Repulsive Spheres Research Articles

Structural fluctuations and thermal stability of proteins in crowded environments: effects of the excluded volume

We perform molecular dynamics simulations for a simple coarse-grained model of a protein placed inside of a softly repulsive sphere of radius R. The protein is surrounded either by a number of same molecules or a number of spherical crowding particles that immitate other biomolecules such as the osmolytes. The two descriptions are shown to lead to distinct results when testing thermal stability as assessed by studying the unfolding times as a function of temperature. We consider three examples of proteins and show that crowding increases the thermal stability provided the inter-protein or protein-crowder interactions are repulsive. On the other hand, an introduction of attraction between the proteins is found to destabilize the proteins. Crowding by repulsive crowder particles is seen to enhance the RMSF in certain exposed regions. The effect grows on decreasing the size of the crowding particles. In the absence of crowding the RMSF anticorrelates with the coordination number related to the residue–residue interaction.

Structural analysis of high-dimensional basins of attraction.

We propose an efficient Monte Carlo method for the computation of the volumes of high-dimensional bodies with arbitrary shape. We start with a region of known volume within the interior of the manifold and then use the multistate Bennett acceptance-ratio method to compute the dimensionless free-energy difference between a series of equilibrium simulations performed within this object. The method produces results that are in excellent agreement with thermodynamic integration, as well as a direct estimate of the associated statistical uncertainties. The histogram method also allows us to directly obtain an estimate of the interior radial probability density profile, thus yielding useful insight into the structural properties of such a high-dimensional body. We illustrate the method by analyzing the effect of structural disorder on the basins of attraction of mechanically stable packings of soft repulsive spheres.

Indirect and Direct Observation of Ionomer Colloidal Systems with Applications to Fuel-Cell Catalyst Layers

Manufacturing methods for fuel cell catalyst layers are critically important for achieving high material utilization and performance. Typically, electrode systems are cast from an ‘ink’ or ‘colloidal’ state, where the solid material is suspended in a solution containing a solvent and a polymer. For polymer-electrolyte fuel cells, a perfluorinated sulfonic-acid (PFSA) ionomer, typically Nafion, is used in the ink and catalyst layer, where its roles are to act as a binding agent and conduit for proton conduction to the reaction site.1 Recently, it has been suggested that the ionomer film that surrounds the platinum reaction site may contribute to increased resistances that limit performance at low Pt loadings.1,2 Thus, it is of great interest to understand the factors controlling the film formation in catalyst layers to optimize material properties and cell performance. The nature of the dispersion and casting process could have significant influence on the morphology and properties of the dispersion-cast membranes.3-5 To isolate these effects, the morphology of PFSA dispersed in various solvents (glycerol, water/2-propanol, and NMP) was reported previously using small angle neutron scattering (SANS), where catalyst layers from the different solvents exhibit different performance.6 The understanding of local‘ink’ structures as a function of active material (polymer and solid) volume fraction (Φ) and across solvent space and length scales can aid in understanding bulk properties and the impact of ink formulation in cast systems. In this talk, a direct observation of the colloidal suspension of the ionomer in different solvents will be described using confocal laser scanning microscopy (CLSM). CLSM has long been utilized as a tool for characterizing the structure of biphasic colloidal gels. We combine dynamic light scattering, ultra-small angle x-ray scattering, and confocal microscopy to understand PFSA size and structure in dilute (1,3, and 5 wt%) ionomer solutions. The structural formation of nafion membranes are observed in-situ with small angle x-ray scattering. Finally, we contrive a model ‘ink’ composed of attractive and repulsive silica spheres and PFSA suspended in different solvents (water, NMP, and isopropyl-alcohol) and use CLSM to gain a greater understanding about solid|PFSA interactions in model inks. 1. A. Z. Weber and A. Kusoglu, Journal of Materials Chemistry A, 2, 17207 (2014). 2. A. Kongkanand and M. F. Mathias, The Journal of Physical Chemistry Letters, 1127 (2016). 3. T. T. Ngo, T. L. Yu and H.-L. Lin, Journal of Power Sources, 225, 293 (2013). 4. C.-H. Ma, T. L. Yu, H.-L. Lin, Y.-T. Huang, Y.-L. Chen, U. S. Jeng, Y.-H. Lai and Y.-S. Sun, Polymer, 50, 1764 (2009). 5. Y. S. Kim, C. F. Welch, R. P. Hjelm, N. H. Mack, A. Labouriau and E. B. Orler, Macromolecules, 48, 2161 (2015). 6. C. Welch, A. Labouriau, R. Hjelm, B. Orler, C. Johnston and Y. S. Kim, Acs Macro Letters, 1, 1403 (2012).

