阅读说明：本技术 基于激光功率激励的差式扫描量热仪温度标定与重构方法 (Temperature calibration and reconstruction method for differential scanning calorimeter based on laser power excitation ) 是由 丁炯 叶树亮 许金鑫 王晓东 于 2021-08-13 设计创作，主要内容包括：本发明公开了一种基于光功率激励的差式扫描量热仪温度标定与重构方法。本发明所述标定方法以激光作为标定激励源,结合差示扫描量热仪工作原理,通过理论推导标定方法的原理,对仪器静态特性、动态特性标定。所述方法提出将DSC分为空坩埚模型以及样品模型,并将其分别看成一阶系统和二阶系统,利用激光负阶跃信号对仪器进行标定,通过对测量结果进行处理得到静态特性标定因子以及模型参数。相对于传统的差式扫描量热仪标定方法存在可用标准物质种类较少且价格昂贵、热流热量标定离散、系统误差来源多等问题,本发明提出的基于激光功率激励的差式扫描量热仪标定方法具有经济、高效的特点。(The invention discloses a temperature calibration and reconstruction method of a differential scanning calorimeter based on optical power excitation. The calibration method provided by the invention uses laser as a calibration excitation source, combines the working principle of a differential scanning calorimeter, and calibrates the static characteristics and the dynamic characteristics of the instrument by theoretically deducing the principle of the calibration method. The method provides that the 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, the instrument is calibrated by using a laser negative step signal, and a static characteristic calibration factor and a model parameter are obtained by processing a measurement result. Compared with the traditional differential scanning calorimeter calibration method, the problems of less available standard substance types, high price, discrete heat flow heat calibration, more system error sources and the like exist, and the differential scanning calorimeter calibration method based on laser power excitation provided by the invention has the characteristics of economy and high efficiency.)

1. The temperature calibration method of the differential scanning calorimeter 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 penetrate through the furnace cover and irradiate the laser beam to the inside of a furnace chamber, opening the furnace cover, placing an empty crucible on a thermopile type differential heat flow sensor, opening a laser, and irradiating laser on the inner surface of the crucible on the sample side;

finely adjusting the position of the laser until the thermopile output signal is observed to have obvious change, then closing the laser, covering a furnace cover, and adopting proper heat preservation measures to reduce convection and heat loss;

turning on a laser, setting laser power, starting an isothermal mode temperature program, turning off the laser after a thermoelectric output signal is stable, and waiting for the thermoelectric output signal to be stable again;

setting different laser powers, and recording the magnitude of thermoelectric potential of the differential heat flow sensor in the whole experiment process;

turning on a laser, enabling a laser beam to aim at a sample substance in a crucible, setting low-power laser, and starting a constant-speed temperature rise program to ensure that the temperature of the sample substance is lower than the phase change temperature of the sample substance in the whole experiment process;

when the thermoelectric voltage output signal is stable, the laser is turned off, and the thermoelectric voltage output signal is stable again; finally, changing the laser power;

putting 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 a 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 the laser calibration temperature experiment, wherein the empty crucible model refers to that the crucibles at the sample side and the reference side are both empty; the sample model refers to the sample placed in the sample side crucible.

2. The method of claim 1, wherein the temperature calibration method comprises: in the experimental measurement process of the differential scanning calorimeter, the measurement signal of the differential heat flow sensor is actually thermoelectric potential, but not heat flow, so that the static characteristic calibration is required to obtain the corresponding relation between a heat flow value and a potential value;

the static characteristic calibration principle is as follows: when the laser power is constant and the heat transfer process enters a stable state, the temperature difference between the two sides of the sample side and the reference side is kept constant; connecting the temperature sensors on the two sides into a measuring circuit to respectively obtain corresponding thermoelectric potentials, and calculating the difference value of the thermoelectric potentials; obtaining a static characteristic calibration factor K_ΦExpression (c):

Φ_ture＝K_Φ·DE_m

in the formula phi_tureFor laser generated heat flow, the unit is W; delta E_mIs the thermoelectric potential difference of the sample side and reference side temperature sensors, and has the unit of V;

and performing a laser calibration experiment by using the empty crucible model, and performing fitting calculation on the input signal and the output signal in a stable state to obtain a static characteristic calibration factor.

