CN113640343B - Differential scanning calorimeter temperature calibration and reconstruction method based on laser power excitation - Google Patents
Differential scanning calorimeter temperature calibration and reconstruction method based on laser power excitation Download PDFInfo
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- G—PHYSICS
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N25/00—Investigating or analyzing materials by the use of thermal means
- G01N25/20—Investigating or analyzing materials by the use of thermal means by investigating the development of heat, i.e. calorimetry, e.g. by measuring specific heat, by measuring thermal conductivity
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N25/00—Investigating or analyzing materials by the use of thermal means
- G01N25/20—Investigating or analyzing materials by the use of thermal means by investigating the development of heat, i.e. calorimetry, e.g. by measuring specific heat, by measuring thermal conductivity
- G01N25/48—Investigating or analyzing materials by the use of thermal means by investigating the development of heat, i.e. calorimetry, e.g. by measuring specific heat, by measuring thermal conductivity on solution, sorption, or a chemical reaction not involving combustion or catalytic oxidation
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- G01N25/4826—Details not adapted to a particular type of sample concerning the heating or cooling arrangements
- G01N25/4833—Details not adapted to a particular type of sample concerning the heating or cooling arrangements specially adapted for temperature scanning
Abstract
The invention discloses a differential scanning calorimeter temperature calibration and reconstruction method based on optical power excitation. The calibration method of the invention uses laser as a calibration excitation source, combines the working principle of a differential scanning calorimeter, and calibrates the static characteristic and the dynamic characteristic of the instrument by theory of a theoretical deduction calibration method. The method provides that DSC is divided into an empty crucible model and a sample model, the empty crucible model and the sample model are respectively regarded as a first-order system and a second-order system, a laser negative step signal is utilized for calibrating an instrument, and a static characteristic calibration factor and model parameters are obtained by processing a measurement result. Compared with the traditional differential scanning calorimeter calibration method, the differential scanning calorimeter calibration method based on laser power excitation has the characteristics of economy and high efficiency, and has the advantages of less available standard substance types, high price, discrete heat flow calibration, multiple sources of systematic errors and the like.
Description
Technical Field
The invention relates to a calibration method of a Differential Scanning Calorimeter (DSC) based on laser power excitation, which is divided into static characteristic calibration and dynamic characteristic calibration of laser power excitation, and also relates to a method for reconstructing sample temperature of calorimetric data for improving thermodynamic analysis results.
Background
For a long time, DSC is used as the principal force of thermal analysis, has the advantages of wide research temperature range, small sample quality, high sensitivity and resolution, and the like, can be used for acquiring various information by being combined with other technologies, and is widely applied to the related fields of chemical safety, high polymer materials, biomedical treatment, fuel cells, agricultural engineering, thermodynamic research and the like. The existing DSC calibration method is mainly divided into two types, namely phase transition of a standard substance and electric Joule heating effect, and is mainly used for calibrating the temperature, heat flow and heat of an instrument. However, the calibration by adopting the standard substance phase transition temperature and the phase transition enthalpy has the limitation of few temperature points and discontinuous; the calibration by adopting the electric joule heating effect is only suitable for cylindrical DSC with a heater installed inside, the calibration cannot be suitable for tower type or tray type DSC, and in addition, the problems of inconsistent positions of the heater and the sample, lead wire heat leakage and the like can also cause systematic errors.
Assessing thermodynamic results is one of the important uses of differential scanning calorimeters. Its credibility is based on good experimental data and reliable dynamic calculation method. When exothermic reaction occurs in the sample to cause heat accumulation, the temperature of the sample can deviate from the measured temperature obviously; also, because the lower thermal conductivity of the sample can lead to significant temperature hysteresis, the DSC can exhibit large thermal inertia, and these factors can lead to significant errors in the thermodynamic analysis. The deconvolution is adopted to correct the heat flow data, so that the method can only reduce the temperature gradient of the sample to a certain extent, and cannot overcome the inherent defect that the temperature of the sample deviates from the measured temperature.
