CN113672843B - Method and device for calculating particle size distribution of Pt particles in Pt/C catalyst - Google Patents
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- 239000002245 particle Substances 0.000 title claims abstract description 330
- 239000003054 catalyst Substances 0.000 title claims abstract description 60
- 238000000034 method Methods 0.000 title claims abstract description 58
- 238000009826 distribution Methods 0.000 title claims abstract description 53
- BASFCYQUMIYNBI-UHFFFAOYSA-N platinum Chemical compound [Pt] BASFCYQUMIYNBI-UHFFFAOYSA-N 0.000 title claims abstract description 41
- 238000007254 oxidation reaction Methods 0.000 claims abstract description 63
- 238000004364 calculation method Methods 0.000 claims abstract description 62
- 238000001016 Ostwald ripening Methods 0.000 claims abstract description 43
- 238000004090 dissolution Methods 0.000 claims abstract description 28
- 238000004458 analytical method Methods 0.000 claims abstract description 22
- 238000002425 crystallisation Methods 0.000 claims abstract description 13
- 230000008025 crystallization Effects 0.000 claims abstract description 13
- 238000006243 chemical reaction Methods 0.000 claims description 81
- 238000006703 hydration reaction Methods 0.000 claims description 31
- 238000004590 computer program Methods 0.000 claims description 16
- 239000000126 substance Substances 0.000 claims description 15
- 239000001257 hydrogen Substances 0.000 claims description 13
- 229910052739 hydrogen Inorganic materials 0.000 claims description 13
- -1 hydrogen ions Chemical class 0.000 claims description 10
- 239000007789 gas Substances 0.000 claims description 7
- 238000009792 diffusion process Methods 0.000 claims description 6
- 230000036571 hydration Effects 0.000 claims description 6
- 239000011164 primary particle Substances 0.000 claims description 6
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- 230000008859 change Effects 0.000 description 11
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- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 4
- UFHFLCQGNIYNRP-UHFFFAOYSA-N Hydrogen Chemical compound [H][H] UFHFLCQGNIYNRP-UHFFFAOYSA-N 0.000 description 3
- 230000003197 catalytic effect Effects 0.000 description 3
- 230000000694 effects Effects 0.000 description 3
- 238000004088 simulation Methods 0.000 description 3
- 230000002776 aggregation Effects 0.000 description 2
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- 238000010248 power generation Methods 0.000 description 2
- 230000005070 ripening Effects 0.000 description 2
- 238000004833 X-ray photoelectron spectroscopy Methods 0.000 description 1
- QVGXLLKOCUKJST-UHFFFAOYSA-N atomic oxygen Chemical compound [O] QVGXLLKOCUKJST-UHFFFAOYSA-N 0.000 description 1
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Abstract
The invention relates to catalyst attenuation analysis, in particular to a method and a device for calculating the particle size distribution of Pt particles in a Pt/C catalyst. The method comprises the following steps: based on an oxidation reaction model of Pt particles in the Pt/C catalyst, obtaining the oxidation reaction rate of the Pt particles; carrying out dissolution and crystallization analysis on the Pt particles to obtain the Ostwald ripening rate of the Pt particles; based on the oxidation reaction rate and ostwald ripening rate, the particle size distribution of Pt particles was obtained. The invention adopts a digital-analog analysis mode, has lower cost, simpler operation and higher efficiency; meanwhile, in the calculation process, the oxidation reaction and Ostwald ripening of the Pt particles are considered, and the actual catalysis process of the Pt particles is attached, so that the digital-to-analog analysis result can be attached to the actual process, and the particle size distribution of the Pt particles in the Pt/C catalyst is obtained at low cost and high efficiency.
Description
Technical Field
The invention relates to catalyst attenuation analysis, in particular to a method and a device for calculating the particle size distribution of Pt particles in a Pt/C catalyst.
Background
With the gradual exhaustion of fossil energy and the increasing environmental pollution, it is urgent to find a new sustainable clean energy. Hydrogen energy is a clean energy source, and its reaction products produce only water. The proton exchange membrane fuel cell takes hydrogen as fuel, the hydrogen firstly reacts with a catalyst of an anode to generate protons, the protons enter a cathode through a proton exchange membrane, oxygen at the cathode is catalyzed by the catalyst to react with the protons, and water is generated while current is generated. The power generation mode is efficient and clean, and is widely focused by various researchers at present. At present, the development of proton exchange membrane fuel cells is mainly limited by higher cost and poorer durability. The proton exchange membrane fuel cell mainly comprises a membrane electrode, a proton exchange membrane, a catalyst layer and a gas diffusion layer. Wherein the catalyst layer is the core of the membrane electrode, its performance determines the power generation capacity of the membrane electrode, and its durable service performance determines the service life of the membrane electrode.