3. The method of claim 1, wherein the temperature calibration method comprises: and during dynamic calibration, a sample model of the differential scanning calorimeter is regarded as a second-order system model, and the temperature of the sample is reconstructed according to the model parameters.

4. The method of claim 3, wherein the temperature calibration method comprises: the temperature T of the sample_restructThe reconstruction expression is as follows:

wherein T is_MSMeasuring temperature, R, for the sample end_SSample end sample thermal resistance from phi_FSThe heat flow from the furnace to the temperature measuring point of the sample end, and C is the equivalent heat capacity of the sample reaction heat flow.

Technical Field

The invention relates to a calibration method of a Differential Scanning Calorimeter (DSC) based on laser power excitation, which comprises static characteristic calibration and dynamic characteristic calibration of laser power excitation, and also relates to a method for reconstructing the temperature of a sample of calorimetric data to improve the result of thermodynamic analysis.

Background

For a long time, DSC, which is the main force of thermal analysis, has the advantages of wide temperature range for research, small mass of used samples, high sensitivity and resolution, and capability of being used in combination with other technologies to obtain various information, and is widely applied to related fields such as chemical safety, polymer materials, biomedical treatment, fuel cells, agricultural engineering, thermodynamic research, and the like. The existing DSC calibration method mainly comprises two methods, namely phase change 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 phase-change temperature and the phase-change enthalpy of the standard substance has the limitations of few and discontinuous temperature points; the calibration by the electric joule heating effect is only suitable for cylindrical DSC in which a heater can be installed, but not suitable for tower or disk type DSC, and in addition, system errors can be caused by the problems of inconsistent positions of the heater and the sample, lead heat leakage and the like.

Evaluation of thermodynamic results is one of the important uses of differential scanning calorimetry. The reliability of the method is based on good experimental data and a reliable dynamic calculation method. When the sample is subjected to exothermic reaction to cause heat accumulation, the temperature of the sample can obviously deviate from the measured temperature; at the same time, the DSC has larger thermal inertia because the sample has lower thermal conductivity, which causes great errors in the thermodynamic analysis. The correction of heat flow data by deconvolution is the main method for solving the problems, but 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 conclusion, aiming at the limitation 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 obviously improves the accuracy and 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 sample temperature reconstruction method, which solves the problem that the sample temperature deviates from the measured temperature in the exothermic reaction of the sample and greatly improves the research level of thermal analysis dynamics and the accuracy of chemical thermal risk evaluation.

Disclosure of Invention

The method aims at solving the problems of difficult calibration, less calibration points, more system error sources and the like of the existing differential scanning calorimeter calibration method in the background art. 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 result of the thermodynamic analysis.

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 thermal current sensor device adopts a thermopile type thermal current sensor to output high-precision thermoelectric force signals; the furnace body temperature measurement and control system comprises four parts, namely a furnace cover, a furnace wall, a furnace bottom and a furnace chamber, wherein a through hole with the diameter of 11.5mm is formed in the center of the upper surface of the furnace cover and can allow laser to pass through, and thermocouples and heating rods are respectively arranged on the furnace cover, the furnace wall and the furnace bottom and can be used for setting a required temperature program, such as an isothermal or constant-speed temperature rise program; the data acquisition device is respectively connected with the heat flow sensor and control software for data display and recording to finish acquisition of the heat potential signal in the temperature control process; the data display and record 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 temperature environment of the furnace body.

The heat flow type DSC is generally composed of a sensor, a support frame, a furnace body and a crucible, and is a differential scanning calorimeter with a simple structure. And (3) putting the heat flow sensor device into the furnace chamber for fixing, and placing the crucible on the thermopiles on two sides of the differential heat flow sensor, thus finishing the construction of a simple heat flow type DSC.