Entropic, electrostatic, and interfacial regimes in concentrated disordered ionic emulsions

We develop a free energy model that describes two key thermodynamic properties, the osmotic pressure Π and the linear elastic shear modulus G′p (i.e. plateau storage modulus), of concentrated monodisperse emulsions which have isotropic, disordered, droplet structures, and are stabilized using ionic surfactants. This model effectively incorporates the concept of random close packing or jamming of repulsive spheres into a free energy F that depends on droplet volume fraction ϕ and shear strain γ both below and above the a critical jamming point ϕ c ≈ 0.646. This free energy has three terms: entropic, electrostatic, and interfacial (EEI). By minimizing F with respect to an average droplet deformation parameter that links all three terms, we show that the entropic term is dominant for ϕ well below ϕ c, the electrostatic term is dominant for ϕ near but below ϕ c, and the interfacial term dominates for larger ϕ. This EEI model describes measurements of G′p(ϕ) for charge-stabilized uniform emulsions having a wide range of droplet sizes, ranging from nanoscale to microscale, and it also is consistent with measurements of Π(ϕ). Moreover, it describes G′p(ϕ) for similar nanoemulsions after adding non-amphiphilic salt, when changes in the interfacial tension and the Debye screening length are properly taken into account. By unifying existing approaches, the EEI model predicts constitutive properties of concentrated ionic emulsions that have disordered, out-of-equilibrium structures through near-equilibrium free energy minimization, consistent with random driving Brownian excitations.

Hydrated nonpolar solute volumes: Interplay between size, Attractiveness, and molecular structure

A solute's partial molar volume determines its response to pressure, which can result in changes in molecular conformation or assembly state. Computing speed advances have made accurate partial molar volume evaluation in water routine, allowing for the dissection of the molecular factors underlying this significant thermodynamic variable. A recent simulation analysis of the volumes of nonpolar molecular solutes in water reported that the apparent solvent-free border thickness enshrouding these solutes grows with increasing solute size, based on the assumption the solute can be treated as an individual sphere [Biophys. Chem. 161 (2012) 46]. This suggests the solvent dewets these solutes as they grow in size. Via simulations of dewetted repulsive spherical solutes, we show that the border thicknesses of the largest non-polar molecular solutes tend towards that of a repulsive sphere. When attractive interactions are accounted for, however, the spherical solute border thicknesses fall below that of the largest molecular solutes. We demonstrate that if the molecular solutes are treated with atomic detail rather than approximated as an individual sphere, the border thickness variation is minimal. A geometric model is put forward that reproduces the inferred border thickening, indicating the implied dewetting results from a breakdown in the spherical volume approximation.

Echoes from anharmonic normal modes in model glasses.

Glasses display a wide array of nonlinear acoustic phenomena at temperatures T ≲ 1 K. This behavior has traditionally been explained by an ensemble of weakly coupled, two-level tunneling states, a theory that is also used to describe the thermodynamic properties of glasses at low temperatures. One of the most striking acoustic signatures in this regime is the existence of phonon echoes, a feature that has been associated with two-level systems with the same formalism as spin echoes in NMR. Here we report the existence of a distinctly different type of acoustic echo in classical models of glassy materials. Our simulations consist of finite-ranged, repulsive spheres and also particles with attractive forces using Lennard-Jones interactions. We show that these echoes are due to anharmonic, weakly coupled vibrational modes and perhaps provide an alternative explanation for the phonon echoes observed in glasses at low temperatures.

Effective potential method for active particles

ABSTRACTWe investigate the steady-state properties of an active fluid modelled as an assembly of soft repulsive spheres subjected to Gaussian coloured noise. Such a noise captures one of the salient aspects of active particles, namely the persistence of their motion and determines a variety of novel features with respect to familiar passive fluids. We show that within the so-called multidimensional unified coloured noise approximation, recently introduced in the field of active matter, the model can be treated by methods similar to those employed in the study of standard molecular fluids. The system shows a tendency of the particles to aggregate even in the presence of purely repulsive forces because the combined action of coloured noise and interactions enhances the effective friction between nearby particles. We also discuss whether an effective two-body potential approach, which would allow to employ methods similar to those of density functional theory, is appropriate. The limits of such an approximation are discussed.

