques are known in the art and thus need not be described herein for clarity and conciseness. Various example optimization techniques will be mentioned by reference later below in example embodiments of the present invention.

[0059] In various embodiments, each of the full-cell thermodynamic data, the cathode half-cell thermodynamic data, and the anode half-cell thermodynamic data comprises a plurality of types of thermodynamic data.

[0060] In various embodiments, the plurality of types of thermodynamic data is selected from a group consisting of an open circuit potential data over a range of SOC, an entropy data over a range of SOC, and an enthalpy data over a range of SOC, an entropy data over a range of open circuit potential, and an enthalpy data over a range of open circuit potential. For example and without limitation, the range of SOC may be from 0% to 100%, 1 % to 99%, 3% to 97%, 5% to 95%, 10% to 90%, 20% to 80%, 30% to 70%, or smaller. The range of open circuit potential may be the range of open circuit potential obtained based on the range of SOC, or a subset thereof. [0061] In various embodiments, the above-mentioned deviation comprises a plurality of deviations associated with the plurality of types of thermodynamic data, respectively. In this regard, the deviation associated with a type of the plurality of types of thermodynamic data is between the obtained full-cell thermodynamic data ("measured full-cell thermodynamic data") of such a type and the computed full-cell thermodynamic data of such a type, and the at least one parameter is determined based on the plurality of deviations associated with the plurality of types of thermodynamic data.

[0062] In various embodiments, the at least one parameter comprises a plurality of parameters, such as the first to fourth parameters as mentioned hereinbefore, and the plurality of parameters are determined (e.g., optimized) collectively based on the plurality of deviations associated with the plurality of types of thermodynamic data.

[0063] By way of an example and without limitation, the plurality of types of thermodynamic data may comprise a thermodynamic data of a first type being an entropy data obtained or measured over a range of SOC and a thermodynamic data of a second type being an enthalpy data obtained or measured over a range of SOC. That is, in this example, full-cell entropy data and full-cell enthalpy data on the electrochemical cell are obtained or measured, and half-cell entropy data and half-cell enthalpy data on each of the cathode and anode half-cells are obtained or measured over a range of SOC. As will be described later in various example embodiments of the present invention, both the full- cell entropy data and the full-cell enthalpy data may be derived from full-cell open circuit potential data obtained based on a measurement of the full-cell open circuit potential on the electrochemical cell, and the half-cell entropy data and half-cell enthalpy data of the cathode or anode half-cell may similarly be derived from half-cell open circuit potential data obtained based on measurements of the half-cell open circuit potential on the respective cathode or anode half-cell.

[0064] However, as mentioned before, according to various embodiments of the present invention, it has been identified that misfits or deviations may exist between the measured full-cell thermodynamic data and the computed full-cell thermodynamic data. For example, following on from the above-mentioned example, a deviation (first deviation) may exist between the measured full-cell entropy data and the computed full- cell entropy data, and a deviation (second deviation) may exist between the measured full-cell enthalpy data and the computed full-cell enthalpy data. Accordingly, the actual SOCs of the anode and the cathode in the electrochemical cell (i.e., in the full-cell) may not match or correspond to the SOC of the electrochemical cell. To address or at least mitigate (or to compensate for) such a problem or issue, various embodiments of the present invention determine a relationship (first relationship) between the SOC of the cathode (in the electrochemical cell) and the SOC of the electrochemical cell, and a relationship between the SOC of the anode (in the electrochemical cell) and the SOC of the electrochemical cell, based on the first and second deviations, such that the actual or more accurate SOCs of the cathode and anode in the electrochemical cell may be determined for assessing the actual performance of the electrochemical cell. In this regard, the first and second relationships depend on a plurality of parameters and such parameters are determined collectively through optimization such that the obtained cathode half-cell thermodynamic data and the obtained anode half-cell thermodynamic data when adjusted based on the determined parameters minimizes the first and second deviations (preferably optimally minimizes). In various embodiments, such an adjustment may be referred to as a shifting and stretching process performed on the obtained cathode and anode half-cell thermodynamic data in view of the obtained full-cell thermodynamic data, for example, such that the computed full-cell thermodynamic data best matches the measured full-cell thermodynamic data, or to optimally minimize the deviation therebetween.

[0065] In various embodiments, the step 108 of assessing a performance of the electrochemical cell comprises determining a utilization rate of the cathode in the electrochemical cell based on the first relationship, and/or determining a utilization rate of the anode in the electrochemical cell based on the second relationship.

[0066] In various embodiments, the step 108 of assessing a performance of the electrochemical cell further comprises determining a composition range of an active chemical element in the cathode in the electrochemical cell based on the determined utilization rate of the cathode and/or determining a composition range of an active chemical element in the anode in the electrochemical cell based the determined utilization rate of the anode. By way of example and without limitation, the utilization rates of the cathode and the anode may be determined to correspond to the above-mentioned first and second parameters, respectively. Furthermore, with the determined utilization rates, the composition range of an active chemical element in the cathode and the composition range of an active chemical element in the anode may be derived as a fraction or a subset of the expected or ideal composition ranges (e.g., achieved at the respective half-cell). By way of an example only and without limitation, assuming the composition of the cathode at a fully discharge state is LiiNii/3Mm/3Coi/302 and the lithium composition range of Li of Li_xNii/3Mni/3Coi/302 in half-cell over 0% to 100% SOC range is or should be 0.46<x<l. In this example, if the cathode utilization rate of the cathode in the full-cell is determined to be 91%, the lithium composition range of the cathode in the full-cell may then be determined to be 0.46<x<0.95 (thus smaller than the expected or ideal composition range), which indicates that the cathode is lithium deficient. In various embodiments, the utilization rate of the cathode ( y_ca ) may be determined by, y_ca =

Δχ C/uii cell)

100——, -. Thus, if the cathode utilization rate is determined to be 91%, it may

Ax_ca(half cell) ^J

0 95-0 46

then be derived that 91% = 100 * ₁__{0 46} , ^and thus the lithium composition range may be determined to be 0.46<x<0.95. In this regard, the minimum "x" value of the lithium composition range of 0.46 is mostly fixed by the highest voltage of the full cell reached during charge (e.g., 4.2V in the example), whereas the highest "x" value at the end of discharge is fixed by lithium vacancies in the cathode due to lithium losses during cycling.

[0067] In various embodiments, the active chemical element in the cathode and/or the active chemical element in the anode is lithium. That is, in various embodiments, the electrochemical cell is a LIB cell.

[0068] In various embodiments, the obtained full-cell thermodynamic data ("measured full-cell thermodynamic data") is based on a measurement of a full-cell open circuit potential on the electrochemical cell over a range of SOC of the electrochemical cell, the obtained cathode half-cell thermodynamic data ("measured cathode half-cell thermodynamic data") is based on a measurement of a half -cell open circuit potential on the cathode over a range of SOC of the cathode (i.e., cathode half-cell), and the obtained anode half-cell thermodynamic data ("measured anode full-cell thermodynamic data") is based on a measurement of a half-cell open circuit potential on the anode over a range of SOC of the anode (i.e., anode half-cell).

[0069] FIG. 2 depicts a schematic drawing of an apparatus 200 configured for assessing a performance of an electrochemical cell comprising a cathode and an anode according to various embodiments of the present invention. The apparatus 200 comprises a memory 202, and at least one processor 204 coupled to the memory 202 and configured to: obtain a full-cell thermodynamic data on the electrochemical cell; obtain a cathode half-cell thermodynamic data and an anode half-cell thermodynamic data on the cathode and the anode (i.e., as cathode and anode half-cells), respectively; determine at least one relationship between a SOC of at least one of the cathode and the anode in the electrochemical cell and a SOC of the electrochemical cell based on the obtained full-cell thermodynamic data, the obtained cathode half-cell thermodynamic data, and the obtained anode half-cell thermodynamic data; and assess the performance of the electrochemical cell based on the at least one relationship.

[0070] It will be appreciated by a person skilled in the art that the at least one processor 204 may be configured to perform the required functions or operations through set(s) of instructions (e.g., software modules) executable by the at least one processor 204 to perform the required functions or operations. Accordingly, as shown in FIG. 2, the apparatus 200 may further comprise a receiving module or circuit 212 configured to obtain a full-cell thermodynamic data on the electrochemical cell and to obtain a cathode half-cell thermodynamic data and an anode half-cell thermodynamic data on the cathode and the anode, respectively, a relationship determining module or circuit (or relationship determinator) 214 configured to determine at least one relationship between a SOC of at least one of the cathode and the anode in the electrochemical cell and a SOC of the electrochemical cell based on the full-cell thermodynamic data, the cathode half-cell thermodynamic data, and the anode half-cell thermodynamic data, and a performance assessment module or circuit (or performance assessor) 216 configured to assess a performance of the electrochemical cell based on the at least one relationship. Accordingly, the at least one processor 204 may be configured to be capable of executing computer-executable instructions (e.g., the receiving module 212, the relationship determining module 214, and/or the performance assessment module 216) to perform one or more the required or desired functions, and the memory (or computer-readable storage medium) 202 may be communicatively coupled to the at least one processor 204 and may have stored therein one or more sets of computer-executable instructions (e.g., the receiving module 212, the relationship determining module 214, and/or the performance assessment module 216)

[0071] In various embodiments, the apparatus 200 corresponds to the method 100 as described hereinbefore with reference to FIG. 1, therefore, various functions or operations configured to be performed by the least one processor 204 described above may correspond to various steps of the method 100 described in further detail hereinbefore, and thus need not be repeated with respect to the apparatus 200 for clarity and conciseness.

[0072] A computing system, a controller, a microcontroller or any other system providing a processing capability may be presented according to various embodiments in the present disclosure. Such a system may be taken to include one or more processors and one or more computer-readable storage mediums. For example, the apparatus 200 described hereinbefore may be a device or a system including a processor (or controller) 204 and a computer-readable storage medium (or memory) 202 which are for example used in various processing carried out therein as described herein. A memory or computer-readable storage medium used in various embodiments may be a volatile memory, for example a DRAM (Dynamic Random Access Memory) or a non-volatile memory, for example a PROM (Programmable Read Only Memory), an EPROM (Erasable PROM), EEPROM (Electrically Erasable PROM), or a flash memory, e.g., a floating gate memory, a charge trapping memory, an MRAM (Magnetoresistive Random Access Memory) or a PCRAM (Phase Change Random Access Memory).

