Glassy correlations and microstructures in randomly crosslinked homopolymer blends

We consider a microscopic model of a polymer blend that is prone to phase separation. Permanent crosslinks 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 emerges upon sufficient crosslinking. 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 crosslinking, 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 lamellae or random structures with a unique wavelength, can be energetically favorable.Comment: 19 pages, 10 figures. Submitted to the Journal of Chemical Physics (http://jcp.aip.org

Three-phase coexistence with sequence partitioning in symmetric random block copolymers

We inquire about the possible coexistence of macroscopic and microstructured phases in random Q-block copolymers built of incompatible monomer types A and B with equal average concentrations. In our microscopic model, one block comprises M identical monomers. The block-type sequence distribution is Markovian and characterized by the correlation \lambda. Upon increasing the incompatibility \chi\ (by decreasing temperature) in the disordered state, the known ordered phases form: for \lambda\ > \lambda_c, two coexisting macroscopic A- and B-rich phases, for \lambda\ < \lambda_c, a microstructured (lamellar) phase with wave number k(\lambda). In addition, we find a fourth region in the \lambda-\chi\ plane where these three phases coexist, with different, non-Markovian sequence distributions (fractionation). Fractionation is revealed by our analytically derived multiphase free energy, which explicitly accounts for the exchange of individual sequences between the coexisting phases. The three-phase region is reached, either, from the macroscopic phases, via a third lamellar phase that is rich in alternating sequences, or, starting from the lamellar state, via two additional homogeneous, homopolymer-enriched phases. These incipient phases emerge with zero volume fraction. The four regions of the phase diagram meet in a multicritical point (\lambda_c, \chi_c), at which A-B segregation vanishes. The analytical method, which for the lamellar phase assumes weak segregation, thus proves reliable particularly in the vicinity of (\lambda_c, \chi_c). For random triblock copolymers, Q=3, we find the character of this point and the critical exponents to change substantially with the number M of monomers per block. The results for Q=3 in the continuous-chain limit M -> \infty are compared to numerical self-consistent field theory (SCFT), which is accurate at larger segregation.Comment: 24 pages, 19 figures, version published in PRE, main changes: Sec. IIIA, Fig. 14, Discussio

Renormalized One-loop Theory of Correlations in Disordered Diblock Copolymers

A renormalized one-loop theory (ROL) is used to calculate corrections to the random phase approximation (RPA) for the structure factor \Sc(q) in disordered diblock copolymer melts. Predictions are given for the peak intensity $S(q^{\star})$, peak position $q^{\star}$, and single-chain statistics for symmetric and asymmetric copolymers as functions of $\chi N$, where $\chi$ is the Flory-Huggins interaction parameter and $N$ is the degree of polymerization. The ROL and Fredrickson-Helfand (FH) theories are found to yield asymptotically equivalent results for the dependence of the peak intensity $S(q^{\star})$ upon $\chi N$ for symmetric diblock copolymers in the limit of strong scattering, or large $\chi N$, but yield qualitatively different predictions for symmetric copolymers far from the ODT and for asymmetric copolymers. The ROL theory predicts a suppression of $S(q^\star)$ and a decrease of $q^{\star}$ for large values of $\chi N$, relative to the RPA predictions, but an enhancement of $S(q^{\star})$ and an increase in $q^{\star}$ for small $\chi N$ ($\chi N < 5$). By separating intra- and inter-molecular contributions to $S^{-1}(q)$, we show that the decrease in $q^{\star}$ near the ODT is caused by the $q$ dependence of the intermolecular direct correlation function, and is unrelated to any change in single-chain statistics, but that the increase in $q^{\star}$ at small values of $\chi N$ is a result of non-Gaussian single-chain statistics.Comment: 16 pages, 13 figures, submitted to J. Chem. Phy

Electronic Excitations and Insulator-Metal Transition in Poly(3-hexylthiophene) Organic Field-Effect Transistors

We carry out a comprehensive theoretical and experimental study of charge injection in Poly(3-hexylthiophene) (P3HT) to determine the most likely scenario for metal-insulator transition in this system. We calculate the optical absorption frequencies corresponding to a polaron and a bipolaron lattice in P3HT. We also analyze the electronic excitations for three possible scenarios under which a first-- or a second--order metal--insulator transition can occur in doped P3HT. These theoretical scenarios are compared with data from infrared absorption spectroscopy on P3HT thin film field-effect transistors (FET). Our measurements and theoretical predictions suggest that charge-induced localized states in P3HT FETs are bipolarons and that the highest doping level achieved in our experiments approaches that required for a first-order metal--insulator transition.Comment: 9 pages, 4 figures. Phys. Rev. B, in pres

Density of Neutral Solitons in Weakly Disordered Peierls Chains

We study the effects of weak off-diagonal disorder on Peierls systems with a doubly degenerate ground state. We show that for these systems disorder in the electron hopping amplitudes induces a finite density of solitons in the minimal-energy lattice configuration of a single chain. These disorder-induced dimerization kinks are neutral and have spin 1/2. Using a continuum model for the Peierls chain and treating the lattice classically, we analytically calculate the average free energy and density of kinks. We compare these results to numerical calculations for a discrete model and discuss the implications of the kinks for the optical and magnetic properties of the conjugated polymer trans-polyacetylene.Comment: 28 pages, revtex, 5 Postscript figures, to appear in Phys. Rev.

Advanced Ginzburg-Landau theory of freezing: A density-functional approach

This paper revisits the weakly fourth-order anisotropic Ginzburg-Landau (GL) theory of freezing (also known as the Landau-Brazowskii model or theory of weak crystallization) by comparing it to a recent density functional approach, the phase-field crystal (PFC) model. First we study the critical behavior of a generalized PFC model and show that (i) the so-called one-mode approximation is exact in the leading order, and (ii) the direct correlation function has no contribution to the phase diagram near the critical point. Next, we calculate the anisotropy of the crystal-liquid interfacial free energy in the phase-field crystal (PFC) model analytically. For comparison, we also determine the anisotropy numerically and show that no range of parameters can be found for which the phase-field crystal equation can quantitatively model anisotropy for metallic materials. Finally, we derive the leading order PFC amplitude model and show that it coincides with the weakly fourth-order anisotropic GL theory, as a consequence of the assumptions of the GL theory being inherent in the PFC model. We also propose a way to calibrate the anisotropy in the Ginzburg-Landau theory via a generalized gradient operator emerging from the direct correlation function appearing in the generating PFC free energy functional