At present, a catalyst widely used in membrane electrodes is a Pt/C catalyst in which Pt particles have a particle diameter of about 3nm, C particles have a particle diameter of about 50nm, and Pt atoms are supported on the C particles. During use of the fuel cell, dissolution, aggregation, etc. of Pt atoms will occur, and the carrier C particles of Pt particles may also be subjected to risk of collapse, cracking, etc. These phenomena will lead to a decrease in the performance of the catalyst and will shorten the service life of the catalyst, which in turn will lead to a decrease in the output of the fuel cell. Therefore, it is necessary to accurately and timely judge the performance degradation of the catalyst with time, and avoid the sudden failure of the fuel cell.
And the acquisition of the particle size distribution of Pt particles in the Pt/C catalyst is an essential data parameter for analyzing the performance of the catalyst. At present, a transmission electron microscope or a scanning electron microscope is generally adopted to observe the particle size distribution of Pt particles, but the method is complex, high in cost and incapable of feeding back the performance condition of the catalyst in real time.
Therefore, how to obtain the particle size distribution of Pt particles in Pt/C catalysts at low cost and high efficiency is a technical problem that needs to be solved at present.
Disclosure of Invention
The invention aims to provide a method and a device for calculating the particle size distribution of Pt particles in a Pt/C catalyst, so as to efficiently obtain the particle size distribution of the Pt particles in the Pt/C catalyst.
In order to achieve the above object, the embodiments of the present invention provide the following solutions:
in a first aspect, an embodiment of the present invention provides a method for calculating a particle size distribution of Pt particles in a Pt/C catalyst, the method including:
based on an oxidation reaction model of Pt particles in a Pt/C catalyst, obtaining the oxidation reaction rate of the Pt particles;
performing dissolution and crystallization analysis on the Pt particles to obtain the Ostwald ripening rate of the Pt particles;
based on the oxidation reaction rate and the ostwald ripening rate, a particle size distribution of the Pt particles is obtained.
In one possible embodiment, the oxidation reaction model of Pt particles includes: one or more of ionization of Pt and hydration of Pt.
In one possible embodiment, the obtaining the oxidation reaction rate of Pt particles based on the oxidation reaction model of Pt particles in the Pt/C catalyst includes:
calculating a first reaction rate of the ionization reaction of PtThe specific calculation formula is as follows:
；
wherein F is Faraday constant; e is the initial voltage set on the cathode; r is an ideal gas constant; t is the temperature at the cathode;a chemical reaction equilibrium constant for the Pt particles in the ionization reaction of the Pt; />Surface tension of the Pt particles; />A chemical equilibrium voltage for the Pt particles in a hydration reaction of the Pt; />Is the molar mass of Pt; />The particle diameter of the ith Pt particle at the moment j; />Is the percentage of the ith Pt particle covered by PtO at time j-1;
calculating a second reaction rate of the hydration reaction of the PtSpecific calculation formulaThe method comprises the following steps:
；
wherein the oxidation reaction rate of the Pt particles comprises the first reaction rateAnd said second reaction rate->One or more of the following; />A chemical reaction equilibrium constant for the Pt particles in the hydration reaction of the Pt; />Is the chemical equilibrium voltage of the Pt particles in the hydration reaction of the Pt.
In one possible embodiment, the performing a dissolution crystallization analysis on the Pt particles to obtain an ostwald ripening rate of the Pt particles includes:
calculating the Ostwald ripening rate of the Pt particlesThe specific calculation formula is as follows:
；
wherein,for Pt in the solution in which the Pt particles are 2+ Is a concentration of (2); />Is the primary particle size of the Pt particles;for the Pt particlesDiffusion coefficient; />The average particle diameter of the Pt particles at the moment j.
In one possible embodiment, the obtaining the particle size distribution of the Pt particles based on the oxidation reaction rate and the ostwald ripening rate includes:
calculation of particle size distribution of ith Pt particles at time jThe specific calculation formula is as follows:
；
wherein,for setting the interval duration.
