arXiv subjects

Stephen Whitelam

Publications and source records attributed to Stephen Whitelam.

At least 91 records · Page 5Linked to original sources

arXiv2012

Random and ordered phases of off-lattice rhombus tiles

We study the covering of the plane by non-overlapping rhombus tiles, a problem well-studied only in the limiting case of dimer coverings of regular lattices. We go beyond this limit by allowing tiles to take any position and orientation on the plane, to be of irregular shape, and to possess different types of attractive interactions. Using extensive numerical simulations we show that at large tile densities there is a phase transition from a fluid of rhombus tiles to a solid packing with broken rotational symmetry. We observe self-assembly of broken-symmetry phases, even at low densities, in the presence of attractive tile-tile interactions. Depending on tile shape and interactions the solid phase can be random, possessing critical orientational fluctuations, or crystalline. Our results suggest strategies for controlling tiling order in experiments involving `molecular rhombi'.

cond-mat.stat-mech↗

arXiv2011

Analyzing mechanisms and microscopic reversibility of self-assembly

We use computer simulations to investigate self-assembly in a system of model chaperonin proteins, and in an Ising lattice gas. We discuss the mechanisms responsible for rapid and efficient assembly in these systems, and we use measurements of dynamical activity and assembly progress to compare their propensities for kinetic trapping. We use the analytic solution of a simple minimal model to illustrate the key features associated with such trapping, paying particular attention to the number of ways that particles can misbind. We discuss the relevance of our results for the design and control of self-assembly in general.

cond-mat.soft↗

arXiv2011

Limit of validity of Ostwald's rule of stages in a statistical mechanical model of crystallization

We have only rules of thumb with which to predict how a material will crystallize, chief among which is Ostwald's rule of stages. It states that the first phase to appear upon transformation of a parent phase is the one closest to it in free energy. Although sometimes upheld, the rule is without theoretical foundation and is not universally obeyed, highlighting the need for microscopic understanding of crystallization controls. Here we study in detail the crystallization pathways of a prototypical model of patchy particles. The range of crystallization pathways it exhibits is richer than can be predicted by Ostwald's rule, but a combination of simulation and analytic theory reveals clearly how these pathways are selected by microscopic parameters. Our results suggest strategies for controlling self-assembly pathways in simulation and experiment.

cond-mat.stat-mech↗

arXiv2011

Design rules for the self-assembly of a protein crystal

Theories of protein crystallization based on spheres that form close-packed crystals predict optimal assembly within a `slot' of second virial coefficients and enhanced assembly near the metastable liquid-vapor critical point. However, most protein crystals are open structures stabilized by anisotropic interactions. Here, we use theory and simulation to show that assembly of one such structure is not predicted by the second virial coefficient or enhanced by the critical point. Instead, good assembly requires that the thermodynamic driving force be on the order of the thermal energy and that interactions be made as nonspecific as possible without promoting liquid-vapor phase separation.

cond-mat.soft↗

arXiv2011

Electrostatics and aggregation: how charge can turn a crystal into a gel

The crystallization of proteins or colloids is often hindered by the appearance of aggregates of low fractal dimension called gels. Here we study the effect of electrostatics upon crystal and gel formation using an analytic model of hard spheres bearing point charges and short range attractive interactions. We find that the chief electrostatic free energy cost of forming assemblies comes from the entropic loss of counterions that render assemblies charge-neutral. Because there exists more accessible volume for these counterions around an open gel than a dense crystal, there exists an electrostatic entropic driving force favoring the gel over the crystal. This driving force increases with increasing sphere charge, but can be counteracted by increasing counterion concentration. We show that these effects cannot be fully captured by pairwise-additive macroion interactions of the kind often used in simulations, and we show where on the phase diagram to go in order to suppress gel formation.

cond-mat.soft↗

arXiv2011

Approximating the dynamical evolution of systems of strongly-interacting overdamped particles