In summary, aiming at the limitations of the traditional differential scanning calorimeter calibration method, the invention provides an economical and efficient differential scanning calorimeter calibration method based on laser power excitation, which remarkably improves the accuracy and the continuity of DSC calibration; meanwhile, in order to obtain an accurate thermodynamic calculation result and develop an accurate chemical safety evaluation process, the invention provides a method for reconstructing the sample temperature, solves the problem that the sample temperature deviates from the measurement temperature in the exothermic reaction of the sample, and greatly improves the research level of the thermodynamic analysis and the accuracy of the thermal risk evaluation of chemicals.
Disclosure of Invention
Aiming at the problems of difficult calibration, fewer calibration points, multiple sources of systematic errors and the like in the conventional calibration method of the differential scanning calorimeter in the background technology. The invention designs a differential scanning calorimeter calibration method based on laser power excitation, which comprises two parts of static characteristic calibration and dynamic characteristic calibration. Meanwhile, the invention also comprises a sample temperature reconstruction method for improving the thermodynamic analysis result.
The laser calibration device comprises a laser generating device, a heat flow sensor device, a furnace body temperature measurement and control system, a data acquisition device and control software for data display and recording.
The laser of the laser generating device has the characteristics of stable laser power, small laser spot diameter, adjustable laser power and the like; the heat flow sensor device adopts a thermopile type heat flow sensor and can output high-precision thermoelectric force signals; the furnace body temperature measurement and control system is divided into four parts, namely a furnace cover, a furnace wall, a furnace bottom and a furnace cavity, wherein the center of the upper surface of the furnace cover is provided with a through hole with the diameter of 11.5mm, so that laser can pass through the through hole, a thermocouple and a heating rod are respectively arranged on the furnace cover, the furnace wall and the furnace bottom, and a required temperature program such as an isothermal or uniform temperature raising program can be set; the data acquisition device is respectively connected with the heat flow sensor and control software for data display and recording to complete the acquisition of the heat potential signal in the temperature control process; the data display and recording control software is connected with the temperature acquisition device through a communication cable to acquire data for recording, and is connected with the furnace body temperature measurement and control system to control the furnace body temperature environment.
The heat flow type DSC is generally composed of a sensor, a supporting frame, a furnace body and a crucible, and is a differential scanning calorimeter with a simple structure. And (3) placing the heat flow sensor device into a furnace chamber for fixing, and placing the crucible on thermopiles at two sides of the differential heat flow sensor, so that a simple heat flow DSC is built.
The invention discloses a temperature calibration method of a differential scanning calorimeter based on laser power excitation, which comprises the following implementation steps:
(1) The laser beam is aligned to the center of the furnace cover, so that the laser beam passes through the furnace cover and irradiates the furnace inside the furnace chamber, the furnace cover is opened, an empty crucible is placed on a thermopile type differential heat flow sensor, the laser is opened, the laser is irradiated on the inner surface of the crucible at the side of the sample, and the position of the laser is finely adjusted until obvious change of a thermopile output signal is observed. And closing the laser, covering a furnace cover, and adopting proper heat preservation measures to reduce convection and heat dissipation.
(2) Then the laser is turned on, the laser power is set, an isothermal mode temperature program is started at the same time, after the thermoelectric voltage output signal is stabilized, the laser is turned off, and the thermoelectric voltage output signal is stabilized again. Different laser powers are set, and the thermoelectric voltage of the differential heat flow sensor in the whole experimental process is recorded.
(3) The laser is turned on to make the laser beam aim at the sample substance in the crucible, the small-power laser is required to be set, and a constant-speed temperature raising program is started to ensure that the temperature of the sample substance is lower than the phase change temperature in the whole experimental process. And when the thermoelectric output signal is stable, the laser is turned off, and when the thermoelectric output signal is stable again, the dynamic response curve is recorded. Finally, the laser power is changed, and the experimental steps are repeated.
And (3) placing different samples into a crucible at the sample side of the differential scanning calorimeter for laser calibration so as to obtain dynamic response curves under different sample models.
And (3) performing fitting calculation on the dynamic response curve of the empty crucible model in the step (2) to obtain the time constant of the instrument. And (3) performing a laser calibration experiment by using the sample model, and processing a dynamic response curve of the sample model to obtain model parameters, wherein the two models are combined to realize the laser calibration experiment.