In one possible embodiment, the method further comprises, after the obtaining the particle size distribution of the Pt particles based on the oxidation reaction rate and the ostwald ripening rate:
calculation of the third reaction Rate of dissolution reaction of PtOThe specific calculation formula is as follows:
；
wherein,a chemical reaction equilibrium constant for the Pt particles in the dissolution reaction of PtO; />The concentration of hydrogen ions in the solution in which the Pt particles are positioned; />Is the concentration of hydrogen ions relative to the solution in which the Pt particles are located;
calculation of particle number of PtO on ith Pt particle at j timeThe specific calculation formula is as follows:
。
in one possible embodiment, the calculation calculates the particle number of PtO on the ith Pt particle at time jThereafter, the method further comprises:
according toAnd->And obtaining the electrochemical active area of the Pt particles.
In a second aspect, an embodiment of the present invention provides a device for calculating a Pt particle size distribution in a Pt/C catalyst, the device including:
the first acquisition module is used for acquiring the oxidation reaction rate of Pt particles based on an oxidation reaction model of the Pt particles in the Pt/C catalyst;
the second acquisition module is used for carrying out dissolution and crystallization analysis on the Pt particles to acquire the Ostwald ripening rate of the Pt particles;
and a third acquisition module for acquiring a particle size distribution of the Pt particles based on the oxidation reaction rate and the ostwald ripening rate.
In one possible embodiment, the oxidation reaction model of Pt particles includes: one or more of ionization of Pt and hydration of Pt.
In one possible embodiment, the first obtaining module includes:
a first calculation module for calculating a first reaction rate of the ionization reaction of PtThe specific calculation formula is as follows:
；
wherein F is Faraday constant; e is the initial voltage set on the cathode; r is an ideal gas constant; t is the temperature at the cathode;a chemical reaction equilibrium constant for the Pt particles in the ionization reaction of the Pt; />Surface tension of the Pt particles; />A chemical equilibrium voltage for the Pt particles in a hydration reaction of the Pt; />Is the molar mass of Pt; />The particle diameter of the ith Pt particle at the moment j; />Is the percentage of the ith Pt particle covered by PtO at time j-1;
a second calculation module for calculating a second reaction rate of the hydration reaction of PtThe specific calculation formula is as follows:
；
wherein the oxidation reaction rate of the Pt particles comprises the first reaction rateAnd said second reaction rate->One or more of the following; />A chemical reaction equilibrium constant for the Pt particles in the hydration reaction of the Pt; />Is the chemical equilibrium voltage of the Pt particles in the hydration reaction of the Pt.
In one possible embodiment, the second obtaining module includes:
a third calculation module for calculating the Ostwald ripening rate of the Pt particlesThe specific calculation formula is as follows:
；
wherein,for Pt in the solution in which the Pt particles are 2+ Is a concentration of (2); />Is the primary particle size of the Pt particles;a diffusion coefficient for the Pt particles; />The average particle diameter of the Pt particles at the moment j.
In one possible embodiment, the third obtaining module includes:
a fourth calculation module for calculating the particle size distribution of the ith Pt particle at the moment jThe specific calculation formula is as follows:
；
wherein,for setting the interval duration.
In one possible embodiment, the apparatus further comprises:
a fifth calculation module for calculating a third reaction rate of the PtO dissolution reactionThe specific calculation formula is as follows:
；
wherein,a chemical reaction equilibrium constant for the Pt particles in the dissolution reaction of PtO; />The concentration of hydrogen ions in the solution in which the Pt particles are positioned; />Is the concentration of hydrogen ions relative to the solution in which the Pt particles are located;
a sixth calculation module for calculating the particle number of PtO on the ith Pt particle at the j timeThe specific calculation formula is as follows:
。
in one possible embodiment, the apparatus further comprises:
a fourth acquisition module for according toAnd->And obtaining the electrochemical active area of the Pt particles.
In a third aspect, an embodiment of the present invention provides an electronic device, including:
a memory for storing a computer program;
a processor for executing the computer program to implement the steps of the Pt particle size distribution calculating method in the Pt/C catalyst as set forth in any one of the first aspects.
In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the method for calculating a Pt particle size distribution in a Pt/C catalyst according to any one of the first aspects.
