DIRECT MEASUREMENT OF THERMAL CONDUCTIVITY COMPONENTS IN RIGID FOAMS

Transcription

1 DIRECT MEASUREMENT OF THERMAL CONDUCTIVITY COMPONENTS IN RIGID FOAMS Valentina Woodcraft, Andrey Soukhojak, Tammy Fowler The Dow Chemical Company, Midland, MI (U.S.A.) Abstract In order to maintain desired properties of insulating products, while also complying with ever-increasing regulatory pressure on blowing agents, emphasis of academic and private sector foams research has shifted to minimizing the radiative and solid conduction components of heat transfer in rigid closed-cell foams. Although methods and equipment for measuring total thermal conductivity of low density, insulating rigid polymeric foams are well established [1], and there are theoretical models [4-6] for estimating individual contribution of each heat transfer mode, experimental methods for direct measurement of the latter are lacking. In this paper, we offer a method for measurement of individual heat transfer modes (conductivity through solid, conductivity through gas, and radiative transfer) in rigid, low density polymeric foams by employing measurements in ambient atmosphere and in vacuum, as well as specific specimen preparation. Introduction The primary function of low density rigid insulating foams used in building and refrigerated transport construction is providing resistance to heat transfer. These low density foams are typically comprised of approximately 5 vol.% solids (polymer and additives), and the balance of the volume is occupied by gas insulating gas (or blend) in closed-cell foams, and mostly air in opencell foams. By design, insulating gas has a much lower thermal conductivity than the solid constituents, and thus total thermal conductivity of a foam insulation product is much lower than that of a non-porous article made of same material. Theoretically, high-molecular weight insulating gasses are most advantageous from the perspective of their low thermal conductivity, but they are also concerning from standpoint of environmental impact. Global regulatory pressure on foam blowing agents with high global warming potential (GWP>150) drives current reformulation efforts for foam insulation products. With limited potential for meeting performance demands through modifications of gas component of thermal conductivity, the industry and academia turned to minimizing contribution of radiative and solid conduction. However, measuring the impact of experimental changes on the solid and radiative components individually has been challenging, as the two are confounded in conventional total thermal conductivity measurement methods. Theory Research pioneers [2-3] in the field of insulating foams postulated that total, or effective, thermal conductivity k t is a superposition of conduction through solid k s, conduction through gas k g, and radiative transfer k r : k " = k $ + k & + k ' (1) Rosseland equation [4] determines contribution from radiative component: k $ = )* +, σt+ (2) Datye and Lemlich [5] proposed the following for the solid contribution: k & = k / (2 f & ) (3) Schuetz et. al. [6] offer expression for the gas contribution: k ' = k => ( ) (4) It is prudent to keep in mind that the above equations are useful approximations in the limit of isotropic, bulk foams. Anisotropy of the cell morphology and density, as well as other factors [7], are known to affect accuracy of agreement between these theoretical descriptors and empirical data. The high potential for discrepancies between the theorybased calculations and experimental results has stimulated our search of a method suitable to accurately measure individual contributions from each of the heat transfer modes in insulating foams. Concept Note that if one were to remove the gas from the insulating foam (e.g. by complete evacuation of the foam cells), the resulting conductivity of the foam would be due only to the radiative component (which is a strong function of temperature, Eqn. 2) and the solid conduction component (which is practically constant in the relevant service temperature interval for insulating foams, [8]). This effect is used in, e.g., vacuum insulation panels [9]. The resulting effective conductivity is then k "@ABC C & + C $ T + (5) where C s and C r are temperature-independent constants within the service temperature interval for insulating foams. This functional form can be utilized to separate contributions from the radiative heat transfer and conduction through solid by measuring heat conductivity SPE ANTEC Anaheim 2017 / 868

