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Abstract
In order to characterize the infrared (IR) radiation absorption and/or emission performances of functional porous polymers which claim to have healthcare functions due to IR excitation and emission by processing technologies, a radiative transfer model was constructed based on the principle of IR radiation, the Beer–Lambert law, the Fresnel’s formula and Planck’s law. The theoretical analysis was conducted for the IR management optical properties of the porous sheet polymer materials, including IR reflection, transmission, absorption and emission behaviours during the dynamic process of IR radiation. A modeling method for characterization and revealing of IR management optical properties and optical and thermal transfer behaviours of the reflection and transmission was then investigated from the structural parameters and the temperature rise characteristics of the porous sheet polymer materials during the dynamic IR radiation process. The model was validated by comparing the predicted values from the radiative transfer model with the measured values from the test results of the validation experiments of eight typical porous sheet polymers in an experimental setup. The model was modified by consideration of the influences of two types of micro-voids defects represented by the porosity of micro structure and the thickness compression ratio. The micro-voids defects factors were added to the structural parameters, and therefore the model was improved and the maximum prediction errors of the transmission and reflection surfaces were mostly less than 10%. The radiative transfer model provides the theoretical fundamentals for the evaluation and guidance of IR management optical performances for new products design, development, fabrication and processing in industrial application of functional porous polymers.
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1. Introduction
The functional porous polymers such as high emissivity infrared radiation materials and far infrared functional textiles which claim to have enhanced infrared emission performances are more and more widely used in healthcare, medical, building, industrial and household application conditions, since porous polymers have many advantages of physical and chemical attributions such as light weight, controllable pore structure, large specific surface area, good chemical and thermal stability, strong adsorption capacity, good permeability and easy surface functionalization. The typical functional porous polymer materials are functional textiles which are used in medical and household products.
With the application of nanoparticles and metal oxides to textile materials, the functional textiles with different performance such as antibacterial, UV shielding, thermal comfort, healthcare and even camouflage with far infrared emission have been developed [1–4]. For household products, the thermal comfort is an important index to evaluate the thermal properties [5]. The thermal comfort is related with the heat transfer through the porous polymer materials such as the functional textiles and textiles based composites. The heat transfer of the microclimate of the air, polymers and skin contains three processes: conduction, convection and radiation. Extensive studies have been conducted for the thermal properties evaluation including heat conduction and convection performances of the polymer materials, and typical methods include the calorimeter [6,7], thermistor [8], IR thermocamera [9–11], Lee’s disk method [12], heat flow meter approaches [13–17], and transient hot disk or hot-wire method [17–19], as well as the transient fluorescence spectroscopy technique [20]. These methods can be applied for the measurement and characterization of the thermal properties of polymer materials.
In the three distinct processes of heat transferring through the clothing in a wearing environment, thermal radiation plays a more important role than the other two ways of conduction and convection [21]. The heat transfer by radiation usually occurs in the form of electromagnetic waves, mainly in the infrared band. The thermal radiation is actually the infrared radiation according to Wein’s Law, and the infrared wavelength range associated with human physiological process is 8–14µm [22]. When the infrared rays interact with the polymer materials, reflection, absorption, transmission and emission occur, and the values of these properties are different with different materials during the dynamic IR radiation process [23]. We define these properties as the IR management optical properties of polymer materials, that is, the overall characteristics of the absorption, reflection, transmission and emission of IR radiation by the coupling of polymer material and environment during the dynamic IR radiation process, which are important physical properties of porous polymer materials and important indices for evaluation of functional textiles.
Traditional studies of thermal radiation properties are based on a radiative thermal/heat conductivity value that obtained via empirical methods or rigorous theories. FTIR is the typical instrument used for the measurement of infrared transmission, reflection and emission ratio in the steady state. Based on FTIR, extensive studies have been carried out for the evaluation of radiative thermal properties of polymeric materials [24–30]. Generally, radiative thermal conductivities were determined from the measurements using FTIR [24–27]. Upon different applications, other radiative properties were obtained in many studies, such as surface emissivity from the spectral radiance measurement [28], spectral absorption coefficient and refractive index calculations from spectral transmissivity and reflectivity measurements [29], and absorption characteristics from absorptivity spectra [30]. Combined with a specially made blackbody, an FTIR spectral radiometer was employed by H. Zhang et al. [28] to measure the spectral radiance of fabrics, which had the advantage that the surface IR emissivity of fabric in the wavelength between 8µm and 14µm was measured. Other studies had advantages in uncertainty analysis for measurement of radiative thermal conductivity [26], transmittance test using KBr as a diluent for composites difficult to determine the spectral extinction coefficient via experiment accurately [27], and investigation of the effect of temperature on absorbance [29]. In recent years, some new technologies have been developed for characterization radiative properties of polymeric materials, such as the experimental apparatus including a thermal imaging camera to detect the radiance in the MIR wavelength range between 7.5–14.0 µm for obtaining the emissivity of the sample [31], and a temperature-controlled spectrophotometry method to obtain the effective radiative properties of heterogeneous semi-transparent media at much higher temperature by measuring the reflectances and transmittances [32]. However, these existing methods are not capable of representing the IR management optical properties of polymer materials directly during the dynamic process of IR radiation.