Compared with the prior art, the invention has the following advantages and beneficial effects:
the method is characterized in that firstly, based on an oxidation reaction model of Pt particles in a Pt/C catalyst, oxidation processes such as dissolution of the Pt particles are simulated, and an oxidation reaction rate capable of reflecting the surface change speed of the Pt particles is obtained; then carrying out dissolution and crystallization analysis on the Pt particles, and simulating the change of the surface morphology of the Pt particles under the influence of the Ostwald ripening phenomenon to obtain the Ostwald ripening rate capable of reflecting the change speed of the surface of the Pt particles; finally, the particle size distribution of the Pt particles is obtained based on the oxidation reaction rate and ostwald ripening rate. Compared with the original electron microscope experimental analysis scheme, the scheme of the invention adopts a digital-analog analysis mode, has lower cost, simpler operation and higher efficiency; meanwhile, in the calculation process, the oxidation reaction and Ostwald ripening of the Pt particles are considered, and the actual catalysis process of the Pt particles is attached, so that the digital-to-analog analysis result can be attached to the actual process, and the particle size distribution of the Pt particles in the Pt/C catalyst is obtained at low cost and high efficiency.
Drawings
In order to more clearly illustrate the embodiments of the present description or the technical solutions in the prior art, the drawings that are required for the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present description, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for calculating the particle size distribution of Pt particles in a Pt/C catalyst according to an embodiment of the present invention;
FIG. 2 is a graphical representation of the electrochemical reaction activity area versus time of Pt particles provided by an embodiment of the present invention;
FIG. 3 is a comparative schematic of the particle size distribution of Pt particles provided by an embodiment of the present invention;
fig. 4 is a schematic structural diagram of a Pt particle size distribution calculating apparatus in a Pt/C catalyst according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the present invention, but not all embodiments, and all other embodiments obtained by those skilled in the art based on the embodiments of the present invention are within the scope of protection of the embodiments of the present invention.
Referring to fig. 1, fig. 1 is a flowchart of a method for calculating a Pt particle size distribution in a Pt/C catalyst according to an embodiment of the present invention, and specifically includes steps 11 to 13.
And 11, obtaining the oxidation reaction rate of the Pt particles based on an oxidation reaction model of the Pt particles in the Pt/C catalyst.
Prior to step 11, pt particles need to be defined mathematicallyThe particles, in this example, define a total of M Pt particles, i in the ith Pt particle, before the catalytic reaction occurs n0 Pt atoms of particle size r i,0 。
Before step 11, an oxidation reaction model of Pt particles is also required to be established, and in this embodiment, the oxidation reaction model of Pt particles includes: one or more of ionization of Pt, hydration of Pt, and dissolution of PtO.
Specifically, the chemical equation for the ionization reaction of Pt can be expressed as:
the method comprises the steps of carrying out a first treatment on the surface of the The reaction belongs to the oxidation reaction of Pt, and can represent the dissolution process of Pt;
the chemical equation for the hydration reaction of Pt can be expressed as:
the method comprises the steps of carrying out a first treatment on the surface of the The reaction belongs to the oxidation reaction of Pt, and can represent the oxidation process of Pt and water in the catalysis process.
In step 11, an oxidation reaction model of Pt particles is adopted to simulate the oxidation processes such as dissolution of Pt particles in the catalytic process, so as to obtain an oxidation reaction rate capable of reflecting the surface change speed of Pt particles.
And step 12, performing dissolution and crystallization analysis on the Pt particles to obtain the Ostwald ripening rate of the Pt particles.
In particular, oswald ripening (or oswald ripening) is a phenomenon that can be observed in solid solutions or liquid sols, which describes the change in a heterogeneous structure over time: smaller crystals or sol particles in the solute dissolve and redeposit onto larger crystals or sol particles. The theory is reversely deduced from the fact that the molecular on the surface of the particles is unstable due to the fact that the energy is higher than that of the molecular inside the particles, and in step 12, thermodynamic analysis is carried out on the Pt particles in a dissolution and crystallization process, so that the change of the surface morphology of the Pt particles under the influence of the Ostwald ripening phenomenon is simulated, and the Ostwald ripening rate capable of reflecting the change of the surface of the Pt particles is obtained.
Step 13, obtaining a particle size distribution of the Pt particles based on the oxidation reaction rate and the ostwald ripening rate.
