van der Ppam Paul Schoot

Dynamical Monte Carlo study of equilibrium polymers. II. The role of rings

We investigate by means of a number of different dynamical Monte Carlo simulation methods the self-assembly of equilibrium polymers in dilute, semidilute and concentrated solutions under good-solvent conditions. In our simulations, both linear chains and closed loops compete for the monomers, expanding on earlier work in which loop formation was disallowed. Our findings show that the conformational properties of the linear chains, as well as the shape of their size distribution function, are not altered by the formation of rings. Rings only seem to deplete material from the solution available to the linear chains. In agreement with scaling theory, the rings obey an algebraic size distribution, whereas the linear chains conform to a Schultz–Zimm type of distribution in dilute solution, and to an exponential distribution in semidilute and concentrated solution. A diagram presenting different states of aggregation, including monomer-, ring-, and chain-dominated regimes, is given. The relevance of our work in...

Parity breaking in nematic tactoids

We theoretically investigate under what conditions the director field in a spindle-shaped nematic droplet or tactoid obtains a twisted, parity-broken structure. By minimizing the sum of the bulk elastic and surface energies, we show that a twisted director field is stable if the twist and bend elastic constants are small enough compared to the splay elastic constant, but only if the droplet volume is larger than some minimum value. We furthermore show that the transition from an untwisted to a twisted director-field structure is a sharp function of the various control parameters. We predict that suspensions of rigid, rod-like particles cannot support droplets with a parity broken structure, whereas they could possibly occur in those of semi-flexible, worm-like particles.

Texture and shape of two-dimensional domains of nematic liquid crystals

We present a generalized approach to compute the shape and internal structure of two-dimensional nematic domains. By using conformal mappings, we are able to compute the director field for a given domain shape that we choose from a rich class, which includes drops with large and small aspect ratios and sharp domain tips as well as smooth ones. Results are assembled in a phase diagram that for given domain size, surface tension, anchoring strength, and elastic constant shows the transitions from a homogeneous to a bipolar director field, from circular to elongated droplets, and from sharp to smooth domain tips. We find a previously unaccounted for regime, where the drop is nearly circular, the director field bipolar, and the tip rounded. We also find that bicircular director fields, with foci that lie outside the domain, provide a remarkably accurate description of the optimal director field for a large range of values of the various shape parameters.

Kinetics of depletion interactions

Depletion interactions between colloidal particles dispersed in a fluid medium are effective interactions induced by the presence of other types of colloid. They are not instantaneous but built up in time. We show by means of Brownian dynamics simulations that the static (mean-field) depletion force between two guest particles in a host dispersion of differently sized colloids is only approached algebraically in time. A simple scaling theory accurately describes the dependence of the magnitude of these fluctuations on time, on the inter-particle distance and on the size ratio of guest and host particles. The consequences in particular for the dynamics of colloidal mixtures are discussed.

Osmotic pressure of solutions containing flexible polymers subject to an annealed molecular weight distribution

The osmotic pressure P of equilibrium polymers (EP) in a good solvent is investigated by means of an off-lattice Monte Carlo simulation. Our results compare well with conformation space renormalisation group theory and the osmotic compressibility K as obtained by recent light scattering measurements of long worm-like micelles. The present study allows for the first time the mapping of the relevant energy scale of a standard coarse-grained model on data from real experiments. We also confirm the scaling predictions for EP in the dilute and semidilute limit. In particular, we find P 2.3 for the scaling of the pressure with the volume fraction and, hence, K −0.3 in the semidilute regime -in agreement with both theory and laboratory experiment. At higher concentrations where the semidilute blobs become too small and hard-core interactions and packing effects become dominant, a much stronger increase is evidenced and, consequently, a compressibility that decreases much more rapidly with than predicted from semidilute polymer theory, but again in agreement with experiment. Our results apply both to EP systems with and without rings.

Geometry explains the large difference in the elastic properties of fcc and hcp crystals of hard spheres

As is well known, hard-sphere crystals of the fcc and hcp type differ very little in their thermodynamic properties. Nonetheless, recent computer simulations by Pronk and Frenkel indicate that the elastic response to mechanical deformation of the two types of crystal should be quite different. By invoking a geometrical argument put forward by R. Martin some time ago, we suggest that this is largely due to the different symmetries of the fcc and hcp crystal structures. Indeed, we find that elastic constants obtained by means of computer simulations for the fcc hard-sphere crystal can be mapped onto the equivalent ones of the hcp crystal to very high accuracy. The same procedure applied to density functional theoretical predictions for the elastic properties of the fcc hard-sphere crystal also produces remarkably accurate predictions for those of the hcp hard-sphere crystal.