In the simulation and prediction model of infrared radiation properties, theoretical models of thermal conductivities for polymer materials were proposed and constructed in many studies, and mainly focused on the model of heat transfer by conduction [33–36], the model of heat transfer by conduction, convection and radiation [37–43], and the model of radiative properties [44–48]. In the model of heat transfer by conduction, S. J. Kim et al. [34] took advantage of phonon scattering and investigated the effects of filler connectivity on the heat conduction of polymer composites using various types of thermally conductive fillers, and a theoretical model of thermal conductivity including the concept of phonon scattering in a two-phase material was proposed. S. Zhai et al. [35] used modeling methods combined with experimental data to qualitatively and quantitatively analyze the impact of various factors on the effective thermal conductivity (ETC) of polymer composites for the guidance of choice and design of particle-filled composites in engineering applications. This study was representative in modeling method and application of heat transfer by conduction. Simultaneously, many studies in this field focused on the heat insulation properties of polymer materials. The influence of morphology and cell gas composition on heat insulation properties of polyurethane (PU) foams was investigated by P. Ferkl et al. [36] using a multi-scale mathematical model.
In the modeling methods of heat transfer by conduction, convection and radiation, the theoretical models of equivalent thermal conductivities were built for polymer materials with consideration of gas and solid phases in many studies. P. Ferkl et al. investigated the heat transfer in one-dimensional multi-layer models [37] and computer-reconstructed three-dimensional (3D) models [40] of polymer foams and determined their equivalent thermal conductivities of conduction and radiation in gas and solid phases and partial photon reflection on phase interfaces. The studies of P. Ferkl et al. were representatives in this field. However, P. Ferkl et al. considered only steady-state heat transfer by conduction and radiation. W. H. Tao et al. [15] also took into account heat transfer by conduction and radiation in the solid and gas phases of the polyurethane foam when a theoretical model was developed based on Maxwell’s equation. M. Jaworski [42] developed a mathematical model of heat transfer coefficient by heat conduction, convection and radiation both inside the PCM incorporated fabrics and interaction with the environment, and had the advantage that different modes of interaction with the environment were taken into account, including radiative heating, cooling in natural convection and direct contact with a solid body of large thermal capacity. In other studies, the heat and moisture transfers including the radiation heat transfer were considered at the same time when the mathematical model was constructed [43].
In the modeling of radiative properties for polymer materials, the existing studies focused on the prediction of the radiative behavior using cell morphology [44] or x-ray tomography methods [45], a full-scale method based on the Rosseland diffusion equation [46], and the radiative transfer equation (RTE) and the Monte Carlo method [47,48]. The radiative properties of extruded polystyrene foams were determined from the morphological data correlated with foam structure cell wall and strut morphology [44]. However, this study was based on ideal representations of the cellular structure that simplified the real porous morphology. A numerical method for computing the directional radiative properties of polymeric foams was developed based on x-ray tomography, allowing a noticeable improvement in the morphological characterization method and achieving a better numerical estimation of radiative properties [45]. Newly proposed modeling methods investigated the influential factors on the radiative properties, such as cell size, porosity, cellular pore shape, volume specific surface area, temperature, refractive index, and extinction index [46,47].
In addition, other studies have proposed special or novel models of heat transfer, such as the model of distribution of temperature in the porous fabric for different material in different environmental conditions [49] and the 3D finite element model to describe heat transfer across heterogeneous polymer composites [10].
Although the existing methods and models can be applied to address certain infrared radiation properties such as radiative thermal conductivity and surface emissivity, they are unable to specify the infrared management optical properties of the porous sheet polymers, including infrared reflection, transmission, absorption and emission during the dynamic process of the infrared radiation, and are difficult to differential dynamic IR functional performances of porous polymers.