Specifically, the oxidation reaction rate of the Pt particles obtained in step 11 and the ostwald ripening rate of the Pt particles obtained in step 12 can be both characterized by the rate at which Pt atoms are obtained or lost by the Pt particles, thereby affecting the variation in the particle size of the Pt particles, and thus are all a function of the Pt particle size distribution。
Thus, the particle size distribution of the ith Pt particle at time jCan be expressed as:
；
wherein,setting interval duration; />The particle diameter of the ith Pt particle at the moment j.
Thus, step 13 can obtain the particle size distribution of Pt particles based on the oxidation reaction rate and ostwald ripening rate.
In order to improve the execution efficiency of step 11, the present embodiment also provides a scheme for obtaining the oxidation reaction rate of Pt particles by calculation, specifically including steps 21 to 22.
Step 21, calculating a first reaction rate of the ionization reaction of PtThe specific calculation formula is as follows:
；
wherein F is Faraday constant; e is the initial voltage set on the cathode; r is an ideal gas constant; t is the temperature at the cathode;a chemical reaction equilibrium constant for the Pt particles in the ionization reaction of the Pt; />Surface tension of the Pt particles; />A chemical equilibrium voltage for the Pt particles in a hydration reaction of the Pt; />Is the molar mass of Pt; />The particle diameter of the ith Pt particle at the moment j; />Is the percentage of the ith Pt particle covered by PtO at time j-1.
Specifically, the first reaction rateSpecifically, pt is dissolved to generate Pt 2+ Is a speed of (2); />The value of (2) may be a variable that varies over time; both E and T may be determined by experimental conditions.
Step 22, calculating a second reaction rate of the hydration reaction of PtThe specific calculation formula is as follows:
；
wherein the oxidation reaction rate of the Pt particles comprises the first reaction rateAnd said second reaction rate->One or more of the following; />A chemical reaction equilibrium constant for the Pt particles in the hydration reaction of the Pt; />Is the chemical equilibrium voltage of the Pt particles in the hydration reaction of the Pt.
Specifically, the second reaction rateSpecifically, the Pt hydration rate is the PtO generation rate; />The value of (2) may be a variable that varies over time; />Is a parameter factor, the value of which is between 0 and 1.
In order to improve the execution efficiency of step 12, the present embodiment also provides a scheme for obtaining the ostwald ripening rate of Pt particles by calculation, specifically comprising step 31.
Step 31, calculating the ostwald ripening rate of the Pt particlesThe specific calculation formula is as follows:
；
wherein,the concentration of Pt < 2+ > in the solution where the Pt particles are positioned; />Is the primary particle size of the Pt particles;a diffusion coefficient for the Pt particles; />The average particle diameter of the Pt particles at the moment j.
At the first reaction rateSecond reaction Rate->Ostwald ripening rateStep 13 may also be directly calculated to obtain the particle size distribution of Pt particles, specifically including step 41.
Step 41, calculating the particle size distribution of the ith Pt particle at the j timeThe specific calculation formula is as follows:
；
wherein,for setting the interval duration.
In the actual catalytic process, pt atoms on the surface of the Pt particles are continuously dissolved into Pt 2+ Continuously hydrating with water to PtO, and at the same time generating PDissolution reaction of tO.
The chemical equation for the dissolution reaction of PtO can be expressed as:
。
this causes the Pt particle surface morphology to change continuously, affecting the catalyst performance. Therefore, in order to accurately analyze the performance of the catalyst, it is also necessary to obtain the real-time amount of PtO on the Pt particle surface.
Here, the present embodiment provides a scheme of obtaining the real-time quantity of PtO on the Pt particle surface by calculation on the basis of the above calculation formula, specifically including steps 51 to 52.
Step 51, calculating the third reaction rate of PtO dissolution reactionThe specific calculation formula is as follows:
；
wherein,a chemical reaction equilibrium constant for the Pt particles in the dissolution reaction of PtO; />The concentration of hydrogen ions in the solution in which the Pt particles are positioned; />Is the concentration of hydrogen ions relative to the solution in which the Pt particles are located.
In particular, the third reaction rateSpecifically PtO is dissolved in solution to generate Pt 2+ Is a speed of (2); />The value of (c) may be a variable that varies over time.
