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Progress in Organic Coatings 47 (2003) 432–442 A multiple-scattering model analysis of zinc oxide pigment for spacecraft thermal control coatings Joel A. Johnson a,∗, John J. Heidenreich a, Robert A. Mantz a, Paul M. Baker b, Michael S. Donley a a Air Force Research Laboratory, Materials & Manufacturing Directorate, Wright-Patterson AFB, Dayton, OH 45433-7750, USA b Department of Physics, Wright State University, Dayton, OH 45435-0001, USA Abstract Space assets inhabit a harsh thermal environment in which the high intensity of direct solar radiation can potentially raise temperatures to harmful levels. Thermal management is obtained through the use of radiators coated with thermal control coatings (TCCs) that diffusely reflect the sun’s high energy visible (VIS) and near infrared (NIR) radiation, while emitting infrared (IR) energy as a method of radiatively cooling. The current state-of-the-art TCC system utilizes a potassium silicate binder and zinc oxide (ZnO) pigment to maintain solar reflectance over a long exposure time. We are investigating improvements to TCCs that will have greater initial performance and significantly better end-of-life properties. We have utilized modeling techniques based upon Mie scattering to determine the theoretical scattering efficiency limits of the currently used materials. An optimized TCC would attain maximum diffuse solar reflectance at a lower film thickness and reduce the pigment volume concentration (PVC) required. These factors would contribute to a reduction in overall weight and possibly extend the durability of the system to longer time scales. Our results of modeling ZnO pigment embedded in a matrix similar to that of potassium silicate under solar irradiance conditions indicate that a narrow particle size distribution centered at 0.35�m would provide the highest overall scattering coefficients, ranging from 0.75�m−1 at 1000 nm to 5.0�m−1 at 380 nm wavelengths. These results indicated that a significant improvement, 2–10 times dependent upon wavelength, in the scattering efficiency of ZnO-based TCCs can be realized by utilizing an optimized particle size distribution rather than the currently used size distribution. © 2003 Elsevier B.V. All rights reserved. Keywords: Thermal control coating; Zinc oxide pigment; Mie scattering; Light scattering efficiency 1. Introduction Space assets inhabit a harsh environment in which high intensity solar radiation can raise temperatures to levels that could render some components inoperable. The additional effect of internal heat generated by onboard electronics adds to this thermal management problem. Unfortunately, in space there is no convection or conduction of heat to allow efficient cooling back to normal operating tempera- tures. The only method to decrease temperature is through radiative heat transfer (i.e., emission of infrared (IR) light). Therefore, thermal management is attained through the use of radiators with thermal control coatings (TCCs) that dif- fusely reflect visible (VIS) and near infrared (NIR) radiation while absorbing/emitting IR wavelengths. ∗ Corresponding author. Present address: 2941 P. St., Bldg. 654, Rm. 136, Wright-Patterson AFB, Dayton, OH 45433-7750, USA. Fax: +1-937-255-2176. E-mail address: joel.johnson@wpafb.af.mil (J.A. Johnson). Temperature is determined by a balance between heat lost through emittance of thermal IR radiation (qR), heat gained through absorption of radiation (qA), and heat internally gen- erated within the spacecraft (qr) at an equilibrium state qR = qA+qr. Assuming that the internal components of the space- craft are not generating any waste heat, the equilibrium sim- plifies to qR = qA, where qR = σεART 4 and qA = SαSAS. T is the absolute temperature in K, αS the solar absorbance of the exterior surface, ε the emissivity at temperature T, σ the Stefan–Boltzmann constant (5.57E−12 W cm−2 K−4), AR the “effective” area in cm2 for heat radiation, S the solar constant (0.135 w/cm2), and AS the cross-sectional area in cm2 exposed to incident radiation. Thus, space asset tem- perature is controlled by the ratio of surface absorption (αS) to its emissivity (ε) as shown in Eq. (1): T = 4 √ SαSAS σεAR (1) It is evident from Eq. (1) that an ideal TCC would minimize solar absorbance and maximize emittance. The basis of TCC 0300-9440/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0300-9440(03)00133-4 J.A. Johnson et al. / Progress in Organic Coatings 47 (2003) 432–442 433 Fig. 1. ASTM average solar spectral irradiances for space [1] and terrestrial [2] environments. Peak space radiation power occurs at 465 nm with the greatest intensities ranging from 300 to 800 nm (UV+ VIS). technology is to provide a coating that diffusely reflects all effective ultraviolet (UV; 200–380 nm), VIS (380–780 nm), and NIR (780–2000 nm) wavelengths to minimize αS, re- sulting in a white coating. In addition, the coating should