Simulation method of local photothermal effect in photovoltaic hydrogen production

Abstract

The present invention provides a simulation method for the local photothermal effect in photoelectric hydrogen production. The main steps include: obtaining parameters and constructing a simplified 3D electromagnetic field model of the photoanode; calculating the thermal power density of the metal nanoparticles on the photoanode and obtaining the average heat production; constructing a macroscopic equivalent temperature field model; calculating the total heat production of the metal nanoparticles according to the experimental data, and substituting it into the model as a heat source term; drawing the local temperature distribution cloud map and the time-domain temperature rise curve. Compared with the traditional simulation method, the macroscopic equivalent model constructed by the present invention achieves the fit with the experimental conditions and saves a lot of computing resources and time; compared with experimental measurements, the size of the local thermal effect obtained by this simulation is more accurate and can more intuitively display its characteristics. The present invention provides a basis for exploring the microscopic mechanism of the photothermal effect, and also provides technical support for the thermal management of large-scale photoelectric water decomposition hydrogen production systems.

Description

Technical Field

[0001] The present invention belongs to the technical field of photoelectric water decomposition to produce hydrogen, and relates to a simulation method for the local photothermal effect generated by a composite photoanode under sunlight conditions based on finite element calculation. Background Art

[0002] Photoelectric water splitting to produce hydrogen can directly convert solar energy into green fuels and is one of the most promising methods to provide sustainable and clean energy. Among them, loading metal nanoparticles on semiconductor substrates is a common method for preparing high-performance composite photoanodes. In recent years, some studies have found that the photothermal effect generated by thermal relaxation of metal nanoparticles also promotes the hydrogen production reaction. However, due to the microscopic nature of nanomaterials, the heat generated by their photothermal effect has limited effect on the overall aqueous solution, and often reflects the local thermal effect near the photoanode. At the same time, in the large-scale exploration of photoelectric water splitting to produce hydrogen, it is found that the temperature of the system has a great influence. Therefore, if you want to explore the influence and mechanism of photothermal in the water splitting hydrogen production system, you first need to get the size and characteristics of the local thermal effect. However, current experimental temperature measurement characterization methods, such as infrared thermal imagers, thermal resistors, etc., cannot accurately measure the size of the thermal effect, and it is even more difficult to characterize the local characteristics of the thermal effect. The previous simulation method is a model constructed at the nanoscale, and its condition setting is far from the experimental conditions and the calculation is large. Therefore, it is very important to find a simulation method that fits the experimental conditions and is simple to calculate to achieve accurate characterization of the local photothermal effect of the photoanode. Summary of the invention

[0003] In view of the above problems, the present invention designs an equivalent simplified temperature field model based on finite element analysis to obtain the local temperature distribution and time-domain temperature rise generated by the photothermal effect of the composite photoanode.

[0004] The present invention adopts the following technical solutions:

[0005] Step 1: According to the size of the prepared semiconductor substrate, the specific size of the metal nanoparticles and their position and density arrangement, a simplified solid 3D model is established in the COMSOL wave optics module;

[0006] Step 2: Select electromagnetic wave and frequency domain physics field, define the electromagnetic properties of dielectric, metal, and semiconductor materials, and set boundary conditions.

[0007] Step 3: Mesh the entire physical field, including selecting the unit type, setting the mesh size, and optimizing the mesh accuracy. The solver is set to parametric sweep, and the independent variable is the incident wavelength;

[0008] Step 4: The electromagnetic field law is calculated based on Maxwell's equations, and the electromagnetic power loss density inside the metal nanoparticles, i.e., the heat source density, is obtained. The expression for the heat generated by the nanoparticles, Q, is:

[0009]

[0010] σ abs is the absorption cross section of the nanoparticle, I is the irradiance of the incident light, n is the optical refractive index of the surrounding medium, c is the speed of light in vacuum, ε ω is the dielectric constant of the nanoparticles, and E0 is the initial electric field of the incident light. E0 is determined by the incident light irradiance I. Substituting the corresponding E0 value into the incident port, the heat generation Q can be calculated by the following formula:

[0011]

[0012] q(r) is the thermal power density, ω is the frequency of the incident light, Im(ε ω ) is the imaginary part of the dielectric constant, ∫ NP It refers to the volume integral of the nanoparticle, and E(r) is the electric field strength inside the metal nanoparticle. Due to the inconsistency of the internal electric field strength, the structural thermal power density q(r) is obviously non-uniform, especially near the particle gap, but due to the large difference in thermal conductivity between metal and water media, for nanoparticles, their internal temperature can be approximated to be uniform, and the heat energy diffuses in the particle boundary and then diffuses out through the water;

