Glassy correlations and microstructures in randomly cross-linked homopolymer blends

We consider a microscopic model of a polymer blend that is prone to phase separation. Permanent cross-links are introduced between randomly chosen pairs of monomers, drawn from the Deam-Edwards distribution. Thereby, not only density but also concentration fluctuations of the melt are quenched-in in the gel state, which emerge upon sufficient cross-linking. We derive a Landau expansion in terms of the order parameters for gelation and phase separation, and analyze it on the mean-field level, including Gaussian fluctuations. The mixed gel is characterized by thermal as well as time-persistent (glassy) concentration fluctuations. Whereas the former are independent of the preparation state, the latter reflect the concentration fluctuations at the instant of cross-linking, provided the mesh size is smaller than the correlation length of phase separation. The mixed gel becomes unstable to microphase separation upon lowering the temperature in the gel phase. Whereas the length scale of microphase separation is given by the mesh size, at least close to the transition, the emergent microstructure depends on the composition and compressibility of the melt. Hexagonal structures, as well as lamellas or random structures with a unique wavelength, can be energetically favorable.     

Magnetic-field enhancement of superconductivity in ultranarrow wires

We study the effect of an applied magnetic field on sub-10-nm wide MoGe and Nb superconducting wires. We find that magnetic fields can enhance the critical supercurrent at low temperatures, and do so more strongly for narrower wires. We conjecture that magnetic moments are present, but their pair-breaking effect, active at lower magnetic fields, is suppressed by higher fields. The corresponding microscopic theory, which we have developed, quantitatively explains all experimental observations, and suggests that magnetic moments have formed on the wire surfaces.     

Scaling of entropic shear rigidity

The scaling of shear modulus near the gelation-vulcanization transition is explored heuristically and analytically. It is found that in a dense melt the effective chains of the infinite cluster have sizes that scale sublinearly with their contour length. Consequently, each chain contributes k(B)T to the rigidity, which leads to a shear-modulus exponent dnu. In contrast, in phantom elastic networks the scaling is linear in the contour length, yielding an exponent identical to that of the random resistor network conductivity, as predicted by de Gennes. For nondense systems, the exponent should cross over to dnu when the percolation correlation length is much larger than the density-fluctuation length.     

Early stages of homopolymer collapse

Interest in the protein folding problem has motivated a wide range of theoretical and experimental studies of the kinetics of the collapse of flexible homopolymers. In this paper, a phenomenological model is proposed for the kinetics of the early stages of homopolymer collapse following a quench from temperatures above to below the straight theta temperature. In the first stage, nascent droplets of the dense phase are formed, with little effect on the configurations of the bridges that join them. The droplets then grow by accreting monomers from the bridges, thus causing the bridges to stretch. During these two stages, the overall dimensions of the chain decrease only weakly. Further growth of the droplets is accomplished by the shortening of the bridges, which causes the shrinking of the overall dimensions of the chain. The characteristic times of the three stages scale as N0, N(1/5), and N(6/5), respectively, where N is the degree of polymerization of the chain.     

Weber blockade theory of magnetoresistance oscillations in superconducting strips

Recent experiments on the conductance of thin, narrow superconducting strips have found periodic fluctuations, as a function of the perpendicular magnetic field, with a period corresponding to approximately two flux quanta per strip area [A. Johansson et al., Phys. Rev. Lett. 95, 116805 (2005)]. We argue that the low-energy degrees of freedom responsible for dissipation correspond to vortex motion. Using vortex-charge duality, we show that the superconducting strip behaves as the dual of a quantum dot, with the vortices, magnetic field, and bias current respectively playing the roles of the electrons, gate voltage, and source-drain voltage. In the bias-current versus magnetic-field plane, the strip conductance displays regions of small vortex conductance (i.e., small electrical resistance) that we term "Weber blockade" diamonds, which are dual to Coulomb blockade diamonds in quantum dots.     

Density-correlator signatures of the vulcanization transition

Certain density correlators, measurable via various experimental techniques, are studied in the context of the vulcanization transition. It is shown that these correlators contain essential information about both the vulcanization transition and the emergent amorphous solid state. Contact is made with various physical ingredients that have featured in experimental studies of amorphous colloidal and gel systems and in theoretical studies of the glassy state. Received 30 September 2000     

Magnetotransport in manganites and the role of quantal phases: theory and experiment

While low-temperature Hall resisitivity rhoxy of La2/3(Ca,Pb)1/3MnO3 single crystals can be separated into ordinary (OHE) and anomalous (AHE) contributions, no such decomposition is possible near the Curie temperature Tc. Rather, the rhoxy data collapse to a single function of the reduced magnetization m=M/Msat, with an extremum at approximately 0.4 m. A new mechanism for the AHE in the inelastic hopping regime is identified that reproduces the scaling curve. An extension of Holstein's model for the hopping OHE, the mechanism arises from the combined effects of the double-exchange-induced quantal phase in triads of Mn ions and spin-orbit interactions.