Model treatments of the heat conductivity of heterogeneous polymers

Abstract

Basic physical concepts and limitations of current approaches to the theoretical description of the composition dependence of heat conductivity of microheterogeneous polymer materials (MHM) are reviewed. All "pragmatic" approaches (i.e., those assuming the existence of a infinitely thin, "mathematieal" interface between the components) fail to account explicitly for salient structural features of MHM such as the onset of an "infinite" duster of a disperse component at the percolation threshold, and the transition of a portion of a continuous component into a structurally different "boundary interphase" (BI). Among the "physical" approaches, it is apparently the Step-by-Step-Averaging (SSA) model which accounts simultaneously for both cited structural features of MHM. The SSA model was shown to provide a quantitative description of the experimental data available by an appropriate choice of relevant BI parameters (i.e., thickness and "partial" heat conductivity): at the present stage, however, the numerical values of the latter should be considered as fitting variables, rather than true material properties of BI.

Structure/Property Relationships for Poly(Vinylidene Fluoride)/Doped Polyaniline Blends

“…V. P. Privalko et al 756 It is pertinent to remark at this point that a jump-like change of a transport property like conductivity at a percolation threshold of a binary composite (Figure 1) is assumed to be a purely geometrical phenomenon, such that the corresponding "partial" properties of components remain unchanged. [20] This is somewhat at variance with the preceding data that revealed a relatively small but definite trend for the decrease of both X DSC and X WAXS for PVDF with w (Table 1). In our opinion, the latter effect can be explained by strong interactions at the PVDF/(PANI/DBSA) interface resulting in the loss of crystallizability of a fraction of sterically immobilized chains of PVDF in boundary layers (BL) around PANI/DBSA particles.…”

“…The apparent thickness, Dr, of the BL can be estimated from the following obvious relationship [20] n BL ð100 À wÞy BL ¼ Drsw;…”

Viscoelastic Behaviour of Polypropylene-Based Nanocomposites in the Melt State

“…2); however, at longer relaxation times the initial decay degenerates into a shallow dip at ô dip » 15 sec, after which the spectrum passes through a maximum around the characteristic relaxation time t 2 » 100 sec. Moreover, one observes strong shifts of these dips to longer relaxation times, the higher the temperature (ô dip » 80 sec and 100 sec at 200 and 220 o C, respectively), suggesting that the final upswings on the corresponding spectra are the shorter-time tails of slow The observed drastic changes in the patterns of relaxation times spectra for the nanocomposite, in particular the absence of decay at the longest relaxation times, are the clear evidence for a shear-resistant, spatial structure (infinite cluster [1]) of filler particles in the PP melt phase. The mean gap between surfaces of neighbouring filler particles, <L> = <d> [(ö max /ö) 1/3 1] »3.5 nm, is comparable to the estimated gyration radius of a macromolecular coil, <R g > = (<h 2 >/6) 1/2 » 4 nm (here ö max »15 % is the maximum packing fraction of Aerosil particles [15]).…”

“…In view of these outstanding properties of TPNC, their further development and characterisation are considered, on line with other areas of nanotechnology , as one of the major goals of the materials science in the oncoming millenium. As could be inferred from previous studies [1, 4, 5], the viscoelastic behaviour of molten TP was strongly affected by polymer-filler interactions; however, up till now no quantitative characterisation of the relaxation times spectra of TPNC was available. It is, therefore, the purpose of the present paper to report on the viscoelastic properties in the melt state of the TPNC based on polypropylene.…”

“…The continuum mechanics theories predict (and the technological experience proves) that the mechanical performance of thermoplastic polymers (TP) can be improved by incorporation of disperse rigid fillers. These theories, however, fail to explain the significant increase of, say, elasticity moduli and concomitant decrease of thermal expansivities of filled TP composites, the smaller the particle size at the same filler loading (e.g., [1]).…”