arXiv subjects

Stephen Whitelam

Publications and source records attributed to Stephen Whitelam.

At least 73 records · Page 4Linked to original sources

arXiv2016

Minimal physical requirements for crystal growth self-poisoning

Self-poisoning is a kinetic trap that can impair or prevent crystal growth in a wide variety of physical settings. Here we use dynamic mean-field theory and computer simulation to argue that poisoning is ubiquitous because its emergence requires only the notion that a molecule can bind in two (or more) ways to a crystal; that those ways are not energetically equivalent; and that the associated binding events occur with sufficiently unequal probability. If these conditions are met then the steady-state growth rate is in general a non-monotonic function of the thermodynamic driving force for crystal growth, which is the characteristic of poisoning. Our results also indicate that relatively small changes of system parameters could be used to induce recovery from poisoning.

cond-mat.stat-mech↗

arXiv2015

The Ramachandran number: an order parameter for protein geometry

Three-dimensional protein structures usually contain regions of local order, called secondary structure, such as $α$-helices and $β$-sheets. Secondary structure is characterized by the local rotational state of the protein backbone, quantified by two dihedral angles called $ϕ$ and $ψ$. Particular types of secondary structure can generally be described by a single (diffuse) location on a two-dimensional plot drawn in the space of the angles $ϕ$ and $ψ$, called a Ramachandran plot. By contrast, a recently-discovered nanomaterial made from peptoids, structural isomers of peptides, displays a secondary-structure motif corresponding to two regions on the Ramachandran plot [Mannige et al., Nature 526, 415 (2015)]. In order to describe such `higher-order' secondary structure in a compact way we introduce here a means of describing regions on the Ramachandran plot in terms of a single Ramachandran number, ${\mathcal{R}}$, which is a structurally meaningful combination of $ϕ$ and $ψ$. We show that the potential applications of ${\mathcal{R}}$ are numerous: it can be used to describe the geometric content of protein structures, and can be used to draw diagrams that reveal, at a glance, the frequency of occurrence of regular secondary structures and disordered regions in large protein datasets. We propose that ${\mathcal{R}}$ might be used as an order parameter for protein geometry for a wide range of applications.

q-bio.BM↗

arXiv2015

Hierarchical assembly may be a way to make large information-rich structures

Self-assembly in the laboratory can now yield `information-rich' nanostructures in which each component is of a distinct type and has a defined spatial position. Ensuring the thermodynamic stability of such structures requires inter-component interaction energies to increase logarithmically with structure size, in order to counter the entropy gained upon mixing component types in solution. However, self-assembly in the presence of strong interactions results in general in kinetic trapping, so suggesting a limit to the size of an (equilibrium) structure that can be self-assembled from distinguishable components. Here we study numerically a two-dimensional hierarchical assembly scheme already considered in experiment. We show that this scheme is immune to the kinetic traps associated with strong `native' interactions (interactions designed to stabilize the intended structure), and so, in principle, offers a way to make large information-rich structures. In this scheme the size of an assembled structure scales exponentially with the stage of assembly, and assembly can continue as long as random motion is able to bring structures into contact. The resulting superstructure could provide a template for building in the third dimension. The chief drawback of this scheme is that it is particularly susceptible to kinetic traps that result from `non-native' interactions (interactions not required to stabilize the intended structure); the scale on which such a scheme can be realized therefore depends upon how effectively this latter kind of interaction can be suppressed.

physics.bio-ph↗

arXiv2015

Crystallization and arrest mechanisms of model colloids

We performed dynamic simulations of spheres with short-range attractive interactions for many values of interaction strength and range. Fast crystallization occurs in a localized region of this parameter space, but the character of crystallization pathways is not uniform within this region. Pathways range from one-step, in which a crystal nucleates directly from a gas, to two-step, in which substantial liquid-like clusters form and only subsequently become crystalline. Crystallization can fail because of slow nucleation from either gas or liquid, or because of dynamic arrest caused by strong interactions. Arrested states are characterized by the formation of networks of face-sharing tetrahedra that can be detected by a local common neighbor analysis.