The principle of the invention is as follows:
in the experimental measurement process of DSC, the measurement signal of the differential heat flow sensor is actually thermoelectric, but not the heat flow itself, so that the static characteristic calibration must be performed to obtain the corresponding relationship between the heat flow value and the potential value.
The static characteristic calibration principle is as follows: when the laser power is constant and the heat transfer process enters steady state, the temperature difference on both sides of the sample side and the reference side will maintain a constant value. And (3) connecting the temperature sensors at two sides to a measuring circuit to obtain corresponding thermoelectric voltages respectively, and calculating the difference value of the thermoelectric voltages. Obtaining the static characteristic calibration factor K Φ Is represented by the expression:
Φ ture ＝K Φ ·DE m (1)
in phi, phi ture The unit of heat flow generated by laser is W; ΔE m The unit is V, which is the difference in thermoelectric voltage between the sample side and reference side temperature sensors.
And performing a laser calibration experiment by using an empty crucible model, and performing fitting calculation on an input signal and an output signal in a steady state to obtain a static characteristic calibration factor. The dynamic characteristic calibration needs to use an empty crucible model and a sample model respectively, so that dynamic response curves of the empty crucible model and the sample model are obtained and processed, and the dynamic response curves of the empty crucible model are subjected to fitting calculation, so that the time constant of the instrument can be obtained. And (3) performing a laser calibration experiment by using the sample model, and processing a dynamic response curve of the sample model to obtain model parameters, wherein the two models are combined to realize the laser calibration experiment.
In the DSC measurement process, when a sample with low heat conductivity undergoes exothermic reaction, heat accumulation is generated, and the heat cannot be timely transmitted, so that the temperature of the sample deviates from the measurement temperature, and the thermal resistance of the sample cannot be ignored. A mathematical model of DSC is derived taking into account that the sample temperature is not equal to the measured temperature. The thermal inertia of the instrument can affect the measured data, so that the DSC curve peak type is distorted, and the thermodynamic calculation result is inaccurate. According to the calibration method, the DSC sample model is regarded as a second-order system model during dynamic calibration, and the sample temperature is reconstructed according to model parameters, so that the accuracy of a thermodynamic calculation result can be greatly improved.
Furthermore, the models used in different calibration experiments are different, and the empty crucible model means that the crucible on the sample side and the crucible on the reference side are empty; the sample model refers to placing a sample into a crucible.
Furthermore, the primary problem of static characteristic calibration is that an excitation source capable of outputting constant heat flow is needed, and the output heat flow is stable and controllable. The laser can meet the conditions, can output step signals and can calibrate static and dynamic characteristics of the instrument.
Compared with the traditional DSC calibration method, the method has the beneficial effects that:
1. the laser power excitation-based differential scanning calorimeter calibration method can effectively improve the calibration precision and simplicity by the combined use of the static and dynamic characteristic calibration methods.
2. For sample heat accumulation caused by sample exothermic reaction in DSC measurement process, the sample temperature reconstruction method accords with practical conditions, and thermodynamic analysis is carried out by using n-level reaction simulation results, so that the accuracy of the thermal analysis can be improved.
Drawings
FIG. 1 is a schematic diagram of a thermal flow DSC laser calibration module;
FIG. 2 is a DSC structure model diagram of a tower structure;
FIG. 3 is an equivalent circuit diagram of a DSC empty crucible model with a tower structure;
FIG. 4 is an equivalent circuit diagram of a DSC sample model of a tower structure;
FIG. 5 is a schematic diagram of the calculation of equivalent thermal resistance results;
FIG. 6 is a schematic diagram of the calculation of equivalent heat capacity results;
FIG. 7 is a graph showing the results of calculating the thermal resistance of a sample;
FIG. 8 is a simplified schematic diagram of a tower DSC;
FIG. 9 relationship of temperature difference and furnace temperature;
FIG. 10 is a graph showing the relationship between the temperature difference and the furnace temperature after the temperature of the sample is reconstructed;
FIG. 11 thermodynamic results of solutions for different datasets;
FIG. 12 is a graph of activation energy residual versus extent of reaction;
in the figure:
FIG. 1,1.1 laser generator; 1.2. a heating furnace; 1.3. a multi-path thermometer; 1.4. and an upper computer.
FIG. 2,2.1. Crucible; 2.2. a sample; 2.3. a reference sample; 2.4. a sensor; 2.5. a support frame; 2.6. a furnace body.
