Orientation fluctuation-induced spinodal decomposition in polymer–liquid-crystal mixtures

We study the early stages of spinodal decomposition (SD) in polymer–liquid-crystal mixtures by solving linearized time-dependent Landau-Ginzburg equations for concentration (conserved order parameter) and orientation (nonconserved order parameter). The theory takes into account a cross term between concentration and orientation gradients, which becomes an important factor for phase separation kinetics. We calculate structure factors for concentration and for orientation, depending on a quench temperature and concentration. We find a new SD process driven by instability of the orientational order parameter. In this case, the average domain size initially grows as a nontrivial and evolving power of time, which starts as t1/3 in our minimal model. The domain growth is advanced by the coupling between the two order parameters

Density functional theory of phase coexistence in weakly polydisperse fluids

The recently proposed universal relations between the moments of the polydispersity distributions of a phase-separated weakly polydisperse system are analyzed in detail using the numerical results obtained by solving a simple density functional theory of a polydisperse fluid. It is shown that universal properties are the exception rather than the rule.Comment: 10 pages, 2 figures, to appear in PR

Modeling phase behavior for quantifying micro-pervaporation experiments

We present a theoretical model for the evolution of mixture concentrations in a micro-pervaporation device, similar to those recently presented experimentally. The described device makes use of the pervaporation of water through a thin PDMS membrane to build up a solute concentration profile inside a long microfluidic channel. We simplify the evolution of this profile in binary mixtures to a one-dimensional model which comprises two concentration-dependent coefficients. The model then provides a link between directly accessible experimental observations, such as the widths of dense phases or their growth velocity, and the underlying chemical potentials and phenomenological coefficients. It shall thus be useful for quantifying the thermodynamic and dynamic properties of dilute and dense binary mixtures.Comment: to be published in EPJ-

Isotropic-nematic phase equilibria in the Onsager theory of hard rods with length polydispersity

We analyse the effect of a continuous spread of particle lengths on the phase behavior of rodlike particles, using the Onsager theory of hard rods. Our aim is to establish whether ``unusual'' effects such as isotropic-nematic-nematic (I-N-N) phase separation can occur even for length distributions with a single peak. We focus on the onset of I-N coexistence. For a log-normal distribution we find that a finite upper cutoff on rod lengths is required to make this problem well-posed. The cloud curve, which tracks the density at the onset of I-N coexistence as a function of the width of the length distribution, exhibits a kink; this demonstrates that the phase diagram must contain a three-phase I-N-N region. Theoretical analysis shows that in the limit of large cutoff the cloud point density actually converges to zero, so that phase separation results at any nonzero density; this conclusion applies to all length distributions with fatter-than-exponentail tails. Finally we consider the case of a Schulz distribution, with its exponential tail. Surprisingly, even here the long rods (and hence the cutoff) can dominate the phase behaviour, and a kink in the cloud curve and I-N-N coexistence again result. Theory establishes that there is a nonzero threshold for the width of the length distribution above which these long rod effects occur, and shows that the cloud and shadow curves approach nonzero limits for large cutoff, both in good agreement with the numerical results.Comment: 20 pages, 13 figure

Phase Diagrams for Deformable Toroidal and Spherical Surfaces with Intrinsic Orientational Order

A theoretical study of toroidal membranes with various degrees of intrinsic orientational order is presented at mean-field level. The study uses a simple Ginzburg-Landau style free energy functional, which gives rise to a rich variety of physics and reveals some unusual ordered states. The system is found to exhibit many different phases with continuous and first order phase transitions, and phenomena including spontaneous symmetry breaking, ground states with nodes and the formation of vortex-antivortex quartets. Transitions between toroidal phases with different configurations of the order parameter and different aspect ratios are plotted as functions of the thermodynamic parameters. Regions of the phase diagrams in which spherical vesicles form are also shown. 82.70, 02.40, 68.15, 64.70.M Typeset using REVT E X 1 I

Non-uniformities in polymer/liquid crystal mixtures

We theoretically study interfacial properties between two coexisting phases in mixtures of a flexible polymer and a low-molecular-weight liquid crystal. By numerically solving Euler equations for compositional and orientational order parameter fields, we calculate the order parameter profiles and interfacial tensions for nematic-isotropic and isotropic-isotropic phase equilibria. We find that the order parameter profiles are non-monotonic at some temperatures. The nematic-isotropic interfacial tension increases with decreasing temperature and is approximately proportional to $(T-T_{\rm{NI}})^n$ at temperatures below the nematic-isotropic transition temperature ($T_{\rm{NI}}$) of the pure nematogen. The value of the exponent $n$ is strongly affected by the existence of a triple point

The self-assembly, elasticity, and dynamics of cardiac thin filaments^☆

Solutions of intact cardiac thin filaments were examined with transmission electron microscopy, dynamic light scattering (DLS), and particle-tracking microrheology. The filaments self-assembled in solution with a bell-shaped distribution of contour lengths that contained a population of filaments of much greater length than the in vivo sarcomere size (∼1 μm) due to a one-dimensional annealing process. Dynamic semiflexible modes were found in DLS measurements at fast timescales (12.5 ns–0.0001 s). The bending modulus of the fibers is found to be in the range 4.5–16 × 10<sup>−27</sup> Jm and is weakly dependent on calcium concentration (with Ca<sup>2+</sup> ≥ without Ca<sup>2+</sup>). Good quantitative agreement was found for the values of the fiber diameter calculated from transmission electron microscopy and from the initial decay of DLS correlation functions: 9.9 nm and 9.7 nm with and without Ca<sup>2+</sup>, respectively. In contrast, at slower timescales and high polymer concentrations, microrheology indicates that the cardiac filaments act as short rods in solution according to the predictions of the Doi-Edwards chopsticks model (viscosity, η ∼c<sup>3</sup>, where c is the polymer concentration). This differs from the semiflexible behavior of long synthetic actin filaments at comparable polymer concentrations and timescales (elastic shear modulus, G′ ∼ c1.4, tightly entangled) and is due to the relative ratio of the contour lengths (∼30). The scaling dependence of the elastic shear modulus on the frequency (ω) for cardiac thin filaments is G′ ∼ω<sup>3/4 ± 0.03</sup>, which is thought to arise from flexural modes of the filaments

The internal dynamic modes of charged self-assembled peptide fibrils

Photon correlation spectroscopy is used to study the internal dynamics of self-assembled charged peptide fibrils. Short neutral and charged polymeric aggregates have diffusive modes due to whole macromolecular motion. For long semiflexible fibrils the logarithm of the intermediate scattering function follows a q2t3/4 scaling at long times consistent with a Kratky-Porod free energy and preaveraged Oseen hydrodynamics. Persistence lengths on the order of micrometers are calculated for the peptide fibrils consistent with estimates from the liquid-crystalline phase behavior. Fibril diameters (5-35 nm) calculated from the initial decay of the correlation functions are in agreement with transmission electron microscopy measurements