[0073] In various embodiments, a "circuit" may be understood as any kind of a logic implementing entity, which may be special purpose circuitry or a processor executing software stored in a memory, firmware, or any combination thereof. Thus, in an embodiment, a "circuit" may be a hard-wired logic circuit or a programmable logic circuit such as a programmable processor, e.g., a microprocessor (e.g., a Complex Instruction Set Computer (CISC) processor or a Reduced Instruction Set Computer (RISC) processor). A "circuit" may also be a processor executing software, e.g., any kind of computer program, e.g., a computer program using a virtual machine code, e.g., Java. Any other kind of implementation of the respective functions which will be described in more detail below may also be understood as a "circuit" in accordance with various alternative embodiments. Similarly, a "module" may be a portion of a system according to various embodiments in the present invention and may encompass a "circuit" as above, or may be understood to be any kind of a logic-implementing entity therefrom.

[0074] Some portions of the present disclosure are explicitly or implicitly presented in terms of algorithms and functional or symbolic representations of operations on data within a computer memory. These algorithmic descriptions and functional or symbolic representations are the means used by those skilled in the data processing arts to convey most effectively the substance of their work to others skilled in the art. An algorithm is here, and generally, conceived to be a self-consistent sequence of steps leading to a desired result. The steps are those requiring physical manipulations of physical quantities, such as electrical, magnetic or optical signals capable of being stored, transferred, combined, compared, and otherwise manipulated.

[0075] Unless specifically stated otherwise, and as apparent from the following, it will be appreciated that throughout the present specification, discussions utilizing terms such as "obtaining", "determining", "assessing", "optimizing", "computing", "minimizing" or the like, refer to the actions and processes of a computer system, or similar electronic device, that manipulates and transforms data represented as physical quantities within the computer system into other data similarly represented as physical quantities within the computer system or other information storage, transmission or display devices.

[0076] The present specification also discloses a system or an apparatus for performing the operations/functions of the methods described herein. Such a system or apparatus may be specially constructed for the required purposes, or may comprise a general purpose computer or other device selectively activated or reconfigured by a computer program stored in the computer. The algorithms presented herein are not inherently related to any particular computer or other apparatus. Various general-purpose machines may be used with computer programs in accordance with the teachings herein. Alternatively, the construction of more specialized apparatus to perform the required method steps may be appropriate.

[0077] In addition, the present specification also at least implicitly discloses a computer program or software/functional module, in that it would be apparent to the person skilled in the art that the individual steps of the methods described herein may be put into effect by computer code. The computer program is not intended to be limited to any particular programming language and implementation thereof. It will be appreciated that a variety of programming languages and coding thereof may be used to implement the teachings of the disclosure contained herein. Moreover, the computer program is not intended to be limited to any particular control flow. There are many other variants of the computer program, which can use different control flows without departing from the spirit or scope of the invention. It will be appreciated by a person skilled in the art that various modules described herein (e.g., the receiving module 212, the relationship determining module 214, and/or the performance assessment module 216) may be software module(s) realized by computer program(s) or set(s) of instructions executable by a computer processor to perform the required functions, or may be hardware module(s) being functional hardware unit(s) designed to perform the required functions. It will also be appreciated that a combination of hardware and software modules may be implemented.

[0078] Furthermore, one or more of the steps of a computer program/module or method described herein may be performed in parallel rather than sequentially. Such a computer program may be stored on any computer readable medium. The computer readable medium may include storage devices such as magnetic or optical disks, memory chips, or other storage devices suitable for interfacing with a general purpose computer. The computer program when loaded and executed on such a general -purpose computer effectively results in an apparatus that implements the steps of the methods described herein.

[0079] In various embodiments, there is provided a computer program product, embodied in one or more computer-readable storage mediums (non-transitory computer- readable storage medium), comprising instructions (e.g., the receiving module 212, the relationship determining module 214, and/or the performance assessment module 216) executable by one or more computer processors to perform a method 100 of assessing a performance of an electrochemical cell as described hereinbefore with reference to FIG. 1 and/or other method(s) described herein. Accordingly, various computer programs or modules described herein may be stored in a computer program product receivable by an apparatus (e.g., a computer system or an electronic device) therein, such as the apparatus 200 shown in FIG. 2, for execution by at least one processor of the apparatus to perform the required or desired functions.

[0080] The software or functional modules described herein may also be implemented as hardware modules. More particularly, in the hardware sense, a module is a functional hardware unit designed for use with other components or modules. For example, a module may be implemented using discrete electronic components, or it can form a portion of an entire electronic circuit such as an Application Specific Integrated Circuit (ASIC). Numerous other possibilities exist. Those skilled in the art will appreciate that the software or functional module(s) described herein can also be implemented as a combination of hardware and software modules.

[0081] The methods or functional modules of the various embodiments as described herein may be implemented in the apparatus 200, which may be realized by a computer system (e.g., portable or desktop computer system), such as a computer system 300 as schematically shown in FIG. 3 as an example only and without limitation. The method or functional module may be implemented as software, such as a computer program being executed within the computer system 300, and instructing the computer system 300 (in particular, one or more processors therein) to conduct the methods/functions of various embodiments described herein. The computer system 300 may comprise a computer module 302, input modules such as a keyboard 304 and mouse 306 and a plurality of output devices such as a display 308, and a printer 310. The computer module 302 may be connected to a computer network 312 via a suitable transceiver device 314, to enable access to e.g. the Internet or other network systems such as Local Area Network (LAN) or Wide Area Network (WAN). The computer module 302 in the example may include a processor 318 for executing various instructions, a Random Access Memory (RAM) 320 and a Read Only Memory (ROM) 322. The computer module 302 may also include a number of Input/Output (I/O) interfaces, for example I/O interface 324 to the display 308, and I/O interface 326 to the keyboard 304. The components of the computer module 302 typically communicate via an interconnected bus 328 and in a manner known to the person skilled in the relevant art.

[0082] It will be appreciated by a person skilled in the art that the terminology used herein is for the purpose of describing various embodiments only and is not intended to be limiting of the present invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.

[0083] In order that the present invention may be readily understood and put into practical effect, various example embodiments of the present invention will be described hereinafter by way of examples only and not limitations. It will be appreciated by a person skilled in the art that the present invention may, however, be embodied in various different forms or configurations and should not be construed as limited to the example embodiments set forth hereinafter. Rather, these example embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the present invention to those skilled in the art.

[0084] In particular, for better understanding of the present invention and without limitation or loss of generality, various example embodiments of the present invention will now be described with respect to the electrochemical cell being a LIB cell. However, it will be appreciated by a person skilled in the art that the electrochemical cell is not limited to a LIB cell and may be other types of electrochemical cells, such as but not limited to, an alkaline battery cell, and an acid battery cell. That is, it will be appreciated that methods and/or apparatuses described herein according to various embodiments of the present invention are not limited to being applied to LIB cells and may also be applied to other types of electrochemical cells. [0085] Various example embodiments of the present invention may seek to obtain accurate determination of lithium composition in anode and cathode in an LIB cell at a defined SOC of the LIB cell by providing a method combining electrochemical thermodynamic measurements (ETM) and computational data fitting technique or protocol. In this regard, as mentioned hereinbefore, it has been identified according to various embodiments of the present invention that in an electrochemical cell such as a LIB, the SOCs of the anode and cathode half-cells may differ from the SOC of the full- cell. Without wishing to be bound by theory, but the differences are understood to be in large part due to irreversible lithium losses within cell and to electrode mass unbalance. Based on this, various embodiments identified that the lithium composition ranges in the anode and cathode in the full-cell during full charge and discharge cycle in the full-cell may be different from the composition ranges achieved in the half-cells of the anode and cathode over their respective full SOC ranges. However, there does not appear to be any conventional unequivocal and practical method to determine the actual or sufficiently accurate lithium composition of electrodes in a LIB, and hence their SOCs. Yet, accurate lithium composition assessment may be important not only for understanding the physics of electrodes but also for optimizing cell performances, particularly energy density and cycle life.

[0086] In various example embodiments, thermodynamic data, including open-circuit potential (OCP) data (e.g., OCP vs. SOC), entropy (AS) data (e.g., AS vs. SOC and/or AS vs. OCP), and enthalpy (ΔΗ) data (e.g., ΔΗ vs. SOC and/or ΔΗ vs. OCP), are collected on full-cells and on their derived lithium half-cells (i.e., anode and cathode half-cells). In theory or in an ideal situation, the thermodynamic data of a full-cell is the arithmetic difference between the corresponding data of cathode and anode achieved in half-cells. However, as mentioned hereinbefore, according to various embodiments of the present invention, it has been identified that misfits exist between the measured full-cell thermodynamic data (or may be referred to experimental full-cell thermodynamic data) and computed full-cell thermodynamic data obtained based on the arithmetic difference between the cathode and anode half-cell thermodynamic data, thus indicating that cells data depart from theory in practice. Furthermore, in various example embodiments, misfits were significantly reduced by applying linear transforms to the cathode and anode half-cell thermodynamic data (e.g., based on the "at least one relationship" determined described hereinbefore) and by an iterative computational method (e.g., to determine the "at least one relationship" described hereinbefore). In various example embodiments, the fitting parameters (e.g., the "at least one parameter" described hereinbefore) are determined collectively through optimization such that the obtained cathode and anode half-cell thermodynamic data when adjusted based on the determined fitting parameters minimizes the differences or deviations (optimally minimizes) between measured and computed full-cell thermodynamics data. Such a technique according to various example embodiments of the present invention has been found to enable accurate Li composition in the anode and cathode in the full-cell, e.g., over the full SOC range of the full-cell to be assessed or determined. Based on such a technique, in examples, it was found that both the anode and cathode in the full-cell may operate under lower Li composition ranges than those achieved in the half-cells, which significantly reduces the full-cell energy density. Moreover, in various example embodiments, the effect of full-cell cycle ageing at the ambient and high temperatures on electrodes composition is investigated independently for anode and cathode so as to better understand their respective contribution to cell's capacity losses.

