Lattice model study of the thermodynamic interplay of polymer crystallization and liquid-liquid demixing

We report Monte Carlo simulations of a lattice-polymer model that can account for both polymer crystallization and liquid-liquid demixing in solutions of semiflexible homopolymers. In our model, neighboring polymer segments can have isotropic interactions that affect demixing, and anisotropic interactions that are responsible for freezing. However, our simulations show that the isotropic interactions also have a noticeable effect on the freezing curve, as do the anisotropic interactions on demixing. As the relative strength of the isotropic interactions is reduced, the liquid-liquid demixing transition disappears below the freezing curve. A simple, extended Flory-Huggins theory accounts quite well for the phase behavior observed in the simulations.Comment: Revtex, 7 pages, the content accepted by J. Chem. Phy

Novel self-assembled morphologies from isotropic interactions

We present results from particle simulations with isotropic medium range interactions in two dimensions. At low temperature novel types of aggregated structures appear. We show that these structures can be explained by spontaneous symmetry breaking in analytic solutions to an adaptation of the spherical spin model. We predict the critical particle number where the symmetry breaking occurs and show that the resulting phase diagram agrees well with results from particle simulations.Comment: 4 pages, 4 figure

Negative thermal expansion in single-component systems with isotropic interactions

We have devised an isotropic interaction potential that gives rise to negative thermal expansion (NTE) behavior in equilibrium many-particle systems in both two and three dimensions over a wide temperature and pressure range (including zero pressure). An optimization procedure is used in order to find a potential that yields a strong NTE effect. A key feature of the potential that gives rise to this behavior is the softened interior of its basin of attraction. Although such anomalous behavior is well known in material systems with directional interactions (e.g., zirconium tungstate), to our knowledge this is the first time that NTE behavior has been established to occur in single-component many-particle systems for isotropic interactions. Using constant-pressure Monte Carlo simulations, we show that as the temperature is increased, the system exhibits negative, zero and then positive thermal expansion before melting (for both two- and three-dimensional systems). The behavior is explicitly compared to that of a Lennard-Jones system, which exhibits typical expansion upon heating for all temperatures and pressures.Comment: 21 pages, 13 figure

Designing colloidal ground state patterns using short-range isotropic interactions

DNA-coated colloids are a popular model system for self-assembly through tunable interactions. The DNA-encoded linkages between particles theoretically allow for very high specificity, but generally no directionality or long-range interactions. We introduce a two-dimensional lattice model for particles of many different types with short-range isotropic interactions that are pairwise specific. For this class of models, we address the fundamental question whether it is possible to reliably design the interactions so that the ground state is unique and corresponds to a given crystal structure. First, we determine lower limits for the interaction range between particles, depending on the complexity of the desired pattern and the underlying lattice. Then, we introduce a `recipe' for determining the pairwise interactions that exactly satisfies this minimum criterion, and we show that it is sufficient to uniquely determine the ground state for a large class of crystal structures. Finally, we verify these results using Monte Carlo simulations.Comment: 19 pages, 7 figure

Chiral surfaces self-assembling in one-component systems with isotropic interactions

We show that chiral symmetry can be broken spontaneously in one-component systems with isotropic interactions, i.e. many-particle systems having maximal a priori symmetry. This is achieved by designing isotropic potentials that lead to self-assembly of chiral surfaces. We demonstrate the principle on a simple chiral lattice and on a more complex lattice with chiral super-cells. In addition we show that the complex lattice has interesting melting behavior with multiple morphologically distinct phases that we argue can be qualitatively predicted from the design of the interaction.Comment: 4 pages, 4 figure

The competition of hydrogen-like and isotropic interactions on polymer collapse

We investigate a lattice model of polymers where the nearest-neighbour monomer-monomer interaction strengths differ according to whether the local configurations have so-called ``hydrogen-like'' formations or not. If the interaction strengths are all the same then the classical $\theta$-point collapse transition occurs on lowering the temperature, and the polymer enters the isotropic liquid-drop phase known as the collapsed globule. On the other hand, strongly favouring the hydrogen-like interactions give rise to an anisotropic folded (solid-like) phase on lowering the temperature. We use Monte Carlo simulations up to a length of 256 to map out the phase diagram in the plane of parameters and determine the order of the associated phase transitions. We discuss the connections to semi-flexible polymers and other polymer models. Importantly, we demonstrate that for a range of energy parameters two phase transitions occur on lowering the temperature, the second being a transition from the globule state to the crystal state. We argue from our data that this globule-to-crystal transition is continuous in two dimensions in accord with field-theory arguments concerning Hamiltonian walks, but is first order in three dimensions

Design of two-dimensional particle assemblies using isotropic pair interactions with an attractive well

Using ground-state and relative-entropy based inverse design strategies, isotropic interactions with an attractive well are determined to stabilize and promote as- sembly of particles into two-dimensional square, honeycomb, and kagome lattices. The design rules inferred from these results are discussed and validated in the dis- covery of interactions that favor assembly of the highly open truncated-square and truncated-hexagonal lattices.Comment: 11 pages, 5 figures and supplemental materia

On Long-Range Order in Low-Dimensional Lattice-Gas Models of Nematic Liquid Crystals

The problem of the orientational ordering transition for lattice-gas models of liquid crystals is discussed in the low-dimensional case $d=1,2$. For isotropic short-range interactions, orientational long-range order at finite temperature is excluded for any packing of molecules on the lattice $Z^d$; on the other hand, for reflection-positive long-range isotropic interactions, we prove existence of an orientational ordering transition for high packing ($\mu > \mu_0$) and low temperatures ($\beta > \beta_c(\mu)$).Comment: 11 page