[0013] Step 5: Calculate the average heat generation Q of the metal nanoparticles according to step 4. V ;

[0014] Step 6: In order to reduce the amount of model calculation and better match the experiment, a macro equivalent temperature field model is constructed in the heat transfer module;

[0015] Step 7. Define the density, specific heat capacity and thermal conductivity of the medium (water), metal and semiconductor materials. Substitute the total heat generated by the metal nanoparticles into the particles in the macro equivalent model as the heat source term, and set the boundary as thermal insulation;

[0016] Step 8: Set the solver to transient state, and keep the time range consistent with the experiment;

[0017] Step 9, draw a local temperature distribution cloud map of the simplified model;

[0018] Step 10: Collect data on the temperature of the center point of the model at different times, and draw a temperature rise curve of the photoanode over time. Compare with the experimental results to verify the accuracy of the simulation results, so as to accurately characterize the local photothermal effect and replace the experimental test method;

[0019] Preferably, in step 2, the boundary conditions are set as follows: a perfectly matched layer PML is constructed at both ends of the model, the thickness of which is one quarter of the initial incident wavelength lda0, ports are set at both ends of the perfectly matched layer as the incident and outgoing electromagnetic fields respectively, and other boundaries are set as scattering boundary conditions.

[0020] Preferably, in step 4, the value of E0 is determined by the incident light irradiance I, and in order to match the experimental conditions (simulated sunlight 1.5M, 100mW / cm 2 ) is consistent with the I value, which is set to 1kW / m 2 Therefore, the corresponding E0 value (868 V / m) is substituted into the incident port.

[0021] Preferably, in step 5, the average heat generation of the metal particles is Q V The calculation method is: perform volume integration on the thermal power density of metal nanoparticles at different positions to obtain the heat generation of metal nanoparticles at different positions at different wavelengths. Continue to integrate over the entire wavelength range to obtain the total heat generation Q of a single metal nanoparticle, and then average it to obtain the average heat generation Q V .

[0022] Preferably, in step 6, the method for constructing the macro equivalent model is: all metal nanoparticles on a photoanode of a certain area (X*Y mm) are equivalently replaced by metal micron particles uniformly distributed on a flat plate of the same area. The flat plate is set to the properties of the semiconductor material, and the thickness of the flat plate is the thickness of the photoanode substrate.

[0023] Preferably, in step 7, the total heat generation is calculated by estimating the number of metal nanoparticles per unit area based on the SEM and TEM images obtained in the experiment and multiplying the result by the average heat generation Q V , and obtain the total heat generated by the metal nanoparticles. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is a simulation configuration in the wave optics module of the present invention.

[0025] Figure 2 According to the present invention, metal nanoparticles at different positions are selected for volume integration according to symmetry to obtain heat generation at different wavelengths.

[0026] Figure 3 This is the macroscopic equivalent photothermal model described in the present invention.

[0027] Figure 4 The three-dimensional local temperature field distribution diagram obtained by the present invention

[0028] Figure 5 Schematic diagram of the local temperature gradient obtained by the present invention

[0029] Figure 6 Schematic diagram of heat flow transfer obtained by the present invention

[0030] Figure 7 This is a comparison chart of the simulation and experimental temperature rise changes described in the present invention.

[0031] Figure 8 It is a schematic diagram of the solar water decomposition hydrogen production system of the present invention. DETAILED DESCRIPTION

[0032] The following, in combination with the accompanying drawings, takes the simulation of the local photothermal effect of the Au / TiO2 photoanode as an example to further illustrate the specific implementation mode of the present invention in detail, with the aim of helping technicians in this field to have a more complete, accurate and in-depth understanding of the concept and technical solution of the present invention, and to facilitate its implementation.

[0033] Step 1: Figure 1 As shown in the figure, according to the size of the prepared TiO2, the specific size of the Au nanoparticles (14-20nm) and their position and density arrangement. A perfect matching layer PML is constructed at both ends of the model, with a thickness of one quarter of the initial incident wavelength lda0 (400nm), and a simplified solid 3D model is established in the COMSOL wave optics module.

[0034] Step 2: Select electromagnetic wave. Frequency domain physics field. Define the real part of the refractive index of the medium water as 1.33 and the imaginary part as 0. The electromagnetic properties of Au and TiO2 materials are selected from the software's own data. Set ports at both ends of the perfect matching layer as the incident and outgoing electromagnetic fields, and set other boundaries as periodic boundary conditions.

