Calculation of the absolute free energy of a smectic-A phase.

In this paper, we provide a scheme to compute the absolute free energy of a smectic-A phase via the "indirect method." The state of interest is connected through a three-step reversible path to a reference state. This state consists of a low-density layer of rods coupled to two external fields maintaining these rods close to the layer's plane and oriented preferably normal to the layer. The low-density free energy of the reference state can be computed on the basis of the relevant second virial coefficients between two rods coupled to the two external fields. We apply this technique to the Gay-Berne potential for calamitics with a parameter set leading to stable isotropic (I), nematic (N), smectic-A (SmA), and crystal (Cr) phases. We locate the I-SmA phase transition at low pressure and the sequence of phase transitions I-N-SmA along higher-pressure isobars and we establish the location of the I-N-SmA triple point. Close to this triple point, we show that the N-SmA transition is clearly first order. Our results are compared to the coexistence lines of the approximate phase diagram elucidated by de Miguel et al. [J. Chem. Phys. 121, 11183 (2004)] established through the direct observation of the sequence of phase transitions occurring along isobars under heating or cooling sequences of runs. Finally, we discuss the potential of our technique in studying similar transitions observed on layered phases under confinement.

Dynamics of dilute solutions of poly(aspartic acid) and its sodium salt elucidated from atomistic molecular dynamics simulations with explicit water.

The use of forward osmosis (FO) process for seawater desalination has attracted tremendous interest in recent years. Besides the manufacture of suitable membranes, the major technical challenge in the efficient deployment of the FO technology lies in the development of a suitable "draw solute". Owing to its inherent advantages, poly(aspartic acid) has arisen to be an attractive candidate for this purpose. However, an investigation of its molecular level properties has not been studied in detail. In this paper, the dynamics of poly(aspartic acid) and its sodium salt in the dilute concentration regime have been reported. The quantification of the polymer conformational properties, its solvation behavior, and the counterion dynamics are studied. The neutral polymer shows a preferentially coiled structure whereas the fully ionized polymer has an extended structure. Upon comparing with poly(acrylic acid) polymer, another polymer which has been used as a draw solute, poly(aspartic acid) forms more number of hydrogen bonds as well as fewer ion pairs.

Compressive force generation by a bundle of living biofilaments.

To study the compressional forces exerted by a bundle of living stiff filaments pressing on a surface, akin to the case of an actin bundle in filopodia structures, we have performed particulate molecular dynamics simulations of a grafted bundle of parallel living (self-assembling) filaments, in chemical equilibrium with a solution of their constitutive monomers. Equilibrium is established as these filaments, grafted at one end to a wall of the simulation box, grow at their chemically active free end, and encounter the opposite confining wall of the simulation box. Further growth of filaments requires bending and thus energy, which automatically limit the populations of longer filaments. The resulting filament sizes distribution and the force exerted by the bundle on the obstacle are analyzed for different grafting densities and different sub- or supercritical conditions, these properties being compared with the predictions of the corresponding ideal confined bundle model. In this analysis, non-ideal effects due to interactions between filaments and confinement effects are singled out. For all state points considered at the same temperature and at the same gap width between the two surfaces, the force per filament exerted on the opposite wall appears to be a function of a rescaled free monomer density ρ1(eff). This quantity can be estimated directly from the characteristic length of the exponential filament size distribution P observed in the size domain where these grafted filaments are not in direct contact with the wall. We also analyze the dynamics of the filament contour length fluctuations in terms of effective polymerization (U) and depolymerization (W) rates, where again it is possible to disentangle non-ideal and confinement effects.

Growth kinetics of circular liquid domains on vesicles by diffusion-controlled coalescence.

Motivated by recent experiments on multicomponent membranes, the growth kinetics of domains on vesicles are theoretically studied. It is known that the steady-state rate of coalescence cannot be obtained by taking the long-time limit of the coalescence rate when the membrane is regarded as an infinite two-dimensional (2D) system. The steady-state rate of coalescence is obtained by explicitly taking into account the spherical vesicle shape. Using the expression for the 2D diffusion coefficient obtained in the limit of small domain size, an analytical expression for domain growth kinetics is obtained when a circular shape is always maintained. For large domains, the growth kinetics are discussed by investigating the size dependence of the coalescence rate, using the expression for the diffusion coefficient of arbitrary domain size.

Autonomous motility of active filaments due to spontaneous flow-symmetry breaking.

We simulate the nonlocal Stokesian hydrodynamics of an elastic filament which is active due a permanent distribution of stresslets along its contour. A bending instability of an initially straight filament spontaneously breaks flow symmetry and leads to autonomous filament motion which, depending on conformational symmetry, can be translational or rotational. At high ratios of activity to elasticity, the linear instability develops into nonlinear fluctuating states with large amplitude deformations. The dynamics of these states can be qualitatively understood as a superposition of translational and rotational motion associated with filament conformational modes of opposite symmetry. Our results can be tested in molecular-motor filament mixtures, synthetic chains of autocatalytic particles, or other linearly connected systems where chemical energy is converted to mechanical energy in a fluid environment.

Hybrid molecular dynamics simulations of living filaments.

We propose a hybrid molecular dynamics/multi-particle collision dynamics model to simulate a set of self-assembled semiflexible filaments and free monomers. Further, we introduce a Monte Carlo scheme to deal with single monomer addition (polymerization) or removal (depolymerization), satisfying the detailed balance condition within a proper statistical mechanical framework. This model of filaments, based on the wormlike chain, aims to represent equilibrium polymers with distinct reaction rates at both ends, such as self-assembled adenosine diphosphate-actin filaments in the absence of adenosine triphosphate (ATP) hydrolysis and other proteins. We report the distribution of filament lengths and the corresponding dynamical fluctuations on an equilibrium trajectory. Potential generalizations of this method to include irreversible steps like ATP-actin hydrolysis are discussed.

Diffusion coefficient of an inclusion in a liquid membrane supported by a solvent of arbitrary thickness.

The diffusion coefficient of an inclusion in a liquid membrane is investigated by taking into account the interaction between membranes and bulk solvents of arbitrary thickness. As illustrative examples, the diffusion coefficients of two types of inclusions, a circular domain composed of fluid with the same viscosity as the host membrane and that of a polymer chain embedded in the membrane, are studied. The diffusion coefficients are expressed in terms of the hydrodynamic screening lengths, which vary according to the solvent thickness. When the membrane fluid is dragged by the solvent of finite thickness, via stick boundary conditions, multiple hydrodynamic screening lengths together with the weight factors to the diffusion coefficients are obtained from the characteristic equation. The conditions for which the diffusion coefficients can be approximated by the expression including only a single hydrodynamic screening length are also shown.

Hydrodynamic coupling between two fluid membranes.

The coupled in-plane diffusion dynamics between point-particles embedded in stacked fluid membranes is investigated. We calculate the contributions to the coupling longitudinal and transverse diffusion coefficients due to particle motion within the different as well as the same membranes. The stacked geometry leads to a hydrodynamic coupling between the two membranes.

Lipid flip-flop driven mechanical and morphological changes in model membranes.

We study, using dissipative particle dynamics simulations, the effect of active lipid flip-flop on model fluid bilayer membranes. We consider both cases of symmetric as well as asymmetric flip-flops. Symmetric flip-flop leads to a steady state of the membrane with an effective temperature higher than that of the equilibrium membrane and an effective surface tension lower than that of the equilibrium membrane. Asymmetric flip-flop leads to transient conformational changes in the membrane in the form of bud or blister formation, depending on the flip rate.