cond-mat.soft↗

arXiv2015

Predicting the outcome of the growth of binary solids far from equilibrium

The growth of multicomponent structures in simulations and experiments often results in kinetically trapped, nonequilibrium objects. In such cases we have no general theoretical framework for predicting the outcome of the growth process. Here we use computer simulations to study the growth of two-component structures within a simple lattice model. We show that kinetic trapping happens for many choices of growth rate and inter-component interaction energies, and that qualitatively distinct kinds of kinetic trapping are found in different regions of parameter space. In a region in which the low-energy structure is an `antiferromagnet' or `checkerboard', we show that the grown nonequilibrium structure displays a component-type stoichiometry that is different to the equilibrium one but is insensitive to growth rate and solution conditions. This robust nonequilibrium stoichiometry can be predicted via a mapping to the jammed random tiling of dimers studied by Flory, a finding that suggests a way of making defined nonequilibrium structures in experiment.

cond-mat.soft↗

arXiv2014

Examples of molecular self-assembly at surfaces

The self-assembly of molecules at surfaces can be caused by a range of physical mechanisms. Assembly can be driven by intermolecular forces, or molecule-surface forces, or both; it can result in structures that are in equilibrium or that are kinetically trapped. Here we review examples of self-assembly at surfaces that have been studied within the User program of the Molecular Foundry at Lawrence Berkeley National Laboratory, focusing on a physical understanding of what causes patterns seen in experiment. Some apparently disparate systems can be described in similar physical terms, indicating that simple factors -- such as the geometry and energy scale of intermolecular binding -- are key to understanding the self-assembly of those systems.

cond-mat.stat-mech↗

arXiv2014

Emergent rhombus tilings from molecular interactions with $M$-fold rotational symmetry

We show that model molecules with particular rotational symmetries can self-assemble into network structures equivalent to rhombus tilings. This assembly happens in an emergent way, in the sense that molecules spontaneously select irregular 4-fold local coordination from a larger set of possible local binding geometries. The existence of such networks can be rationalized by simple geometrical arguments, but the same arguments do not guarantee networks' spontaneous self-assembly. This class of structures must in certain regimes of parameter space be able to reconfigure into networks equivalent to triangular tilings.

cond-mat.stat-mech↗

arXiv2014

The Statistical Mechanics of Dynamic Pathways to Self-assembly

We describe some of the important physical characteristics of the `pathways', i.e. dynamical processes, by which molecular, nanoscale and micron-scale self-assembly occurs. We highlight the fact that there exist features of self-assembly pathways that are common to a wide range of physical systems, even though those systems may be different in respect of their microscopic details. We summarize some existing theoretical descriptions of self-assembly pathways, and highlight areas -- notably, the description of self-assembly pathways that occur `far' from equilibrium -- that are likely to become increasingly important.

cond-mat.stat-mech↗

arXiv2014

Modeling sequence-specific polymers using anisotropic coarse-grained sites allows quantitative comparison with experiment

Certain sequences of peptoid polymers (synthetic analogs of peptides) assemble into bilayer nanosheets via a nonequilibrium assembly pathway of adsorption, compression, and collapse at an air-water interface. As with other large-scale dynamic processes in biology and materials science, understanding the details of this supramolecular assembly process requires a modeling approach that captures behavior on a wide range of length and time scales, from those on which individual sidechains fluctuate to those on which assemblies of polymers evolve. Here we demonstrate that a new coarse-grained modeling approach is accurate and computationally efficient enough to do so. Our approach uses only a minimal number of coarse-grained sites, but retains independently fluctuating orientational degrees of freedom for each site. These orientational degrees of freedom allow us to accurately parameterize both bonded and nonbonded interactions, and to generate all-atom configurations with sufficient accuracy to perform atomic scattering calculations and to interface with all-atom simulations. We have used this approach to reproduce all available experimental X-ray scattering spectra (for stacked nanosheets, and for peptoids adsorbed at air-water interfaces and in solution), in order to resolve the microscopic, real-space structures responsible for these Fourier-space features. By interfacing with all-atom simulations, we have also laid the foundations for future multiscale simulations of sequence-specific polymers that communicate in both directions across scales.