The radiative transfer model in this paper was built to predict the IR management optical properties of porous sheet polymers based on the principle of infrared radiation. Three stages including the initial stage, the dynamic stage and the steady stage were applied and the impacts of micro-voids were considered in the modeling. For the given thickness and unit weight of the porous sheet polymers, the IR management optical properties can be predicted by the dynamic changes of the IR reflectivity and transmissivity from the radiative transfer model.
2. Methods
It is assumed that the sheet polymer material is a homogeneous medium with a certain thickness d and its optical property is consistent with its constituent substance such as fiber. The medium model is shown in Fig. 1. The top surface of the medium model is the incident surface of the IR source, which is called the reflection surface, and the other surface called the transmission surface.
Since the sheet polymer materials have the IR absorption property, the absorption of IR radiation energy is a dynamic process when the IR source is incident on the sheet material constantly. This dynamic process of IR radiation can be divided into three stages including the initial stage, the dynamic stage and the steady stage. The initial stage refers to the instantaneous time when the IR source is just incident on the reflection surface of the sheet material. In this moment, the temperature rise caused by the IR absorption and the emitted IR energy are negligible, and the incident IR energy is divided into the reflection energy, the absorption energy and the transmission energy. The dynamic stage refers to the temperature rise process in which the sheet material keeps absorbing and emitting IR energy simultaneously. In this stage, the IR intensity measured by the reflection surface includes the reflected intensity of the incident IR energy and the emitted intensity by the sheet material due to the temperature rise, and the IR intensity measured by the transmission surface consists of the transmitted intensity of the incident IR energy and the emitted intensity t from the sheet material due to the temperature rise. The steady stage means the equilibrium state of IR absorption and emission and the IR intensity of both surfaces keeps a constant value.
2.1 Initial stage
In this stage, the propagation of IR light in the medium model of the sheet polymer is shown in Fig. 2. When the IR source is incident on the reflection surface of the medium model, the IR ray propagation follows the law of optical propagation. The reflection and transmission happens at the interface of the environment and the medium, and the IR energy inside the medium is attenuated according to Lambert-Beer’s law for the optical absorption property of sheet polymers.
In Fig. 2, The IR ray propagation trajectories in the ideal medium are in vertical direction under vertically incidence light. The coordinate axis n represents the contact times between the IR ray and the two surfaces of the medium. When the IR source with intensity ${{\textrm I}_{0}}$ is incident on the reflection surface of the medium, the incident IR is reflected and transmitted, which is divided into two parts, the reflected part with intensity ${I}_{0}^{{\textrm r}}$ and the transmitted part with intensity ${I}_{0}^{{\textrm t}}$. When the transmitted light ${I}_{0}^{{\textrm t}}$ reaches the transmission surface with intensity ${{I}_{1}}$ due to the absorption of the sheet polymer and attenuation, it is further divided into the reflected light with intensity ${I}_{1}^{{\textrm r}}$ and the transmitted light with intensity ${I}_{1}^{{\textrm t}}$, ${I}_{1}^{{\textrm r}}$ is then continually attenuated and propagated inside the medium and its intensity is reduced to ${{I}_{2}}$ when it reaches the reflection surface. Followed by a reflection-transmission and an optical absorption effect successively, ${{I}_{2}}$ is reduced to ${{\textrm I}_{3}}$ when reaching the transmission surface. According to the propagation law of the IR light, the expressions of the total reflected light with intensity ${{I}_{r}}$ and the total transmitted light with intensity ${{I}_{t}}$ can be obtained.
According to Fresnel formula, by introducing the coefficients of reflectivity ${\textrm R^{\prime}}$ and the transmissivity ${{\textrm T}^{{^{\prime\prime}}}}$ at the surfaces of the medium, the relationship between the incident light ${{I}_{m}}$ and the reflected light ${I}_{m}^{{\textrm r}}$ and the transmitted light ${I}_{m}^{{\textrm t}}$ are expressed as Eqs. (3) and (4).
where the reflectivity ${R^{\prime}}$ at the surfaces of the medium has a relationship with the refractivity n as:Since the radiation energy does not decay on the surface of the medium and the absorption rate is considered to be zero, the relationship between the transmissivity ${{T}^{{^{\prime\prime}}}}$ and the reflectivity ${R^{\prime}}$ can be expressed as:
When light propagates inside the medium of the sheet polymer, the light intensity will be attenuated and change as Eq. (7) according to Lambert-Beer’s law.