2 of an evacuated foam sample at several temperatures within the relevant range, and plotting it against T 3. Should the data fall along a straight line, as expected, the intercept can be interpreted as the solid contribution: k & = C &, and the slope as the coefficinent C r of the cubic term reflecting the radiative component: k $ = C $ T + Of course, one should keep in mind the range of applicability of this method is limited to that where bulk solid polymer conductivity is essentially independent of temperature. If k s exhibits a linear trend vs. temperature, i.e. k & = C &F + C &) T, one may still be able to separate k r as the only non-linear term in the equation for k t-vac (T) k "@ABC C &F + C &) T + C $ T + (6) provided the k t-vac is measured in a temperature range wide enough to exhibit substantial curvature in its plot vs. temperature. If the above curvature is not well-pronounced, the confidence intervals for the fit parameters of Eqn. 6 will be broad, and thus the accuracy of separation of k s and k r will be poor. Measuring temperature dependence of k s using dense samples may help improve the accuracy of measuring k r by providing the ratio C s1 /C s0, which should be porosity-independent. Moreover, if C s1 /C s0 turns out to be temperature-dependent, this dependency measured using a dense sample can be plugged into a modified Eqn. 6, where C s1 is a product of C s0 and some function of temperature. Measuring k t of the same sample prior to evacuation and comparing to k t-vac should isolate the gas contribution: k ' = k " k "@ABC (7) Generally, gas contribution is not temperatureindependent, as thermal conductivity of most gasses utilized as foam blowing agents is a moderately strong function of temperature. Some blowing agent gas mixtures (e.g. most pentanes and some hydrofluoroolefins) have a tendency to condense at some point within the applicable range of service conditions. The main limitation of the method is the temperature range of applicability: it is restricted to about -20 to +50, where the base polymer conductivity is practically temperature-independent. Additional limitations can be uniformity of the foam cell size distribution, and structural stability of the foam under conditions of high vacuum. Method Development and Validation Open Cell Foam Icynene Classic TM (LD-C-50) Spray Foam Insulation [12] product from Icynene, Inc. was used to prepare samples for validation of the method. First, 50 ml of B Side was added to a 1000 ml plastic beaker and agitated for 5 seconds using a mechanical stirrer. Subsequently, 50 ml of A Side was added to the same beaker and agitated for 3 seconds using a mechanical stirrer. The foaming mixture was guided upward using a wooden depressor to prevent tipping over during rise. When foam stopped rising, the depressor was removed, and the foam allowed to fully cure for at least 3 days. Resulting foam had effective density of 8 kg/m 3 and open cell content in excess of 95%. It was sliced transverse to the rise direction into approximately 25 mm thick sections. Portion of this material was utilized for thermal resistivity (R-value) measurement using a FOX 314 Heat Flow Meter (TA Instruments) unit augmented to accommodate measurements from -15 to 50. Another portion was used to prepare three types of specimens: (a) rectangular blocks, (b) thick sliced blocks, and (c) thin sliced blocks. Two specimens (a) were prepared, with dimensions 55 mm x 50 mm x 25 mm. Two specimens (b) were prepared, with dimensions 55 mm x 50 mm x 25 mm, each block cut into slices 1 mm thick, transverse to the rise direction. Two specimens (c) were prepared, with dimensions 55 mm x 50 mm x 25 mm, each block cut into slices 0.3 to 0.5 mm thick, transverse to the rise direction. Hobart Meat Slicer was used for slicing foam. It was noted that voids far in excess of overall foam cell size were present randomly throughout the sample. This is characteristic for spray foams, but for the purpose of this study sampling targeted areas without such large voids. Hot Disk Method Transient Plane Source [10], also known as Hot Disk method, was used for measurements of thermal conductivity (TC) in this work. Transient heating method yields TC and thermal diffusivity in a single experiment by fitting a curve of average temperature rise vs. time for a disk-shaped sensor sandwiched between two identical samples and subjected to a constant electric current. Range of TC that Hot Disk method can accommodate is from to 1000 W/m K. The specific device used for this work was TPS 2500S. Typical instrument variability of the Hot Disk method is well below 1% of signal. For the measurements, the Hot Disk probe was sandwiched between two identical specimens of a given sample, and the assembly was placed into a chamber with locally controlled atmosphere and temperature. TC measurements were conducted on the open cell foam samples under conditions of (a) ambient pressure and (b) high vacuum (0.08 Pa, or 8*10-7 bar), at several target temperatures, using Hot Disk probe. Corresponding results are presented in Figure 1. The data points in Figure 1 are plotted against cube of temperature (as expressed in degrees Kelvin), T 3. Thermal conductivity data follow the anticipated linear trend very well, especially under high vacuum. Additionally, data sets collected under vacuum for all three sample forms are nearly identical, as to be expected. There are more pronounced deviations for measurements carried out in atmosphere of lab air. One can SPE ANTEC Anaheim 2017 / 869