Detailed Description
In order to make the steps, technical solutions and advantages of the embodiment examples of the present invention more clear, the technical solutions in the implementation of the present invention will be more clearly, fully described below with reference to the accompanying drawings in the embodiment examples of the present invention.
The differential scanning calorimeter calibration method based on laser power excitation comprises the following steps:
1. as shown in fig. 1, a laser generator 1.1 is used as an excitation source, and when a differential scanning calorimeter empty crucible model is used for laser calibration experiments, a laser beam is first aligned to the center of a furnace cover, so that the laser beam passes through the furnace cover and irradiates the inside of a furnace cavity of a heating furnace 1.2.
2. The furnace cover is opened, the empty crucible is placed on a thermopile type differential heat flow sensor by using tweezers, the heat flow sensor is transmitted to a multi-path thermometer 1.3 (Fluke 1586A), the laser is opened, the position of the laser generator is moved, and the laser is only irradiated on the inner surface of the crucible at the side of the sample. The heat generated by the laser is transferred along the crucible to the temperature sensor,
3. setting laser power of the laser, starting an isothermal mode temperature program in the upper computer 1.4 by the upper computer, and stopping the laser after the thermoelectric output signal is stabilized, and waiting for the thermoelectric output signal to be stabilized again. Different laser powers are set, and the thermoelectric voltage of the differential heat flow sensor in the whole experimental process is recorded. And (5) completing a DSC empty crucible model dynamic response experiment.
4. And (3) placing different samples into a crucible at the sample side of the differential scanning calorimeter for laser calibration so as to obtain dynamic response curves under different sample models. Firstly, placing a certain mass of sample substance in a crucible at the sample side, turning on a laser to enable a laser beam to be aligned to the sample substance in the crucible, taking care of setting low-power laser, starting a constant-speed temperature raising program, and ensuring that the temperature of the sample substance is lower than the phase change temperature of the sample substance in the whole experimental process. And when the thermoelectric output signal is stable, the laser is turned off, and the thermoelectric output signal is stable again. Finally, the laser power is changed, and the experimental steps are repeated.
By combining the above, the empty crucible model is used for carrying out a laser calibration experiment, the input signal and the output signal under the steady state are subjected to fitting calculation, the static characteristic calibration factor can be obtained, the dynamic response curve of the empty crucible model is subjected to fitting calculation, and the time constant of the instrument can be obtained. And (3) performing a laser calibration experiment by using the sample model, and processing a dynamic response curve of the sample model to obtain model parameters, wherein the two models are combined to realize the laser calibration experiment.
The dynamic characteristic calibration theory and the deduction process of the differential scanning calorimeter based on laser power excitation are as follows:
as shown in fig. 2, a tower structure DSC is selected for analysis, a mathematical model of the tower structure DSC is deduced in detail through an equivalent circuit diagram, and an equivalent model of a differential scanning calorimeter is obtained, wherein the tower structure DSC in fig. 2 comprises a crucible 2.1; sample 2.2; reference sample 2.3; a heat flow sensor 2.4; 2.5 parts of a supporting frame; 2.6 parts of furnace body.
The derivation process of the DSC equivalent model of the tower structure is as follows:
for the empty crucible model of the tower structure DSC, the equivalent circuit diagram is shown in FIG. 3, the influence of heat convection and heat radiation is ignored in the deduction process, only the effect of heat conduction is considered, and the temperature in the sample and the crucible is considered to be uniform. In fig. 3, subscripts S and R represent the sample end and the reference sample end, respectively, F represents the furnace, and M represents the temperature measurement point; the measured temperature of the sample end and the reference end is T respectively MS 、T MR The temperature of the furnace is T F The unit is K; the thermal resistance from the furnace to the temperature measurement point at the sample end is R FMS The unit is K/W; heat capacity of C FMS The unit is J/K; the thermal resistance of the reference sample end is R FMR Heat capacity of C FMR . Setting the furnace temperature as T under a certain temperature program F Heat flows from the furnace to the crucible, with the final system in steady state equilibrium.
