Melts athermal

An example of the changes in blend pair correlations upon cooling from the athermal (pure melt) limit to the critical temperature is shown in Figure 23 for the two values of N and a highly asymmetric blend composition. Strong deviations of the from the athermal melt... 

Fig. 5.3. Log-log plot of the self-diffusion constant D of polymer melts vs. chain length N. D is normalized by the diffusion constant of the Rouse limit, DRoUse> which is reached for short chain lengths. N is normalized by Ne, which is estimated from the kink in the log-log plot of the mean-square displacement of inner monomers vs. time [gi (t) vs. t]. Molecular dynamics results [177] and experimental data on PE [178] are compared with the MC results [40] for the athermal bond fluctuation model. From [40]...

Fig. 8 Theoretical liquid-liquid demixing curve (solid line) and the bulk melting temperature (dashed line) of a flexible-polymer blend with one component crystallizable and with athermal mixing. The chain lengths are uniform and are 128 units, the linear size of the cubic box is 64, and the occupation density is 0.9375 [86]...

Let us first consider a network immersed in a melt of polymer chains with degree of polymerization p. In the athermal case, the network should be swollen. As polymer-network interaction parameter Xnp increases, the volume of the network decreases until a practically complete segregation of the gel from polymer melt occurs. It has been found [34, 35] that two qualitatively different regimes can be realized either a smooth contraction of the network (Fig. 8, curve 1) or a jumpwise transition (Fig. 8, curve 2). The discrete first order phase transition takes place only for the networks prepared in the presence of some diluent and when p is larger than a critical value pcr m1/2. The jump of the... 

We will briefly discuss the molecular dynamics results obtained for two systems—protein-like and random-block copolymer melts— described by a Yukawa-type potential with (i) attractive A-A interactions (saa < 0, bb = sab = 0) and with (ii) short-range repulsive interactions between unlike units (sab > 0, aa = bb = 0). The mixtures contain a large number of different components, i.e., different chemical sequences. Each system is in a randomly mixing state at the athermal condition (eap = 0). As the attractive (repulsive) interactions increase, i.e., the temperature decreases, the systems relax to new equilibrium morphologies. 

This assumption is based on the fact that the polymer-solvent interaction parameter [see Eq. (8)] of the tributyrin-cellulose tributyrate system, as evaluated from melting-point depressions, is nearly zero at about 100° C [Mandelkern and Flory (160)]. It does not follow, however, that the system is athermal, for the parameter generally involves an entropy contribution. Furthermore, the heat and entropy parts of this parameter vary with the concentration in a complicated way, especially in polar systems [see, for example, Takenaka (243) Zimm (22) Kurata (154)]. Thus it is extremely hazardous to predict dilute solution properties from concentrated solution properties such as the melting-point depression, at least on a highly quantitative level as in the present problem. 

The above calculations assume that the gross chain conformations are those of a random walk, which is the case in the melt. However, for an isolated polymer molecule in a dilute solution, the average conformation is affected by excluded-volume interactions between one part of the chain and another. Because the chain must avoid self-intersection, the conformation of the chain will be that of a self-avoiding walk, rather than a random walk, if the solution is athermal—that is, if all interactions are negligible except excluded volume. Self-avoiding walks lead, on average, to more expanded coil dimensions, since expanded configurations are less likely than contracted ones to lead to self-intersection of the chain. Thus, in an athermal solution, the mean-square end-to-end dimension of a polymer molecule scales as... 

The crossover volume fraction is of order unity (f) 1) in an athermal solvent, meaning that the chains are partially swollen at all concentrations. The excluded volume in an athermal solvent is fully screened only in the melt state (. rs b 7- at 0 = 1). 

Table 9.1 shows that the number of Kuhn monomers in an entanglement strand in the melt state varies over a wide range (7 < A e(l) < 80) making 4 < 0e/0 < 30 for solutions in an athermal solvent. Since the entanglement concentration

overlap concentration (p, the expressions for a -solvent [Eqs (9.31), (9.33), and (9.34)] are valid for [A e(l)] - This condition is not very restrictive and it is satisfied for all experimental studies to date. 

Combining Eqs 3.32 and 3.33 and rearranging, gives a relation between the experimental and equilibrium melting point in athermal polymer blends ... 

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