3 extract the solid and radiative components of thermal conductivity, following Eqn. 5, as, respectively, the intercept and the linear term of the linear regression of the thermal conductivity data measured in vacuum. Table 1A 1C summarize findings. Note that k g, extracted per Eqn. 6 from the thin slices data, is in good agreement (within 3%) with reference data [11]. Origin of deviation in k g extracted out of the bulk and thick slices data from the reference values for air at the same temperatures is unclear, but can be potentially attributed to uncontrolled retained atmosphere within the bulk of the foam blocks and thick slices. Table 1A. Thermal conductivity components of the open cell foam samples in lab air Environment Sample form Table 1C. Thermal conductivity components of the open cell foam samples in vacuum Sample Source k g intercept k g slope form FOX Heat Flow Meter Trendline intercept Trendline slope Bulk Lab Air E-07 Thick Slices Lab Air E-07 Thin Slices Lab Air E-07 Table 1B. Thermal conductivity components of the open cell foam samples in vacuum Sample Environment Trendline Trendline slope form intercept = k s = k r slope Bulk Vacuum E-07 Thick Slices Vacuum E-07 Thin Slices Vacuum E-07 Bulk Calculated E-07 Thick Slices Calculated E-07 Thin Slices Calculated E-07 Dry Air Reference E-07 Table 2 lists results of thermal conductivity measurements using FOX 314 Heat Flow Meter at four target mean temperatures (-7, 13, 24, 43 ) with temperature differential between the opposing sample surfaces of 22.4 (40 ), in a laboratory with controlled climate of 24, 50% relative humidity (RH). Heat Flow Meter relies on steady-state heat flux through a sample. Prior to measurement, the sample specimens were conditioned at 24, 50% RH conditions for at least 48 hours, as prescribed by ASTM C518. Table 2. Thermal conductivity k t and resistivity R/in of open cell foam samples via FOX Heat Flow Meter. Temp., Thickness, kt, R/in, Age, o C m W/m. o K F*ft2*h/Btu*in Days Apparent difference of thermal conductivity of the same sample measured using two different methods may well be due to significant propensity of the resulting foam product to water absorption (per Technical Product Data [12], up to 5 wt.%) and substantial difference in laboratory air humidity. Influence of the absorbed water content on thermal conductivity of low density foams is well appreciated in the industry [13, 14]. Considering this, the study team is currently pursuing the Hot Disk measurements in atmosphere of dry nitrogen. Method Application Four samples of commercially available closed cell polyisocyanurate foam insulation from various manufacturers were selected for evaluation using this method. Table 3 provides description of the samples. A pair of blocks of each sample were cut to approximately 50 mm x 50 mm x foam thickness dimensions. Each block was then sliced as described above, with planes of the slices parallel to the parent boardstock plane. During specimen preparation, it was noted that most samples contained irregularities such as gradients in cell morphology, with either pores in excess of the bulk foam cell size present near surfaces of the foam boards, or knit lines where cells of much smaller size where dominant. For the purpose of this study, we avoided sampling foam with such features, to minimize variability in the experiments. All four samples of closed cell foams had similar cell size. Therefore, the slice thickness was targeted to be same for all four samples, mm, which was commensurate with approximately twice the average foam cell size. Table 3. Closed Cell Foam Samples Sample ID Producer Product Name Density, kg/m 3 Sample A Hunter Hunter Xci Panels Sample B Rmax ThermoSheath-3 32 Sample C Rmax TSX Sample D Dow Chemical THERMAX XARMOR (ci) 30 SPE ANTEC Anaheim 2017 / 870