The invention relates to a temperature calibration method of a differential scanning calorimeter based on laser power excitation, which comprises the following steps:

(1) aligning the laser beam to the center of the furnace cover, enabling the laser beam to penetrate through the furnace cover and irradiate the furnace cavity, opening the furnace cover, placing the empty crucible on the thermopile type differential heat flow sensor, opening the laser, only irradiating the laser on the inner surface of the crucible on the sample side, and finely adjusting the position of the laser until the output signal of the thermopile is observed to have obvious change. Then the laser is closed, the furnace cover is covered, and proper heat preservation measures are adopted to reduce convection and heat loss.

(2) And then turning on the laser, setting laser power, starting an isothermal mode temperature program, turning off the laser after the thermoelectric output signal is stable, and waiting for the thermoelectric output signal to be stable again. And setting different laser powers, and recording the magnitude of the thermoelectric potential of the differential heat flow sensor in the whole experimental process.

(3) And opening a laser to enable laser beams to aim at the sample substance in the crucible, paying attention to the fact that low-power laser needs to be set, and starting a constant-speed temperature rise program to ensure that the temperature of the sample substance is lower than the phase change temperature of the sample substance in the whole experiment process. And when the thermoelectric voltage output signal is stable, the laser is turned off, the thermoelectric voltage output signal is stable again, and the dynamic response curve of the thermoelectric voltage output signal is recorded. And finally, changing the laser power and repeating the experimental steps.

Different samples are put 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, processing the dynamic response curve of the sample model to obtain model parameters, and combining the two models to realize the laser calibration experiment.

The principle of the invention is as follows:

in the experimental measurement process of the DSC, the measurement signal of the differential heat flow sensor is actually the thermoelectric potential, not the heat flow itself, so 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 a steady state, the temperature difference between the two sides of the sample side and the reference side will be maintained constant. And connecting the temperature sensors on the two sides into a measuring circuit to respectively obtain corresponding thermoelectric potentials, and calculating the difference value of the thermoelectric potentials and the corresponding thermoelectric potentials. Obtaining a static characteristic calibration factor K_ΦExpression (c):

Φ_ture＝K_Φ·DE_m (1)

in the formula phi_tureFor laser generated heat flow, the unit is W; delta E_mThe thermoelectric potential difference between the sample-side and reference-side temperature sensors is given in V.

And performing a laser calibration experiment by using the empty crucible model, and performing fitting calculation on the input signal and the output signal in a stable state to obtain a static characteristic calibration factor. The dynamic characteristic calibration needs to use an empty crucible model and a sample model respectively to obtain and process the dynamic response curves of the empty crucible model and the sample model, and the time constant of the instrument can be obtained by performing fitting calculation on the dynamic response curve of the empty crucible model. The sample model is used for carrying out a laser calibration experiment, the dynamic response curve of the sample model is processed, model parameters can be obtained, and the two models are combined to realize the laser calibration experiment.

In the DSC measurement process, when a sample with low thermal conductivity is subjected to an exothermic reaction, heat is accumulated and cannot be timely transferred out, 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 the 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 pattern is distorted, and the thermodynamic calculation result is further inaccurate. According to the calibration method, the DSC sample model is taken as a second-order system model during dynamic calibration, and the sample temperature is reconstructed according to the model parameters, so that the accuracy of the thermodynamic calculation result can be greatly improved.

Furthermore, different calibration experiments use different models, and the empty crucible model means that crucibles on the sample side and the reference side are both empty; the sample model refers to a crucible in which a sample is placed.

Furthermore, the first problem of static characteristic calibration is that there is an excitation source capable of outputting constant heat flow, and the output heat flow is stable and controllable. The laser can meet the conditions, can output step signals, and can calibrate the static and dynamic characteristics of the instrument.

Compared with the traditional DSC calibration method, the method has the beneficial effects that:

1. the calibration method of the differential scanning calorimeter based on laser power excitation is used in combination with the static and dynamic characteristic calibration methods, and can effectively improve the precision and the simplicity of calibration.

2. For sample heat accumulation caused by exothermic reaction of a sample in the DSC measurement process, the sample temperature reconstruction method accords with the actual situation, and thermodynamic analysis is carried out by using n-level reaction simulation results, so that the accuracy of thermal analysis can be improved.