Step 52, calculating the particle number of PtO on the ith Pt particle at the j-th timeThe specific calculation formula is as follows:
。
in practical applications, the morphology of the catalyst has a direct correspondence to the electrochemically active area (Electrochemical Active Surface Area, ECSA) of the catalyst, and therefore step 61 is further included after step 52.
Step 61, according toAnd->And obtaining the electrochemical active area of the Pt particles.
Specifically, after the real-time particle size distribution of the Pt particles and the real-time number of PtO on the surface of the Pt particles are obtained, the electrochemically active area of the Pt particles at that time can be obtained by performing cumulative calculation of the effective surface area of the Pt particles.
The electrochemical active area of the Pt particles and the catalytic performance of the Pt particles directly have a direct relationship, so that the relationship between the reaction time and the catalyst attenuation degree in the Pt particles can be obtained in this embodiment, and thus the attenuation of the catalyst in the membrane electrode can be accurately known in real time.
Application case
To illustrate the good simulation results of this embodiment, this embodiment also provides the following application cases.
In this application case, the relevant initial parameter values for the Pt/C catalyst are detailed in Table 1.
TABLE 1
Based on the simulated calculation procedure provided in the above examples, the operation process was repeated up to 100h (settable), outputting the particle size distribution of Pt particles and ESCA of Pt particles.
As shown in fig. 2, which is a schematic diagram showing the relationship between the electrochemical reaction activity area of the Pt particles provided by the embodiment of the present invention and the time variation, and as shown in fig. 3, which is a schematic diagram showing the particle size distribution of the Pt particles provided by the embodiment of the present invention, it can be seen that the results obtained by the simulation calculation of the embodiment of the present invention maintain higher consistency with the numerical results obtained by the experiment, and meanwhile, the deviation between the two results is smaller, which indicates that the scheme of the embodiment of the present invention can accurately calculate the relevant numerical values of the Pt particles in a simulation manner.
Therefore, the embodiment is more in line with the actual running situation, and not only considers the situation that the Pt particles possibly appear in the reaction process when the catalyst is dissolved in the solution, but also considers the Ostwald ripening of the Pt particles when the reaction is carried out, namely the process of gradual aggregation and particle size increase in the reaction, thereby realizing real-time monitoring on the attenuation situation of the Pt/C catalyst.
Based on the same inventive concept as the method, the embodiment of the invention also provides a device for calculating the particle size distribution of Pt particles in a Pt/C catalyst, as shown in fig. 4, which is a schematic structural diagram of the embodiment of the device, and the device comprises:
a first obtaining module 71, configured to obtain an oxidation reaction rate of Pt particles in the Pt/C catalyst based on an oxidation reaction model of the Pt particles;
a second obtaining module 72, configured to perform a dissolution crystallization analysis on the Pt particles, and obtain an ostwald ripening rate of the Pt particles;
a third acquisition module 73 for acquiring a particle size distribution of the Pt particles based on the oxidation reaction rate and the ostwald ripening rate.
In one possible embodiment, the oxidation reaction model of Pt particles includes: one or more of ionization of Pt and hydration of Pt.
In one possible embodiment, the first obtaining module includes:
a first calculation module for calculating a first reaction rate of the ionization reaction of PtThe specific calculation formula is as follows:
wherein F is Faraday constant; e is the initial voltage set on the cathode; r is an ideal gas constant; t is the temperature at the cathode;a chemical reaction equilibrium constant for the Pt particles in the ionization reaction of the Pt; />Surface tension of the Pt particles; />A chemical equilibrium voltage for the Pt particles in a hydration reaction of the Pt; />Is the molar mass of Pt; />The particle diameter of the ith Pt particle at the moment j; />Percent of the ith Pt particle covered by PtO at time j-1 +.>
A second calculation module for calculating a second reaction rate of the hydration reaction of PtThe specific calculation formula is as follows:
；
wherein the oxidation reaction rate of the Pt particles comprises the first reaction rateAnd said second reaction rate->One or more of the following; />A chemical reaction equilibrium constant for the Pt particles in the hydration reaction of the Pt; />For the chemical equilibrium voltage of the Pt particles in the hydration reaction of the Pt +.>
In one possible embodiment, the second obtaining module includes:
a third calculation module for calculating the Ostwald ripening rate of the Pt particlesThe specific calculation formula is as follows:
；
wherein,for Pt in the solution in which the Pt particles are 2+ Is a concentration of (2); />Is the primary particle size of the Pt particles;a diffusion coefficient for the Pt particles; />The average particle diameter of the Pt particles at the moment j.