We describe collective-move Monte Carlo algorithms designed to approximate the overdamped dynamics of self-assembling nanoscale components equipped with strong, short-ranged and anisotropic interactions. Conventional Monte Carlo simulations comprise sequential moves of single particles, proposed and accepted so as to satisfy detailed balance. Under certain circumstances such simulations provide an approximation of overdamped dynamics, but the accuracy of this approximation can be poor if e.g. particle-particle interactions vary strongly with distance or angle. The twin requirements of simulation efficiency (trial moves of appreciable scale are needed to ensure reasonable sampling) and dynamical fidelity (true in the limit of vanishingly small trial moves) then become irreconcilable. As a result, single-particle moves can underrepresent important collective modes of relaxation, such as self-diffusion of particle clusters. However, one way of using Monte Carlo simulation to mimic real collective modes of motion, retaining the ability to make trial moves of reasonable scale, is to make explicit moves of collections of particles. We will outline ways of doing so by iteratively linking particles to their environment. Linking criteria can be static, conditioned upon properties of the current state of a system, or dynamic, conditioned upon energy changes resulting from trial virtual moves of particles. We argue that the latter protocol is better-suited to approximating real dynamics.

cond-mat.stat-mech↗

arXiv2010

Microscopic implications of S-DNA

Recent experiments [J. van Mameren et al. PNAS 106, 18231 (2009)] provide a detailed spatial picture of overstretched DNA, showing that under certain conditions the two strands of the double helix separate at about 65 pN. It was proposed that this observation rules out the existence of an elongated, hybridized form of DNA ('S-DNA'). Here we argue that the S-DNA picture is consistent with the observation of unpeeling during overstretching. We demonstrate that assuming the existence of S-DNA does not imply DNA overstretching to consist of the complete or near-complete conversion of the molecule from B- to S-form. Instead, this assumption implies in general a more complex dynamic coexistence of hybridized and unhybridized forms of DNA. We argue that such coexistence can rationalize several recent experimental observations.

cond-mat.soft↗

arXiv2010

Nonclassical assembly pathways of anisotropic particles

Advances in synthetic methods have spawned an array of nanoparticles and bio-inspired molecules of diverse shapes and interaction geometries. Recent experiments indicate that such anisotropic particles exhibit a variety of 'nonclassical' self-assembly pathways, forming ordered assemblies via intermediates that do not share the architecture of the bulk material. Here we apply mean field theory to a prototypical model of interacting anisotropic particles, and find a clear thermodynamic impetus for nonclassical ordering in certain regimes of parameter space. In other parameter regimes, by contrast, assembly pathways are selected by dynamics. This approach suggests a means of predicting when anisotropic particles might assemble in a manner more complicated than that assumed by classical nucleation theory.

cond-mat.stat-mech↗

arXiv2010

Self-assembly of amphiphilic peanut-shaped nanoparticles

We use computer simulation to investigate the self-assembly of Janus-like amphiphilic peanut-shaped nanoparticles, finding phases of clusters, bilayers and micelles in accord with ideas of packing familiar from the study of molecular surfactants. However, packing arguments do not explain the hierarchical self-assembly dynamics that we observe, nor the coexistence of bilayers and faceted polyhedra. This coexistence suggests that experimental realizations of our model can achieve multipotent assembly of either of two competing ordered structures.

cond-mat.soft↗

arXiv2009

Transformation from spots to waves in a model of actin pattern formation

Actin networks in certain single-celled organisms exhibit a complex pattern-forming dynamics that starts with the appearance of static spots of actin on the cell cortex. Spots soon become mobile, executing persistent random walks, and eventually give rise to traveling waves of actin. Here we describe a possible physical mechanism for this distinctive set of dynamic transformations, by equipping an excitable reaction-diffusion model with a field describing the spatial orientation of its chief constituent (which we consider to be actin). The interplay of anisotropic actin growth and spatial inhibition drives a transformation at fixed parameter values from static spots to moving spots to waves.