Drawings

FIG. 1 is a schematic diagram of a heat flow type DSC laser calibration module;

FIG. 2 is a diagram of a tower structure DSC structural model;

FIG. 3 is an equivalent circuit diagram of a tower structure DSC empty crucible model;

FIG. 4 is an equivalent circuit diagram of a tower structure DSC sample model;

FIG. 5 is a diagram illustrating the equivalent thermal resistance calculation results;

FIG. 6 is a schematic diagram illustrating the equivalent heat capacity calculation result;

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 construction DSC;

FIG. 9 is a relationship between temperature difference and furnace temperature;

FIG. 10 is a graph of temperature difference versus oven temperature after sample temperature reconstruction;

FIG. 11 thermodynamic results of different dataset solutions;

FIG. 12 is a graph of activation energy residual versus degree of reaction;

in the figure:

FIG. 1, 1.1 laser generator; 1.2. heating furnace; 1.3. a plurality of temperature measuring instruments; 1.4. and (4) 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 embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be described more clearly, in detail and completely in the following with reference to the accompanying drawings in the embodiments of the present invention.

A 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 laser calibration experiment is performed on an empty crucible model of a differential scanning calorimeter, a laser beam is firstly aligned to the center of a furnace cover, so that the laser beam penetrates through the furnace cover and irradiates the inside of a furnace chamber of a heating furnace 1.2.

2. The empty crucible was placed on a thermopile type differential heat flow sensor with tweezers by opening the lid, the heat flow sensor was transferred to a multi-channel thermometer 1.3(Fluke1586A), the laser was turned on, the laser generator was moved, and the laser was irradiated only on the inner surface of the crucible on the sample side. The heat generated by the laser is transferred to the temperature sensor along the crucible,

3. setting laser power of the laser, starting an isothermal mode temperature program in the upper computer 1.4 by the upper computer, turning off the laser after the thermoelectric force output signal is stable, and waiting for the thermoelectric force output signal to be stable again. And setting different laser powers, and recording the magnitude of the thermoelectric potential of the differential heat flow sensor in the whole experimental process. And (5) completing a dynamic response experiment of the DSC empty crucible model.

4. Different samples are put 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, a certain mass of sample substances are put into a crucible on the sample side, a laser is started to enable laser beams to aim at the sample substances in the crucible, small-power laser needs to be set, a constant-speed temperature rise program is started, and the temperature of the sample substances in the whole experiment process is guaranteed to be lower than the phase change temperature of the sample substances. And when the thermoelectric voltage output signal is stable, the laser is turned off, and the thermoelectric voltage output signal is stable again. And finally, changing the laser power and repeating the experimental steps.

In summary, the empty crucible model is used for laser calibration experiments, fitting calculation is carried out on input signals and output signals under a stable state, static characteristic calibration factors can be obtained, fitting calculation is carried out on a dynamic response curve of the empty crucible model, and a time constant of an instrument can be obtained. The sample model is used for carrying out a laser calibration experiment, the dynamic response curve of the sample model is processed, model parameters can be obtained, and the two models are combined to realize the laser calibration experiment.

The dynamic characteristic calibration theory and the derivation process of the differential scanning calorimeter based on laser power excitation are as follows:

as shown in fig. 2, a tower-type structure DSC is selected for analysis, and a mathematical model thereof is derived in detail through an equivalent circuit diagram to obtain an equivalent model of a differential scanning calorimeter, wherein the tower-type structure DSC in fig. 2 comprises a crucible 2.1; sample 2.2; reference sample 2.3; a heat flow sensor 2.4; a support frame 2.5; and 2.6 of a furnace body.

The derivation process of the tower structure DSC equivalent model is as follows:

for the empty crucible model of tower structure DSC, the equivalent circuit diagram is shown in fig. 3, and the derivation process ignores the influence of thermal convection and thermal radiation, only considers the effect of thermal conduction, and considers that the temperature in the sample and crucible is uniform. In FIG. 3, subscripts S and R represent the sample end and the reference end, respectively, F represents the furnace, and M represents the temperature measurement point; the measured temperatures of the sample end and the reference end are respectively T_MS、T_MRThe temperature of the furnace is T_FThe unit is K; the thermal resistance from the furnace to the point of temperature measurement at the sample end is R_FMSThe unit is K/W; heat capacity of C_FMSThe unit is J/K; similarly, the thermal resistance of the reference sample end is R_FMRHeat capacity of C_FMR. Setting the furnace temperature to be T under a certain temperature program_FHeat flows from the furnace to the crucible and finally the system is in steady state equilibrium.

