Athermal blends

Because for most systems the entropy of mixing is small, attractive interactions between both components are needed to obtain a homogeneous mixed state. In the opposite case miscible polymer blends for which k 0 (no or weak interactions) are called athermal blends. 

Concerning the localized p-relaxation, it was found if the interaction of the two components are weak (athermal blends) the effect of blending on fliis relaxation process is small (see, for instance, Schartel and Wendorff 1995 Pathmanathan et al. 1986 Cendoya et al. 1999 Urakawa et al. 2001 Dionissio et al. 2000). These dielectric results are also in agreement with quasielastic neutron scattering investigations (Arbe et al. 1999) and are probably a consequence of the rather small length scale (localized fluctuations) of motions involved in these processes. This is further discussed also in reference Fischer et al. (1985). 

The model athermal blend is defined [59,62] as the hypothetical limit of vanishing interchain attractive potentials relative to the thermal energy, i.e., Pvmm-W = 0- For this situation the atomic site-site Percus-Yevick closure approximation of Eq. (2.7) is employed where the subscripts now refer to the spedes type. The constant volume athermal blend is of theoretical interest since it isolates the purely entropic packing effects. However, as emphasized by several workers [2,62,63,67], the athermal reference blend is not an adequate model of any real phase separating system. Its primary importance is as a reference system for the theories of thermally-induced phase separation discussed in Sect 8. 

The reference direct correlation functions assodated with the athermal blend are denoted by Rtc computed separately using the Percus-... 

The well-known mean-field incompressible Flory-Huggins theory of polymer mixtures assumes random mixing of polymer repeat units. However, it has been demonstrated that the radial distribution functions gay(r) of polymer melts are sensitive to the details of the polymer architecture on short length scales. Hence, one expects that in polymer mixtures the radial distribution functions will likewise depend on the intramolecular structure of the components, and that the packing will not be random. Since by definition the heat of mixing is zero for an athermal blend, Flory-Huggins theory predicts athermal mixtures are ideal solutions that exhibit complete miscibility. 

An important question is whether PRISM theory can predict the packing in athermal blends with the same good accuracy found for one-component melts. To address this question Stevenson and co-workers performed molecular dynamics simulations on binary, repulsive force blends of 50 unit chains at a liquidlike packing fraction of -17 = 0.465. The monomeric interactions were very similar to earlier one-component melt simulations which served as benchmark tests of melt PRISM theory. Nonbonded pairs of sites (both on the same and different chains) were taken to interact via shifted, purely repulsive Lennard-Jones potentials. These repulsive potentials were adjusted so that the effective hard site diameters, obtained from Eq. (3.12), were 1-015 and = 1.215 for the chains of type A or B, respectively. Chain connectivity was maintained using an intramolecular FENE potential between bonded sites on the same chain. The resulting chain model has nearly constant bond lengths that are nearly equal to the effective hard-core site diameter. 

Figure 14. A comparison between PRISM theory and MD simulations for the radial distribution functions in an athermal blend of 50 unit chains, The composition was maintained at 0 = 0.368, The points are the simulations and the curves are the PRISM predictions.

Another important question regarding the structure of athermal blends is whether the single-chain conformation changes with composition. In the molecular dynamics simulations, small changes (at most 10-15%) were observed in in ih mean-square end-to-end distance... 

Assuming that the intramolecular structure of the chains in the athermal blend is independent of composition, then the elements of the 4x4 Cl y(k) intramolecular matrix for the blend are already available from the corresponding one-component melt Intramolecular structure functions. The noy(k) for a, -y = A, B, C were obtained from Monte Carlo simulations of a single, rotational isomeric state chain using the parameterization of Suter and Flory discussed in Section III.B. Likewise, dd( ) was obtained from the RIS calculations of Honnell and coworkers for polyethylene... 

It should be mentioned that Eq. (4.3) is only one of several possible thermodynamic routes to the entropy of mixing in the athermal blend. Another possible route is through the charging formula of Chandler used earlier in Eq. (3.9b) for the one-component polymer melt. 

Fredrickson and co-workers have obtained entropic corrections to Flory-Huggins theory using a field theoretic approach. They considered athermal or nearly athermal blends where the corrections appeared from differences in the architecture or flexibility of the components. Using a field theoretic approach they demonstrated that conformational asymmetry will favor a demixing of the blends, and derived quasi universal conditions by which the miscibility could be maximized. Many qualitative features of the theory were consistent with experiments on polyolefin blends. This theory does not, however, attempt to rectify the many other approximations in the FH theory and is really intended only for nearly athermal blends, which are difficult to fabricate. 

The majority of experimental data has been measured for two blend systems PS/PVME, and isotopic blends of PS and poly(perdeutero-styrene). The surface compositions for PS/PVME blends were found to scale directly with the surface energy difference between the constituents (23), showing that the latter factor dominates the surface behavior, a result that might be expected for these nearly athermal blends with large surface energy differences. (The PS/PVME system has an interaction parameter estimated to be —0.0011 and can be considered as effectively athermal.) The square gradient theory with the Flory-Huggins free... 

The aim of the current work is to investigate the relationship between Tg, the length scale of the dynamic heterogeneity, the fragility, and the activation energy of pure poly(a-methyl styrene) and blends of poly(a-methyl styrene) with its oligomers. Our previous work [17] has shown that the mixture is an athermal blend. 

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