Building up DNA, bit by bit: a simple description of chain assembly.

We simulate the assembly of DNA copolymers from two types of short duplexes (short double strands with a single-stranded overhang at each end), as described by the oxDNA model. We find that the statistics of chain lengths can be well reproduced by a simple theory that treats the association of particles into ideal (i.e., non-interacting) clusters as a reversible chemical reaction. The reaction constants can be predicted either from SantaLucia's theory or from Wertheim's thermodynamic perturbation theory of association for spherical patchy particles. Our results suggest that theories incorporating very limited molecular detail may be useful for predicting the broad equilibrium features of copolymerisation.

Remnants of the disappearing critical point(s) in patchy fluids with distinct interaction patches.

We investigate the disappearance of the critical points of a model consisting of particles decorated with two patches of type A and a variable number (n) of patches of type B (2AnB patchy particles), in which only AA and AB bonds can form. This has been shown to exhibit a very rich phase behavior including one, two, or no liquid-vapor critical points, depending on two parameters: the ratio of the volumes available to each type of bond and the ratio of the bond strengths. We apply Wertheim's theory in the limit of strong AA bonds to a lattice version of the model [Almarza et al., J. Chem. Phys. 137, 244902 (2012)] and show that the critical point does not always vanish at zero density and temperature, in contrast with results for particles decorated with only one type of patch. We uncover two remnants of the critical points-the lines of maximum and ideal compressibility-that survive even when no critical points are present.

Patchy particles at a hard wall: Orientation-dependent bonding.

The well-known and widely used Wertheim thermodynamic perturbation theory (TPT) of associating fluids averages over the orientational dependence of the bonding interactions. For this reason, density functional theories based on the otherwise very successful TPT have been unable to describe the structure of patchy particle fluids at hard walls, when the coupling of positional and orientational degrees of freedom becomes important at low temperatures [N. Gnan et al., J. Chem. Phys. 137, 084704 (2012)]. As a first attempt at remedying this, we propose to introduce into the theory an additional, nonbonding, anisotropic interparticle potential that enforces end-to-end alignment of two-patch particles. Within the simplest mean-field approximation, this additional potential does not change the thermodynamics of the bulk system and hence preserves its phase diagram but has the qualitatively correct effect on the order parameter and density profiles at a hard wall, as determined from computer simulation.

Criticality of colloids with three distinct interaction patches: As simple as A,B,C?

We systematically study the phase behavior of a simple model of associating fluids which consists of hard spherical particles with three short-ranged attractive sites on their surfaces (sticky spots or patches), of types A,B, and C, that can form bonds with energy ε_{ij} (i,j=A,B,C). We consider realizations of the model with one, two, or three nonzero ε_{ij}. Using Wertheim's first order perturbation theory of association, we establish the minimum requirements on the bond energies for the model to exhibit a liquid-vapor critical point, and investigate the nature of criticality in each case. As a preliminary, we rigorously show that, within this theory, particles with M identical sites do not condense if M<3, a result that was previously conjectured, but never proved.

Liquid-vapor interfaces of patchy colloids.

We investigate the liquid-vapor interface of a model of patchy colloids. This model consists of hard spheres decorated with short-ranged attractive sites ("patches") of different types on their surfaces. We focus on a one-component fluid with two patches of type A and nine patches of type B (2A9B colloids), which has been found to exhibit reentrant liquid-vapor coexistence curves and very low-density liquid phases. We have used the density-functional theory form of Wertheim's first-order perturbation theory of association, as implemented by Yu and Wu [J. Chem. Phys. 116, 7094 (2002)], to calculate the surface tension, and the density and degree of association profiles, at the liquid-vapor interface of our model. In reentrant systems, where AB bonds dominate, an unusual thickening of the interface is observed at low temperatures. Furthermore, the surface tension versus temperature curve reaches a maximum, in agreement with Bernardino and Telo da Gama's mesoscopic Landau-Safran theory [Phys. Rev. Lett. 109, 116103 (2012)]. If BB attractions are also present, competition between AB and BB bonds gradually restores the monotonic temperature dependence of the surface tension. Lastly, the interface is "hairy," i.e., it contains a region where the average chain length is close to that in the bulk liquid, but where the density is that of the vapor. Sufficiently strong BB attractions remove these features, and the system reverts to the behavior seen in atomic fluids.