In one possible embodiment, the third obtaining module includes:
a fourth calculation module for calculating the particle size distribution of the ith Pt particle at the moment jThe specific calculation formula is as follows:
；
wherein,for setting the interval duration.
In one possible embodiment, the apparatus further comprises:
a fifth calculation module for calculating a third reaction rate of the PtO dissolution reactionThe specific calculation formula is as follows:
；
wherein,a chemical reaction equilibrium constant for the Pt particles in the dissolution reaction of PtO; />The concentration of hydrogen ions in the solution in which the Pt particles are positioned; />Is the concentration of hydrogen ions relative to the solution in which the Pt particles are located;
a sixth calculation module for calculating the particle number of PtO on the ith Pt particle at the j timeThe specific calculation formula is as follows:
。
in one possible embodiment, the apparatus further comprises:
a fourth acquisition module for according toAnd->And obtaining the electrochemical active area of the Pt particles.
Based on the same inventive concept as in the previous embodiments, the present embodiments further provide an electronic device including a memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor implements the steps of the method for calculating the Pt particle size distribution in any one of the Pt/C catalysts described above when the processor executes the program.
Based on the same inventive concept as in the previous embodiments, the embodiments of the present invention further provide a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the method for calculating the Pt particle size distribution in any of the Pt/C catalysts described above.
The technical scheme provided by the embodiment of the invention has at least the following technical effects or advantages:
according to the embodiment of the invention, firstly, based on an oxidation reaction model of Pt particles in a Pt/C catalyst, an oxidation process such as dissolution of the Pt particles is simulated, and an oxidation reaction rate capable of reflecting the surface change speed of the Pt particles is obtained; then carrying out dissolution and crystallization analysis on the Pt particles, and simulating the change of the surface morphology of the Pt particles under the influence of the Ostwald ripening phenomenon to obtain the Ostwald ripening rate capable of reflecting the change speed of the surface of the Pt particles; finally, the particle size distribution of the Pt particles is obtained based on the oxidation reaction rate and ostwald ripening rate. Compared with the original electron microscope experimental analysis scheme, the scheme provided by the embodiment of the invention adopts a digital-analog analysis mode, and has the advantages of lower cost, simpler operation and higher efficiency; meanwhile, in the calculation process, the oxidation reaction and Ostwald ripening of the Pt particles are considered, and the actual catalysis process of the Pt particles is attached, so that the digital-to-analog analysis result can be attached to the actual process, and the particle size distribution of the Pt particles in the Pt/C catalyst is obtained at low cost and high efficiency.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (modules, systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. It is therefore intended that the following claims be interpreted as including the preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (8)
1. A method for calculating a Pt particle size distribution in a Pt/C catalyst, the method comprising:
based on an oxidation reaction model of Pt particles in a Pt/C catalyst, obtaining the oxidation reaction rate of the Pt particles;
performing dissolution and crystallization analysis on the Pt particles to obtain the Ostwald ripening rate of the Pt particles;
obtaining a particle size distribution of the Pt particles based on the oxidation reaction rate and the ostwald ripening rate;
the method for obtaining the oxidation reaction rate of the Pt particles based on the oxidation reaction model of the Pt particles in the Pt/C catalyst comprises the following steps:
calculating a first reaction rate of the ionization reaction of PtThe specific calculation formula is as follows:
；
wherein F is Faraday constant; e is the initial voltage set on the cathode; r is an ideal gas constant; t is the temperature at the cathode;a chemical reaction equilibrium constant for the Pt particles in the ionization reaction of the Pt; />Surface tension of the Pt particles; />A chemical equilibrium voltage for the Pt particles in a hydration reaction of the Pt; />Is the molar mass of Pt; />The particle diameter of the ith Pt particle at the moment j; />Is the percentage of the ith Pt particle covered by PtO at time j-1;
calculating a second reaction rate of the hydration reaction of the PtThe specific calculation formula is as follows:
；
wherein the oxidation reaction rate of the Pt particles comprises the first reaction rateAnd the second reaction rateOne or more of the following; />A chemical reaction equilibrium constant for the Pt particles in the hydration reaction of the Pt;a chemical equilibrium voltage for the Pt particles in a hydration reaction of the Pt;
the dissolving crystallization analysis is performed on the Pt particles to obtain the Ostwald ripening rate of the Pt particles, which comprises the following steps:
calculating the Ostwald ripening rate of the Pt particlesThe specific calculation formula is as follows:
；
wherein,for Pt in the solution in which the Pt particles are 2+ Is a concentration of (2); />Is the primary particle size of the Pt particles; />A diffusion coefficient for the Pt particles; />The average particle diameter of the Pt particles at the moment j.
