Effect of Temperature Cycling on Ostwald Ripening.

We study the effect of temperature cycling on the rate of Ostwald ripening (or coarsening) of spherical particles dispersed in a binary solution. A widespread view, which states a temperature cycle generally enhances the rate of Ostwald ripening by first dissolving the smallest particles (heating) and then regrowing the dissolved amount of material on the remaining particles (cooling), is shown to be inadequate as it does not include transient effects. On the basis of a simulation method that assumes mass transfer as the limiting growth mechanism, we show that each temperature cycle is followed by a significant relaxation of the particle-size distribution, during which the number of particles remains constant, and the average particle size decreases. The relaxation is shown to be crucial to obtain a linear scaling of the average particle radius cubed with the number of cycles applied (or time), which is the behavior generally observed for the evolution of ice crystals in cycling experiments on frozen aqueous solutions or frozen foods. We show the experimentally observed increase in the proportionality constant (or "coarsening rate") as compared to isothermal ripening, or the increase of the coarsening rate with increasing cycle frequency, can be reproduced convincingly only if some (transient) ripening is allowed to take place at the elevated temperature of each cycle. Our results thus suggest the effect of temperature cycling on Ostwald ripening is governed by a dissolution-ripening-regrowth-relaxation mechanism.

Predicting the Kinetics of Ice Recrystallization in Aqueous Sugar Solutions.

The quality of stored frozen products such as foods and biomaterials generally degrades in time due to the growth of large ice crystals by recrystallization. While there is ample experimental evidence that recrystallization within such products (or model systems thereof) is often dominated by diffusion-limited Ostwald ripening, the application of Ostwald-ripening theories to predict measured recrystallization rates has only met with limited success. For a model system of polycrystalline ice within an aqueous solution of sugars, we here show recrystallization rates can be predicted on the basis of Ostwald ripening theory, provided (1) the theory accounts for the fact the solution can be nonideal, nondilute and of different density than the crystals, (2) the effect of ice-phase volume fraction on the diffusional flux of water between crystals is accurately described, and (3) all relevant material properties (involving binary Fick diffusion coefficients, the thermodynamic factor of the solution, and the surface energy of ice) are carefully estimated. To enable calculation of material properties, we derive an alternative formulation of Ostwald ripening in terms of the Maxwell-Stefan instead of the Fick approach to diffusion. First, this leads to a cancellation of the thermodynamic factor (a measure for the nonideality of a solution), which is a notoriously difficult property to obtain. Second, we show that Maxwell-Stefan diffusion coefficients can to a reasonable approximation be related to self-diffusion coefficients, which are relatively easy to measure or predict in comparison to Fick diffusion coefficients. Our approach is validated for a binary system of water and sucrose, for which we show predicted recrystallization rates of ice compare well to experimental results, with relative deviations of at most a factor of 2.

Mesoscale simulation of semiflexible chains. I. Endpoint distribution and chain dynamics.

The endpoint distribution and dynamics of semiflexible fibers are studied by numerical simulation. A brief overview is given over the analytical theory of flexible and semiflexible polymers. In particular, a closed expression is given for the relaxation spectrum of wormlike chains, which determines polymer diffusion and rheology. Next a simulation model for wormlike chains with full hydrodynamic interaction is described, and relations for the bending and torsion modulus are given. Two methods are introduced to include torsion stiffness into the model. The model is validated by simulating single chains in a heat bath, and comparing the endpoint distribution of the chains with established Monte Carlo results. It is concluded that torsion stiffness leads to a slightly shorter effective persistence length for a given bending stiffness. To further validate the simulation model, polymer diffusion is studied for fixed persistence length and varying polymer length N. The diffusion constant shows crossover from Rouse (D [proportionality] N(-1)) to reptation behaviour (D [proportionality] N(-2)). The terminal relaxation time obtained from the monomer displacement is consistent with the theory of wormlike chains. The probability for chain crossing has also been studied. This probability is so low that it does not influence the present results.

Mesoscale simulation of semiflexible chains. II. Evolution dynamics and stability of fiber bundle networks.

Network formation of associative semiflexible fibers and mixtures of fibers and colloidal particles is simulated for the Johnson-Kendall-Roberts model of elastic contacts, and a phase diagram in terms of particle elasticity and surface energy is presented. When fibers self-assemble, they form a network for sufficiently large fiber-solvent surface energy. If the surface energy is above the value where single particles crystallize, the adhesion forces drive diffusion-limited aggregation. Two mechanisms contribute to coarsening: non-associated chains joining existing bundles, and fiber bundles merging. Coarsening stops when the length of the network connections is roughly the persistence length, independent of surface energy. If the surface energy is below the value where single particles crystallize, a network can still be formed but at a much slower (reaction limited) rate. Loose (liquid-like) assemblies between chains form when they happen to run more-or-less parallel. These assemblies grow by diffusion and aggregation and form a loose network, which sets in micro-phase separation, i.e., syneresis. Only when the clusters crystallize, the coarsening process stops. In this case, the length of the network connections is larger than the persistence length of a single chain, and depends on the value of the surface energy. All networks of semiflexible homopolymers in this study show syneresis. Mixtures of fibers and colloid particles also form fiber bundle networks, but by choosing the colloid volume fraction sufficiently low, swelling gels are obtained. Applications of this model are in biological systems where fibers self-assemble into cell walls and bone tissue.