In the deduction, it is assumed that only the heat capacity of the sample and the heat resistance between the sample and the furnace are considered, which causes measurement errors, and if the heat capacity and the heat resistance of all structures in the instrument are considered, the problem is complicated, so that the heat capacity from the furnace to the crucible is regarded as a whole, and is called equivalent heat capacity C, and the heat resistance from the furnace to the crucible is called equivalent heat resistance R. Also because the tower structure DSC is a symmetrical structure, R is assumed FMS ＝R FMR ＝R；C FMS ＝C FMR ＝C。
After placing samples in the crucibles at two sides, an equivalent circuit diagram of a DSC sample model with a tower structure is obtained as shown in figure 4, wherein the sample thermal resistances of the sample end and the reference end are respectively R S 、R R The method comprises the steps of carrying out a first treatment on the surface of the The heat capacity of the sample and the reference sample are C respectively S 、C R The method comprises the steps of carrying out a first treatment on the surface of the The reaction heat flow of the sample is phi r The unit is W.
Heat flow Φ from furnace to sample/reference end temperature measurement point FS /Φ FR The expression is as follows, the heat flow difference phi m For measuring signals.
Formula (2) minus formula (3) gives:
the reaction heat flow of the sample is phi r For exothermic reactions, Φ r Negative, for endothermic reactions Φ r Is positive. The heat flow expressions for the sample and reference ends are derived as follows:
formula (5) minus formula (6), parallel vertical (4) is obtained:
as can be seen from equation (7), the expression of the DSC mathematical model is first order. Heat flow phi of sample reaction r Regarded as input signal, heat flow difference phi m Regarding the output signal, the mathematical model of the instrument can be equivalently:
coefficient a in the formula 1 ～a 3 Known as model parameters, can be calculated from the instrument characteristics. Under the empty crucible model, laser irradiates the inner surface of the empty crucible at the side of the sampleThe generated heat flow is phi r From equation (7), the mathematical expression of the DSC empty crucible model can be deduced:
where τ is the instrument time constant, equal to the product of the equivalent heat capacity and the equivalent thermal resistance, in s.
Considering the empty crucible model as a first order system, equation (9) can be considered as a first order differential equation, thus yielding the output signal Φ m The solution is expressed as follows:
fitting calculation is carried out on the step response curve of the empty crucible model according to equation (10), so that the time constant of the instrument can be obtained.
In the DSC empty crucible model with the tower structure, the equivalent thermal resistance is equal to the static characteristic calibration factor K as known by the equation (1) Φ The product of the equivalent heat capacity and the equivalent thermal resistance is the instrument time constant, and the static characteristic calibration factor K is obtained through laser calibration Φ And the instrument time constant, the values of the equivalent heat capacity and the equivalent thermal resistance can be calculated as shown in fig. 5 and 6.
Placing a sample which does not undergo chemical reaction at the reference end, the temperature change rate of the reference sample can be considered to be equal to the heating rate beta, namely:
substituting the formula (11) into the formula (7), and performing corresponding conversion to obtain:
from the equivalent circuit diagram shown in fig. 4, the relationship between the sample temperature and the measurement point temperature can be deduced:
subtracting formula (14) from formula (13) to obtain the temperature difference between the sample temperature and the reference sample temperature:
substituting the formula (4) into the formula (15), and performing corresponding conversion to obtain:
then, the formulas (6) and (11) are substituted into formula (16), and the following can be obtained:
substituting formula (17) into formula (12) to obtain sample reaction heat flow phi r And measuring signal phi m I.e. mathematical expression of DSC sample model:
as can be seen from equation (18), the DSC sample model with the tower structure is a second-order system, and the sample reaction heat flow is subjected to equivalent heat capacity C, equivalent thermal resistance R, and heat capacities C of the sample and the reference sample S 、C R Sample thermal resistance R S And the effect of the set temperature program.
In the tower structure DSC sample model, the same applies equation (18) as the second order ordinary differential equation:
coefficient A 0 ～A 3 Are all constant terms, phi r Is an input signal phi m Is the output signal. Then output signal phi m The solution is in the form of:
the characteristic equation is:
in the experiment, a dynamic response curve of a sample model is obtained, and nonlinear fitting is carried out on data by using a formula (20) to obtain two characteristic roots. Substituting the required parameters into the characteristic equation (21) to solve the thermal resistance R of the sample S As shown in fig. 7.