q-bio.SC↗

arXiv2009

The role of collective motion in examples of coarsening and self-assembly

The simplest prescription for building a patterned structure from its constituents is to add particles, one at a time, to an appropriate template. However, self-organizing molecular and colloidal systems in nature can evolve in much more hierarchical ways. Specifically, constituents (or clusters of constituents) may aggregate to form clusters (or clusters of clusters) that serve as building blocks for later stages of assembly. Here we evaluate the character and consequences of such collective motion in a set of prototypical assembly processes. We do so using computer simulations in which a system's capacity for hierarchical dynamics can be controlled systematically. By explicitly allowing or suppressing collective motion, we quantify its effects. We find that coarsening within a two dimensional attractive lattice gas (and an analogous off-lattice model in three dimensions) is naturally dominated by collective motion over a broad range of temperatures and densities. Under such circumstances, cluster mobility inhibits the development of uniform coexisting phases, especially when macroscopic segregation is strongly favored by thermodynamics. By contrast, the assembly of model viral capsids is not frustrated but is instead facilitated by collective moves, which promote the orderly binding of intermediates consisting of several monomers.

cond-mat.stat-mech↗

arXiv2008

Stretching chimeric DNA: a test for the putative S-form

Double-stranded DNA `overstretches' at a pulling force of about 65 pN, increasing in length by a factor of 1.7. The nature of the overstretched state is unknown, despite its considerable importance for DNA's biological function and technological application. Overstretching is thought by some to be a force-induced denaturation, and by others to consist of a transition to an elongated, hybridized state called S-DNA. Within a statistical mechanical model we consider the effect upon overstretching of extreme sequence heterogeneity. `Chimeric' sequences possessing halves of markedly different AT composition elongate under fixed external conditions via distinct, spatially segregated transitions. The corresponding force-extension data display two plateaux at forces whose difference varies with pulling rate in a manner that depends qualitatively upon whether the hybridized S-form is accessible. This observation implies a test for S-DNA that could be performed in experiment. Our results suggest that qualitatively different, spatially segregated conformational transitions can occur at a single thermodynamic state within single molecules of DNA.

cond-mat.stat-mech↗

arXiv2008

Avoiding unphysical kinetic traps in Monte Carlo simulations of strongly attractive particles

We introduce a `virtual-move' Monte Carlo (VMMC) algorithm for systems of pairwise-interacting particles. This algorithm facilitates the simulation of particles possessing attractions of short range and arbitrary strength and geometry, an important realization being self-assembling particles endowed with strong, short-ranged and angularly specific (`patchy') attractions. Standard Monte Carlo techniques employ sequential updates of particles and suffer from low acceptance rates when attractions are strong. Our algorithm avoids this slowing-down by proposing simultaneous moves of collections (clusters) of particles according to gradients of interaction energies. One particle first executes a `virtual' trial move. We determine which of its neighbours move in a similar fashion by calculating individual bond energies before and after the proposed move. We iterate this procedure and update simultaneously the positions of all affected particles. Particles move according to an approximation of realistic dynamics without requiring the explicit computation of forces, and without the step size restrictions required when integrating equations of motion. We also employ a size- and shape-dependent hydrodynamic damping of cluster movements. We discuss the virtual-move algorithm in the context of other Monte Carlo cluster-move schemes, and demonstrate its utility by applying it to a model of biological self-assembly.

cond-mat.stat-mech↗

arXiv2007

There and (slowly) back again: Entropy-driven hysteresis in a model of DNA overstretching