[0087] Accordingly, various example embodiments of the present invention provide a method of assessing a performance of an electrochemical cell based on a combined ETM and computational technique, for example, to seek to determine or estimate the actual active chemical element (e.g., lithium) composition in anode and cathode at any SOC of the full-cell. In various example embodiments, half-cell thermodynamic data are measured and collected on the anode and cathode half-cells, and then such half-cell thermodynamic data collected are processed in order to best fit the experimental data on the full-cell (e.g., corresponding to the "measured full-cell thermodynamic data" described hereinbefore). In various example embodiments, thermodynamic data (ETM data) including OCP data, AS data and ΔΗ data are processed with the same fitting parameters for minimizing (preferably optimally minimizing) differences between the measured and computed full-cell thermodynamic data to seek to accurately reveal or determine the lithium composition in the anode and cathode in the full-cell. [0088] For illustration purpose and without limitation, an exemplary combined ETM and computational technique will now be described in detail according to various example embodiments of the present invention (e.g., corresponding to the step 106 of "determining at least one relationship" described hereinbefore).

[0089] In theory, at a defined SOC (X_fc) of a full-cell, the full-cell's OCP ( E_f°_c ) equals the difference between the cathode (ca) and anode (an) half-cells' OCPs at their respective SOC (X_ca and X_an), that is:

E_f°_c (X_fc ) = E_c°_a {X_ca) - E_a°_n {X_an ) (Equation 5)

[0090] In a half-cell, OCP may relates to free energy {AG) of cell reaction according to:

^G X = -nFE° X , (Equation 6) and

G_an (X_an ) = -nFE_a°_n {X_an ) , (Equation 7) where "«" is the number of exchanged electron per mole (e.g., n = 1 for lithium).

[0091] Also, in theory, the SOC of an optimized full-cell should be equal to or correspond to the SOC of each electrode as follows:

X_/e = X_efl = 100 - X_fl„, (Equation s)

[0092] In Equation 8, it will be appreciated by a person skilled in the art that the "100-Xm" expression applies because the anode and the cathode in the full-cell theoretically have complementary SOCs.

[0093] The free energy AG relates to enthalpy AH(X) and entropy AS(X) according to:

Gca,an (^X ca.an ) = ^ ca.an (^X ca.an ) ^{" T} S ca.an (^X ca.an ) > (Equation 9) where "7" is the cell temperature.

[0094] Deriving Equation (9) vs T yields AS and enthalpy AH according to: Δ5_Μ,απ ) = F ^dE-^ - ⁾ , _{(Equation 10}) oT

and

dE c°a. ' T)

AH an (X ca.an ,

ca.an ( X ca.an ~ >) E 'ccaa.,aann ccaa.,aann '' T) + T - . (Equation 11) dT [0095] By combining the above equations, the following equations can be derived:

AS_fi (X_fi ) = AS_ca(X_ca) - AS_an(lQQ - X_an) , (Equation 12) and

AH_fc {X_fc ) = AH_ca{X_ca) - AH_an{\QO - X_an) . (Equation 13) [0096] However, as explained hereinbefore, in practice, full-cells may usually depart from optimized electrode mass balance and incur lithium losses. Therefore, Equation (8) provided above may not hold or apply. To address this problem, such as in order to determine or estimate the SOCs (e.g., actual SOCs) of the anode and cathode in the full- cell at a well-defined SOC of the full-cell, an approach or a method according to various example embodiments of the present invention involves fitting OCP, AS and ΔΗ data of half-cells (measured half-cell thermodynamic data) to corresponding OCP, AS and ΔΗ data of full-cells (measured full-cell thermodynamic data) by applying a linear transform of X_ca and X_an against X_c (e.g., a process or method which may be referred to as "shift and stretch") according to the following relationships (e.g., corresponding to the "at least one relationship" described hereinbefore):

xca = ca^x fc + ea . (Equation 3) and

* an = "an* ft + Pan , (Equation 4) where , β α and βαη (e.g., corresponding to the first, second, third, and fourth parameters described hereinbefore) are adjustable/fitting parameters determined and/or optimized to best fit Equations 12 and 13.

[0097] Let Ή' be a lithium host electrode structure. The electrode reaction can be schematized as:

H + xLi⁺ + xe^~ -> Li_xH , x_min < x < _max. (Equation 14) [0098] The electrode theoretical specific capacity (mAh/g), qth may be derived according to Equation 15 as follows:

F

q_th = Ax , Ax = x_max - x - , (Equation 15)

* 3.6 (H)

where F is the Faraday constant (about 96500 C/mole) and M(H) is the molecular mass of electrode Ή' (g/mole). [0099] Assuming x_max and x_min correspond respectively to 100% SOC and 0% SOC of electrode Ή', the relationship between SOC 'X' and Li composition may be given by:

x x 3.6 (H)¾ _ . _{Λ ^} x = x_min + Ax = x ■ + (Equation 16) mm 100 F

[00100] Assuming 100% SOC and 0% SOC correspond to x_m,„ and x_max, respectively, Equation 16 becomes:

x x 3.6 (HV^, _ . , AX = _{m ax} + — (Equation 17) m ax 100 F

[00101] Equations 16 and 17 may thus be used to convert SOC to lithium composition in anode and cathode, respectively. Accordingly, composition ranges of an active chemical element in the anode and cathode in the electrochemical cell may be determined or estimated based on the determined or estimated SOCs of the anode and cathode in the electrochemical cell.

[00102] According to an example embodiment of the present invention, in order to verify the effectiveness of the above-mentioned linear transform ("shift and stretch" method), a plurality of sets or types of thermodynamic data (e.g., OCP vs. SOC, AS vs. SOC, AS vs. OCP, ΔΗ vs. SOC, and/or ΔΗ vs. OCP) were used (e.g., three or five types, or any number of types as appropriate or desired) to compute the four parameters a_ca, βοα, dan, and βαη of Equations 3 and 4. In the example embodiment, the purpose of the curve fitting is to find the optimal values of these four parameters by shifting and stretching the curves (or graphs or profiles) of the half-cell thermodynamic data of the cathode and the anode such that the reformed curves (computed curves) in full-cell (i.e., computed full- cell curves based on a difference between the shifted/adjusted half-cell curves of the cathode and anode) can match (e.g., best match or optimally minimizes differences therebetween) with the measured full-cell values for entropy, enthalpy and OCP (measured full-cell thermodynamic data).

[00103] In an example embodiment, the root mean square error (RMSE) is used to evaluate the difference between the computed curve and the measured curve in the full cell, that is, between the computed full-cell curve (curve produced by the computed full- cell thermodynamic data) and the measured full-cell curve (curve produced by the measured full-cell thermodynamic data). In the example embodiment, as the three curves (i.e., E vs. SOC, AS vs. SOC, and ΔΗ vs. SOC) shift and stretch in the same format, the RMSE of these three functions are combined. Thus, the problem of finding the optimal values of these four parameters can be simplified as an optimization or minimization problem by minimizing the RMSE according to: rrrin RMSE (Equation 18)

where y_p ^J _red . and y_r'_ef . are given by: y_p ^J _nd = M + £⁾ - fl (a_a (10Q - xj ) + /3_a), H 2, ... , N),j = a, 2, 3),

(Equation 19) and

;: _{; i} ./V (.v). (Equation 20) where N is the number of data points, f_x ^j (x) represent E° vs. SOC (when j = 1), AS vs. SOC (when j = 2), and ΔΗ vs. SOC (when j = 3) of the cathode, / ^' (J ) represent E° vs. SOC (when j = 1), AS vs. SOC (when j = 2), and ΔΗ vs. SOC (when j = 3) of the anode, and f₃ ^J (x) represent E° vs. SOC (when j = 1), AS vs. SOC (when j = 2), and ΔΗ vs. SOC

(when j = 3) of the full-cell. In various example embodiments, Equations 18 to 20 are subject to the conditions: 0.6 < a_ca, a_an≤ 1.2 and -20 < β_αα, and β_αη≤ 20.

[00104] When performing the linear transform or curve fitting process, since the thermodynamics of the cathode and anode are very sensitive to the amount of lithium at 0 and 100 % SOC, the two points (0 and 100 % SOC) may exhibit high deflection from the average. Therefore, in various example embodiments, such two points are removed in the process.

[00105] Global optimization techniques/algorithms, such as evolutionary computing heuristic algorithms, have been widely used in various applications, such as disclosed in the following references, the contents of which being hereby incorporated by reference in their entirety for all purposes: Storn et al, "Differential Evolution - A simple and Efficient Heuristic for Global Optimization over Continuous Spaces", J. Global Optimization, 1997, 11(4), pages 341-359; Plagianakos, et al., "A Review of Major Application Areas of Differential Evolution, in Advances in Differential Evolution", U. Chakraborty, Editor 2008, Springer Berlin Heidelberg, pages 197-238; Jiang et al., "A novel ant colony optimization-based maximum power point tracking for photovoltaic systems under partially shaded conditions", Energy and Buildings, 2013, 58, pages 227- 236; and Jiang et al., "Parameter estimation of solar cells and modules using an improved adaptive differential evolution algorithm", Applied Energy, 2013, 112, pages 185-193.

[00106] One of the most popular algorithms in use is the differential evolution (DE) algorithm, a population based stochastic function optimization technique developed by the above-mentioned Storn reference. Extensive implementation details of the DE algorithm are available in the literatures, such as in the above-mentioned Storn reference \and the above-mentioned Jiang reference ("Parameter estimation of solar cells and modules using an improved adaptive differential evolution algorithm"), and thus need not be reproduced herein for clarity and conciseness. In an example, by applying the adaptive DE algorithm described in the above-mentioned Jiang reference ("Parameter estimation of solar cells and modules using an improved adaptive differential evolution algorithm") above into the optimization or minimization problem, the optimized parameters a_ca, βοα, dan, and βαη for a fresh cell (un-aged cell) were determined as [0.9118, 9.4862, 0.8178, -1.7511], respectively. After substituting the obtained parameters to the E° vs. SOC, AS vs. SOC, ΔΗ vs. SOC curves of the half-cells (measured half-cell curves), shifted or adjusted measured half-cell curves can be obtained, based on which the corresponding adjusted computed full-cell curves may be obtained.

[00107] In various experiments conducted according to example embodiments of the present invention, the combined ETM and computational technique was also applied to cells aged at 25°C and 55°C for various cycles. For ease of reference, the aged cells are indicated as "RT" for 25°C and "HT" for 55°C, and the number after the abbreviation RT or HT (e.g., HT100, RT300) denote the number of cycles performed.