By combining the above, the empty crucible model is used for carrying out a laser calibration experiment, the input signal and the output signal under the steady state are subjected to fitting calculation, the static characteristic calibration factor can be obtained, the dynamic response curve of the empty crucible model is subjected to fitting calculation, and the time constant of the instrument can be obtained. And (3) performing a laser calibration experiment by using the sample model, and processing a dynamic response curve of the sample model to obtain model parameters, wherein the two models are combined to realize the laser calibration experiment.
Compared with the traditional differential scanning calorimeter calibration method, the method has the following advantages: (1) the invention adopts laser as excitation source, which has non-contact advantage and will not pollute the instrument. (2) The invention adopts the laser to output step signals, performs static characteristic and dynamic characteristic calibration on the instrument, and can conveniently measure the instrument time constant. (3) The invention is suitable for all types of differential scanning calorimeters, and solves the problem that a heater is difficult to install in a heat flow DSC in an electric heating calibration method. (4) The invention can shut down the laser at any time to check the position of the base line in the experimental process, thereby judging whether the experiment is carried out smoothly.
Based on the static and dynamic characteristic calibration, the invention also provides a sample temperature reconstruction method, which comprehensively considers the influence of two factors of sample heat accumulation and instrument heat inertia on a thermodynamic result, and combines a laser calibration theory to acquire model parameters to correct calorimetric data, thereby greatly improving the accuracy of a thermodynamic calculation result.
The principle of the sample temperature reconstruction method is as follows:
for samples with good thermal conductivity such as metals, the thermal resistance is small, and the measured temperature can be considered to be equal to the sample temperature. However, for samples with low thermal conductivity, the sample thermal resistance cannot be ignored. When the sample undergoes exothermic reaction, heat accumulation is generated, and the heat cannot be timely transmitted, so that the temperature of the sample is increased and obviously deviates from the measured temperature. Based on the relation between the sample temperature and the measured temperature, the sample reconstruction temperature T can be deduced from equation (13) restruct Is represented by the expression:
it can be seen from equations (18) and (22) that if the measurement data is to be optimized, it is critical to find the equivalent heat capacity and equivalent thermal resistance of the instrument and the sample thermal resistance. By combining with the laser calibration theory, the required parameters can be obtained through laser static characteristic and dynamic characteristic calibration.
In order to prove the sample temperature reconstruction method provided by the invention, the accuracy of the thermodynamic calculation result can be effectively improved. And (3) designing a DSC heat transfer model with a tower structure by adopting an ANSYS software thermal analysis module, and verifying the heat transfer model by simulating and calculating the heat release effect of the n-level reaction of the substance.
The step of establishing the DSC simulation model by the ANSYS software is as follows:
the simplified tower structure DSC architecture diagram according to FIG. 8 is modeled and imported into ANSYS software. And (5) performing simulation. After the model mesh is divided, the material properties of the model are set, and the preprocessing of the simulation process is completed.
The specific theory of the n-level reaction is as follows:
the Arrhenius (Arrhenius) equation describes the reaction rate versus temperature, from which an n-stage reaction model can be derived:
in phi, phi r Is the heat flow of the sample reaction, W; q is the heat of reaction, J; dα/dt is the reaction rate, s -1 The method comprises the steps of carrying out a first treatment on the surface of the A is a forefinger factor, s -1 The method comprises the steps of carrying out a first treatment on the surface of the E is activation energy, J/mol; r is the gas constant, and r= 8.314J/(mol·k), T is the sample temperature, K; alpha is the degree of reaction; f (α) is a kinetic model; n is the reaction order.
The activation energy E can be obtained by adopting differential equal conversion rate method α The relation with the reaction degree alpha, and specific information of the dynamic model f (alpha) is not needed to be known, so that the influence of inaccurate measurement results caused by incorrect model selection can be reduced. Taking the logarithm of the reaction rate in equation (23) yields equation (24):
in DSC, α may be the ratio of the current heat change to the heat of reaction Q; e (E) α ，A α F (α) is the forefinger factor, activation energy, and kinetic model, respectively, for a given α. Index i indicates different heating rates, T α,i Is the sample temperature at which α is reached at the ith heating rate. Selecting ln (dα/dt) at different heating rates for the same reaction degree α α,i And 1/T α,i The values are subjected to linear fitting, and E is determined according to the slope of a fitting straight line α Is a value of (2).