How to impose stick boundary conditions in coarse-grained hydrodynamics of Brownian colloids and semi-flexible fiber rheology.

Long-range hydrodynamics between colloidal particles or fibers is modelled by the fluid particle model. Two methods are considered to impose the fluid boundary conditions at colloidal surfaces. In the first method radial and transverse friction forces between particle and solvent are applied such that the correct friction and torque follows for moving or rotating particles. The force coefficients are calculated analytically and checked by numerical simulation. In the second method a collision rule is used between colloidal particle and solvent particle that imposes the stick boundary conditions exactly. The collision rule comprises a generalisation of the Lowe-Anderson thermostat to radial and transverse velocity differences.

Close packing density of polydisperse hard spheres.

The most efficient way to pack equally sized spheres isotropically in three dimensions is known as the random close packed state, which provides a starting point for many approximations in physics and engineering. However, the particle size distribution of a real granular material is never monodisperse. Here we present a simple but accurate approximation for the random close packing density of hard spheres of any size distribution based upon a mapping onto a one-dimensional problem. To test this theory we performed extensive simulations for mixtures of elastic spheres with hydrodynamic friction. The simulations show a general (but weak) dependence of the final (essentially hard sphere) packing density on fluid viscosity and on particle size but this can be eliminated by choosing a specific relation between mass and particle size, making the random close packed volume fraction well defined. Our theory agrees well with the simulations for bidisperse, tridisperse, and log-normal distributions and correctly reproduces the exact limits for large size ratios.

Mesoscopic model for colloidal particles, powders, and granular solids.

A simulation model is presented, comprising elastic spheres with a short-range attraction. Besides conservative forces, radial and shear friction, and radial noise are added. The model can be used to simulate colloids, granular solids, and powders, and the parameters may be related to experimental systems via the range of attraction and the adhesion energy. The model shares the simplicity and speed of dissipative particle dynamics, yet the predictions are rather nontrivial. We demonstrate that the model predicts the correct scaling relations for fracture of granular solids, and we present a schematic phase diagram. This shows liquid-vapor coexistence for a sufficiently large interaction range, with a surface tension that follows Ising criticality. For smaller interaction range only solid-vapor coexistence is found, but for a very small attractive interaction range stable liquid-vapor coexistence reappears due to pathological stability of the solid phase. At very low temperature the model forms a glassy state.

A Local Galilean Invariant Thermostat.

The thermostat introduced recently by Stoyanov and Groot (J. Chem. Phys. 2005, 122, 114112) is analyzed for inhomogeneous systems. This thermostat has one global feature, because the mean temperature used to drive the system toward equilibrium is a global average. The consequence is that the thermostat locally conserves energy rather than temperature. Thus, local temperature variations can be long-lived, although they do average out by thermal diffusion. To obtain a faster local temperature equilibration, a truly local thermostat must be introduced. To conserve momentum and, hence, to simulate hydrodynamic interactions, the thermostat must be Galilean invariant. Such a local Galilean invariant thermostat is studied here. It is shown that, by defining a local temperature on each particle, the ensemble is locally isothermal. The local temperature is obtained from a local square velocity average around each particle. Simulations on the ideal gas show that this local Nosé-Hoover algorithm has a similar artifact as dissipative particle dynamics: the ideal gas pair correlation function is slightly distorted. This is attributed to the fact that the thermostat compensates fluctuations that are natural within a small cluster of particles. When the cutoff range rc for the square velocity average is increased, systematic errors decrease proportionally to rc(-)(3/2); hence, the systematic error can be made arbitrary small.

From molecular dynamics to hydrodynamics: a novel Galilean invariant thermostat.

This paper proposes a novel thermostat applicable to any particle-based dynamic simulation. Each pair of particles is thermostated either (with probability P) with a pairwise Lowe-Andersen thermostat [C. P. Lowe, Europhys. Lett. 47, 145 (1999)] or (with probability 1-P) with a thermostat that is introduced here, which is based on a pairwise interaction similar to the Nosé-Hoover thermostat. When the pairwise Nosé-Hoover thermostat dominates (low P), the liquid has a high diffusion coefficient and low viscosity, but when the Lowe-Andersen thermostat dominates, the diffusion coefficient is low and viscosity is high. This novel Nosé-Hoover-Lowe-Andersen thermostat is Galilean invariant and preserves both total linear and angular momentum of the system, due to the fact that the thermostatic forces between each pair of the particles are pairwise additive and central. We show by simulation that this thermostat also preserves hydrodynamics. For the (noninteracting) ideal gas at P = 0, the diffusion coefficient diverges and viscosity is zero, while for P > 0 it has a finite value. By adjusting probability P, the Schmidt number can be varied by orders of magnitude. The temperature deviation from the required value is at least an order of magnitude smaller than in dissipative particle dynamics (DPD), while the equilibrium properties of the system are very well reproduced. The thermostat is easy to implement and offers a computational efficiency better than (DPD), with better temperature control and greater flexibility in terms of adjusting the diffusion coefficient and viscosity of the simulated system. Applications of this thermostat include all standard molecular dynamic simulations of dense liquids and solids with any type of force field, as well as hydrodynamic simulation of multiphase systems with largely different bulk viscosities, including surface viscosity, and of dilute gases and plasmas.