Experiments

[00108] Commercial Li-ion battery (18650) rated 2 Ah were used in various experiments performed according to example embodiments of the present invention. According to electrode materials ex-situ XRD (X-Ray Diffraction), TEM (Transmission Electron Microscopy), EDX (Energy-Dispersive X-ray) and ICP (Inductively Coupled Plasma) analyses, the active cathode and anode materials include ½, ½, ½ type NMC material and graphitic carbon, respectively. From cell capacity and total anode and cathode geometrical surface areas measurements, the surface capacity of the electrodes was found to be around 2.15 mAh/cm².

Disassembly of Full-Cells and Reassembly of Half-Cells

[00109] Prior to disassembly, full-cell were each discharged to 2.5 V at 400 mA on BioLogic Multi Potentiostats/Galvanostats and were each held at 2.5 V until the current was lower than 40 mA (C/50). The full-cells were then each disassembled in a glove box filled with argon with the moisture and oxygen contents of lower than 1 ppm to make the cathode and anode half-cells. The double coated electrodes were separated and washed with dimethyl carbonate to remove the electrolyte, followed by overnight drying in vacuum at 50 °C. Subsequently, one side of the double coated electrodes was removed with N-methyl-2-pyrrolidone. The electrodes were then dried again in vacuum at 50 °C for 24 hours. The single side coated electrodes were cut into discs of 12 mm in diameter (1.13 cm²) for half-cells assembly.

[00110] The half-cells, CR2016, were assembled in an argon filled glove box. A Lithium metal foil was used as the counter and reference electrode. Celgard 2320 was used as a separator, and 1M LiPF₆ in ethylene carbonate and ethyl methyl carbonate (volume ratio 1: 1) was used as the electrolyte.

Cycling and Accelerate Ageing Conditions

[00111] The full-cells and the cathode half-cells were cycled at C/3 rate between 2.5 V to 4.2 V and 3 V to 4.3 V, respectively. The anode half-cells were cycled at C/6.3 between 0.005 V to 1.5 V. At the end of the charging process of the full-cell, a constant voltage was applied at 4.2 V until the current falls below 40 mA. The detailed cycling condition is summarized in Table 1 below. Table 1 - Cycling Condition for the Full Cell and Half Cells

[00112] For ageing tests, the full-cells were cycled at 25 °C (RT) and 55 °C (HT) at C/3 rate between 2.5 V to 4.2 V with an Arbin Instruments Battery Cycler for up to 500 cycles and 300 cycles at 25 °C and 55 °C, respectively. After each completed 200 cycles at 25 °C and 100 cycles at 55 °C, an ETM test was run. The full-cell was then dismounted to make cathode and anode half-cells for further ETM tests. Electrochemical Thermodynamic Measurements

[00113] Electrochemical Thermodynamic Measurement Systems (ETMS), BA-1000 and BA-2000 (KVI PTE LTD, Singapore), were used for measurements of the half-cells and the full-cells, respectively. In the experiments according to example embodiments of the present invention, the following steps were performed in sequence:

a. Conditioning cycle: the full-cells were each charged to 4.2 V and then discharged to 2.5V at 667 mA. The cathode half-cells were each charged to 4.3 V and then discharged to 3 V at 0.7 mA. The anode half-cells were each charged to 1.5 V and then discharged to 0.005 V at 0.35 mA. In each test, the ETMS measure the charge/discharge capacities of the cells, which were then used for the next ETM step.

b. ETM test: the full-cells and the half-cells were discharged (or charged) by 5% SOC increments up to full charge (or full discharge). At each SOC, the cells were rested for 30 minutes at ambient temperatures, then rested at different set temperatures (T) of 25 °C, 20 °C, 15 °C, and 10 °C. The open-circuit potentials (OCP) of the cells, E°(SOC, T), were measured and recorded.

[00114] In various example embodiments, entropy and enthalpy of the cells were then derived or calculated according to Equations 10 and 11, respectively. [00115] In various experiments, ETM tests on several identical cells show good data reproducibility. The ETM data (thermodynamic data) presented in various figures to be described below may be an average over several tests with error bars shown as appropriate.

[00116] In the context of various embodiments, the term "charge" in the cathode and anode half-cells may be used in relation to electrode processes during discharge of a full- cell, that is, lithium intercalation in the cathode and lithium deintercalation in the anode.

Materials Characterization

[00117] After the electrodes were washed with dimethyl carbonate and dried overnight in a vacuum oven at 50°C, the coatings of the anodes and the cathodes were scratched off for material analysis. The scratched powders were dried in a vacuum oven for 24 hours at 50°C. The electrode material morphology and chemical composition were investigated using a Field-Emission Scanning Electron Microscopy (FESEM; JEOL, JSM-7600F) and an Energy-Dispersive X-ray spectroscopy (EDX) attached to the electron microscope, respectively. Crystallographic data of the powders was collected using a powder X-ray diffractometer (Bruker, Cu Ka radiation with λ =1.5406 A).

Experimental Results

1. XRD, EDX and ICP analyses

[00118] X-ray diffractograms of the anode and the cathode are shown in FIGs. 4A and 4B, respectively. The anode structure can be indexed to hexagonal graphite with (002) sharp peak at 2Θ = 26.6° corresponding to an interlayer spacing of d = 3.35 A. The cathode has the hexagonal crystal structure typical of a-NaFe0₂ (space group R3 m). The peak at 2Θ = 18.8° is indexed as the (003) peak characteristic of layered structures with d = 4.721 A. Rietveld structure refinement yields lattice parameters of a = 2.861 A and c = 14.160 A with unit cell volume of 100.4 A³, in agreement with the literature (e.g., see Yabuuchi et al, "Novel lithium insertion material of LiCol/3Nil/3Mnl/302 for advanced lithium-ion batteries", J. Power Sources, 2003, 119, pages 171-174). EDX analysis of the cathode as shown in FIG. 4C indicates the presence of Mn, Co, and Ni with an atomic ratio of about 1 : 1 : 1. This was confirmed by ICP elemental analysis, which yielded a composition of Lio.965Nio.332Mno.337Coo.33i02. Small amounts of Fluorine (F) and Sulfur (S) were also detected by EDX. SEM (Scanning Electron Microscope) image analysis showed that the cathode material includes agglomerated particles of 2 μπι to 5 μπι in size. 2. ETM and Computational

a. Fresh Cells

[00119] Charge/discharge profiles (graphs or curves) of the full-cell, the half-cell having a cathode (cathode half-cell), and the half-cell having an anode (anode half-cell), are shown in FIGs. 5A, 5B, and 5C, respectively. All cells were in good operation conditions with cycle coulombic efficiency close to 100%. The voltage profile of the anode half-cell (FIG. 5C) was found to correspond to graphitic carbon with characteristic multiple phase transitions (staging) (e.g., see Billaud et al., "Electrochemical Intercalation of Lithium into Carbon Materials", Molecular Crystals and Liquid Crystals Science and Technology, Section A. Molecular Crystals and Liquid Crystals, 1994, 245(1), pages 159-164; Sawai et al, "Carbon Materials For Lithium-Ion (Shuttlecock) Cells", Solid State Ionics, 1994, 69(3-4); pages 273-283; Yazami et al., "A Reversible Graphite-Lithium Negative Electrode for Electrochemical Generators", J. Power Sources, 1983, 9(3), pages 365-371; and Yazami et al., "Carbon-Fibers and Natural Graphite as Negative Electrodes for Lithium Ion-Type Batteries", J. Power Sources, 1994, 52(1), pages 55-59). The voltage profile of the cathode half-cell (FIG. 5B) was found to be consistent with LiNii/3Mm/3Coi/302 (e.g., see Li et al, "Effect of Synthesis Method on the Electrochemical Performance of LiNil/3Mnl/3Col/302", J. Power Sources, 2004, 132(1-2), pages 150-155" and Yabuuchi et al, "Electrochemical Behaviors of LiCol/3Nil/3Mnl/302 in Lithium Batteries at Elevated Temperatures", J. Power Sources, 2005, 146(1-2), pages 636-639).

[00120] The OCP vs. SOC, AS vs. SOC, AH vs. SOC profiles of the full-cell (e.g., corresponding to the "measured full-cell thermodynamic data" or "obtained full-cell thermodynamic data" described hereinbefore) during discharge are shown in FIGs. 6A, 6B, and 6C, respectively. Since discharge of the full-cell corresponds to the reduction of the cathode (i.e. lithium intercalation) and the oxidation of the anode (i.e. lithium deintercalation), the OCP vs. SOC, AS vs. SOC, AH vs. SOC profiles for cathode and anode shown in FIGs. 7A, 7B, and 7C (e.g., corresponding to the "measured cathode half-cell thermodynamic data" or "obtained cathode half-cell thermodynamic data" described hereinbefore) and in FIGs. 8A, 8B, and 8C (e.g., corresponding to the "measured anode half-cell thermodynamic data" or "obtained anode half-cell thermodynamic data" described hereinbefore), respectively, were taken during the same electrode processes (in this example, lithium intercalation and de-intercalation in anode and cathode) as during the full-cell discharge.

[00121] The OCP vs. SOC profile of the full-cell depicted in FIG. 6A shows a monotonous increase with little changes in slope. Broad peaks can be observed in the enthalpy and entropy profiles in the SOC range of 20% to 60% as depicted in FIGs. 6B and 6C, respectively. However, the peak in the entropy profile is more pronounced than that of the enthalpy profile.

[00122] The OCP vs. SOC, AS vs. SOC, ΔΗ vs. SOC profiles of the cathode half-cell during discharge (lithium intercalation) are shown in FIGs. 7A, 7B, and 7C, respectively. It can be seen that the OCP and enthalpy profiles increase and decrease monotonously as function of the SOC, respectively, whereas the entropy trace makes broad maximum (labelled "C I" in FIG. 7B) and minimum (labelled "C2" in FIG. 7B) at about 50% and 90% SOC, respectively. A broad peak at about 50% SOC in the entropy profile may be attributed to changes in the 'a' and 'c' parameters of the hexagonal lattice, which go through a minimum and a maximum in the 50% to 60% SOC range, respectively (e.g., see Choi et al, "Investigation of the Irreversible Capacity Loss in the Layered LiNil/3Mnl/3Col/302 Cathodes", Electrochem. Solid-State Lett., 2005, 8(8), pages C102-C 105). A minimum in the calculated relative formation energy of Li_xNii/3Mni/3Coi/302 has also been reported at around 0.4, which corresponds to about 60% SOC (e.g. , see Li et al. , "Effect of Synthesis Method on the Electrochemical Performance of LiNil/3Mnl/3Col/302", J. Power Sources, 2004, 132(1 -2), pages 150- 155" and Yabuuchi et al, "Electrochemical Behaviors of LiCol/3Nil/3Mnl/302 in Lithium Batteries at Elevated Temperatures", J. Power Sources, 2005, 146(1 -2), pages 636-639).