In the derivation, measurement errors are made if only the sample heat capacity and the thermal resistance between the sample and the furnace are taken into account, if anyThe thermal capacity resistance of all the structures in the apparatus again complicates the problem, so the invention regards the thermal capacity from the furnace to the crucible as a whole, called equivalent thermal capacity C, and similarly the thermal resistance from the furnace to the crucible, called equivalent thermal resistance R. Since the tower structure DSC is a symmetrical structure, it is assumed that R is_FMS＝R_FMR＝R；C_FMS＝C_FMR＝C。

An equivalent circuit diagram of a tower-type DSC sample model obtained after samples are put in crucibles at two sides is shown in FIG. 4, wherein the sample thermal resistances of the sample end and the reference end are R respectively_S、R_R(ii) a The heat capacities of the sample and the reference sample are respectively C_S、C_R(ii) a Reaction heat flow of the sample is phi_rAnd the unit is W.

Heat flow phi from the furnace to the sample/reference temperature measurement point_FS/Φ_FRExpressed as follows, heat flow difference phi_mTo measure the signal.

Equation (2) minus equation (3) yields:

the reaction heat flow of the sample is phi_rFor exothermic reactions,. phi.,. phi_rIs negative, for endothermic reactions,. phi_rIs positive. The heat flow expressions for the sample and reference terminals were derived as follows:

formula (5) minus formula (6), the parallel connection of vertical (4) yields:

as can be seen from equation (7), the expression of the DSC mathematical model is first order. Reacting the sample with heat flow phi_rAs input signal, heat flow difference phi_mThe mathematical model of the instrument, considered as the output signal, can be equivalent to:

coefficient a in the formula₁～a₃Referred to as model parameters, can be derived from instrument characteristics. Under the empty crucible model, laser is irradiated on the inner surface of the empty crucible on the side of the sample to generate heat flow phi_rFrom equation (7), the mathematical expression of the DSC empty crucible model can be derived:

in the formula, tau is an instrument time constant and is equal to the product of equivalent heat capacity and equivalent heat resistance, and the unit is s.

Considering the empty crucible model as a first order system, equation (9) can be considered as a first order differential equation, thus obtaining the output signal Φ_mThe expression of the solution is as follows:

the time constant of the instrument can be obtained by fitting the step response curve of the empty crucible model according to equation (10).

In the tower-type structure DSC hollow crucible model, the equivalent thermal resistance value is equal to the static characteristic calibration factor according to the equation (1)Seed K_ΦThe product of the equivalent heat capacity and the equivalent heat resistance is the instrument time constant, and the static characteristic calibration factor K is obtained through laser calibration_ΦAnd instrument time constants, the values of equivalent heat capacity and equivalent heat resistance can be calculated as shown in fig. 5 and 6.

Placing a sample that does not undergo a chemical reaction at the reference end, the temperature rate of change of the reference sample can be considered to be equal to the heating rate β, i.e.:

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 derived:

equation (13) minus equation (14) yields 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:

by substituting formulae (6) and (11) for formula (16), it is possible to obtain:

substituting formula (17) for formula (12) to obtain sample reaction heat flow phi_rAnd the measurement signal phi_mThe relationship of (a) or (b), i.e. the mathematical expression of the DSC sample model:

as can be seen from equation (18), the tower-type structure DSC sample model 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_RSample thermal resistance R_SAnd the influence of the set temperature program.

In the tower structure DSC sample model, equation (18) is treated as a second order ordinary differential equation in the same way:

coefficient A₀～A₃Are all constant terms, phi_rIs an input signal, phi_mIs the output signal. Then the output signal phi_mThe solution is in the form:

the characteristic equation is as follows:

in the experiment, a sample model dynamic response curve is obtained and nonlinear fitting is performed on the data by using the formula (20), so that two characteristic roots are obtained. The required parameters are substituted into a characteristic equation (21), and the thermal resistance R of the sample can be solved_SAs in fig. 7.

