Polymer blends athermal

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]...

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

In immiscible polymer blends with a high degree of immiscibility such as PP/PS, it has been shown that nucleation at the interface affects the crystallization behavior. Wenig et al. [1990] showed that, with increasing the amount of PS in a blend with PP, the nucleation shifted from preferentially thermal (related to the degree of undercooling) to more athermal. This was... 

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. 

In this section we examine athermal binary mixtures using PRISM theory. Tests of both the structural and thermodynamic predictions of PRISM theory with the PY closure against large-scale computer simulations are discussed in Section IV.A. Atomistic level PRISM calculations are presented in Section IV.B, and the possibility of nonlocal entropy-driven phase separation is discussed in Section IV.C at the SFC model level. Section IV.D presents analytic predictions based on the idealized Gaussian thread model. The limitations of overly coarse-grained chain models for treating athermal polymer blends are briefly discussed. 

Summarizing, the major conclusion of this section is that PRISM theory provides an excellent description of the structure and (constant volume) free energy of mixing of high-density athermal polymer blends composed of the short and modest chain length molecules presently accessible to computer simulation. This has motivated the application of the theory to experimentally relevant situations such as long chain N lO -lO ) and chemically realistic atomistic models. 

Gaussian thread limit for N—For many physical problems (e.g., polymer solutions and melts, liquid-vapor equilibria, and thermal polymer blends and block copolymers), the Gaussian thread model has been shown to be reliable in the sense that it is qualitatively consistent with many aspects of the behavior predicted by numerical PRISM for more realistic semiflexible, nonzero thickness chain models. However, there are classes of physical problems where this is not the case. The athermal stiffness blend in certain regions of parameter space is one case, both in... 

Singh C, Schweizer KS (1995) Correlation-effects and entropy-driven phase-separation in athermal polymer blends. J Chem Phys 103(13) 5814—5832... 

Taking into account that polyolefins can be blended in spite of only small van der Waals enthalpic interactions, in a series of papers theoretical models were developed to explain the miscibility in such nearly athermal and/or athermal polymeric mixtures. Thus Schweizer et al. [85] found by extending the RISM ( reference interaction side model ) theory, that structural asymmetry between the polymer components leads to negative interaction parameters because of significant noncombinatorial mixing entropy contributions which stabilize the polymer blend by spatially... 

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. 

Benchmark Monte Carlo simulations of a different class of athermal polymer mixtures have recently been carried out by Weinhold et al. An equimolar = 0.5), constant-volume binary blend was considered. The polymers were modeled as semiflexible, tangent bead chains of equal degrees of polymerization, N, interacting via a purely hard-core potential... 

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. 

Finally, field theoretic approaches have recently predicted athermal phase separation driven by nonlocal-entropic considerations for incompressible blends of Gaussian thread polymers. This prediction is at odds with PRISM theory in the thread limit. However, for the effective chi parameter PRISM theory has been shown to be equivalent to the field theory if the free energy route is employed in conjunction with the extremely simple RPA closure (not PY). The RPA closure, Cmm ( ) = -/8mmm ( ) for all r, is known to be very poor for repulsive force systems and violates the hard-core impenetrability condition. Thus, the field-theoretic prediction has been suggested to be a consequence of the combined use of a long-wavelength incompressibility approximation in conjunction with a RPA closure. ... 

The favorable effect on polyolefin miscibility of statistical segment length asymmetry due to the entropy contributions required for conformational adjustments has also been emphasized by Bates et al. [87]. In a series of papers. Bates and Fredrickson [88] attributed the miscibility of athermal or nearly athermal polymer mixtures mainly to these conformational asymmetries which contribute substantially to a nonlocal conformational excess entropy of mixing. The effect is exemplified for the amorphous polyethylene/poly-(ethylethylene) blend. Due to the fact that unperturbed PE and PEE molecules cannot be randomly interchanged, a positive excess free energy of mixing caused by nonlocal excess entropy contribution is anticipated by the authors. The effect of asymmetry on polymer miscibility is also supported by computer simulations, which suggest additional contributions due to entropy density differences of the pure polymeric phases [89]. 

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