4 Results of thermal conductivity measurements, conducted on these four samples under conditions of high vacuum (0.08 Pa, or 8*10-7 bar) at several target temperatures using Hot Disk probe, are presented in Figure 1. Thermal conductivity k t of open cell foam samples in vacuum and at ambient pressure, plotted against T 3. Reference k air and calculated k g are added. Figure 2. The data points, plotted against cube of temperature (as expressed in degrees Kelvin), appear to closely follow the anticipated straight line behavior. One can extract the solid and radiative components of thermal conductivity, following Eq. 5, from the linearized trendline expressions within the graph as, respectively, the intercept and the linear term of each sample-specific equation. Table 4. Extinction coefficient K, solid component k s and radiative component k r of TC for closed cell foams Sample ID K, k s, k r, 1/cm mw/m.k mw/m.k Sample A Sample B Sample D Data from these samples measured via Hot Disk in atmosphere of dry nitrogen is pending. Limitations of the method. We have already mentioned the boundaries of this new method in thermal range. This method works well with rigid foams that can be cut into slices such that the slice thickness does not exceed twice the average foam cell size. Typically, sell size of insulation grade commercially available polymeric foams is not monodispersed, commonplace range is from 10-5 m to 10-2 m, and average size about 2*10-4 m. So usually the slices are relatively easy to prepare using commercially available cutting instruments. Time to produce each data point using TPS is rather long, about 6-10 hours, depending on how fast the environmental chamber stabilizes the sample environment. Conclusions A method to separately assess the three components of TC in low density insulating foams (solid conduction, gas conduction, and radiative transfer) has been developed and validated using open cell foam samples. The method relies on comparison of TC at ambient pressure and in carefully sliced and evacuated specimens of same foam. Reasonably good agreement was found between the extracted k g (where cell gas is air) and reference data for TC of air. The method was further used to assess K, k s and k r in closed cell polyisocyanurate foams. Nomenclature f s Fraction of struts in the foam structure k Thermal conductivity k p Thermal conductivity of solid bulk polymer k BA Thermal conductivity of bulk blowing agent K extinction coefficient r foam density of foam r poly density of solid bulk polymer s - Stephan Boltzman constant T Absolute temperature (in o K) Acknowledgements Thanks to the product development teams at The Dow Chemical Co. for locating and supplying foam samples for this work. References SPE ANTEC Anaheim 2017 / 871

5 1. ASTM C518-15, Standard Test Method for Steady-State Thermal Transmission Properties by Means of the Heat Flow Meter Apparatus, ASTM International, West Conshohocken, PA, 2015, 2. O. R. McIntire, R.N. Kennedy, Styrofoam for low temperature insulation, Chem. Eng. Progress, 44 (9), pp (1948) 3. R.L. Gorring, S.W. Churchill, Thermal conductivity of heterogeneous materials, Chem. Eng. Progress, 57 (7), pp (1961) 4. J.R. Howell et al, Thermal Radiation Heat Transfer (5 th edition), pp. 591, Taylor & Francis, A.B. Datye, R. Lemlich, Liquid distribution and electrical conductivity in foam, Int. J. Multiphase Flow, 9 (6), pp (1983) 6. M.A. Schuetz, L.R. Glickman, A basic study of heat transfer through foam insulation, J. Cellular Plastics, 20 (2), pp , (1984) 7. N.C. Hilyard, A. Cunningham, Low Density Cellular Plastics, pp , Chapman & Hall, C.L. Choy, Thermal Conductivity of Polymers, Polymer, 18, pp (1977) ASHRAE Handbook - Fundamentals (I-P Edition), American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., DIPPR 801 Thermophysical Property Database, Icynene Classic LD-C-50 Technical Product Data, Owens Corning Technical Bulletin, Pub. No Printed in U.S.A. June H.R. Trechsel, Moisture Control in Buildings: (MNL 18), ASTM International, 1994 SPE ANTEC Anaheim 2017 / 872

6 Figure 1. Thermal conductivity k t of open cell foam samples in vacuum and at ambient pressure, plotted against T 3. Reference k air and calculated k g are added. Figure 2. Thermal conductivity of sliced closed cell foams samples in vacuum. SPE ANTEC Anaheim 2017 / 873