[0035] Step 3: Mesh the entire physical field, including selecting the unit type, setting the mesh size, and optimizing the mesh accuracy. The solver is set to parametric sweep with a range of 300-700nm.

[0036] Step 4: The electromagnetic field law is calculated based on Maxwell's equations, and the electromagnetic power loss density inside the Au nanoparticles, i.e., the heat source density, is obtained. The expression for the heat generated by the nanoparticles, Q, is:

[0037]

[0038] σ abs is the absorption cross section of the nanoparticle, I is the irradiance of the incident light, n is the optical refractive index of the surrounding medium, c is the speed of light in vacuum, ε ω is the dielectric constant of the nanoparticles, E0 is the initial electric field of the incident light, and the value of E0 is determined by the incident light irradiance I. In order to match the experimental conditions (simulating sunlight 1.5M, 100mW / cm 2 ) is consistent with the I value, and the I value is set to 1kW / m2 Therefore, the corresponding E0 value (868V / m) is substituted into the incident port. The heat generation Q can be calculated by the following formula:

[0039]

[0040] q(r) is the thermal power density, ω is the frequency of the incident light, Im(ε ω ) is the imaginary part of the dielectric constant, ∫ NP It refers to the volume integral of the nanoparticle, and E(r) is the electric field strength inside the metal nanoparticle. The magnitude of the thermal power density is proportional to the magnitude of the electric field, and because the internal electric field strength E(r) is inconsistent, the structural thermal power density q(r) is obviously non-uniform, especially near the particle gap. However, due to the large difference in thermal conductivity between Au and water media, for nanoparticles, their internal temperature can be approximated to be uniform, and the heat energy diffuses in the particle boundary and then diffuses out through the water.

[0041] Step 5: According to the principle of symmetry, we selected Figure 2 The heat generation of Au nanoparticles at different positions in the image was obtained by integrating their thermal power density by volume. The total heat generation Q of a single Au nanoparticle was obtained by integrating the entire wavelength range, and the average heat generation Q was obtained by averaging. V .

[0042] Step 6: Construct a macroscopic equivalent temperature field model in the heat transfer module, which can reduce the amount of model calculation and maintain better consistency with the experiment. Figure 3 As shown, 1cm 2 All Au nanoparticles per unit area are equivalently replaced by Au micron particles with a diameter of 300 um uniformly distributed (21*21) on a 1cm*1cm*0.1cm TiO2 flat plate.

[0043] Step 7: Define the density, specific heat capacity and thermal conductivity of the medium (water), Au and TiO2 materials. According to the SEM and TEM images obtained from the experiment, estimate the number of metal nanoparticles per unit area and multiply it by the average heat generation Q V , the total heat generated by Au nanoparticles is about 0.6 W. Substitute 0.6 W into the macroparticles in the macro equivalent model as the heat source term. The boundary is set as thermal insulation.

[0044] Step 8. Set the solver to transient with a time range of 0-120 minutes.

[0045] Step 9: Draw the local temperature distribution cloud diagram of the Au / TiO2 simplified model. Figure 4,5 is the 3D local temperature field distribution diagram and temperature gradient diagram of the model at 60 minutes. It clearly shows the strong local temperature rise around the composite photoanode, proving the effectiveness of the local photothermal effect. Figure 6 It shows the heat transfer direction of the heat source Au particles to the surrounding environment.

[0046] Step 10: Collect data on the temperature of the center point of the model at different times, and draw a temperature rise curve of the photoanode over time. Figure 7 , the temperature at the photoanode rises from 25°C to 42.3°C within 0-60min. For comparison, an infrared thermal imager was used in the experiment to test the temperature changes of the photoanode in air and water under simulated sunlight. When in air, the thermal conductivity of air is much lower than that of water, and there is no radiation attenuation, so the measured temperature of the photoanode is higher. When in water, due to the errors of temperature measuring instruments such as infrared thermal imagers or thermal resistors, and the locality of the temperature rise of the photoanode in water, the temperature measured in the experiment is only the temperature of the surface water (60min--35°C), which is much lower than the actual temperature around the photoanode. Comparing the three sets of data, it can be seen that the simulated temperature is between the experiment (air) and the experiment (water), which also verifies the rationality and accuracy of the simulation results. Therefore, our macro equivalent model can replace experimental testing and more accurately characterize the size and local distribution characteristics of the photothermal effect.