[00123] The OCP vs. SOC, AS vs. SOC, ΔΗ vs. SOC profiles of the anode half-cell during charge (lithium deintercalation) are shown in FIGs. 8A, 8B, and 8C, respectively. It is noted that OCP plateaus and minima and maxima in the entropy and enthalpy profiles are consistent with a carbon anode with graphitization degree of 75% corresponding to a specific capacity of about 275 mAh/g (e.g., see Reynier et al., "Thermodynamics of Lithium Intercalation into Graphites and Disordered Carbons", J. Electrochem. Soc, 2004, 151(3), pages A422-A426). It is also noted that a broad minimum appears in the entropy and enthalpy profiles (labelled "A2" and "Al" in FIGs. 8B and 8C, respectively) in the 30% to 70% SOC range.

[00124] FIGs. 9A, 9B, and 9C depict two sets of OCP vs. SOC, AS vs. SOC, AH vs. SOC profiles, namely, measured full-cell thermodynamic data (i.e., obtained based on measurements on the full-cell, and labelled as "full cell" in the figures) and computed full-cell thermodynamic data (derived by computing a difference (e.g., arithmetic subtraction) between the measured cathode half-cell thermodynamic data (on the cathode half-cell) and measured anode half-cell thermodynamic data (on the anode half-cell), and labelled as "cathode-anode" in the figures). It can be seen that the measured and computed curves ("full cell" and "cathode-anode" curves) do not match indicating anode and cathode SOCs in half-cells are different from or are not equivalent to the SOC of the full-cell.

[00125] From FIGs. 9D and 9E, it can be seen that the misfit between the measured and computed full-cell thermodynamic data is lower when AS and AH are plotted against OCP as compared with when AS and AH are plotted vs. SOC, respectively.

[00126] According to various example embodiments, to reduce or to account for data deviation, the thermodynamic data of the cathode and the anode half-cells were adjusted or altered (e.g., stretched/compressed and/or shifted/translated) by performing computations according to Equations 3, 4, 12 and 13 described hereinbefore. Full-cell thermodynamic data computed based on the adjusted half-cell thermodynamic data may herein be referred to as adjusted full-cell thermodynamic data, and the curves produced based on the adjusted full-cell thermodynamic data may thus herein be referred to as adjusted curves (labelled as "adjusted" in the figures). Adjusted curves of OCP vs. SOC, AS vs. SOC, and AH vs. SOC are shown in FIGs. 10A to IOC, respectively, along with the corresponding measured and computed curves. Adjusted curves of AS vs. OCP and AH vs. OCP are shown in FIGs. 10D and 10E, respectively, along with the corresponding measured and computed curves. From FIGs. 10A to 10E, it can be seen that the adjusted curves show much less deviation from the measured curves, especially in the range of 20% to 60% SOC of the enthalpy and entropy. [00127] Data computing allows the a_ca, βοα, -an, and β_αη parameters to be determined. The data computed in experiments for all cells are displayed in the Table shown in FIG. 19 for reference only and without limitation. In an example according to various example embodiments, for the fresh cell, the relationship between the actual SOC (X_ca) of the cathode (in the full-cell) and the SOC (Xf_c) of the full-cell, and the relationship between the actual SOC (X_an) of the anode (in the full-cell) and the SOC (X_fc) of the full-cell are respectively determined as:

X_ca = 0.91X _t + 9.5 , (Equation 21 ) and

X_an = -O.S2X_fi + 80.03 . (Equation 22)

[00128] Therefore, when the SOC of the full-cell varies between 0 to 100%, the SOC of cathode in the full-cell ranges between 9.5% and 100.5% and SOC of anode in the full- cell varies between -2% and 80.03 %. Slightly over 100% SOC of cathode and negative OCP in anode may result from differences in the voltage experienced by cathode and anode in the full-cell and in the half-cells at end of charge and discharge. The utilization rates of the cathode and the anode in fresh full-cell are determined to be about 91 % and 82%, respectively. In this regard, the utilization rates of the cathode and anode are determined or estimated based on the parameters a_ca and a_an (e.g., determined or estimated to be equal to or to correspond to the parameters a_Ca and aan), respectively. This indicates that the anode and cathode in the full-cell are not operating to its full capability and features at least 20% energy shortage, which is undesirably high. Although the unused energy may not be reduced to zero, according to various embodiments of the present invention, better electrode construction and cell engineering are provided for more efficient use of cell capability.

[00129] As an example, assuming that the specific capacity of the NMC cathode material in half-cell is qth(ca) = 150 mAh/g in the 3 V to 4.3 V range (e.g., see Choi et al., "Investigation of the Irreversible Capacity Loss in the Layered LiiNii/3Mni/3Coi/302 cathodes", Electrochem., Solid-State Lett., 2005, 8(8), pages C102-C105) and assuming the cathode composition at a fully discharged state is LiiNii/3Mm/3Coi/302, the lithium composition range of Li_xNii/3Mni/3Coi/302 in a half-cell over 100% SOC should be 0.46<x<l. However, with the determined 91% cathode utilization rate, the lithium composition range may be derived to be 0.46<x<0.95.. Similarly, assuming that the anode specific capacity in half-cell is qth(ca) = 275 mAh/g, and corresponds to lithium composition range of 0<y<0.74 in Li_yC₆, with 82% anode utilization rate, the lithium composition range may be derived to be 0.072<y<0.74. For example, according to various example embodiments, based on Equations 14 to 17, the utilization rates of the cathode and the anode are defined as: v_ca = 100 X ^^{XcaifuU celV)} or 100 X l^ca Ax_ca(half cell)

(Xmax-Xmin)ca (full cell) _ ^ Ay_an(full cell) _χ (yma_X-ymin)an (full cell)

(Xmax-Xmin)ca (half cell) ' ^an &y_an(half cell) (Vmax-y 'min) an (half cell) respectively. For example, in the above example where the cathode utilization rate is determined to be 91 %, the lithium composition range in the cathode in the full-cell may

0 95-0 46

be determined to be 0.46<x<0.95, that is, 91% = 100 X — . This indicates that at

1-0.46

the end of the full-cell discharge, some lithium are still retained in the anode (e.g., Lio.o72C₆ vs. LioC₆) and the cathode is lithium deficient. For example, based on ICP analysis, the cathode composition is determined to be Lio.95Nii/3Mm/3Coi/302, which is lower than the expected or ideal cathode composition of Lio.965Nio.332Mno.337Coo.33i02.

[00130] According to various example embodiments, in order to evaluate the cathode and anode contributions to the entropy and the enthalpy of the full-cell, the corresponding profiles are plotted in FIGs. 1 1A and 1 IB, respectively. It can be seen that the broad peak of entropy of the full-cell in the 20% to 60% SOC range in FIG. 1 1A is mostly dominated by the anode as compared to a rather flat entropy profile of cathode. The anode effect is milder on the enthalpy profile as can be seen in FIG. 1 IB. In FIG. 1 IB, it should be noted that the enthalpy scales of the anode and the cathode are difference.

[00131] According to various example embodiments, the combined ETM and computation method is also applied to full-cells and half-cells cycled at 25 °C and 55 °C for various cycle numbers ('η'), and the results are presented in FIGs. 12 to 17. It can be seen that the adjusted curves both against SOC (FIGs. 12A, 12B, and 12C to 17A, 17B, and 17C) and against OCP (FIGs. 12D and 12E to 17D and 17E) exhibit reduced deviation from measured curves than the computed curves (directly subtracted curves). The fitting parameters are listed in the Table shown in FIG. 19.

[00132] The corresponding upper (xmax) and lower limits (x_min) of lithium composition in the cathode ("x" in Li_xNi½Co½Mn½02) and in the anode (} and j_m,„ Li_yC₆) are plotted in FIGs. 18A and 18B for cells aged at 25 °C (RTn) and 55 °C (HTn), respectively, where 'n' is the number of cycles. The lithium composition limits x_max, Xmin, } 'max and} 'min relate to Δχ and Ay since the actual capacities (mAh) of the cathode (Q_ca) and the anode (Qan) are respectively given by:

Q_ca = Axm_caq:_h ^a, (Equation 23) and

Q_m = l ym_mq2 , (Equation 24) where "m_ca" and "m_an" are the active mass (g) of the cathode and the anode in the full- cell, respectively, and " q^ " and " q™ " are the specific capacitites (mAh/g) (i.e., theoretical specific capacities) of the cathode and the anode, respectively. The capacity of the full-cell capacity is the lowest value of Q_an and Q_ca.

[00133] In various example embodiments, two equations relating x_ca in LixMCh and y_an in Li_yC₆ to Xf_C, respectively, are as follows:

x_ca = -aXfc + b , (Equation 25) and

y_an = cX_fc + d . (Equation 26)

[00134] FIGs. 18A and 18B show the evolution of lithium composition limits x_m,„,

Xmax, ymin, and y_max during ageing at 55 °C and 25 °C, respectively. At 55 °C, it can be seen that the cathode upper limit x_max increases from about 0.9 to about 1.0 after 100 cycles then slightly decreases, whereas the lower limit x_min increases for the first 200 cycles then stabilizes at about 0.6 for the following 100 cycles. The lithium composition range Ax deceases after 100 cycles mostly because x_m,„ increases relatively faster than χ_Μαχ increases. For anode, it can be seen that y_max increases for the first 100 cycles from about 0.49 to about 0.67 and then stabilizes about 0.62 to 0.67, whereas j_m,„ remains almost unchanged for the first 200 cycles at about 0.06 to 0.12 then it increases for the following 100 cycles up to about 0.23. Therefore, the capacity loss in anode is mostly due to lithium retention at the end of discharge (delithiation). This is reflected in the electrode utilization rates presented in FIG. 18C, which shows an increase for both anode and cathode for the first 100 cycles, then a decrease in the following 200 cycles. From the experiments conducted, it is interesting to note that none of the cathode and the anode has 100% utilization rate, even in the fresh cells. From the experiments conducted, the utilization rates of the cathode and the anode were found to vary, respectively, from about 75% and about 53% in fresh cells to about 58% and about 56% after 300 cycles at 55 °C.