absorb all (2–20�m) wavelengths to maximize ε. The ma- terials used in conventional TCCs have inherently high IR emissivities and, as such, potential improvements in total emittance are rather limited. While it is possible to heat an object through IR absorption, a low percentage of the total solar energy is in the form of IR radiation as seen in the graph of solar irradiance for both space and earth’s surface (Fig. 1) [1,2]. A simplified schematic diagram of the desired TCC radi- ation interactions is shown in Fig. 2 in which both the binder and pigment are transparent to UV/VIS/NIR but have a suf- ficient enough difference in refractive indices to promote Fig. 2. A schematic diagram of the scattering and emittance of an idealized TCC system. Unfortunately, the use of ZnO as a pigment results in nearly complete absorption of UV wavelengths. In addition to being irradiated by the sun’s electromagnetic rays, the coating is also bombarded with electrons (e−) and protons (p+). scattering. The most widely used TCC formulations consist of a potassium silicate binder and zinc oxide (ZnO) pigment. Unfortunately, the presence of ZnO pigment deviates from this idealized scheme due to strong absorption of UV light. There are several potential benefits to optimizing the scattering efficiency of the ZnO pigment through control of particle size. An ideal coating design would obtain the the- oretical maximum reflectance (i.e., opacity) with the lowest pigment volume concentration (PVC) and dry film thick- ness (DFT). Any additional pigment does not contribute to scattering and is detrimental to the physical properties of the film. Given a specific pigment/binder material combination, the optimal PVC is that which yields effective opacity at the thinnest DFT. The advantages of obtaining UV/VIS/NIR opacity with a minimal PVC and DFT include weight re- duction, improved mechanical properties, minimization of pigment related degradation, and lower porosity. The purpose of this study was to utilize modeling tech- niques to investigate the optimum particle size of ZnO pigment required to obtain the most efficient scattering mechanism in an approach to reduce the overall PVC and film thickness required. This approach does not alter any of the existing materials being used, but examines the potential impact of purely formulational changes to existing TCCs. 2. ZnO multiple-scattering model The scattering of light by pigment particles embedded in a coating matrix has been previously investigated to estab- lish the theoretical limits of opacity for particular material compositions. There have been several excellent publica- tions [3–7] that have modeled the physics of light scattering by small particles in an effort to predict the optimal particle 434 J.A. Johnson et al. / Progress in Organic Coatings 47 (2003) 432–442 size and scattering efficiencies for specific pigments. Most importantly, the work of Bohren and Huffman [8] contains a computer program (named BHMIE) written in FORTRAN that will calculate the linear scattering cross-sectional area, Csca/A, of a spherical particle with a given refractive index surrounded by a medium of a different specified refractive index. Csca/A is easily converted to the volumetric scatter- ing cross-section, Csca/V, based on spherical geometry. The scattering coefficient, S, is then calculated by multiplying Csca/V by one minus the asymmetry parameter. The asym- metry parameter, g, is the average cosine of the scattering angle, and accounts for the angular intensity of the scattered light. The value of g is unitless and varies between −1.0 for perfect backward scattering, and 1.0 for perfect forward scattering. The equation for calculating S from Mie theory results is provided in Eq. (2): S = ( Csca V ) (1− g) (2) While there are a number of reports [3,7,9–11] modeling the scattering efficiency of TiO2 pigments, no such analysis has been performed for ZnO because it is not commercially used as a primary opacifying pigment. However, TiO2 is not well suited for TCC applications due to the formation of absorbing color centers under a vacuum UV environment, [12], whereas ZnO is used almost exclusively for this pur- pose. Therefore, a similar modeling approach for ZnO is warranted to determine not only the optimal particle size, but also the theoretical limits of opacity under the unique TCC irradiance conditions. 