The n-level reaction calculation steps are as follows:
setting the heating rate of the furnace body to be 1, 2, 4 and 8K/min, and selecting Ba (TFA) as a sample 3 Ginseng radixAlumina was selected for the comparative sample. The kinetic parameters used for the simulation are as follows: activation energy e=177 kJ/mol, forefinger factor a=4.5e13s -1 Reaction heat q=9.2j, reaction model f (α) = (1- α). And generating discrete heat flow data according to the n-level reaction model by utilizing the dynamic parameters, converting the discrete heat flow data into heat flow density, and applying the heat flow density to a sample of the DSC sample model of the tower structure. Setting an ambient initial temperature T 0 The simulation results were read from the reaction degree α=0 to the reaction degree α=1, which= 508.18K.
In the process of simulating n-level reaction, under different heating rates, the temperature T of the sample S And measuring temperature T MS Temperature difference and furnace temperature T F The relationship of (2) is shown in FIG. 9. It can be seen that the greater the heating rate, the greater the hysteresis of the output signal. The maximum temperature differences between the sample temperature and the measured temperature were 0.53, 0.94, 1.66 and 2.99K at heating rates of 1, 2, 4 and 8K/min, respectively.
The sample model used for simulating the n-level reaction is the same as the sample model used for calibrating the static characteristic and the dynamic characteristic, so parameters such as the thermal resistance of the sample, the equivalent thermal resistance and the like which are obtained by fitting and solving before can be universal. From equation (22), the sample reconstruction temperature T can be obtained restruct . Sample temperature T at different heating rates S Temperature T for sample reconstruction restruct The relationship between the temperature difference and the furnace temperature is shown in FIG. 10. After temperature reconstruction, the maximum temperature difference between the sample temperature and the sample reconstruction temperature is respectively 0.015, 0.03, 0.06 and 0.12K, the temperature difference is greatly reduced, and the result shows that the temperature of the sample temperature after the reconstruction is closer to the sample temperature.
To further verify the effect of different types of data processing on assessing thermodynamic results, four data sets were set up:
(a) Output signal (raw data);
(b) Only the data of the heat flow are corrected;
(c) Reconstructing only data of the sample temperature;
(d) And simultaneously correcting the heat flow and reconstructing the data of the sample temperature.
Correcting only the heat flow data refers to correcting the output signal according to equation (18). Figure 12 shows the thermodynamic results of solutions for different datasets, where the solid line is the thermodynamic result calculated from datasets (a) - (d), the dashed line is the true value of the thermodynamic result, and dataset a, b, c, d corresponds to curve a, b, c, d.
As can be seen from fig. 11, the curve a deviates significantly from the true value, the curve c is obtained only after temperature reconstruction, and the curve b is obtained only after heat flow correction. It can be found that the effect of temperature modification on the thermodynamic parameter is greater than the effect of heat flow modification. And after temperature and heat flow correction are carried out simultaneously, a curve d is obtained, and the consistency of the curve d and a true value is best.
Taking the data with the reaction degree alpha=0.05-0.95, calculating the residual error of the activation energy and the activation energy true value corresponding to the data sets (a) - (d), and calculating the Root Mean Square Error (RMSE) according to the formula (25), and the results are shown in fig. 12 and table 2.
Wherein E is k Is an activation energy measurement; e (E) 0 For the activation energy true value, m is the corresponding data length.
TABLE 1 root mean square error
As can be seen from table 1, the root mean square error of the thermodynamic results solved from the raw data is large. During exothermic reactions of the sample, heat build up inside the sample accelerates the reaction, and thus the apparent activation energy is greater than the actual activation energy. And after the temperature reconstruction and the heat flow correction of the sample are carried out simultaneously, the root mean square error of the activation energy is reduced from the original 21.13kJ/mol to 0.64kJ/mol, and the accuracy of the thermodynamic result is effectively improved.
The experimental result shows that the method for reconstructing the sample temperature effectively reduces the deviation between the sample temperature and the measured temperature, and the experimental heat release obtained by adopting the method for reconstructing the sample temperature provided by the invention is more practical.