[00135] From the composition limits profiles shown in FIG. 18C during ageing at 25 °C, it can be seen that the cathode utilization increased from about 75% to about 85% during the first 100 cycles, then it decreased to about 72% after 500 cycles as depicted in FIG. 18D. The anode utilization rate also increased from about 53% to about 84% for the first 100 cycles, then it decreased and almost stabilized at about 65% after 500 cycles. It is interesting to see that for the anode, both y_max and j_m,„ decreased between 300 and 500 cycles, keeping Ay almost constant. The Table shown in FIG. 19 includes all the fitting parameters and lithium composition ranges in the cathode and the anode on fresh and aged cells collected in experiments conducted according to various example embodiments of the present invention for illustration purpose only and without limitation.

[00136] The trends that both cathode and anode utilization rate increase during the first 100 cycles as shown in FIGs. 18C and 18D suggest that more active lithium is involved in the cathode and anode intercalation/de-intercalation processes. This may be related to: 1) electrodes conductivity enhancement, therefore allowing additional electrode materials to become active (increased m_ca and m_an) and/or 2) more lithium is extracted from or incorporated in the active material (increased Δχ and Ay). It is also noted that in the following 400 cycles, the electrode utilization rate decreased uniformly to about 70% and about 65% for the anode and the cathode, respectively, after 500 cycles.

[00137] Accordingly, various embodiments of the present invention provide a method of assessing a performance of an electrochemical cell, such as in relation to the utilization rate of the cathode and/or the anode in the electrochemical cell. For example, as described hereinbefore according to various example embodiments of the present invention, in the case of the electrochemical cell being a LIB cell, a method of assessing a performance of the LIB cell may be based on a method of assessing the lithium composition (e.g., actual composition) in the anode and the cathode in the LIB cell. As described hereinbefore, in various example embodiments, the method of assessing a performance of the LIB cell (or the method of assessing the lithium composition in the anode and the cathode in the LIB cell) is based on a combined ETM (e.g., OCP, entropy, and enthalpy) applied to full-cells and half-cells and iterative computational data processing to minimize differences between measured and computed full-cell thermodynamic data. In an example and without limitation, five sets of thermodynamic data profiles were fitted with same parameters so as to achieve the best fits. The fitting parameters may then be used for accurate assessment of lithium composition limits in the anode and the cathode together with electrode utilization rates. Accordingly, according to various embodiments of the present invention, composition limits in the cathode and the anode may advantageously be accurately and simultaneously determined using a nondestructive in-situ method.

[00138] Various experiments conducted verified the theoretical prediction of lithium deficiency in discharged cathode in example embodiments of the present invention. According to various embodiments of the present invention, an important and surprising finding is that both the anode and the cathode of a fresh full-cell operate significantly below their active chemical element composition ranges achieved in half-cells. For example, in experiments conducted on a LIB cell, the Li composition ranges were about 45% and about 25% below for anode and cathode, respectively (e.g., see FIGs. 18A to 18D and Table in FIG. 19). It can be understood that such an unused capacity affects cell performances, including energy density and power density. Experiments conducted also found an enhancement of both anode and cathode utilization rates after 100 cycles at 25 °C and 55 °C, which may be attributed to either an enhanced electrode conductance and/or deeper charge/discharge rates. Following the first 100 cycles, the electrode utilization rates decreased to about 55% after 300 cycles at 55 °C and 65% to 70% after 500 cycles at 25 °C for the anode and the cathode, respectively.

[00139] Accordingly, various embodiments of the present invention advantageously provide a method of assessing a performance of an electrochemical cell in order to reduce or minimize unused capacity of anode and cathode in an electrochemical cell, such as a fresh LIB cell, or to maximize utilization of the capacity of the anode and cathode, thereby increasing the energy density of the electrochemical cell (such as by up to 25% or more). Furthermore, according to various embodiments of the present invention, various manufacturing or fabrication conditions and/or materials (electrochemical cell engineering) may be tuned or selected based on the assessed performance of the electrochemical cell to seek to enhance the performance of the electrochemical cell, such as but not limited to, electrode materials selection, electrode formulation and engineering, electrolyte formation, anode/cathode mass ratio, and so on. In other words, the method of assessing a performance of an electrochemical cell according to various embodiments of the present invention may be utilized or implemented as a tool to tune (e.g., optimize) the manufacturing or fabrication conditions and/or materials of electrochemical cells, such as loop-wise iterative improvements before mass production of the electrochemical cells.

[00140] FIG. 20 depicts a flow diagram of a method 2000 of improving or optimizing the performance of an electrochemical cell, such as a LIB cell, according to various example embodiments of the present invention. In other words, the method 2000 may be for manufacturing electrochemical cell(s) which are improved or optimized. In particular, the method 2000 seeks to improve the performance of the electrochemical cell by configuring or adjusting the electrode (cathode and anode) formulation process based on the assessed performance of the electrochemical cell including the electrodes in a loop- wise iterative improvement manner.

[00141] By way of an example and without limitation, the method 2000 will now be described further for the example of the electrochemical cell being a LIB cell. The method 2000 illustrates a process for the manufacturing of a full-cell that seeks to optimize the cell performances based on electrode formulation in a loop-wise iterative manner. The method 2000 includes a step 2010 of acquiring ETM data (thermodynamic data) on a newly made full-cell, and steps 2020, 2022 of acquiring ETM data on cathode and anode half cells (disassembled from the full-cell at step 2014). After the full-cell thermodynamic data and the half-cells thermodynamics data have been obtained, the method 2000 further includes a step 2024 of computing or adjusting the half cells thermodynamic data to best fit the full-cell thermodynamic data (e.g., corresponding to the parameters (e.g., the first, second, third, and fourth parameters) optimization process as described hereinbefore), a step 2026 of determining the Li compositions of the anode and the cathode in the full-cell, and a step 2028 of determining the utilization rate of anode and cathode in the full-cell, such as in a manner as described hereinbefore according to various example embodiments of the present invention. With the utilization rates of the anode and cathode determined, reformulation of anode and cathode formulation according to such utilization rates determined is then performed in step 2030. Such an iterative process has been found to result in improved formulation of cathode and anode in the full-cell with optimized utilization rates

[00142] In various example embodiments, by way of example only and without limitation, the electrode formulation process may include or be based on one or more of the following:

• slurry composition (e.g., active electrode material, binder, and conductive additive);

• slurry mixing (e.g., solvent, grinder-mixing materials and technique, temperature, atmosphere, and duration);

· electrode coating (e.g., slurry viscosity, coating rate (m/min), coating film thickness, temperature, and atmosphere);

• electrode drying (e.g., temperature, pressure, atmosphere, and duration);

• electrode calendaring (e.g., roll press temperature and pressure, rate (m/min), and pressed film thickness); and

· electrode slitting (e.g., slitting rate (m/min), and blade interspacing).

[00143] In various example embodiments, parameters for controlling an electrode performance, including utilization rate are:

• electrode chemistry relating to electrode reaction mechanisms during charge storage and release;

· electrode physical characteristics, such as crystallinity, particle size, specific surface area, density, porosity, electrical conductivity, and thickness; and

• thermal and chemical stability.

[00144] In various example embodiments, all of the above-mentioned parameters are adjusted to seek to achieve the highest electrode utilization rate.

[00145] In various example embodiments, cell engineering is tuned or configured based on one or more factors, such as but not limited to, anode/cathode mass ratio adjustment, electrolyte formulation, anode and cathode stacking technology, and cell's form factor and assembly.

[00146] FIG. 21 depicts a flow diagram of a method 2100 of improving or optimizing the performance of an electrochemical cell, such as a LIB cell, according to various example embodiments of the present invention. In particular, the method 2100 seeks to improve the performance of the electrochemical cell by configuring or adjusting the electrode (cathode and anode) formulation process based on the assessed performance of the electrochemical cell including the electrodes in a loop-wise iterative improvement manner. The method 2100 is the same or similar as the method 2000 described hereinbefore with reference to FIG. 20, except that the electrochemical cell (e.g., fresh cell) is specifically subjected to a step 2110 of ageing (e.g., full-cell cycle ageing at various temperatures as described hereinbefore with respect to experiments performed according to various example embodiments of the present invention), and a step 2120 of evaluating the effects of ageing. The electrode formulation process 2030 takes into account the performance of the aged cells, such as to minimize undesirable effects of cell ageing. In other words, the method 2100 illustrates the optimization of full-cells according to their ageing mode. The method 2100 is thus also capable of detecting aged LIB. In particular, during ageing, one electrode may deteriorate faster than the other electrode, which may thus be referred to as the "capacity limiting electrode" as identified in step 2120 in FIG. 21. The method 2100 allows an accurate identification of which of the cathode and anode is the "capacity limiting electrode". The electrode formulation 2030 then takes into account this information for the optimization of the full-cell according to the ageing mode.

[00147] Various embodiments of the present invention seek to improve the performance of an electrochemical cell by forming an electrochemical cell comprising one or more additional electrodes, which may be referred to as buffer or auxiliary electrodes. In this regard, the one or more buffer electrodes may be configured to function to supplement or top-up active chemical element (e.g., lithium in the case of the electrochemical cell being a LIB cell) with respect to the anode and/or cathode, which are found to be deficient of the active chemical element. FIG. 22 depicts a schematic representation of an electrochemical cell (e.g., a LIB cell) 2200 comprising buffer electrodes 2202, 2260 according to various embodiments of the present invention. As depicted in FIG. 22, the electrochemical cell 2200 comprises an anode 2220 and a cathode 2240, with a first separator 2230 disposed therebetween. For example, in the case of the electrochemical cell 2200 being a LIB cell, the anode 2220 and cathode 2240 may be found to be lithium deficient, such as based on the assessed performance of the electrochemical cell determined according to a method of assessing a performance of an electrochemical cell described hereinbefore according to various embodiments of the present invention. In this regard, to compensate for the lithium deficient anode 2220 and cathode 2240, the electrochemical cell 2200 may further comprise a first buffer electrode 2202 to compensate for the lithium deficient anode 2220, along with a second separator 2210 disposed therebetween, and a second buffer electrode 2260 to compensate for the lithium deficient cathode 2240, along with a third separator 2250 disposed therebetween. For example, the buffer electrodes 2202, 2260 may be different in nature (e.g., of different chemical composition) from the anode 2220 and the cathode 2240 which can be used to compensate for the lithium deficient anode 2220 and cathode 2240, using lithium from electrolyte. In this regard, the buffer electrode 2202, 2260 may incorporate or de- incorporate both Li and the Lithium salt anion, such as X ^~ = PF₆ , BF₄ , TFSI, Triflate, Bis(oxalate)borate, and so on.