2.1. ZnO refractive index anisotropy In order to accurately model the scattering properties of ZnO over the VIS to NIR spectrum, the refractive index as a function of wavelength must be known. Early attempts at pigment scattering models used single values for refrac- tive index, often taken at the center of the VIS spectrum (550 nm). This approach has led to serious errors in the re- sults, especially for materials that exhibit a high degree of optical dispersion, such as the case for both TiO2 and ZnO. The refractive index function for ZnO is complicated by the fact that this material is crystalline (predominantly in a wurtzite structure). Like many crystalline materials, ZnO is optically anisotropic and thus will have a different refrac- tive index for light polarized parallel and perpendicular to the optic axis. Unfortunately, there is no exact solution to Mie scattering of spherical particles that have discrete re- fractive indices for different states of polarization [7]. The incident radiation in most modeling studies, including this effort, is incoherent, and therefore an average refractive in- dex of the anisotropic substance is generally used despite theoretical justification. Palmer et al. [7] have investigated this issue for rutile TiO2, a material with an even greater anisotropy, by comparing the scattering coefficient (S) com- puted from the average refractive index versus the average S for individual computations of parallel and perpendicular polarizations. They concluded that use of the average re- fractive index in the modeling computations did not produce significant deviations from the averaged S results, allowing simplification of the modeling effort. Fortunately, since wurtzite ZnO is only slightly anisotropic it was not expected to be problematic. Nevertheless, we also have computed both single and averaged Csca/V, g, and S results as a function of particle diameter for both the average refractive index and polarity-specific refractive indices, respectively. The data used in our ZnO modeling program was generated from spectroscopic ellipsometry measurements and fit to the first-order Sellmeier equation as reported by Yoshikawa and Adachi [13]. The equation and fitting parameters from this work for both parallel and perpendicular polarizations of wurtzite ZnO are provided in Eq. (3) and plotted in Fig. 3: n = √ A+ Bλ 2 λ2 − C (3) where A = 2.850, B = 0.870, C = 0.096 for parallel val- ues, A = 2.840, B = 0.840, C = 0.101 for perpendicular values and λ units are in �m. 2.2. Computation of ZnO scattering coefficient A slightly modified version of the BHMIE program sup- plied in Appendix A of Bohren and Huffman [8] was used to calculate the scattering coefficient of ZnO as a function of particle diameter for the wavelengths of 380–1000 nm. No computations were performed below 380 nm due to strong absorption in this region. Furthermore, since the ab- sorption of ZnO is essentially zero from 380 to 1000 nm, the absorption coefficient was not included in the compu- tations. The supplied code permitted calculation of Csca/V from Mie theory [14,15] for a homogenous sphere in a medium, both of known refractive indices. The results of this program have been verified by Bohren and Huffman [8]. Our first modification to the code involved including a loop to automatically generate results over a set range of sphere diameters. Second, we have included an additional outer loop to generate results over a range of selected wave- lengths. With this, our modification also requires that the refractive index as a function of wavelength equation be known and included for both the pigment and medium to account for optical dispersion. Lastly, we have included the necessary equations to calculate the asymmetry parameter, g, associated with each particular Csca/V result generated. Using both the parallel and perpendicular polarized re- fractive index data for ZnO from Eq. (3), the Csca/V values for 546.1 nm wavelength light and spheres ranging in di- ameter from 0.02 to 1.00�m immersed in a medium of refractive index 1.0 were computed and averaged to produce the solid line in Fig. 4. These conditions were specifically chosen to make a direct comparison against the results for a J.A. Johnson et al. / Progress in Organic Coatings 47 (2003) 432–442 435 Fig. 3. Wurtzite ZnO refractive index as a function of wavelength for both parallel and perpendicular polarized incident light as reported by Yoshikawa and Adachi [13]. similar modeling study on rutile TiO2 by Palmer et al. [7]. Similarly, the averaged refractive index of ZnO under the same conditions was also used to produce the open circle data points in Fig. 4. It is clear that the difference between average refractive index and averaged Csca/V values is negligible for the slight anisotropy of wurtzite ZnO. Interestingly, there is a bimodal distribution of the diameters that yield the greatest Csca/V values; the largest peak is 0.26�m and the secondary peak is at 0.36�m. Palmer’s results for rutile TiO2 show much narrower single mode distribution with the maximum scat- tering occurring at a diameter of 0.19�m. Fig. 4. Volumetric scattering cross-section (Csca/V) of ZnO at 546.1 nm as a function of particle diameter. The refractive index of the medium was 1.0. The solid curve represents the average Csca/V values for parallel and perpendicular polarization. The open circle data points represent the values obtained using the averaged refractive index. For opaque coatings in which all incident radiation is preferred to be diffusely scattered backwards, 1− g values closest to 1 are preferred. Fig. 5 shows a plot of 1−g for ZnO under the same conditions previously mentioned for Fig. 4. Once again, the anisotropic effects of ZnO are negligible for this computed value, suggesting that the average refrac- tive index can also be effectively utilized in this calculation as well. In comparison with results of Palmer et al. [7] for ru- tile TiO2, the major valleys tend to be broader as a function of particle diameter and slightly more forward-reflective, particularly for the optimal Csca/V diameter ranges. Fi- nally, the scattering coefficient, S, which correlates to 436 J.A. Johnson et al. / Progress in Organic Coatings 47 (2003) 432–442 Fig. 5. 