Free energy of singular sticky-sphere clusters

The emergence of bulk structure in clusters via isotropic multi-well pair potentials

The mechanical, optical, and chemical properties of a wide variety of soft materials are enabled and constrained by their bulk structure. How this structure emerges at small system sizes during self-assembly has been the subject of decades of research, with the aim of designing and controlling material functionality. Despite these efforts, it is still not fundamentally understood how nontrivial interparticle interactions in a finite N-body system influence resultant structure, and how that structure depends on N. In this study, we investigate the emergence of non-close packings using multi-well isotropic pair potentials to simulate finite cluster formation of four distinct two-dimensional crystal structures. These pair potentials encode multiple preferred length scales into the system, allowing us to understand how anisotropic structural motifs-as opposed to close-packing-emerge as cluster size N increases. We find a tendency toward close-packing at small system sizes irrespective of the bulk structure; however, the system size at which bulk structure emerges is influenced by the coordination number of the bulk and the shape of the pair potential. Anisotropic structure emerges through the formation of bonds at a secondary bonding length at larger system sizes, and it is also dependent upon the shape of the pair potential. Our findings demonstrate that tuning particle-particle interactions can enable the engineering of nano- or mesoscale soft matter clusters, in applications as diverse as drug delivery and hierarchical materials design.

Application of a Simple Short-Range Attraction and Long-Range Repulsion Colloidal Model toward Predicting the Viscosity of Protein Solutions

Some hard-sphere colloidal models have been criticized for inaccurately predicting the solution viscosity of complex biological molecules like proteins. Competing short-range attractions and long-range repulsions, also known as short-range attraction and long-range repulsion (SALR) interactions, have been thought to affect the microstructure of a protein solution at low to moderate ionic strength. However, such interactions have been implicated primarily in causing phase transition, protein gelation, or reversible cluster formation, and their effect on protein solution viscosity change is not fully understood. In this work, we show the application of a hard-sphere colloidal model with SALR interactions toward predicting the viscosity of dilute to semi-dilute protein solutions. The comparison is performed for a globular-shaped albumin and Y-shaped therapeutic monoclonal antibody that are not explained by previous colloidal models. The model predictions show that it is the coupling between attractions and repulsions that gives rise to the observed experimental trends in solution viscosity as a function of pH, concentration, and ionic strength. The parameters of the model are obtained from measurements of the second virial coefficient and net surface charge/zeta-potential, without additional fitting of the viscosity.

Thermal Fluctuations of Singular Bar-Joint Mechanisms

A bar-joint mechanism is a deformable assembly of freely rotating joints connected by stiff bars. Here we develop a formalism to study the equilibration of common bar-joint mechanisms with a thermal bath. When the constraints in a mechanism cease to be linearly independent, singularities can appear in its shape space, which is the part of its configuration space after discarding rigid motions. We show that the free-energy landscape of a mechanism at low temperatures is dominated by the neighborhoods of points that correspond to these singularities. We consider two example mechanisms with shape-space singularities and find that they are more likely to be found in configurations near the singularities than others. These findings are expected to help improve the design of nanomechanisms for various applications.

Simulating sticky particles: A Monte Carlo method to sample a stratification

Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their equilibrium distribution, and there are several methods to sample probability distributions subject to fixed constraints. We introduce a Monte Carlo method to handle the case when constraints can break and form. More generally, the method samples a probability distribution on a stratification: a collection of manifolds of different dimensions, where the lower-dimensional manifolds lie on the boundaries of the higher-dimensional manifolds. We show several applications of the method in polymer physics, self-assembly of colloids, and volume calculation in high dimensions.

From canyons to valleys: Numerically continuing sticky-hard-sphere clusters to the landscapes of smoother potentials

We study the energy landscapes of particles with short-range attractive interactions as the range of the interactions increases. Starting with the set of local minima for 6≤N≤12 hard spheres that are "sticky," i.e., they interact only when their surfaces are exactly in contact, we use numerical continuation to evolve the local minima (clusters) as the range of the potential increases, using both the Lennard-Jones and Morse families of interaction potentials. As the range increases, clusters merge, until at long ranges only one or two clusters are left. We compare clusters obtained by continuation with different potentials and find that for short and medium ranges, up to about 30% of particle diameter, the continued clusters are nearly identical, both within and across families of potentials. For longer ranges, the clusters vary significantly, with more variation between families of potentials than within a family. We analyze the mechanisms behind the merge events and find that most rearrangements occur when a pair of nonbonded particles comes within the range of the potential. An exception occurs for nonharmonic clusters, i.e., those that have a zero eigenvalue in their Hessian, which undergo a more global rearrangement.

Morphology of depletant-induced erythrocyte aggregates

Red blood cells suspended in quiescent plasma tend to aggregate into multicellular assemblages, including linearly stacked columnar rouleaux, which can reversibly form more complex clusters or branching networks. While these aggregates play an essential role in establishing hemorheological and pathological properties, the biophysics behind their self-assembly into dynamic mesoscopic structures remains under-explored. We employ coarse-grained molecular simulations to model low-hematocrit erythrocytes subject to short-range implicit depletion forces, and demonstrate not only that depletion interactions are sufficient to account for a sudden dispersion-aggregate transition, but also that the volume fraction of depletant macromolecules controls small aggregate morphology. We observe a sudden transition from a dispersion to a linear column rouleau, followed by a slow emergence of disorderly amorphous clusters of many short rouleaux at larger volume fractions. This work demonstrates how discocyte topology and short-range, non-specific, physical interactions are sufficient to self-assemble erythrocytes into various aggregate structures, with markedly different morphologies and biomedical consequences.

From sticky-hard-sphere to Lennard-Jones-type clusters

A relation M_{SHS→LJ} between the set of nonisomorphic sticky-hard-sphere clusters M_{SHS} and the sets of local energy minima M_{LJ} of the (m,n)-Lennard-Jones potential V_{mn}^{LJ}(r)=ɛ/n-m[mr^{-n}-nr^{-m}] is established. The number of nonisomorphic stable clusters depends strongly and nontrivially on both m and n and increases exponentially with increasing cluster size N for N≳10. While the map from M_{SHS}→M_{SHS→LJ} is noninjective and nonsurjective, the number of Lennard-Jones structures missing from the map is relatively small for cluster sizes up to N=13, and most of the missing structures correspond to energetically unfavorable minima even for fairly low (m,n). Furthermore, even the softest Lennard-Jones potential predicts that the coordination of 13 spheres around a central sphere is problematic (the Gregory-Newton problem). A more realistic extended Lennard-Jones potential chosen from coupled-cluster calculations for a rare gas dimer leads to a substantial increase in the number of nonisomorphic clusters, even though the potential curve is very similar to a (6,12)-Lennard-Jones potential.