where d is the vertical transmission distance of the light in the medium of the sheet polymer, I is the initial intensity, ${{\textrm I}_{\textrm d}}$ is the residual light intensity after the propagation in the medium for a d distance vertically, and u is the attenuation coefficient which is composed of absorption coefficient u’ and scattering extinction coefficient s as:The scattering extinction coefficient s can be calculated as:
The absorption coefficient u’, also known as Rosseland mean extinction coefficient, can be calculated from the Rosseland approximation as [50]:
According to Lambert-Beer’s law and Eqs. (3), (4) and (7), the relationship between the residual light intensities ${{I}_{0}}$, ${{I}_{1}}$, ${{I}_{2}}$, ${{I}_{3}}$, …, ${{I}_{m}}$ can be expressed as Eq. (12).
Then the Eqs. (3) and (4) can be converted to Eqs. (13) and (14).
In accordance with the conservation of energy, the characteristic parameters IR reflectivity and transmissivity of the IR management optical properties of the sheet polymer materials, in the initial stage can be obtained after normalization as Eqs. (15) and (16).
2.2 Dynamic stage
According to Lambert-Beer’s law and the principle of temperature rise due to heat absorption of polymer materials, the temperature rise with time of the two surfaces of the sheet polymer due to the IR radiation absorption during the dynamic stage of IR radiation can be defined as:
where ${{\textrm T}_{{\textrm{r0}}}}$ and ${{\textrm T}_{{\textrm{t0}}}}$ are the initial temperatures (t = 0) of the reflection surface and transmission surface respectively, and the values are approximate to the ambient temperature. ${{\textrm T}_{\textrm r}}{(\textrm t)}$ and ${{\textrm T}_{\textrm t}}{(\textrm t)}$ are the dynamic temperatures of the two surfaces at time t. ${{\textrm A}_{\textrm r}}$, ${{\textrm B}_{\textrm r}}$, ${{\textrm A}_{\textrm t}}$ and ${{\textrm B}_{\textrm t}}$ represent the parameters related to the sample’s characteristics of optical and thermal properties, including the absorption coefficient, extinction coefficient, refractive index, scattering of refracted light, unit weight, specific heat capacity and heat transfer coefficient, which can be obtained by the temperature rise experiment and the nonlinear regression function.According to Planck’s law, the definition of emissivity and the relationship between the full-band radiation intensity and the spectral radiation intensity, the wavelength range to be investigated is from ${{\lambda }_{1}}$ to ${{\lambda }_{2}}$, then the IR intensity emitted from the sheet polymer ${{\textrm I}_{\textrm e}}$ is :
According to Eqs. (18)-(20), the IR management optical properties of the sheet polymer materials in the dynamic stage can be obtained as:
2.3 Steady stage
When the temperature of the sheet polymer surface rises to a steady state, the increased IR intensity caused by the emitted IR radiation of the sheet polymer in the dynamic stage also reaches to a steady value.
According to the analysis of the three stages of the dynamic IR radiation process, the radiative transfer model of the IR management optical properties of sheet polymer materials can be obtained from the reflectivity ${{\alpha }_{r}}{(t)}$ and the transmissivity ${{\alpha }_{t}}{(t)}$ as:
The initial values (${{\alpha }_{{r0}}}$, ${{\alpha }_{{t0}}}$) of the reflectivity and transmissivity and the emissivity (ε) in the radiative transfer model can be calculated from the structural parameters of the sheet polymer.
3. Materials and validation experiments
In order to evaluate the effectiveness of the radiative transfer model, the validation experiments were conducted in an experimental setup. As shown in Fig. 3, the experimental setup consists of five main components: the test platform, the support arm of the IR sensor for the transmission surface, the specimen transfer mechanism for the moving of the platform, the support arm of the IR sensor for the reflection surface, and IR source.
The IR sensors are installed on the support arms of the transmission and reflection surfaces to measure the IR intensities on both surfaces of the sheet polymer. The test platform is hollow square frame, which has a square hole in the middle to ensure that it does not affect the IR intensity detection of transmission and emission from the test sample. The IR source is thermal radiation type. The wavelength range of IR source spectrum is 8∼14µm, which is near the IR band of human radiation.