[00148] By way of an example in relation to the first buffer electrode 2202, let the carbon anode composition at the end of the battery discharge be: Li_ymin C₆ (y_min as in the Table shown in FIG. 19). In order to fully discharge the anode 2220 to Li₀C₆ composition, an electrochemical cell comprising a first buffer electrode 2202, a second separator 2210 and an anode 2220 may be implemented. In this regard, the cell reaction can be schematized as:

Anode 2220 Side

^Liy_min ^C6 *~* min L<-⁺ + min e^~ + Li₀C₆ (Equation 27)

First Buffer Electrode (B) 2202 Side

B + y_min Li⁺ + y_min e^~ <→ B(Li)_y (Equation 28) or

^B (^X min + ymin ^~ <→ B + y_min X^~ (Equation 29)

[00149]

Equation 27 describes the anode reaction during the cell regeneration process. In this regard, Lithium is extracted from anode.

[00150] By way of an example in relation to the second buffer electrode 2260, let the LMO carbon composition at the end of the battery discharge be: li_x M0₂ (x_max as in the

Table shown in FIG. 19). In order to fully discharge the cathode 2240 to Li_xM0₂ composition, an electrochemical cell comprising a second buffer electrode 2260, a third separator 2250, and a cathode 2240 may be implemented. In this regard, the cell reaction can be schematized as:

Cathode 2240 Side

Li_Im M0₂ + (l-x_m Li ⁺ +(1- j_max)e^" →> U_xM0₂ (Equation 30)

Second Buffer electrode (D) 2260 Side D -» D{U)^ +(i-x_m Li⁺+(i-x_m e- (Equation 31)

D + (l-x_m X-^D(X)_(i__Xm) +(l-x_m e- (Equation 32)

Alternatively, lithium can be provided to the cathode from the first buffer electrode (B). B(Li)y_m._n «→ B(Li)_{(ymin i}__{Xmax )} + (1 - x_max))Li⁺ + (1 - x_max))e- (Equation 33)

[00151] FIG.23 depicts a flow diagram of a method 2300 of improving or optimizing the performance of an electrochemical cell, such as a LIB cell, according to various example embodiments of the present invention. The method 2300 is similar to the method 2100 described hereinbefore with reference to FIG. 21, but further implements cathode and anode regeneration steps 2320, 2325 based on one or more buffer electrodes2310. For example, at a fully discharged state of a full cell, cathode and anode regeneration can take place as follows: 1) residual lithium is extracted from anode to reach Li₀C₆ composition. Extracted lithium is then stored in a first buffer (auxiliary) electrode (e.g., Buffer Electrode 1) at step 2320, 2) lithium vacancies in the cathode are filled at step 2325 to reach composition Li₁M0₂. Lithium is provided from either the first buffer electrode or a second buffer electrode (e.g., Buffer Electrode 2). At the end of the regeneration process, the anode composition is Li₀C₆ and the cathode composition is Li₁M0₂. The regenerated full cell at step 2330 is then ready for recharge.

[00152] It is understood from the above that full cell regeneration requires at least one buffer electrode to accommodate lithium ions and/or electrolyte anions. According to various example embodiments, regeneration can proceed by one of the two-step processes A and B as follows. Process A: 1) full delithiation of anode to reach Li₀C₆ composition followed by 2) cathode full re-lithiation to reach Li₁M0₂- Process B: 1) Full charging the cathode (delithiation) to reach Li_XminM0₂ , followed by 2) full re-lithiation of anode to reach Li₁C₆ composition. At the end of Process A, the regenerated full cell is fully discharged. On the other hand, at the end of Process B, the regenerated full cell is fully charged.

[00153] Buffer electrodes comprise materials able to store lithium cations and/or electrolyte anions. For example, ions (cations and anions) storage include but not limited to intercalation/de-intercalation, alloying/de-alloying, surface deposition/stripping including in material pores, micropores, mesopores, and nanopores.

[00154] In various example embodiments, buffer electrode materials may include, but not limited to: metals, metal alloys, demi-metals, metalloids, carbon-based materials and silicon based materials.

[00155] In various example embodiments, the regeneration process may take place in several steps at each step either the cell is partly discharged (Process A) or partly charged (Process B). The number of steps is fixed when the cell reaches full discharge state (Process A) and full charge state (process B). [00156] For better understanding of the present invention and without limitation or loss of generality, various example embodiments of the present invention will now be described with respect to LIB regeneration involving one buffer (auxiliary) electrode (auxiliary electrode approach or technique). A schematic drawing of a prismatic lithium ion cell with one auxiliary electrode is shown in FIG. 24. In the example, the auxiliary electrode is U-shaped for illustration purpose only and without limitation. It will be appreciated by a person skilled in the art that other form factors for the auxiliary electrode and locations in the full-cell may be implemented as appropriate or desired.

[00157] In various example embodiments, the auxiliary (or third) electrode (JE) approach or technique may involve the following steps:

1. Residual lithium is extracted from anode:

Anode: Li_rC₆ rLi⁺ + re ^" + C₆ (Equation 34)

2. Li is stored either in electrolyte (Li⁺) or in JE

Auxiliary electrode: (^E)_n+ rLi⁺ + re ^~ -> + (Li_r JE)_a (Equation 35) 3. Li stored in JE is transferred to the lithium deficient cathode

Cathode: (JE)_n+ rLi⁺ + re ^" - + (Li_r JE)_n (Equation 36)

[00158] For better understanding, the above-mentioned LIB regeneration will now be described in further detail with reference to FIGs. 25 according to various example embodiments of the present invention. For illustration purpose only and without limitation, FIG. 26 depicts a schematic drawing of an electrochemical cell 2600 comprising three electrodes, namely, a cathode 2610, an anode 2612, and an auxiliary electrode 2614, according to various example embodiments of the present invention. For example, the electrochemical cell 2600 may be referred to as a 3 -electrode electrochemical cell. In the example of FIG. 25, a lithium ion cell with an aluminum strip auxiliary electrode is used. The anode comprises graphite and the cathode comprises L1C0O2. Full-cell and half-cell thermodynamics data were measured in the process of cycling and the results are shown in FIG. 27. The cell was cycled between 2.5V and 4.2V under 6 mA rate (about CAS). The initial discharge capacity of the cell was about 36 mAh. It dropped to about 30.5 mAh after 400 cycles, which is about 15% capacity loss. OCP, entropy and enthalpy data were measured after 400 cycles on the full and half-cells. After computation according embodiments of the present invention described hereinbefore, the following data were obtained: cathode composition limits: x_max=0.92, x_min=0.60; anode composition limits: y_max=0.62 and y_min=0.06. Accordingly, cell regeneration may be performed including two steps according to various example embodiments of the present invention as illustrated in FIG. 25. In a first step (Step 1): about 0.06 lithium mole (about 3.5 mAh) was extracted from the anode and deposited in the auxiliary electrode, and in a second step (Step 2): the same amount of about 3.5 mAh is transferred from the auxiliary electrode and intercalated in the cathode. After regeneration was completed the cell was cycled again under 6 mA between 2.5V and 4.2V. The discharge capacity increased from 30.5 mAh to 34 mAh (about 11.5% increase). The cell was cycled for an additional 400 cycles until capacity reached about 30 mAh.

[00159] Accordingly, various embodiments of the present invention have demonstrated that in a lithium ion battery cell, anode and cathode are not used at their maximum lithium storage capabilities. Instead, at the end of the cell discharge, residual lithium ions are present in anode whereas lithium ion vacancies are present in cathode. Residual lithium and lithium vacancies contribute to the cell' capacity decay and to its premature end of life. Accordingly, to extend the cell life, a method of electrochemical cell regeneration (regeneration process) is provided according to various example embodiments of the present invention as illustrated in FIGs. 23 to 25 described hereinabove.

[00160] FIG. 28 depicts a schematic drawing of a method 2800 of electrochemical cell regeneration according to various embodiments of the present invention (e.g., corresponding to the electrochemical cell regeneration described hereinbefore with reference to FIGs. 23 to 25). The method 2800 comprises a step 2802 of assessing a performance of an electrochemical cell comprising a cathode and an anode according to various embodiments of the present invention as described hereinbefore, such as with reference to FIG. 1, and a step 2804 of regenerating the anode and the cathode based on the performance of the electrochemical cell determined. In various embodiments, the step 2804 of regenerating the anode and the cathode comprises determining a residual amount of an active chemical element in the anode based on the performance of the electrochemical cell determined, transferring the residual amount of the active chemical element from the anode to an auxiliary electrode, and transferring the residual amount of the active chemical element from the auxiliary electrode to the cathode. For example, the residual amount of an active chemical element in the anode may be determined based on the determined composition range of the active chemical element in the anode.

[00161] In various example embodiments, the electrochemical cell comprises at least one auxiliary electrode in addition to anode and cathode (e.g., a 3-electrode or 4-electrode cell). In various example embodiments, the regeneration process may involve the following steps:

1) fully discharge the cell comprising anode and cathode;

2) applying the method of assessing a performance of an electrochemical cell (e.g., corresponding to step 2802 of FIG. 28) as described hereinbefore according to various embodiments of the present invention to determine:

a. the amount of residual lithium in the anode at end of discharge. For example, if the anode in based on carbon (graphite) material, the amount of residual lithium may be the value of y_min in Li_v min C_fi; and/or

b. the amount of lithium vacancies in the cathode. For example, if the cathode comprises lithiated metal oxide (LiMCh, where M = Mn, Co, Ni, or Al, or various other appropriate elements), lithium vacancies may be given by the value of (1- x_max) m Li_XmaxM0₂;

3) transfer the determined amount of residual lithium from anode to the auxiliary electrode (e.g., corresponding to step 2804 of FIG. 28). In various example embodiments, this process involves the anode and the auxiliary electrode without involving (i.e., independent of) the cathode. For example, the transfer may be performed in one step or in multiple successive steps according to the auxiliary electrode capacity. As a result, less (or no) residual lithium is present in the anode; and

4) transfer the amount of residual lithium in the auxiliary electrode to the cathode (e.g., corresponding to step 2804 of FIG. 28). In various example embodiments, this process involves the cathode and the auxiliary electrode without involving the anode. For example, the transfer may also be performed in one step or in multiple successive steps according to the auxiliary electrode capacity and to the amount of lithium vacancies. As a result less (or no) lithium vacancies are present in cathode. [00162] In various example embodiments, excess lithium present in electrode may be used to complete the vacancies filing if y_min<l-Xmax.