Density-induced reentrant melting of colloidal Wigner crystals

Electrostatic repulsions can drive crystallization in many-particle systems. For charged colloidal systems, the phase boundaries as well as crystal structure are highly tunable by experimental parameters such as salt concentration and pH. By using projections of the colloid-ion mixture to a system of (soft) repulsive spheres and the one-component plasma (OCP), we study the hitherto unexplained experimentally observed reentrant melting of electrostatically repelling colloids upon increasing the colloid density. Our study shows that the surface chemistry should involve a competition between adsorption of cations and anions to explain the observed density-induced reentrant melting.

Configurational entropy and effective temperature in systems of active Brownian particles.

We propose a method to determine the effective density of states and configurational entropy in systems of active Brownian particles by measuring the probability distribution function of potential energy at varying temperatures. Assuming that the entropy is a continuous and monotonically increasing function of energy, we provide support that two-dimensional systems of purely repulsive active Brownian spheres can be mapped onto an equilibrium system with a Boltzmann-like distribution and an effective temperature. We find that the effective temperature depends even for a large number of particles on system size, suggesting that active systems are non-extensive. In addition, the effective Helmholtz free energy can be derived from the configurational entropy. We verify our results regarding the configurational entropy by using thermodynamic integration of the effective Helmholtz free energy with respect to temperature.

Thermalized connectivity networks of jammed packings.

Jammed packings of repulsive elastic spheres have emerged as a rich model system within which the elastic properties of disordered glassy materials may be elucidated. Most of the work on these packings has focused on the case of vanishing temperature. Here, we explore the elastic properties of the associated connectivity network for finite temperatures, ignoring the breaking of bonds and the formation of new ones. Using extensive Monte Carlo simulations, we find that, as the temperature is increased, the resulting spring network shrinks and exhibits a rapidly softening bulk modulus via a cusp. Moreover, the shear modulus stiffens in a fixed volume ensemble but not in a fixed pressure ensemble. These counter-intuitive behaviors may be understood from the characteristic spectrum of soft modes near isostaticity, which resembles the spectrum of a rod near its buckling instability. Our results suggest a generic mechanism for negative thermal expansion coefficients in marginal solids. We discuss some consequences of bond breaking and an apparent analogy between thermalization and shear.

Bridging between macroscopic behavior of shale gas reservoirs and confined fluids in nanopores

The macroscopic behavior of gas flow in multi-porosity shale gas reservoirs is rigorously derived within the framework of the reiterated homogenization procedure in conjunction with the Thermodynamics of Inhomogeneous Gases in nanopores. At the nanoscale, the Density Functional Theory is applied to reconstruct general adsorption isotherms and local density profiles of pure methane in the intraparticle porosity of the gas-wet organic matter. The description of adsorption incorporates both repulsive hard sphere effects and Lennard–Jones attractive intermolecular interactions between fluid-fluid supplemented by a fluid-solid exterior potential. Such local description reproduces the monolayer surface adsorption ruled by the Langmuir isotherm in the asymptotic regime of large pore size distributions. The nanoscopic model is upscaled to the microscale where kerogen particles and nanopores are viewed as overlaying continua forming the organic aggregates with adsorbed gas at local thermodynamic equilibrium with the free gas in the water partially saturated interparticle pores. The reaction/diffusion equation for pure gas movement in the kerogen aggregates is coupled with the Fickian diffusion of dissolved gas in the water phase and free gas Darcy flow in the adjacent interparticle pores which also lye in the vicinity of the inorganic solid phase (clay, quartz, calcite) assumed impermeable. By postulating continuity of fugacity between free and dissolved gas in the interparticle pores and neglecting the water movement, we upscale the microscopic problem to the mesoscale, where organic and inorganic matters along with interparticle pores are viewed as overlaying continua. The upscaling gives rise to a new nonlinear pressure equation for gas hydrodynamics in the interparticle pores including a new storativity coefficient dependent on water saturation, total organic carbon content (TOC), and intra- and interparticle porosities. When coupled with the nonlinear single phase gas flow in the hydraulic fractures, the homogenization of the mesoscopic model leads to a new microstructural model of triple porosity type with distributed mass transfer function between the different levels of porosity. Computational simulations illustrate the potential of the multiscale approach proposed herein in providing accurate numerical simulations of methane flow in shale gas reservoirs.

