Heat generation and conduction in PDMS-carbon nanoparticle membranes irradiated with optical fibers

Abstract

Carbon based materials have recently been used to fabricate highly photo-absorbing surfaces for heat generation purposes. In this report we present experimental measurements of the temperature increments ΔT in polymer (PDMS)-carbon nanopowder membranes irradiated by a light source via an optical fiber. In particular, we analyze experimentally the effects of the optical depth, τλ=βL, on the transient and steady state temperature profiles. In order to analyze the experimental data under the heat conduction theory, we also constructed a 2D axi-symmetric heat transfer solution for a semi-transparent finite membrane using Green's functions. With this approach we obtained two analytical expressions: one for the axial unsteady profile and another for the steady ΔT profile in the r−z plane using the delta function approximation. We found a linear relationship between the experimental ΔT steady values and the optical intensity Io; this linear relationship was maintained until incandescence at the membrane surface appeared. We also found that the steady ΔT values had little dependance on the membrane thickness L; conversely, the transient ΔT values exhibited a clear dependance on L, as expected. The theoretical solution fitted the experimental data only for a thermal diffusivity smaller than that of pristine PDMS. Our analysis suggests that such heat transfer retardation may be due to the nonlinear scattering behavior of the composite or due to additional interfacial resistances imposed by the experiment. Finally, experiments and theory showed that the L−ΔT curves have a maximum point (maximum temperature) at an optimal membrane thickness Lop; this optimal point in turn decreases as the extinction coefficient increases. Additional analysis of the results were also conducted regarding the area of the membranes, and both, experiments and theory, suggest that the heat generation induced by irradiating a surface with optical fibers is indeed highly localized.