2. The method for calculating a Pt particle size distribution in a Pt/C catalyst according to claim 1, wherein the model of the oxidation reaction of Pt particles comprises: one or more of ionization of Pt and hydration of Pt.
3. The method according to claim 1, wherein the obtaining the particle size distribution of the Pt particles based on the oxidation reaction rate and the ostwald ripening rate comprises:
calculation of particle size distribution of ith Pt particles at time jThe specific calculation formula is as follows:
；
wherein,for setting the interval duration.
4. The method for calculating a particle size distribution of Pt particles in a Pt/C catalyst according to claim 3, wherein after the obtaining of the particle size distribution of Pt particles based on the oxidation reaction rate and the ostwald ripening rate, the method further comprises:
calculation of the third reaction Rate of dissolution reaction of PtOThe specific calculation formula is as follows:
；
wherein,a chemical reaction equilibrium constant for the Pt particles in the dissolution reaction of PtO; />The concentration of hydrogen ions in the solution in which the Pt particles are positioned; />Is the concentration of hydrogen ions relative to the solution in which the Pt particles are located;
calculation of particle number of PtO on ith Pt particle at j timeThe specific calculation formula is as follows:
。
5. the method for calculating a particle diameter distribution of Pt particles in a Pt/C catalyst according to claim 4, wherein said calculating the number of PtO particles on the ith Pt particle at the j-th momentThereafter, the method further comprises:
according toAnd->And obtaining the electrochemical active area of the Pt particles.
6. A Pt particle size distribution calculating apparatus for a Pt/C catalyst, comprising:
the first acquisition module is used for acquiring the oxidation reaction rate of Pt particles based on an oxidation reaction model of the Pt particles in the Pt/C catalyst;
the second acquisition module is used for carrying out dissolution and crystallization analysis on the Pt particles to acquire the Ostwald ripening rate of the Pt particles;
a third acquisition module for acquiring a particle size distribution of the Pt particles based on the oxidation reaction rate and the ostwald ripening rate;
the method for obtaining the oxidation reaction rate of the Pt particles based on the oxidation reaction model of the Pt particles in the Pt/C catalyst comprises the following steps:
calculating a first reaction rate of the ionization reaction of PtThe specific calculation formula is as follows:
；
wherein F is Faraday constant; e is the initial voltage set on the cathode; r is an ideal gas constant; t is the temperature at the cathode;a chemical reaction equilibrium constant for the Pt particles in the ionization reaction of the Pt; />Surface tension of the Pt particles; />A chemical equilibrium voltage for the Pt particles in a hydration reaction of the Pt; />Is the molar mass of Pt; />The particle diameter of the ith Pt particle at the moment j; />Is the percentage of the ith Pt particle covered by PtO at time j-1;
calculating a second reaction rate of the hydration reaction of the PtThe specific calculation formula is as follows:
；
wherein the oxidation reaction rate of the Pt particles comprises the first reaction rateAnd the second reaction rateOne or more of the following; />A chemical reaction equilibrium constant for the Pt particles in the hydration reaction of the Pt;a chemical equilibrium voltage for the Pt particles in a hydration reaction of the Pt;
the dissolving crystallization analysis is performed on the Pt particles to obtain the Ostwald ripening rate of the Pt particles, which comprises the following steps:
calculating the Ostwald ripening rate of the Pt particlesThe specific calculation formula is as follows:
；
wherein,for Pt in the solution in which the Pt particles are 2+ Is a concentration of (2); />Is the primary particle size of the Pt particles; />A diffusion coefficient for the Pt particles; />The average particle diameter of the Pt particles at the moment j.
7. An electronic device, comprising:
a memory for storing a computer program;
a processor for executing the computer program to implement the steps of the method of any one of claims 1 to 5.
8. A computer readable storage medium, on which a computer program is stored, characterized in that the computer program is executed by a processor to implement the steps of the method of any of claims 1 to 5.
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