[00163] Accordingly, various embodiments of the present invention determine the utilization rate of the anode and the cathode in order to improve the performance of the electrochemical cell, such as to increase the discharge capacity (Q) and optimize the performance of the electrochemical cell. For example, various embodiments of the present invention enable how much of the cathode and/or anode's capability or capacity is actually being used or utilized in operation to be determined or estimated. As described hereinbefore, various example embodiments of the present invention provide a method of assessing a performance of an electrochemical cell based on a combined ETM and computational technique, for example, to seek to determine the actual active chemical element (e.g., lithium) composition in anode and cathode at any SOC of the full-cell. In this regard, experiments conducted according to various example embodiments of the present invention reveal that in an electrochemical cell such as a LIB cell, anode and cathode in the electrochemical cell are not utilized to their maximum capacity or capability. Various embodiments of the present invention advantageously enable the performance of the electrochemical cell, such as the energy density W™ or W to be improved significantly, such as 50% or higher. As described hereinbefore, the data or assessed performance of the electrochemical cell advantageously enables electrochemical manufacturers to significantly increase the performance of the electrochemical cell (e.g., energy density W™ or ), such as by optimization of electrode formulation and electrochemical cell engineering. Various embodiments of the present invention also provide enable incrase battery calendar and cycle life during ageing.

[00164] While embodiments of the invention have been particularly shown and described with reference to specific embodiments, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. The scope of the invention is thus indicated by the appended claims and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced.

Claims

What is claimed is:

1. A method of assessing a performance of an electrochemical cell comprising a cathode and an anode, the method comprising:

2. The method according to claim 1, wherein the at least one relationship is dependent on at least one parameter, and said determining at least one relationship comprises determining the at least one parameter based on a deviation between the obtained full-cell thermodynamic data and a computed full-cell thermodynamic data, the computed full-cell thermodynamic data being computed based on the obtained cathode half-cell thermodynamic data and the obtained anode half-cell thermodynamic data.

3. The method according to claim 2, wherein the computed full-cell thermodynamic data is computed based on a difference between the obtained cathode half-cell thermodynamic data and the obtained anode half-cell thermodynamic data.

4. The method according to claim 2 or 3, wherein said determining the at least one parameter comprises determining the at least one parameter through optimization such that the obtained cathode half-cell thermodynamic data and the obtained anode half-cell thermodynamic data when adjusted based on the determined at least one parameter minimize the deviation.

5. The method according to any one of claims 2 to 4, wherein each of the obtained full-cell thermodynamic data, the obtained cathode half-cell thermodynamic data, and the obtained anode half-cell thermodynamic data comprises a plurality of types of thermodynamic data.

6. The method according to claim 5, wherein the plurality of types of thermodynamic data is selected from a group consisting of an open circuit potential data over a range of state of charge, an entropy data over a range of state of charge, and an enthalpy data over a range of state of charge, an entropy data over a range of open circuit potential, and an enthalpy data over a range of open circuit potential.

7. The method according to claim 5 or 6, wherein the deviation comprises a plurality of deviations associated with the plurality of types of thermodynamic data, respectively, wherein the deviation associated with a type of the plurality of types of thermodynamic data is between the obtained full-cell thermodynamic data of the type and the computed full-cell thermodynamic data of the type, and the at least one parameter is determined based on the plurality of deviations associated with the plurality of types of thermodynamic data.

8. The method according to claim 7, wherein the at least one parameter comprises a plurality of parameters, and the plurality of parameters are determined collectively based on the plurality of deviations associated with the plurality of types of thermodynamic data.

9. The method according to claim 8, wherein the at least one relationship comprises a first relationship between the state of charge of the cathode in the electrochemical cell and the state of charge of the electrochemical cell, and a second relationship between the state of charge of the anode in the electrochemical cell and the state of charge of the electrochemical cell, and wherein the at least one parameter comprises a first parameter and a second parameter, the first relationship is dependent on at least the first parameter, and the second relationship is dependent on at least the second parameter.

10. The method according to claim 9, wherein the first and second relationships are based on first and second linear functions, respectively, the first linear function being dependent on the first parameter and a third parameter, and the second linear function being dependent on the second parameter and a fourth parameter, and wherein the first, second, third, and fourth parameters are determined collectively based on the plurality of deviations associated with the plurality of types of thermodynamic data.

11. The method according to claim 9 or 10, wherein said assessing a performance of the electrochemical cell comprises determining a utilization rate of the cathode in the electrochemical cell based on the first relationship, and/or determining a utilization rate of the anode in the electrochemical cell based on the second relationship.

12. The method according to claim 11, wherein said assessing a performance of the electrochemical cell further comprises determining a composition range of an active chemical element in the cathode in the electrochemical cell based on the determined utilization rate of the cathode and/or determining a composition range of an active chemical element in the anode in the electrochemical cell based the determined utilization rate of the anode.

13. The method according to claim 12, wherein the active chemical element in the cathode and/or the active chemical element in the anode is lithium. The method according to any one of claims 1 to 13, wherein the obtained full-cell thermodynamic data is based on a measurement of a full-cell open circuit potential on the electrochemical cell over a range of state of charge of the electrochemical cell, the obtained cathode half-cell thermodynamic data is based on a measurement of a half-cell open circuit potential on the cathode over a range of state of charge of the cathode, and the obtained anode half-cell thermodynamic data is based on a measurement of a half-cell open circuit potential on the anode over a range of state of charge of the anode. 15. An apparatus configured for assessing a performance of an electrochemical cell comprising a cathode and an anode, the apparatus comprising:

a memory; and

at least one processor coupled to the memory and configured to:

The apparatus according to claim 15, wherein the at least one relationship is dependent on at least one parameter, and said determine at least one relationship comprises determining the at least one parameter based on a deviation between the obtained full-cell thermodynamic data and a computed full-cell thermodynamic data, the computed full-cell thermodynamic data being computed based on the obtained cathode half-cell thermodynamic data and the obtained anode half-cell thermodynamic data.

17. The apparatus according to claim 16, wherein the computed full-cell thermodynamic data is computed based on a difference between the obtained cathode half-cell thermodynamic data and the obtained anode half-cell thermodynamic data.

18. The apparatus according to claim 16 or 17, wherein said determining the at least one parameter comprises determining the at least one parameter through optimization such that the obtained cathode half-cell thermodynamic data and the obtained anode half-cell thermodynamic data when adjusted based on the determined at least one parameter minimize the deviation.

19. The apparatus according to any one of claims 16 to 18, wherein each of the obtained full-cell thermodynamic data, the obtained cathode half-cell thermodynamic data, and the obtained anode half-cell thermodynamic data comprises a plurality of types of thermodynamic data.

20. The apparatus according to claim 19, wherein the plurality of types of thermodynamic data is selected from a group consisting of an open circuit potential data over a range of state of charge, an entropy data over a range of stage of charge, and an enthalpy data over a range of state of charge, an entropy data over a range of open circuit potential, and an enthalpy data over a range of open circuit potential.

21. The apparatus according to claim 19 or 20, wherein the deviation comprises a plurality of deviations associated with the plurality of types of thermodynamic data, respectively, wherein the deviation associated with a type of the plurality of types of thermodynamic data is between the obtained full-cell thermodynamic data of the type and the computed full-cell thermodynamic data of the type, and the at least one parameter is determined based on the plurality of deviations associated with the plurality of types of thermodynamic data. The apparatus according to claim 21, wherein the at least one parameter comprises a plurality of parameters, and the plurality of parameters are determined collectively based on the plurality of deviations associated with the plurality of types of thermodynamic data.

The apparatus according to claim 22, wherein the at least one relationship comprises a first relationship between the state of charge of the cathode in the electrochemical cell and the state of charge of the electrochemical cell, and a second relationship between the state of charge of the anode in the electrochemical cell and the state of charge of the electrochemical cell, and wherein the at least one parameter comprises a first parameter and a second parameter, the first relationship is dependent on at least the first parameter, and the second relationship is dependent on at least the second parameter.

The apparatus according to claim 23, wherein the first and second relationships are based on first and second linear functions, respectively, the first linear function being dependent on the first parameter and a third parameter, and the second linear function being dependent on the second parameter and a fourth parameter, and wherein the first, second, third, and fourth parameters are determined collectively based on the plurality of deviations associated with the plurality of types of thermodynamic data.

The apparatus according to claim 23 or 24, wherein said assess a performance of the electrochemical cell comprises determining a utilization rate of the cathode in the electrochemical cell based on the first relationship, and/or determining a utilization rate of the anode in the electrochemical cell based on the second relationship. 26. The apparatus according to claim 25, wherein said assess a performance of the electrochemical cell further comprises determining a composition range of an active chemical element in the cathode in the electrochemical cell based on the determined utilization rate of the cathode and/or determining a composition range of an active chemical element in the anode in the electrochemical cell based the determined utilization rate of the anode.

27. The apparatus according to claim 26, wherein the active chemical element in the cathode and/or the active chemical element in the anode is lithium.

28. The apparatus according to any one of claims 15 to 27, wherein the obtained full- cell thermodynamic data is based on a measurement of a full-cell open circuit potential on the electrochemical cell over a range of state of charge of the electrochemical cell, the obtained cathode half-cell thermodynamic data is based on a measurement of a half-cell open circuit potential on the cathode over a range of state of charge of the cathode, and the obtained anode half-cell thermodynamic data is based on a measurement of a half-cell open circuit potential on the anode over a range of state of charge of the anode.

29. A computer program product, embodied in one or more computer-readable storage mediums, comprising instructions executable by at least one processor to perform the method of assessing a performance of an electrochemical cell according to any one of claims 1 to 14.

30. A method of electrochemical cell regeneration, the method comprising:

assessing a performance of an electrochemical cell comprising a cathode and an anode according to the method of any one of claims 1 to 14; and

31. The method according to claim 30, wherein said regenerating the anode and the cathode comprises: determining a residual amount of an active chemical element in the anode based on the performance of the electrochemical cell determined;