When pulled along its axis, double-stranded DNA elongates abruptly at a force of about 65 pN. Two physical pictures have been developed to describe this overstretched state. The first proposes that strong forces induce a phase transition to a molten state consisting of unhybridized single strands. The second picture instead introduces an elongated hybridized phase, called S-DNA, structurally and thermodynamically distinct from standard B-DNA. Little thermodynamic evidence exists to discriminate directly between these competing pictures. Here we show that within a microscopic model of DNA we can distinguish between the dynamics associated with each. In experiment, considerable hysteresis in a cycle of stretching and shortening develops as temperature is increased. Since there are few possible causes of hysteresis in a system whose extent is appreciable in only one dimension, such behavior offers a discriminating test of the two pictures of overstretching. Most experiments are performed upon nicked DNA, permitting the detachment (`unpeeling') of strands. We show that the long-wavelength progression of the unpeeled front generates hysteresis, the character of which agrees with experiment only if we assume the existence of S-DNA. We also show that internal melting (distinct from unpeeling) can generate hysteresis, the degree of which is strongly dependent upon the nonextensive loop entropy of single-stranded DNA.

cond-mat.stat-mech↗

arXiv2005

Two-stage coarsening mechanism in a kinetically constrained model of an attractive colloid

We study an attractive version of the East model using the real-space renormalization group (RG) introduced by Stella et al. The former is a kinetically constrained model with an Ising-like interaction between excitations, and shows striking agreement with the phenomonology of attractive colloidal systems. We find that the RG predicts two nonuniversal dynamic exponents, which suggests that in the out-of-equilibrium regime the model coarsens via a two-stage mechanism. We explain this mechanism physically, and verify this prediction numerically. In addition, we find that the characteristic relaxation time of the model is a non-monotonic function of attraction strength, again in agreement with numerical results.

cond-mat.stat-mech↗

arXiv2004

Renormalization group study of a kinetically constrained model for strong glasses

We derive a dynamic field theory for a kinetically constrained model, based on the Fredrickson--Andersen model, which we expect to describe the properties of an Arrhenius (strong) supercooled liquid at the coarse-grained level. We study this field theory using the renormalization group. For mesoscopic length and time scales, and for space dimension d \geq 2, the behaviour of the model is governed by a zero-temperature dynamical critical point in the directed percolation universality class. We argue that in d=1 its behaviour is that of compact directed percolation. We perform detailed numerical simulations of the corresponding Fredrickson-Andersen model on the lattice in various dimensions, and find reasonable quantitative agreement with the field theory predictions.

cond-mat.stat-mech↗

arXiv2004

Facilitated spin models in one dimension: a real-space renormalization group study

We use a real-space renormalization group (RSRG) to study the low temperature dynamics of kinetically constrained Ising chains (KCICs). We consider the cases of the Fredrickson-Andersen (FA) model, the East model, and the partially asymmetric KCIC. We show that the RSRG allows one to obtain in a unified manner the dynamical properties of these models near their zero-temperature critical points. These properties include the dynamic exponent, the growth of dynamical lengthscales, and the behaviour of the excitation density near criticality. For the partially asymmetric chain the RG predicts a crossover, on sufficiently large length and time scales, from East-like to FA-like behaviour. Our results agree with the known results for KCICs obtained by other methods.

cond-mat.stat-mech↗

arXiv2004

Geometrical picture of dynamical facilitation

Kinetically constrained models (KCMs) are models of glass formers based on the concept of dynamic facilitation. This concept accounts for many of the characteristics of the glass transition. KCMs usually display a combination of simple thermodynamics and complex glassy dynamics, the latter being a consequence of kinetic constraints. Here we show that KCMs can be regarded as systems whose configuration space is endowed with a simple energy surface but a complicated geometry. This geometry is determined solely by the kinetic constraints, and determines the dynamics of the system. It does not affect the overall distribution of states. Low temperature dynamical slow-down is then a consequence of the competition between the paths allowed by the geometry of configuration space, and those leading to energy relaxation. This competition gives rise to dynamical bottlenecks unrelated to static properties. This view of the dynamics is distinct from that based on an underlying static rugged energy landscape. We illustrate our ideas with simple examples.

cond-mat.stat-mech↗