Super-cooled polymer melts

Starting from the Liouville equation as the fundamental microscopic evolution equation for the dynamics of all phase-space variables, MCT uses 

In this generalized oscillator equation, the frequency is related to the restoring force acting on a particle and Q is a friction constant. The key quantity of the theory is the memory kernel mq(l — t ), which involves higher order correlation functions and hence needs to be approximated. The memory kernel is expanded as a power series in terms of S(q, t) 

The coefficients of this mode-coupling functional are the basic control parameters of this idealized version of MCT. One sees that Eqs. [46] and [47] amount to a set of nonlinear equations for the correlators S(q,t) that must be solved self-consistently. 

This time t a actually is the maximum time for which Eq. [48] is valid, to C t C t a. The exponent y characterizes the behavior of the a-relaxation or structural relaxation. Typical a time scales diverge as 

As indicated, the power law approximations to the fS-correlator described above are only valid asymptotically for a — 0, but corrections to these predictions have been worked out.102,103 More important, however, is the assumption of the idealized MCT that density fluctuations are the only slow variables. This assumption breaks down close to Tc. The MCT has been augmented by coupling to mass currents, which are sometimes termed inclusion of hopping processes, but the extension of the theory to temperatures below Tc or even down to Tg has not yet been successful.101 Also, the theory is often not applied to experimental density fluctuations directly (observed by neutron scattering) but instead to dielectric relaxation or to NMR experiments. These latter techniques probe reorientational motion of anisotropic molecules, whereas the MCT equation describes a scalar quantity. Using MCT results to compare with dielectric or NMR experiments thus forces one to assume a direct coupling of orientational correlations with density fluctuations exists. The different orientational correlation functions and the question to what extent they directly couple to the density fluctuations have been considered in extensions to the standard MCT picture.104-108 

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Finding that the scattering functions at low temperature are amenable to an MCT description, we are faced with a dilemma. On the one hand, the high-temperature mean-square displacement curves lead us to conclude that dihedral barriers constitute a second mechanism for time scale separation in super-cooled polymer melts besides packing effects. On the other hand, the... 

Let us now turn to a discussion of the relation of the temperature dependence of the polymer melt s configurational entropy with its glass transition and address the famous paradox of the Kauzmann temperature of glass-forming systems.90 It had been found experimentally that the excess entropy of super-cooled liquids, compared with the crystalline state, seemed... 

In order for the ordered phase to crystallize from an amorphous melt a nucleation barrier must be overcome. This barrier is a result of interfacial energy between the ordered phase and the melt that causes super cooling. Sirota [44] suggested that in order for the nucleation barrier of the stable phase to be sufficiently high to form out of the melt, another phase with a lower nucleation barrier and a free energy intermediate between that of the stable phase and the melt must form. This, he points out, is implied by Oswald s rule [45] and evidence presented by Keller [35] that crystallization in semicrystalline polymer systems is mediated by a transient metastable phase [47, 48]. 

AY [)mr were measured by a Rheovibron (Toyo Seiki) at a heating rate of 2°C/min and a frequency of lOH over the temperature range from 150 C to 200° C. These phenomenological results suggest that the activation energy for the molecular transport term in polymer crystallization is associated with molecular diffusion in the super-cooled melt above T. This indicates that the activation process in molecular transport in polymer crystalUzation could be similar to that in the confined molecular motion in the rubbery state above T... 

The properties of incompatible polymer blends depend to a large extent on the mutual dispersion of the components, on the super-molecular structure within the phase of a single component, and on the structure of the interface. These structural parameters, in turn, depend on the processing or mixing conditions and on the strength of the thermodynamic incompatibility of the components as well. These boundary conditions together with the cooling rate control also the solidification process of a melt. 

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