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We investigate the static shear viscosity on the sol side of the vulcanization transition within a minimal mesoscopic model for the Rouse-dynamics of a randomly crosslinked melt of phantom polymers. We derive an exact relation between the viscosity and the resistances measured in a corresponding random resistor network. This enables us to calculate the viscosity exactly for an ensemble of crosslinks without correlations. The viscosity diverges logarithmically as the critical point is approached. For a more realistic ensemble of crosslinks amenable to the scaling description of percolation, we prove the scaling relation $k=\phi-\beta$ between the critical exponent $k$ of the viscosity, the thermal exponent $\beta$ associated with the gel fraction and the crossover exponent $\phi$ of a random resistor network., Comment: 8 pages, uses Europhysics Letters style; Revisions: results extended

We discuss the critical dynamics of dipolar glasses as observed in the dynamic dielectric response and the dynamic structure factor. Our analysis is based on a hydrodynamic model, generalized to include slow (dipolar) fluctuations near the glass transition. The critical slowing-down of the dipoles gives rise to anomalies in the dynamic dielectric response, the appearance of a central peak and a divergent sound damping. All three phenomena are interrelated and determined by the critical exponents of an Ising spin glass. We work out the consequences of a dynamic scaling hypothesis for the dipolar autocorrelation and discuss two examples of such a scaling function. One is calculated within mean-field theory and the other is taken from numerical simulations. We compare our results to recent experiments on (NH4I)x(KI)1 − x.

When a sufficient density of permanent random crosslinks is incorporated into a system of macromolecules, the system undergoes a continuous equilibrium phase transition from a liquid to an amorphous solid state. In this solid state, a certain fraction of monomers are entirely delocalised. The remaining fraction (i.e. the gel-fraction) are localised about random mean positions, and have random r.m.s. displacements (i.e. localisation lengths). A microscopic mean-field theory of this so-called vulcanisation transition is presented, in which the gel-fraction and statistical distribution of localisation lengths are determined self-consistently. A scaling form for the distribution of localisation lengths, valid for all near-critical crosslink densities, is obtained, and it is found that both the fraction of localised monomers and the typical inverse localisation length vanish continuously at the transition.

We present a statistical-mechanical analysis of a system of randomly cross-linked macromolecules, focusing on the emergence of random static-density fluctuations as the solidification transition is approached. In mean-field theory the problem can be formulated in terms of a single macromolecule in an effective random potential. The distribution of the random potential, which must be calculated self-consistently, determines all moments of the static-density fluctuations. We find that the solidification transition occurs when an infinite network of cross-linked macromolecules is formed, and that a sequence of nonlinear density response functions diverges simultaneously at this transition.

We derive a semi-microscopic model for a mixed crystal with orientable molecules in the presence of lattice anisotropy. Fluctuations in the orientational degrees of freedom can be related exactly to fluctuations in the strain field. The phase diagram is calculated approximately: depending on the degree of disorder, we find either a state with long-range orientational order and a uniform lattice distortion or a glassy state. Enhanced orientational fluctuations near the transition give rise to a pronounced softening of the lattice in symmetry directions, which are determined by the anisotropy fields.