Eight typical samples of porous sheet polymers with different thickness and unit weight were tested in the experiments (Table 1). All the testings were carried out in the conditioning room (21 ± 1°C, 65 ± 2% RH) in accordance with ASTM D1776. Each test was conducted until the IR intensities at two surfaces of the sample reached a steady state.
Table 1. Sample construction parameters
The validation experiments and the temperature rise experiments were conducted simultaneously. The sample was laid flat on the test platform with the four edges clamped by clamping clips. The flexible mounting type temperature sensors with measuring head less than 2 mm were attached on the two surfaces of the sample, with three sensors each surface in a circular distribution.
4. Results and analysis
4.1 Predicted values
The temperature rise process in the dynamic stage is shown in Fig. 4. The temperature rise curves of the reflection surface (R) and the transmission surface (T) for test and fit are presented. Based on the analysis of the test results, the parameters (Tr0, Ar, Br, Tt0, At, Bt) in Eqs. (20) and (21) derived from the nonlinear regression method are shown in Fig. 5.
Fig. 5. The fitting parameters in the temperature rise model. (a) The fitting parameters Tr0 and Tt0. (b) The fitting parameters Ar and At. (c) The fitting parameters Br and Bt.
Based on the measured refractivity n and the transmittance percentage τλ, and the calculated attenuation coefficient u from Eqs. (8) – (11), the prediction values from the initial stage to the steady stage in the radiative transfer model can be calculated from Eqs. (23) and (24), as shown in Fig. 8 (line in red color). The parameters αr0 and αesr represent the predicted values of the reflectivity in the initial and steady stage on the reflection surface, and αt0 and αest represent the predicted values of the transmissivity in the initial and steady stage on the transmission surface (Fig. 6). Due to the short action time in the initial stage (imaginary frame part), the results of the initial stage are presented in the way of partial magnification in Fig. 8.
Fig. 6. The predicted values of the IR management optical properties in the initial stage and the steady stage.
4.2 Measured Values
Based on the IR intensities measured from the reflection surface and the transmission surface of the sample, the measured values of reflectivity (αr-T) and transmissivity (αt-T) of the IR management optical properties can be obtained as:
The test results of ${{\alpha }_{{\textrm r - \textrm T}}}$ and ${{\alpha }_{{\textrm t - \textrm T}}}$ are shown in Fig. 8 (line in black color). The parameters ${{\alpha }_{{\textrm{r0} - \textrm T}}}$ and ${{\alpha }_{{\textrm{esr - T}}}}$ represent the measured values of reflectivity in the initial and steady stage on the reflection surface, and αt0-T and ${{\alpha }_{{\textrm{est - T}}}}$ represent the measured values of transmissivity in the initial and steady stage on the transmission surface (Fig. 7). Due to the reflection value of the support frame of the experimental setup when the sample does not enter the test position, the initial value of reflectivity is not zero (Fig. 8). However, the influence of the reflection value of the experimental setup frame can be ignored due to the sample barrier after the sample fully enters the test position, and has no effect on the reflectivity value at the end of the initial stage. Therefore, the test value of reflectivity is only valid when the sample is completely in the test position.
Fig. 7. The measured values of the IR management optical properties in the initial stage and the steady stage.
Fig. 8. The comparison results of the predicted values and the measured values. (a)–(h) Comparison results of samples A–H.
4.3 Comparative analysis
The predicted values and the measured values are compared as Fig. 8, and the relative errors of the predicted values and the measured values are calculated. The maximum relative errors of the in different stages are listed in Table 2. The parameters δ1r, δ2r and δ3r are the maximum relative errors of the three stages on the reflection surface, and δ1 t, δ2 t and δ3 t are the maximum relative errors of the three stages on the transmission surface. In Fig. 8, δ1r is the relative error at the end of the initial stage since the test value of reflectivity is only valid after the sample has fully entered the test position.
Table 2. The relative errors of the experimental results
Since the absolute values of most maximum relative errors are greater than 20% from the comparison results, the model cannot effectively predict the IR management optical properties of the porous sheet polymers, which needs to be modified.
4.4 Modification of the radiative transfer model
In the initial modeling process, the model was constructed from a macro perspective and only the thickness parameter of the porous sheet polymer material was considered in modeling. The internal structures of the porous sheet polymers were considered to be uniform, and the influence of micro-voids defects on IR light propagation was ignored. The validation experiment results show that the internal construction difference of the sample should be considered in modeling.
