Thermal expansion linear chains

Figure 9.33 The dependence of the thermal expansion linear coefficient a p on the fractal dimension of the chain part between nanoclnsters for epoxy polymers. The designations are the same as in Figure 9.32. The straight line 3 shows the dependence cc(D ) for phenylone [62]...

Since this meta-substituted diamine was much more reactive than OFB, a variety of polyimides could be made, aUowing the synthesis of such structures as PMDA-PFMB, a polyimide with a very low thermal expansion coefficient (CTE) that may provide many advantages for microelectronic fabrication. Linear polyimide structures have generally been found to have low CTEs even when bulky groups were attached to the main chain. 

Finally, making use the equation of state of Eq. (28) one can demonstrate that the linear thermal expansion coefficient depends on the deformation as follows (for isoenergetic chains)26 211... 

These expressions show that a deformed polymer network is an extremely anisotropic body and possesses a negative thermal expansivity along the orientation axis of the order of the thermal expansivity of gases, about two orders higher than that of macromolecules incorporated in a crystalline lattice (see 2.2.3). In spite of the large anisotropy of the linear thermal expansivity, the volume coefficient of thermal expansion of a deformed network is the same as of the undeformed one. As one can see from Eqs. (50) and (51) Pn + 2(iL = a. Equation (50) shows also that the thermoelastic inversion of P must occur at Xim (sinv) 1 + (1/3) cxT. It coincides with F for isoenergetic chains [see Eq. (46)]. 

If one reverts to the constant volume data of Fig. 15, a law such as p,(7) T fits the data fairly well above 7 , i.e. a = 0.7. Below 60 K, there is hardly any difference between constant T and constant P variations since the thermal expansion is greatly suppressed there. As for the longitudinal transport, the result is displayed in Fig. 14, where a cross-over from a superlinear to a linear (or sublinear) power law temperature dependence is observed in the vicinity of 80 K. Figure 15 emphasizes the remarkable feature of (TMTSF)2PF6, namely, opposite temperature dependencies for interplane and chain resistivities above T . 

If we consider the process of cooling molten polyethylene, there will be a progressive decrease in the volume that the chains occupy. This specific volume, V, is the reciprocal of the density and this is shown in Figure 1.7 for the case on cooling the polymer from 150 C to — 150 °C. It is seen that there is a linear decrease in with decreasing temperature, which is consistent with the coefficient of thermal expansion. 

They observed that in injection-molded copolyesters containing 40-90 mol% of p-hydroxybenzoic acid (PHB), the linear thermal expansions were highly anisotropic. They also observed that the linear thermal expansion is zero along the flow but not across the flow. The anisotropy in linear thermal expansion is due to the orientation of polymer chains during molding. 

Coefficient of linear thermal expansion measurements can also be used to estimate some important characteristic parameters of polymers, such as free volume (Vf), hard-core volume (v ), and magnitude of intermolecular interactions (T ) in the materials (Brostow and Szymanski 1986). As temperature increases, polymers expand and their conformational entropy, a measure of disorder in polymer chains, increases. Theoretically, at a sufficiently high temperature, volume expansion allows each polymer chain to relax individually without interacting with its neighbors. This temperature is defined as T. In polymers, T is an extrapolated value above the degradation temperature, and for many commercial polymers T is above 500°C (Matsuoka 1997). Variables such as Vt, v, and T can be evaluated by the application of an equation of state such as the Hartman equation shown below (where V = v/v, T = TIT, and F = PIP ). (Hartman and Haque 1985a, b) ... 

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