19 research outputs found
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 , peak position , and single-chain
statistics for symmetric and asymmetric copolymers as functions of ,
where is the Flory-Huggins interaction parameter and 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 upon for symmetric diblock copolymers in the
limit of strong scattering, or large , but yield qualitatively
different predictions for symmetric copolymers far from the ODT and for
asymmetric copolymers. The ROL theory predicts a suppression of
and a decrease of for large values of , relative to the RPA
predictions, but an enhancement of and an increase in
for small (). By separating intra- and
inter-molecular contributions to , we show that the decrease in
near the ODT is caused by the dependence of the intermolecular
direct correlation function, and is unrelated to any change in single-chain
statistics, but that the increase in at small values of 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