Model-based description of peptide retention on doped reversed-phase media

Reversed-phase (RP) chromatography is one of the main tools for the preparative purification of therapeutic peptides. In previous works [1,2], a new type of RP chromatography, doped reversed-phase chromatography (DRP) was presented. By adding small amounts (up to 15% of the surface ligands) of repulsive ion exchange ligands to a traditional RP material, significant improvements in peptide purification performance were observed, at the same or in similar operating conditions. These improvements included increases in selectivity in diluted conditions (up to twice as high), increases in yield in preparative conditions (up to 20% higher) and in productivity in preparative conditions (up to twice as high), when compared to RP materials [2]. A proper physical model is developed in this work to quantitatively explain and rationalize this behavior. The developed model is then used to correctly fit the retention data of several peptides in different buffering conditions. The increase in selectivity is related to a controlled decrease in free surface area available for adsorption due to the ionic ligands creating a repulsive sphere the analytes cannot enter. This decrease in adsorption surface is calculated using Debye–Hückel theory, and in combination with linear solvent strength theory, allows for the quantitative description of peptide retention on DRP media.

Self-assembly of patchy colloidal dumbbells.

We employ Monte Carlo simulations to investigate the self-assembly of patchy colloidal dumbbells interacting via a modified Kern-Frenkel potential by probing the system concentration and dumbbell shape. We consider dumbbells consisting of one attractive sphere with diameter σ1 and one repulsive sphere with diameter σ2 and center-to-center distance d between the spheres. For three different size ratios, we study the self-assembled structures for different separations l = 2d/(σ1 + σ2) between the two spheres. In particular, we focus on structures that can be assembled from the homogeneous fluid, as these might be of interest in experiments. We use cluster order parameters to classify the shape of the formed structures. When the size of the spheres is almost equal, q = σ2/σ1 = 1.035, we find that, upon increasing l, spherical micelles are transformed to elongated micelles and finally to vesicles and bilayers. For size ratio q = 1.25, we observe a continuously tunable transition from spherical to elongated micelles upon increasing the sphere separation. For size ratio q = 0.95, we find bilayers and vesicles, plus faceted polyhedra and liquid droplets. Our results identify key parameters to create colloidal vesicles with attractive dumbbells in experiments.

Jamming in finite systems: stability, anisotropy, fluctuations, and scaling.

Athermal packings of soft repulsive spheres exhibit a sharp jamming transition in the thermodynamic limit. Upon further compression, various structural and mechanical properties display clean power-law behavior over many decades in pressure. As with any phase transition, the rounding of such behavior in finite systems close to the transition plays an important role in understanding the nature of the transition itself. The situation for jamming is surprisingly rich: the assumption that jammed packings are isotropic is only strictly true in the large-size limit, and finite-size has a profound effect on the very meaning of jamming. Here, we provide a comprehensive numerical study of finite-size effects in sphere packings above the jamming transition, focusing on stability as well as the scaling of the contact number and the elastic response.

Jamming graphs: A local approach to global mechanical rigidity

We revisit the concept of minimal rigidity as applied to frictionless, repulsive soft sphere packings in two dimensions with the introduction of the jamming graph. Minimal rigidity is a purely combinatorial property encoded via Laman's theorem in two dimensions. It constrains the global, average coordination number of the graph, for example. However, minimal rigidity does not address the geometry of local mechanical stability. The jamming graph contains both properties of global mechanical stability at the onset of jamming and local mechanical stability. We demonstrate how jamming graphs can be constructed using local moves via the Henneberg construction such that these graphs fall under the jurisdiction of correlated percolation. We then probe how jamming graphs destabilize, or become unjammed, by deleting a bond and computing the resulting rigid cluster distribution. We also study how the system restabilizes with the addition of new contacts and how a jamming graph with extra (redundant) contacts destabilizes. The latter endeavor allows us to probe a disk packing in the rigid phase and uncover a potentially new diverging length scale associated with the random deletion of contacts as compared to the study of cut-out (or frozen-in) subsystems.