In summary, the empty crucible model is used for laser calibration experiments, fitting calculation is carried out on input signals and output signals under a stable state, static characteristic calibration factors can be obtained, fitting calculation is carried out on a dynamic response curve of the empty crucible model, and a time constant of an instrument can be obtained. The sample model is used for carrying out a laser calibration experiment, the dynamic response curve of the sample model is processed, model parameters can be obtained, and the two models are combined to realize the laser calibration experiment.

Compared with the traditional differential scanning calorimeter calibration method, the differential scanning calorimeter calibration method has the following advantages: the laser is used as an excitation source, so that the laser has the advantage of non-contact and cannot pollute an instrument. The laser can output step signals to calibrate the static characteristics and the dynamic characteristics of the instrument, and the time constant of the instrument can be conveniently measured. 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 type DSC in an electric heating calibration method. The invention can close the laser at any time to check the position of the baseline in the experimental process so as to judge 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, namely sample heat accumulation and instrument thermal inertia, on thermodynamic results and corrects calorimetric data by combining with model parameters obtained by a laser calibration theory, thereby greatly improving the accuracy of thermodynamic calculation results.

The principle of the sample temperature reconstruction method is as follows:

for a sample having good thermal conductivity such as a metal, the thermal resistance is small, and the measurement temperature is considered to be equal to the sample temperature. But for samples with lower thermal conductivity, the sample thermal resistance cannot be neglected. When the sample is subjected to an exothermic reaction, heat is accumulated and cannot be transmitted out in time, so that the temperature of the sample rises and deviates from the measurement temperature obviously. Based on the relationship between the sample temperature and the measured temperature, the reconstructed temperature T of the sample can be derived from equation (13)_restructExpression (c):

it can be seen from the equations (18) and (22) that, if the measurement data is optimized, the key is to find the equivalent heat capacity and the equivalent heat resistance of the instrument and the sample heat resistance. And by combining the laser calibration theory, the required parameters can be obtained through laser static characteristic and dynamic characteristic calibration.

The sample temperature reconstruction method provided by the invention can effectively improve the accuracy of thermodynamic calculation results. An ANSYS software thermal analysis module is adopted to design a tower-type structure DSC heat transfer model, and the exothermic effect of n-level reaction of the substance is verified through simulation calculation.

The steps of establishing the DSC simulation model by ANSYS software are as follows:

and drawing a model according to the simplified tower structure DSC structure diagram in figure 8 and importing the model into ANSYS software. And (6) carrying out simulation. After the model is divided into meshes, the material attribute of the model is required to be set, and the pretreatment of the simulation process is completed.

The specific theory of the n-stage reaction is as follows:

the Arrhenius (Arrhenius) equation describes the relationship between reaction rate and temperature, from which n-order reaction models can be derived:

in the formula phi_rIs the sample reaction heat flow, W; q is the heat of reaction, J; d α/dt is the reaction rate, s^-1(ii) a A is an antecedent factor, s^-1(ii) a E is activation energy, J/mol; r is the gas constant and R is 8.314J/(mol · K), T is the sample temperature, K; α is the degree of reaction; f (α) is a kinetic model; n is the reaction order.

The activation energy E can be obtained by differential equal transformation rate method_αThe relation between the degree of reaction alpha and the dynamic model f (alpha) is not needed to know specific information, so that the measurement caused by improper model selection can be reducedThe effect of inaccurate results. 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_α，A_αAnd f (alpha) is the index factor, activation energy and kinetic model given alpha respectively. Index i indicates different heating rates, T_α,iIs the sample temperature at which alpha is reached at the ith heating rate. Selecting ln (d alpha/dt) at different heating rates at the same reaction degree alpha_α,iAnd 1/T_α,iThe values are fitted linearly, and E is determined from the slope of the fitted line_αThe value of (c).