In summary, the calibration method of the differential scanning calorimeter and the sample temperature reconstruction method based on laser power excitation provided by the invention comprise static and dynamic characteristic calibration and a correction thermal data method. The calibration method of the differential scanning calorimeter provided by the invention overcomes the disadvantages of few types of available standard substances, high price, discrete heat flow heat calibration points, multiple sources of systematic errors and the like in the traditional calibration method. Therefore, the invention has great significance for the research of the calibration method of the differential scanning calorimeter. In addition, the sample temperature reconstruction method solves the problem that in practical application, the thermodynamic result calculation is inaccurate due to the fact that the measured temperature deviates from the sample temperature and the thermal inertia of the instrument. Therefore, the result of the invention has great significance for improving the calibration efficiency of the differential scanning calorimeter and the accuracy of thermodynamic analysis results.
Claims (1)
1. The differential scanning calorimeter temperature calibration method based on laser power excitation is characterized by comprising the following steps of:
aligning a laser beam to the center of a furnace cover, enabling the laser beam to pass through the furnace cover, irradiating the laser beam into the furnace cover, opening the furnace cover, placing an empty crucible on a thermopile type differential heat flow sensor, opening the laser, and irradiating laser on the inner surface of a crucible at the side of a sample;
the position of the laser is finely adjusted until obvious change of the output signal of the thermopile is observed, then the laser is closed, a furnace cover is covered, and proper heat preservation measures are taken to reduce convection and heat dissipation;
step (2) turning on the laser, setting laser power, starting an isothermal mode temperature program, and turning off the laser after the thermoelectric voltage output signal is stabilized, and waiting for the thermoelectric voltage output signal to be stabilized again;
setting different laser powers, and recording the thermal potential of a differential heat flow sensor in the whole experimental process;
step (3), turning on a laser to enable a laser beam to be aligned with sample substances in a crucible, setting low-power laser, and starting a constant-speed temperature raising program to ensure that the temperature of the sample substances is lower than the phase change temperature of the sample substances in the whole experimental process;
when the thermoelectric output signal is stable, the laser is turned off, and the thermoelectric output signal is stable again; finally, changing the laser power;
placing different samples into a crucible at the sample side of a differential scanning calorimeter for laser calibration so as to obtain dynamic response curves under different sample models;
performing fitting calculation on the dynamic response curve of the empty crucible model in the step (2) to obtain the time constant of the instrument, performing a laser calibration experiment by using the sample model in the step (3), processing the dynamic response curve of the sample model to obtain model parameters, and combining the two models to realize a laser calibration temperature experiment, wherein the empty crucible model refers to that the crucible on the sample side and the crucible on the reference side are empty; the sample model refers to that a sample is put into a sample side crucible;
in the experimental measurement process of the differential scanning calorimeter, the measurement signal of the differential heat flow sensor is actually thermoelectric force, but not heat flow itself, so that static characteristic calibration is necessary to obtain the corresponding relationship between the heat flow value and the potential value;
the static characteristic calibration principle is as follows: when the laser power is constant and the heat transfer process enters a steady state, the temperature difference between the two sides of the sample side and the reference side is maintained to be a constant value; the temperature sensors at two sides are connected into a measuring circuit to respectively obtain corresponding thermoelectric voltages, and the difference value of the thermoelectric voltages is calculated; obtaining the static characteristic calibration factor K Φ Is represented by the expression:
Φ ture ＝K Φ ·ΔE m
in phi, phi ture The unit of heat flow generated by laser is W; ΔE m The unit is V, which is the difference in thermoelectric voltage between the temperature sensors on the sample side and the reference side;
performing a laser calibration experiment by using an empty crucible model, and performing fitting calculation on an input signal and an output signal in a steady state to obtain a static characteristic calibration factor;
the differential scanning calorimeter sample model is regarded as a second-order system model during dynamic calibration, and the temperature of the sample is reconstructed according to model parameters; the sample temperature T restruct The reconstruction expression is:
wherein T is MS For measuring temperature at sample end, R S For the thermal resistance of the sample at the sample end, from phi FS The heat flow from the furnace to the temperature measuring point at the sample end is C, and the heat flow of the sample reaction is equivalent heat capacity.
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