Phase behavior of shape-changing spheroids.

We introduce a simple model for a biaxial nematic liquid crystal. This consists of hard spheroids that can switch shape between prolate (rodlike) and oblate (platelike) subject to an energy penalty Δε. The spheroids are approximated as hard Gaussian overlap particles and are treated at the level of Onsager's second-virial description. We use both bifurcation analysis and a numerical minimization of the free energy to show that, for additive particle shapes, (i) there is no stable biaxial phase even for Δε=0 (although there is a metastable biaxial phase in the same density range as the stable uniaxial phase) and (ii) the isotropic-to-nematic transition is into either one of two degenerate uniaxial phases, rod rich or plate rich. We confirm that even a small amount of shape nonadditivity may stabilize the biaxial nematic phase.

Neural-network approach to modeling liquid crystals in complex confinement.

Finding the structure of a confined liquid crystal is a difficult task since both the density and order parameter profiles are nonuniform. Starting from a microscopic model and density-functional theory, one has to either (i) solve a nonlinear, integral Euler-Lagrange equation, or (ii) perform a direct multidimensional free energy minimization. The traditional implementations of both approaches are computationally expensive and plagued with convergence problems. Here, as an alternative, we introduce an unsupervised variant of the multilayer perceptron (MLP) artificial neural network for minimizing the free energy of a fluid of hard nonspherical particles confined between planar substrates of variable penetrability. We then test our algorithm by comparing its results for the structure (density-orientation profiles) and equilibrium free energy with those obtained by standard iterative solution of the Euler-Lagrange equations and with Monte Carlo simulation results. Very good agreement is found and the MLP method proves competitively fast, flexible, and refinable. Furthermore, it can be readily generalized to the richer experimental patterned-substrate geometries that are now experimentally realizable but very problematic to conventional theoretical treatments.

Longitudinal versus polar wrinkling of core-shell fibers with anisotropic size mismatches.

We consider a fiber made of a soft elastic material, encased in a stiff elastic shell (core-shell geometry). If the core and shell dimensions are mismatched, e.g., because the core shrinks while the shell does not, but the two remain attached, then an elastic instability is triggered whereby wrinkles may appear on the shell. The wrinkle orientation may be longitudinal (along the fiber axis), polar (along the fiber perimeter), or a mixture of both, depending on the fiber's geometrical and material parameters. Here we investigate under what conditions longitudinal or polar wrinkling will occur.

Effective isotropic potential for dipolar hard spheres.

A new effective isotropic potential is proposed for the dipolar hard-sphere fluid, on the basis of recent results by others for its angle-averaged radial distribution function. The new effective potential is shown to exhibit oscillations even for moderately high densities and moderately strong dipole moments, which are absent from earlier effective isotropic potentials. The validity and significance of this result are briefly discussed.

Phase diagrams of particles with dissimilar patches: X-junctions and Y-junctions.

We use Wertheim's first-order perturbation theory to investigate the phase behaviour and the structure of coexisting fluid phases for a model of patchy particles with dissimilar patches (two patches of type A and f(B) patches of type B). A patch of type α = {A,B} can bond to a patch of type ß = {A,B} in a volume v(αß), thereby decreasing the internal energy by ϵ(αß). We analyse the range of model parameters where AB bonds, or Y-junctions, are energetically disfavoured (ϵ(AB) < Ïµ(AA)/2) but entropically favoured (v(AB) â‰« v(αα)), and BB bonds, or X-junctions, are energetically favoured (ϵ(BB) > 0). We show that, for low values of ϵ(BB)/ϵ(AA), the phase diagram has three different regions: (i) close to the critical temperature a low-density liquid composed of long chains and rich in Y-junctions coexists with a vapour of chains; (ii) at intermediate temperatures there is coexistence between a vapour of short chains and a liquid of very long chains with X- and Y-junctions; (iii) at low temperatures an ideal gas coexists with a high-density liquid with all possible AA and BB bonds formed. It is also shown that in region (i) the liquid binodal is reentrant (its density decreases with decreasing temperature) for the lower values of ϵ(BB)/ϵ(AA). The existence of these three regions is a consequence of the competition between the formation of X- and Y-junctions: X-junctions are energetically favoured and thus dominate at low temperatures, whereas Y-junctions are entropically favoured and dominate at higher temperatures.

