Coarsening dynamics of ternary amphiphilic fluids and the self-assembly of the gyroid and sponge mesophases: lattice-Boltzmann simulations

By means of a three-dimensional amphiphilic lattice-Boltzmann model with short-range interactions for the description of ternary amphiphilic fluids, we study how the phase separation kinetics of a symmetric binary immiscible fluid is altered by the presence of the amphiphilic species. We find that a gradual increase in amphiphile concentration slows down domain growth, initially from algebraic, to logarithmic temporal dependence, and, at higher concentrations, from logarithmic to stretched-exponential form. In growth-arrested stretched-exponential regimes, at late times we observe the self-assembly of sponge mesophases and gyroid liquid crystalline cubic mesophases, hence confirming that (a) amphiphile-amphiphile interactions need not be long-ranged in order for periodically modulated structures to arise in a dynamics of competing interactions, and (b) a chemically-specific model of the amphiphile is not required for the self-assembly of cubic mesophases, contradicting claims in the literature. We also observe a structural order-disorder transition between sponge and gyroid phases driven by amphiphile concentration alone or, independently, by the amphiphile-amphiphile and the amphiphile-binary fluid coupling parameters. For the growth-arrested mesophases, we also observe temporal oscillations in the structure function at all length scales; most of the wavenumbers show slow decay, and long-term stationarity or growth for the others. We ascribe this behaviour to a combination of complex amphiphile dynamics leading to Marangoni flows.Comment: 16 pages, 13 figures. Accepted for publication in Phys. Rev. E. (Replaced for the latest version, in press.) Higher-quality figures can be sent upon reques

A new class of highly efficient exact stochastic simulation algorithms for chemical reaction networks

We introduce an alternative formulation of the exact stochastic simulation algorithm (SSA) for sampling trajectories of the chemical master equation for a well-stirred system of coupled chemical reactions. Our formulation is based on factored-out, partial reaction propensities. This novel exact SSA, called the partial propensity direct method (PDM), is highly efficient and has a computational cost that scales at most linearly with the number of chemical species, irrespective of the degree of coupling of the reaction network. In addition, we propose a sorting variant, SPDM, which is especially efficient for multiscale reaction networks.Comment: 23 pages, 3 figures, 4 tables; accepted by J. Chem. Phy

Stress response and structural transitions in sheared gyroidal and lamellar amphiphilic mesophases: lattice-Boltzmann simulations

We report on the stress response of gyroidal and lamellar amphiphilic mesophases to steady shear simulated using a bottom-up lattice-Boltzmann model for amphiphilic fluids and sliding periodic (Lees-Edwards) boundary conditions. We study the gyroid per se (above the sponge-gyroid transition, of high crystallinity) and the molten gyroid (within such a transition, of shorter-range order). We find that both mesophases exhibit shear-thinning, more pronounced and at lower strain rates for the molten gyroid. At late times after the onset of shear, the skeleton of the crystalline gyroid becomes a structure of interconnected irregular tubes and toroidal rings, mostly oriented along the velocity ramp imposed by the shear, in contradistinction with free-energy Langevin-diffusion studies which yield a much simpler structure of disentangled tubes. We also compare the shear stress and deformation of lamellar mesophases with and without amphiphile when subjected to the same shear flow applied normal to the lamellae. We find that the presence of amphiphile allows (a) the shear stress at late times to be higher than in the case without amphiphile, and (b) the formation of rich patterns on the sheared interface, characterised by alternating regions of high and low curvature.Comment: 15 pages, 10 figures, Physical Review E, in pres

Noise-Induced Modulation of the Relaxation Kinetics around a Non-Equilibrium Steady State of Non-Linear Chemical Reaction Networks

Stochastic effects from correlated noise non-trivially modulate the kinetics of non-linear chemical reaction networks. This is especially important in systems where reactions are confined to small volumes and reactants are delivered in bursts. We characterise how the two noise sources confinement and burst modulate the relaxation kinetics of a non-linear reaction network around a non-equilibrium steady state. We find that the lifetimes of species change with burst input and confinement. Confinement increases the lifetimes of all species that are involved in any non-linear reaction as a reactant. Burst monotonically increases or decreases lifetimes. Competition between burst-induced and confinement-induced modulation may hence lead to a non-monotonic modulation. We quantify lifetime as the integral of the time autocorrelation function (ACF) of concentration uctuations around a non-equilibrium steady state of the reaction network. Furthermore, we look at the first and second derivatives of the ACF, each of which is affected in opposite ways by burst and confinement. This allows discriminating between these two noise sources. We analytically derive the ACF from the linear Fokker-Planck approximation of the chemical master equation in order to establish a baseline for the burst-induced modulation at low confinement. Effects of higher confinement are then studied using a partial-propensity stochastic simulation algorithm. The results presented here may help understand the mechanisms that deviate stochastic kinetics from its deterministic counterpart. In addition, they may be instrumental when using uorescence-lifetime imaging microscopy (FLIM) or uorescence-correlation spectroscopy (FCS) to measure confinement and burst in systems with known reaction rates, or, alternatively, to correct for the effects of confinement and burst when experimentally measuring reaction rate

Discreteness-induced concentration inversion in mesoscopic chemical systems

Molecular discreteness is apparent in small-volume chemical systems, such as biological cells, leading to stochastic kinetics. Here we present a theoretical framework to understand the effects of discreteness on the steady state of a monostable chemical reaction network. We consider independent realizations of the same chemical system in compartments of different volumes. Rate equations ignore molecular discreteness and predict the same average steady-state concentrations in all compartments. However, our theory predicts that the average steady state of the system varies with volume: if a species is more abundant than another for large volumes then the reverse occurs for volumes below a critical value, leading to a concentration inversion effect. The addition of extrinsic noise increases the size of the critical volume. We theoretically predict the critical volumes and verify by exact stochastic simulations that rate equations are qualitatively incorrect in sub-critical volumes

Three-dimensional lattice-Boltzmann simulations of critical spinodal decomposition in binary immiscible fluids

We use a modified Shan-Chen, noiseless lattice-BGK model for binary immiscible, incompressible, athermal fluids in three dimensions to simulate the coarsening of domains following a deep quench below the spinodal point from a symmetric and homogeneous mixture into a two-phase configuration. We find the average domain size growing with time as $t^\gamma$, where $\gamma$ increases in the range $0.545 < \gamma < 0.717$, consistent with a crossover between diffusive $t^{1/3}$ and hydrodynamic viscous, $t^{1.0}$, behaviour. We find good collapse onto a single scaling function, yet the domain growth exponents differ from others' works' for similar values of the unique characteristic length and time that can be constructed out of the fluid's parameters. This rebuts claims of universality for the dynamical scaling hypothesis. At early times, we also find a crossover from $q^2$ to $q^4$ in the scaled structure function, which disappears when the dynamical scaling reasonably improves at later times. This excludes noise as the cause for a $q^2$ behaviour, as proposed by others. We also observe exponential temporal growth of the structure function during the initial stages of the dynamics and for wavenumbers less than a threshold value.Comment: 45 pages, 18 figures. Accepted for publication in Physical Review

Lattice-Boltzmann and lattice-gas simulations of binary immiscible and ternary amphiphilic fluids in two and three dimensions

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