physics.bio-ph↗

arXiv2014

Growth of equilibrium structures built from a large number of distinct component types

We use simple analytic arguments and lattice-based computer simulations to study the growth of structures made from a large number of distinct component types. Components possess 'designed' interactions, chosen to stabilize an equilibrium target structure in which each component type has a defined spatial position, and 'undesigned' interactions that allow components to bind in a compositionally-disordered way. We find that high-fidelity growth of the equilibrium target structure can happen in the presence of substantial attractive undesigned interactions, as long as the energy scale of the set of designed interactions is chosen appropriately. This observation may help explain why equilibrium DNA 'brick' structures self-assemble even if undesigned interactions are not suppressed [Ke et al. Science 338, 1177 (2012)]. We also find that high-fidelity growth of the target structure is most probable when designed interactions are drawn from a distribution that is as narrow as possible. We use this result to suggest how to choose complementary DNA sequences in order to maximize the fidelity of multicomponent self-assembly mediated by complementary DNA interactions. We also comment on the prospect of growing macroscopic structures in this manner

cond-mat.soft↗

arXiv2014

Self-assembly at a nonequilibrium critical point

We use analytic theory and computer simulation to study patterns formed during the growth of two-component assemblies in 2D and 3D. We show that these patterns undergo a nonequilibrium phase transition, at a particular growth rate, between mixed and demixed arrangements of component types. This finding suggests that principles of nonequilibrium statistical mechanics can be used to predict the outcome of multicomponent self-assembly, and suggests an experimental route to the self-assembly of multicomponent structures of a qualitatively defined nature.

cond-mat.stat-mech↗

arXiv2014

Common physical framework explains phase behavior and dynamics of atomic, molecular and polymeric network-formers

We show that the self-assembly of a diverse collection of building blocks can be understood within a common physical framework. These building blocks, which form periodic honeycomb networks and nonperiodic variants thereof, range in size from atoms to micron-scale polymers, and interact through mechanisms as different as hydrogen bonds and covalent forces. A combination of statistical mechanics and quantum mechanics shows that one can capture the physics that governs assembly of these networks by resolving only the geometry and strength of building block interactions. The resulting framework reproduces a broad range of phenomena seen experimentally, including periodic and nonperiodic networks in thermal equilibrium, and nonperiodic supercooled and glassy networks away from equilibrium. Our results show how simple `design criteria' control assembly of a wide variety of networks, and suggest that kinetic trapping can be a useful way of making functional assemblies.

cond-mat.stat-mech↗

arXiv2013

Competing thermodynamic and dynamic factors select molecular assemblies on a gold surface

Controlling the self-assembly of surface-adsorbed molecules into nanostructures requires understanding physical mechanisms that act across multiple length and time scales. By combining scanning tunneling microscopy with hierarchical ab initio and statistical mechanical modeling of 1,4-substituted benzenediamine (BDA) molecules adsorbed on a gold (111) surface, we demonstrate that apparently simple nanostructures are selected by a subtle competition of thermodynamics and dynamics. Of the collection of possible BDA nanostructures mechanically stabilized by hydrogen bonding, the interplay of intermolecular forces, surface modulation, and assembly dynamics select at low temperature a particular subset: low free energy oriented linear chains of monomers, and high free energy branched chains.

cond-mat.mes-hall↗

arXiv2013

Selective nucleation in porous media

Geometrical arguments suggest that pore-mediated nucleation happens in general in a two-step fashion, the first step being nucleation within the pore, the second being nucleation from the filled pore into solution [Page & Sear, Phys. Rev. Lett. 97, 65701 (2006)]. The free energy barriers controlling the two steps of this process show opposite dependencies on pore size, implying that for given thermodynamic conditions there exists a pore size for which nucleation happens fastest. Here we show, within the two- and three-dimensional Ising lattice gas, that this preferred pore size tracks the size of the bulk critical nucleus, up to a numerical prefactor. This observation suggests a simple prescription for directing nucleation to certain locations within heterogeneous porous media.

cond-mat.soft↗

arXiv2012

Do hierarchical structures assemble best via hierarchical pathways?

