Fluid-Fluid and Fluid-Solid transitions in the Kern-Frenkel model from Barker-Henderson thermodynamic perturbation theory

We study the Kern-Frenkel model for patchy colloids using Barker-Henderson second-order thermodynamic perturbation theory. The model describes a fluid where hard sphere particles are decorated with one patch, so that they interact via a square-well (SW) potential if they are sufficiently close one another, and if patches on each particle are properly aligned. Both the gas-liquid and fluid-solid phase coexistences are computed and contrasted against corresponding Monte-Carlo simulations results. We find that the perturbation theory describes rather accurately numerical simulations all the way from a fully covered square-well potential down to the Janus limit (half coverage). In the region where numerical data are not available (from Janus to hard-spheres), the method provides estimates of the location of the critical lines that could serve as a guideline for further efficient numerical work at these low coverages. A comparison with other techniques, such as integral equation theory, highlights the important aspect of this methodology in the present context.Comment: Accepted for publication in The Journal of Chemical Physics (2012

Self-assembly of two-dimensional binary quasicrystals: A possible route to a DNA quasicrystal

We use Monte Carlo simulations and free-energy techniques to show that binary solutions of penta- and hexavalent two-dimensional patchy particles can form thermodynamically stable quasicrystals even at very narrow patch widths, provided their patch interactions are chosen in an appropriate way. Such patchy particles can be thought of as a coarse-grained representation of DNA multi-arm `star' motifs, which can be chosen to bond with one another very specifically by tuning the DNA sequences of the protruding arms. We explore several possible design strategies and conclude that DNA star tiles that are designed to interact with one another in a specific but not overly constrained way could potentially be used to construct soft quasicrystals in experiment. We verify that such star tiles can form stable dodecagonal motifs using oxDNA, a realistic coarse-grained model of DNA

Coarse-grained simulations of DNA overstretching

We use a recently developed coarse-grained model to simulate the overstretching of duplex DNA. Overstretching at 23C occurs at 74 pN in the model, about 6-7 pN higher than the experimental value at equivalent salt conditions. Furthermore, the model reproduces the temperature dependence of the overstretching force well. The mechanism of overstretching is always force-induced melting by unpeeling from the free ends. That we never see S-DNA (overstretched duplex DNA), even though there is clear experimental evidence for this mode of overstretching under certain conditions, suggests that S-DNA is not simply an unstacked but hydrogen-bonded duplex, but instead probably has a more exotic structure.Comment: 11 pages, 11 figure

Nucleation barriers in tetrahedral liquids spanning glassy and crystallizing regimes

Crystallization and vitrification of tetrahedral liquids are important both from a fundamental and a technological point of view. Here, we study via extensive umbrella sampling Monte Carlo computer simulations the nucleation barriers for a simple model for tetrahedral patchy particles in the regime where open tetrahedral crystal structures (namely cubic and hexagonal diamond and their stacking hybrids) are thermodynamically stable. We show that by changing the angular bond width, it is possible to move from a glass-forming model to a readily crystallizing model. From the shape of the barrier we infer the role of surface tension in the formation of the crystalline clusters. Studying the trends of the nucleation barriers with the temperature and the patch width, we are able to identify an optimal value of the patch size that leads to easy nucleation. Finally, we find that the nucleation barrier is the same, within our numerical precision, for both diamond crystals and for their stacking forms.Comment: 12 pages, 11 figure

The effect of topology on the structure and free energy landscape of DNA kissing complexes

We use a recently developed coarse-grained model for DNA to study kissing complexes formed by hybridization of complementary hairpin loops. The binding of the loops is topologically constrained because their linking number must remain constant. By studying systems with linking numbers -1, 0 or 1 we show that the average number of interstrand base pairs is larger when the topology is more favourable for the right-handed wrapping of strands around each other. The thermodynamic stability of the kissing complex also decreases when the linking number changes from -1 to 0 to 1. The structures of the kissing complexes typically involve two intermolecular helices that coaxially stack with the hairpin stems at a parallel four-way junction

Measuring internal forces in single-stranded DNA: Application to a DNA force clamp

We present a new method for calculating internal forces in DNA structures using coarse-grained models and demonstrate its utility with the oxDNA model. The instantaneous forces on individual nucleotides are explored and related to model potentials, and using our framework, internal forces are calculated for two simple DNA systems and for a recently-published nanoscopic force clamp. Our results highlight some pitfalls associated with conventional methods for estimating internal forces, which are based on elastic polymer models, and emphasise the importance of carefully considering secondary structure and ionic conditions when modelling the elastic behaviour of single-stranded DNA. Beyond its relevance to the DNA nanotechnological community, we expect our approach to be broadly applicable to calculations of internal force in a variety of structures -- from DNA to protein -- and across other coarse-grained simulation models.Comment: 39 pages, 9 figure