[0047] It is worth noting that in the future industrial application of solar photovoltaic water splitting to produce hydrogen ( Figure 8 ), the comprehensive thermal management of the system is very important. Low system temperature is not conducive to the decomposition of water, while too high temperature will lead to the generation of a large amount of water vapor, affecting the stability of the system and not conducive to the purification of H2. The present invention can provide technical support for the thermal management of the system.

[0048] Those skilled in the art should note that the embodiments described in the present invention are merely exemplary, and various other substitutions, changes and improvements may be made within the scope of the present invention. Therefore, the present invention is not limited to the above embodiments, but is only limited by the claims.

Claims

1. A simulation method for the local photothermal effect in photoelectric hydrogen production, characterized in that The following steps are involved: Step 1: According to the size of the prepared semiconductor substrate, the specific size of the metal nanoparticles and their position and density arrangement, a simplified solid 3D model is established in the COMSOL wave optics module; Step 2: Select the electromagnetic wave-frequency domain physical field, define the electromagnetic properties of dielectric, metal, and semiconductor materials, and set boundary conditions; Step 3: Mesh the entire physical field, including selecting the unit type, setting the mesh size, and optimizing the mesh accuracy; the solver is set to parametric sweep, and the independent variable is the incident wavelength; Step 4: The electromagnetic field law is calculated based on Maxwell's equations, and the electromagnetic power loss density inside the metal nanoparticles, i.e., the heat source density, is obtained; the expression of the heat generated by the nanoparticles, Q, is: σ abs is the absorption cross section of the nanoparticle, I is the irradiance of the incident light, n is the optical refractive index of the surrounding medium, c is the speed of light in vacuum, ε ω is the dielectric constant of the nanoparticles, E0 is the initial electric field of the incident light; E0 is determined by the incident light irradiance I, and the corresponding E0 value is substituted into the incident port, so the heat generation Q is calculated by the following formula: q(r) is the thermal power density, ω is the frequency of the incident light, Im(ε ω ) is the imaginary part of the dielectric constant, ∫ NP refers to the volume integral of the nanoparticle, E(r) is the electric field intensity inside the metal nanoparticle; Step 5: Calculate the average heat generation Q of the metal nanoparticles according to step 4. V ; Step 6. In order to reduce the amount of model calculation and better match the experiment, a macro equivalent temperature field model is constructed in the heat transfer module. The construction method of the macro equivalent model is as follows: all metal nanoparticles on a certain area of ​​the photoanode are equivalently replaced by metal micron particles uniformly distributed on a flat plate of the same area; the flat plate is set to the properties of the semiconductor material, and the thickness of the flat plate is the thickness of the photoanode substrate; Step 7: Define the density, specific heat capacity and thermal conductivity of dielectric, metal and semiconductor materials; substitute the total heat generated by metal nanoparticles into the particles in the macro equivalent model as the heat source term, and set the boundary as thermal insulation; Step 8: Set the solver to transient state, and keep the time range consistent with the experiment; Step 9, draw a local temperature distribution cloud map of the simplified model; Step 10: Collect data on the temperature of the center point of the model at different times, and draw a temperature rise curve of the photoanode over time.

2. The method according to claim 1, characterized in that The boundary conditions in step 2 are set as follows: a perfectly matched layer PML is constructed at both ends of the model, with a thickness of one quarter of the initial incident wavelength lda0, ports are set at both ends of the perfectly matched layer as the incident and outgoing electromagnetic fields respectively, and other boundaries are set as scattering boundary conditions.

3. The method according to claim 1, characterized in that The value of E0 in step 4 is determined by the incident light irradiance I, which is similar to the experimental conditions of sunlight 1.5M, 100mW / cm 2 The I value is set to 1kW / m 2 ; Therefore, the corresponding E0 value of 868 V / m is substituted into the incident port.

4. The method according to claim 1, characterized in that: The average heat generation Q of the metal particles in step 5 V The calculation method is as follows: the thermal power density of metal nanoparticles at different positions is volume integrated to obtain the heat generation of metal nanoparticles at different positions at different wavelengths; the total heat generation Q of a single metal nanoparticle is obtained by integrating the entire wavelength range, and the average heat generation Q is obtained by averaging. V .

5. The method according to claim 1, characterized in that The total heat generation in step 7 is calculated by estimating the number of metal nanoparticles per unit area based on the experimental SEM and TEM images, and multiplying the average heat generation Q by V , and obtain the total heat generated by the metal nanoparticles.

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