Re-entrant phase behaviour of network fluids: a patchy particle model with temperature-dependent valence.

We study a model consisting of particles with dissimilar bonding sites ("patches"), which exhibits self-assembly into chains connected by Y-junctions, and investigate its phase behaviour by both simulations and theory. We show that, as the energy cost ε(j) of forming Y-junctions increases, the extent of the liquid-vapour coexistence region at lower temperatures and densities is reduced. The phase diagram thus acquires a characteristic "pinched" shape in which the liquid branch density decreases as the temperature is lowered. To our knowledge, this is the first model in which the predicted topological phase transition between a fluid composed of short chains and a fluid rich in Y-junctions is actually observed. Above a certain threshold for ε(j), condensation ceases to exist because the entropy gain of forming Y-junctions can no longer offset their energy cost. We also show that the properties of these phase diagrams can be understood in terms of a temperature-dependent effective valence of the patchy particles.

Reentrant phase diagram of network fluids.

We introduce a microscopic model for particles with dissimilar patches which displays an unconventional "pinched" phase diagram, similar to the one predicted by Tlusty and Safran in the context of dipolar fluids [Science 290, 1328 (2000)]. The model-based on two types of patch interactions, which account, respectively, for chaining and branching of the self-assembled networks-is studied both numerically via Monte Carlo simulations and theoretically via first-order perturbation theory. The dense phase is rich in junctions, while the less-dense phase is rich in chain ends. The model provides a reference system for a deep understanding of the competition between condensation and self-assembly into equilibrium-polymer chains.

Equilibrium self-assembly of colloids with distinct interaction sites: thermodynamics, percolation, and cluster distribution functions.

We calculate the equilibrium thermodynamic properties, percolation threshold, and cluster distribution functions for a model of associating colloids, which consists of hard spherical particles having on their surfaces three short-ranged attractive sites (sticky spots) of two different types, A and B. The thermodynamic properties are calculated using Wertheim's perturbation theory of associating fluids. This also allows us to find the onset of self-assembly, which can be quantified by the maxima of the specific heat at constant volume. The percolation threshold is derived, under the no-loop assumption, for the correlated bond model: In all cases it is two percolated phases that become identical at a critical point, when one exists. Finally, the cluster size distributions are calculated by mapping the model onto an effective model, characterized by a--state-dependent--functionality f and unique bonding probability p. The mapping is based on the asymptotic limit of the cluster distributions functions of the generic model and the effective parameters are defined through the requirement that the equilibrium cluster distributions of the true and effective models have the same number-averaged and weight-averaged sizes at all densities and temperatures. We also study the model numerically in the case where BB interactions are missing. In this limit, AB bonds either provide branching between A-chains (Y-junctions) if epsilon(AB)/epsilon(AA) is small, or drive the formation of a hyperbranched polymer if epsilon(AB)/epsilon(AA) is large. We find that the theoretical predictions describe quite accurately the numerical data, especially in the region where Y-junctions are present. There is fairly good agreement between theoretical and numerical results both for the thermodynamic (number of bonds and phase coexistence) and the connectivity properties of the model (cluster size distributions and percolation locus).

Percolation of colloids with distinct interaction sites.

We generalize the Flory-Stockmayer theory of percolation to a model of associating (patchy) colloids, which consists of hard spherical particles, having on their surfaces f short-ranged-attractive sites of m different types. These sites can form bonds between particles and thus promote self-assembly. It is shown that the percolation threshold is given in terms of the eigenvalues of a m X m matrix, which describes the recursive relations for the number of bonded particles on the ith level of a cluster with no loops; percolation occurs when the largest of these eigenvalues equals unity. Expressions for the probability that a particle is not bonded to the giant cluster, for the average cluster size and the average size of a cluster to which a randomly chosen particle belongs, are also derived. Explicit results for these quantities are computed for the case f=3 and m=2 . We show how these structural properties are related to the thermodynamics of the associating system by regarding bond formation as a (equilibrium) chemical reaction. This solution of the percolation problem, combined with Wertheim's thermodynamic first-order perturbation theory, allows the investigation of the interplay between phase behavior and cluster formation for general models of patchy colloids.

Simulation of defects in bubble clusters.