In general woven structures of porous sheet polymers such as fabrics, there are two types of micro-voids existing including the micro-voids between fiber layers in multilayer fabric (Fig. 9) and the micro-voids between fiber bundles in single layer fabric (Fig. 10). When the IR ray propagates inside the multilayer fabric (Fig. 9), its energy is not attenuated in the micro-voids. Therefore, the actual energy attenuation distance is d’ after the porous sheet polymer is compressed at the pressure of 4.14 kPa in accordance with ASTM D1777 as shown in Fig. 9(b).
Fig. 9. The IR propagation model in compressible multilayer sample. (a) Before compression. (b) After compression.
Setting κ as the compression ratio of thickness after compression (equivalent compressed thickness, d’) to thickness before compression (d), the model was updated by the parameter κ due to the air gap between layers in multilayer sample as:
For the single-layer porous sheet polymer (Fig. 10), part of the IR light passes through the sheet polymer directly from the pores in the process of IR light propagating from the reflection surface to the transmission surface. The IR radiation actually propagating inside the solid skeletons of the sheet polymer materials such as fiber bundles of fabric is the effective radiation intensity irradiating the solid skeletons (E1), which is the total incident radiation (E0) minus the IR radiation directly passing through the pores (E2). The model was updated due to the micro-voids between solid skeletons in single-layer sheet polymer as:
${{\theta }_{{E1}}}$ is related to the porosity of the single-layer porous sheet polymer and can be obtained as:
where ${{P}_{{sl}}}$ is the porosity of the single-layer porous sheet polymer.By considerations of the two types of micro-voids represented by porosity and compression ratio of thickness, the radiative transfer model can be modified as:
The morphological observation using SEM was conducted for the porosity measurement, as shown in Fig. 11. From the morphological observation results, the porosity ${{P}_{{ect}}}$ can be calculated and θE1’ and θE2’ can be obtained from Eqs. (35) and (36). The compression ratio of thickness (κ) of test sample can be calculated from the thickness measurement results including thickness after compression (d’) and thickness before compression (d, Table 1). The modification parameters of the eight samples for the modified model are list in Table 3.
Fig. 11. The morphological observation results of the porous polymer samples. (a)–(h) SEM images of samples A–H.
Table 3. The modification parameters of the modified model
Using the parameters in Table 3, the predicted values of the IR management optical properties of samples B∼H are modified based on Eqs. (33) and (34). The predicted values of the IR management optical properties of sample A do not need to be modified since κ is 0.98 and ${{\theta }_{{E1}}}^{^{\prime}}$ is 0.93 for sample A. The comparison results of the predicted values after modification and the measured values in the validation experiment are shown in Fig. 12. The relative errors are listed in Table 4, and the maximum prediction errors are less than 15%. Furthermore, the prediction errors of the transmission surface are mostly less than 10% except for samples A and H. The results show that the modified model can effectively predict the IR management optical properties of porous sheet polymers.
Fig. 12. The comparison results of the predicted values and the measured values after the model modification. (a)–(g) Comparison results of samples B–H.
Table 4. The relative errors of the experimental results after the model modification
5. Conclusion
A radiative transfer model was established and the theoretical analysis was conducted for the characterization of IR management optical properties of porous sheet polymer materials, including the IR reflection, transmission, absorption and emission during the dynamic process of the IR radiation. In the modeling, three stages of the dynamic radiation process were considered, including the initial stage, the dynamic stage and the steady stage. Based on the initial reflectivity and transmissivity in the initial stage and the dynamic components represented by the ratio of the emitted IR intensity to the IR source intensity in the dynamic stage, the initial model was built by describing the reflectivity change vs. time of the reflection surface and the transmissivity change vs. time of the transmission surface with consideration of the IR absorption and emission during the dynamic process. Eight typical porous sheet polymers were tested for the IR management optical properties in an experimental setup. The comparison analysis results of the predicted values and the measured values showed that the initial model needed to be improved. By considerations of the two types of micro-voids defects including the micro-voids between layers in multilayer sample and the micro-voids between material bundles in single layer sample and the thickness compression ratio, the radiative transfer model was modified. The maximum prediction errors of the modification model are less than 15%, and the maximum prediction errors of the transmission and reflection surfaces are mostly less than 10%. The modeling method provides the theoretical fundamentals and evaluation of the IR management optical properties of porous polymer materials for new products development, fabrication and processing in industrial application.
Funding
National Natural Science Foundation of China (51675500, 51175487).
Acknowledgments
We would like to thank Prof. Henry Yi Li of University of Manchester for his suggestions on experimental setup in this research.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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