1− asymmetry parameter (1− g) of ZnO at 546.1 nm as a function of particle diameter. The refractive index of the medium was 1.0. The solid curve represents the average 1− g values for parallel and perpendicular polarization. The open circle data points represent the values obtained using the averaged refractive index. experimentally determined values though Kubelka–Munk analysis, is shown in Fig. 6 for similar conditions. As expected, the effects of ZnO anisotropy are negli- gible for computation of scattering coefficients. Since the anisotropy does not change appreciably for other frequen- cies, it was concluded to be justifiable in using the average refractive index function for all further computations. As can be seen in Fig. 6, the most effective particle diameter for ZnO to scatter light under these conditions is 0.27�m. This is in contrast to an optimal rutile TiO2 particle diameter of 0.19�m from the work of Palmer et al. [7]. Furthermore, the theoretical maximum scattering coefficient for ZnO un- der these conditions was found to be 13.5 versus 37.0 for rutile TiO2. The expected lower scattering efficiency of ZnO is a direct result of the material’s overall lower refractive in- Fig. 6. Scattering coefficient of ZnO at 546.1 nm as a function of particle diameter. The refractive index of the medium was 1.0. The solid curve represents the average S values for parallel and perpendicular polarization. The open circle data points represent the values obtained using the averaged refractive index. dex and verifies why it is not used commercially as a white pigment. 2.3. ZnO spectral scattering in coating films In order to model the scattering properties of ZnO under the realistic conditions of being embedded in a TCC binder medium, we have used a similar procedure and added several components to the model, such as examining the various wavelengths of the solar spectrum and including the wavelength-dependent refractive index function of the medium as well. Since no ellipsometry data was available for potassium silicate, we have substituted a similar material into the model, BK7 Schott glass. The refractive index function for this material was determined by non-linear regression J.A. Johnson et al. / Progress in Organic Coatings 47 (2003) 432–442 437 Fig. 7. Contour plot of the theoretical ZnO scattering coefficient as a function of sphere diameter and wavelength in BK7 Schott glass. from literature data [16] and is provided in Eq. (4): nBK7 Schott = (−1.879E − 10)λ3 + (4.650E − 07)λ2 +(−3.985E − 04)λ+ 1.628 (4) Our modified BHMIE program was used to generate the theoretical scattering coefficient for ZnO spheres in a BK7 Schott glass medium for diameters ranging from 0.02 to 5.00�m (in 0.02�m increments) throughout a 380–1000 nm wavelength range (in 5 nm increments). The results of this scenario are provided in a contour plot (Fig. 7). Fig. 8. Theoretical ZnO scattering coefficient as a function of sphere diameter in BK7 Schott glass for selected wavelengths. It is quite evident from the contour plot that ZnO par- ticle diameters greater than approximately 1.5�m do not scatter light efficiently at any wavelength. At shorter wave- lengths there is a greater dependency on particle size than at longer wavelengths, with the highest computed scattering coefficient (7.65�m−1) occurring with a 0.16�m particle at 380 nm. The theoretical scattering coefficients as a func- tion of ZnO diameter for selected wavelengths are shown in Fig. 8 for convenient comparison. From this plot, the general trend in greater scattering efficiency and dependency on particle diameter for shorter 438 J.A. Johnson et al. / Progress in Organic Coatings 47 (2003) 432–442 wavelengths is clearly evident. For all wavelengths, the shape of the S value distribution curve tends to be lognormal with respect to ZnO diameter. The particle diameter range that covers the maximums of these curves is from 0.16 to 0.55�m and thus any ZnO particles present in a formula- tion outside this range will not contribute to an increase in overall scattering efficiency. 3. Experimental In an effort to examine the effectiveness of a common TCC formulation, Z-93P from Illinois Institute of Technol- ogy Research Institute (IITRI), as well as compa