Topological defects in a foam, either isolated (disclinations and dislocations) or in pairs, affect the energy and stress, and play an important role in foam deformation. Surface evolver simulations were performed on large finite clusters of bubbles. These allow us to evaluate the effect of the topology of the defects, and the distance between defects, on the energy and pressure of foam clusters of different sizes. The energy of such defects follows trends similar to known analytical results for a continuous medium.

Criticality of colloids with distinct interaction patches: the limits of linear chains, hyperbranched polymers, and dimers.

We use a simple model of associating fluids which consists of spherical particles having a hard-core repulsion, complemented by three short-ranged attractive sites on the surface (sticky spots). Two of the spots are of type A and one is of type B; the bonding interactions between each pair of spots have strengths epsilon(AA), epsilon(BB), and epsilon(AB). The theory is applied over the whole range of bonding strengths and the results are interpreted in terms of the equilibrium cluster structures of the phases. In addition to our numerical results, we derive asymptotic expansions for the free energy in the limits for which there is no liquid-vapor critical point: linear chains (epsilon(AA) not equal to 0, epsilon(AB)=epsilon(BB)=0) , hyperbranched polymers (epsilon(AB) not equal to 0, epsilon(AA)=epsilon(B)=0) , and dimers (epsilon(BB) not equal to 0, epsilon(AA)=epsilon(AB)=0) . These expansions also allow us to calculate the structure of the critical fluid by perturbing around the above limits, yielding three different types of condensation: of linear chains (AA clusters connected by a few AB or BB bonds); of hyperbranched polymers (AB clusters connected by AA bonds); or of dimers (BB clusters connected by AA bonds). Interestingly, there is no critical point when in(AA) vanishes despite the fact that AA bonds alone cannot drive condensation.

Contact angle of a hemispherical bubble: an analytical approach.

We have calculated the equilibrium shape of the axially symmetric Plateau border along which a spherical bubble contacts a flat wall, by analytically integrating Laplace's equation in the presence of gravity, in the limit of small Plateau border sizes. This method has the advantage that it provides closed-form expressions for the positions and orientations of the Plateau border surfaces. Results are in very good overall agreement with those obtained from a numerical solution procedure, and are consistent with experimental data. In particular we find that the effect of gravity on Plateau border shape is relatively small for typical bubble sizes, leading to a widening of the Plateau border for sessile bubbles and to a narrowing for pendant bubbles. The contact angle of the bubble is found to depend even more weakly on gravity.

Simulation and theory of hybrid aligned liquid crystal films.

We present a study of the effects of nanoconfinement on a system of hard Gaussian overlap particles interacting with planar substrates through the hard-needle-wall potential, extending earlier work by two of us [D. J. Cleaver and P. I. C. Teixeira, Chem. Phys. Lett. 338, 1 (2001)]. Here, we consider the case of hybrid films, where one of the substrates induces strongly homeotropic anchoring, while the other favors either weakly homeotropic or planar anchoring. These systems are investigated using both Monte Carlo simulation and density-functional theory, the latter implemented at the level of Onsager's second-virial approximation with Parsons-Lee rescaling. The orientational structure is found to change either continuously or discontinuously depending on substrate separation, in agreement with earlier predictions by others. The theory is seen to perform well in spite of its simplicity, predicting the positional and orientational structure seen in simulations even for small particle elongations.

Demixing instability in coil-rod blends undergoing polycondensation reactions.

The authors extend their earlier work on the stability of a reacting binary polymer blend with respect to demixing [D. J. Read, Macromolecules 31, 899 (1998); P. I. C. Teixeira et al., Macromolecules 33, 387 (2000)] to the case where one of the polymers is rod-like and may order nematically. As before, the authors combine the random phase approximation for the free energy with a Markov chain model for the chemistry to obtain the spinodal as a function of the relevant degrees of reaction. These are then calculated by assuming a simple second-order chemical kinetics. Results are presented, for linear systems, which illustrate the effects of varying the proportion of coils and rods, their relative sizes, and the strength of the nematic interaction between the rods.

Line tension and excess energy of a wall Plateau border.

We have calculated the equilibrium shape of the axially symmetric Plateau border (PB) along which a spherical bubble contacts a flat wall, by numerical integration of Laplace's equation. We found that the (spherical) film prolongation into the PB meets the wall at an internal angle varphi