The n-stage reaction calculation steps are as follows:

setting the heating rate of the furnace to be 1, 2, 4 and 8K/min, and selecting Ba (TFA) as a sample₃The reference sample was alumina. The kinetic parameters used for the simulation were as follows: activation energy E177 kJ/mol, presymptor A4.5E 13s^-1The reaction heat Q was 9.2J, and the reaction model f (α) was (1- α). According to the n-level reaction model, discrete heat flow data is generated by utilizing the kinetic parameters, and the data is converted into heat flow density and then applied to a sample of the tower-type structure DSC sample model. Setting an ambient initial temperature T₀The simulation results were read by running from reaction degree α of 0 to reaction degree α of 1 at 508.18K.

In the process of simulating n-stage reaction, the temperature T of the sample is different at different heating rates_SAnd measuring the temperature T_MSTemperature difference and furnace temperature T_FThe 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 difference between the sample temperature and the measured temperature was 0.53, 0.94, 1.66 and 2.99K at heating rates of 1, 2, 4, 8K/min, respectively.

The sample model used for simulating n-stage reaction is the same as the sample model used for calibrating static characteristic and dynamic characteristic, so the parameters of sample thermal resistance, equivalent thermal resistance and the like are solved by fittingThe numbers may be general. According to the formula (22), the sample reconstitution temperature T can be obtained_restruct. Sample temperature T at different heating rates_STemperature T of sample reconstruction_restructThe relationship between the temperature difference of (a) and the furnace temperature is shown in FIG. 10. After temperature reconstruction, the maximum temperature difference between the obtained sample temperature and the sample reconstruction temperature is respectively 0.015K, 0.03K, 0.06K and 0.12K, the temperature difference is greatly reduced, and the result shows that the temperature after the sample temperature reconstruction is closer to the sample temperature.

To further verify the impact of different types of data processing on the evaluation of thermodynamic outcomes, four data sets were set:

(a) output signal (raw data);

(b) correcting only the data for heat flow;

(c) reconstructing data only of the sample temperature;

(d) while correcting the heat flow and reconstructing the data for the sample temperature.

Correcting only the heat flow data refers to correcting the output signal according to equation (18). Fig. 12 shows thermodynamic results of different data set solutions, in which the solid line is a thermodynamic result calculated from the data sets (a) - (d), the dotted line is a true value of the thermodynamic result, and the data sets a, b, c, d correspond to the curves a, b, c, d.

As can be seen from fig. 11, the curve a deviates significantly from the true value, and only the temperature reconstruction is performed to obtain the curve c, and only the heat flow correction is performed to obtain the curve b. It has been found that the effect of temperature correction on thermodynamic parameters is greater than the effect of heat flow correction. And after the temperature and the heat flow are corrected simultaneously, a curve d is obtained, and the consistency of the curve d and the true value is the best.

And (3) taking data with the reaction degree alpha of 0.05-0.95, calculating the residual difference between the activation energy and the true activation energy corresponding to the data sets (a) - (d), and calculating the Root Mean Square Error (RMSE) according to the formula (25), wherein the results are shown in FIG. 12 and Table 2.

In the formula, E_kIs an activation energy measurement; e₀For the true value of activation energy, 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 the exothermic reaction of the sample, the heat build up inside the sample accelerates the reaction, and thus the apparent activation energy is greater than the actual activation energy. 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 to 0.64kJ/mol from the original 21.13kJ/mol, and the accuracy of the thermodynamic result is effectively improved.

According to the experimental result, the deviation between the sample temperature and the measured temperature is effectively reduced by the sample temperature reconstruction method, and the experiment heat release obtained by the sample temperature reconstruction method is closer to the reality.

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 include static and dynamic characteristic calibration and a method for correcting calorimetric data. The differential scanning calorimeter calibration method provided by the invention overcomes the disadvantages of fewer types of available standard substances, high price, discrete heat flow heat calibration points, more system error sources and the like in the traditional calibration method. Therefore, the invention has great significance for the research of the calibration method of the errand scanning calorimeter. In addition, the sample temperature reconstruction method solves the problem that thermodynamic result calculation is inaccurate due to deviation of the measured temperature from the sample temperature and thermal inertia of an instrument in practical application in principle. Therefore, the achievement of the invention has great significance for improving the calibration efficiency of the differential scanning calorimeter and the accuracy of the thermodynamic analysis result.