Hierarchically structured natural materials possess functionalities unattainable to the same components organized or mixed in simpler ways. For instance, the bones and teeth of mammals are far stronger and more durable than the mineral phases from which they are derived because their constituents are organized hierarchically from the molecular scale to the macroscale. Making similarly functional synthetic hierarchical materials will require an understanding of how to promote the self-assembly of structure on multiple lengthscales, without falling foul of numerous possible kinetic traps. Here we use computer simulation to study the self-assembly of a simple hierarchical structure, a square crystal lattice whose repeat unit is a tetramer. Although the target material is organized hierarchically, it self-assembles most reliably when its dynamic assembly pathway consists of the sequential addition of monomers to a single structure. Hierarchical dynamic pathways via dimer and tetramer intermediates are also viable modes of assembly, but result in general in lower yield: these intermediates have a stronger tendency than monomers to associate in ways not compatible with the target structure. In addition, assembly via tetramers results in a kinetic trap whereby material is sequestered in trimers that cannot combine to form the target crystal. We use analytic theory to relate dynamical pathways to the presence of equilibrium phases close in free energy to the target structure, and to identify the thermodynamic principles underpinning optimum self-assembly in this model: 1) make the free energy gap between the target phase and the most stable fluid phase of order kT, and 2) ensure that no other dense phases (liquids or close-packed solids of monomers or oligomers) or fluids of incomplete building blocks fall within this gap.

cond-mat.soft↗

arXiv2012

Patterning a surface so as to speed nucleation from solution

Motivated by the question of how to pattern a surface in order to best speed nucleation from solution, we build on the work of Page and Sear [Phys. Rev. Lett. 97, 65701 (2006)] and calculate rates and free energy profiles for nucleation in the 3d Ising model in the presence of cuboidal pores. Pores of well-chosen aspect ratio can dramatically speed nucleation relative to a planar surface made of the same material, while badly-chosen pores provide no such enhancement. For a given pore, the maximum nucleation rate is achieved when one of its two horizontal dimensions attains a critical length, largely irrespective of the other dimension (provided that the latter is large enough). This observation implies that patterning a surface in a raster-like fashion is a better strategy for speeding nucleation than e.g. scoring long grooves in it.

cond-mat.stat-mech↗

arXiv2012

Self-assembly of multicomponent structures in and out of equilibrium

Theories of phase change and self-assembly often invoke the idea of a `quasiequilibrium', a regime in which the nonequilibrium association of building blocks results nonetheless in a structure whose properties are determined solely by an underlying free energy landscape. Here we study a prototypical example of multicomponent self-assembly, a one-dimensional fiber grown from red and blue blocks. If the equilibrium structure possesses compositional correlations different from those characteristic of random mixing, then it cannot be generated without error at any finite growth rate: there is no quasiequilibrium regime. However, by exploiting dynamic scaling, structures characteristic of equilibrium at one point in phase space can be generated, without error, arbitrarily far from equilibrium. Our results thus suggest a `nonperturbative' strategy for multicomponent self-assembly in which the target structure is, by design, not the equilibrium one.

cond-mat.stat-mech↗

arXiv2012

Control of pathways and yields of protein crystallization through the interplay of nonspecific and specific attractions

We use computer simulation to study crystal-forming model proteins equipped with interactions that are both orientationally specific and nonspecific. Distinct dynamical pathways of crystal formation can be selected by tuning the strengths of these interactions. When the nonspecific interaction is strong, liquidlike clustering can precede crystallization; when it is weak, growth can proceed via ordered nuclei. Crystal yields are in certain parameter regimes enhanced by the nonspecific interaction, even though it promotes association without local crystalline order. Our results suggest that equipping nanoscale components with weak nonspecific interactions (such as depletion attractions) can alter both their dynamical pathway of assembly and optimize the yield of the resulting material.

cond-mat.soft↗