Particle-scale reversibility in athermal particulate media below jamming

We perform numerical simulations of repulsive, frictionless athermal disks in two and three spatial dimensions undergoing cyclic quasistatic simple shear to investigate particle-scale reversible motion. We identify three classes of steady-state dynamics as a function of packing fraction φ and maximum strain amplitude per cycle γ(max). Point-reversible states, where particles do not collide and exactly retrace their intracycle trajectories, occur at low φ and γ(max). Particles in loop-reversible states undergo numerous collisions and execute complex trajectories but return to their initial positions at the end of each cycle. For sufficiently large φ and γ(max), systems display irreversible dynamics with nonzero self-diffusion. Loop-reversible dynamics enables the reliable preparation of configurations with specified structural and mechanical properties over a broad range of φ.

Linear and nonlinear rheology of dense emulsions across the glass and the jamming regimes

We discuss the linear and nonlinear rheology of concentrated microscale emulsions, amorphous disordered solids composed of repulsive and deformable soft colloidal spheres. Based on recent results from simulation and theory, we derive quantitative predictions for the dependences of the elastic shear modulus and the yield stress on the droplet volume fraction. The remarkable agreement with experiments we observe supports the scenario that the repulsive glass and the jammed state can be clearly identified in the rheology of soft spheres at finite temperature while crossing continuously from a liquid to a highly compressed yet disordered solid.

Transient behavior of a model fluid under applied shear

We study the transient behavior of a model fluid composed by soft repulsive spheres subjected to a planar uniform shear. To this aim, we use a dynamical non-equilibrium molecular dynamics method originally developed by Ciccotti and Jacucci [Phys. Rev. Lett. 35, 789 (1975)] and recently applied to the study of the transient regimes in various fluid systems. We show that the dynamical method allows one to study the transient behavior of the viscous time-dependent response over a wide range of applied shear rates, provided that a temperature control is enforced on the system. In this study, we adopt in particular the configurational thermostat of Braga and Travis [J. Chem. Phys. 123, 134101 (2005)]. The initial behavior of the dynamical response to a θ-like perturbation is characterized by a rapid increase, culminating in a pronounced peak, later relaxing to a plateau value. The latter positively reproduces the values of the viscosity observed in standard steady-state non-equilibrium molecular dynamics.

Thermodynamic scaling and corresponding states for the self-diffusion coefficient of non-conformal soft-sphere fluids

In this work, we explore transport properties of a special type of repulsive spheres that exhibit remarkable scaling of their thermodynamic properties. In order to accomplish that we propose a new way to derive and express effective hard-sphere diameters for transport properties of simple fluids. The procedure relies on mapping the system's transport properties, in the low density limit, to the hard-sphere fluid. We have chosen a set of soft-sphere systems characterised by a well-defined variation of their softness. These systems represent an extension of the repulsive Lennard-Jones potential widely used in statistical mechanics of fluids and are an accurate representation of the effective repulsive potentials of real systems. The self-diffusion coefficient of the soft-sphere fluids is obtained by equilibrium molecular dynamics. The soft-sphere collision integrals of different systems are shown to follow quite simple relationships between each other. These collision integrals are incorporated, through the definition of the effective hard-sphere diameter, in the resulting equation for the self-diffusion coefficient. The approach followed exhibits a density rescaling that leads to a single master curve for all systems and temperatures. The scaling is carried through to the level of the mean-squared displacement.

Dynamic criticality at the jamming transition

We characterize vibrational motion occurring at low temperatures in dense suspensions of soft repulsive spheres over a broad range of volume fractions encompassing the jamming transition at (T = 0, ϕ = ϕJ). We find that characteristic time and length scales of thermal vibrations obey critical scaling in the vicinity of the jamming transition. We show in particular that the amplitude and the time scale of dynamic fluctuations diverge symmetrically on both sides of the transition, and directly reveal a diverging correlation length. The critical region near ϕJ is divided in three different regimes separated by a characteristic temperature scale T(⋆)(ϕ) that vanishes quadratically with the distance to ϕJ. While two of them, (T < T(⋆)(ϕ), ϕ > ϕJ) and (T < T(⋆)(ϕ), ϕ < ϕJ), are described by harmonic theories developed in the zero temperature limit, the third one for T > T(⋆)(ϕ) is inherently anharmonic and displays new critical properties. We find that the quadratic scaling of T(⋆)(ϕ) is due to nonperturbative anharmonic contributions, its amplitude being orders of magnitude smaller than the perturbative prediction based on the expansion to quartic order in the interactions. Our results show that thermal vibrations in colloidal assemblies directly reveal the critical nature of the jamming transition. The critical region, however, is very narrow and has not yet been attained experimentally, even in recent specifically-dedicated experiments.