Hard-body Interactions Research Articles

The role of the second virial coefficient in the vapor-liquid phase coexistence of anisotropic square-well particles

We examine the role of the second virial coefficient in the vapor-liquid (VL) phase coexistence of anisotropic hard bodies with square-well attractions of variable range. According to the extended law of corresponding states, the parameters of hard body interactions and attractions can be built into the reduced density and the reduced second virial coefficients, respectively, which gives rise to the collapse of all VL binodals in the reduced second virial coefficient vs. reduced density plane. The second virial perturbation theory shows that the shape dependence appears as an extra parameter in the phase behavior of anisotropic particles, which does not make possible the perfect collapse of the VL binodals for varying shapes. Interestingly, the binodal curves go closely together and even cross each other in the liquid side allowing to define a quasi-master curve. The existence of an almost perfect master curve is confirmed by replica-exchange Monte Carlo simulations for oblate square-well ellipsoids with several shape anisotropies.

Protein adsorption on ion exchange adsorbers: A comparison of a stoichiometric and non-stoichiometric modeling approach

For mechanistic modeling of ion exchange (IEX) processes, a profound understanding of the adsorption mechanism is important. While the description of protein adsorption in IEX processes has been dominated by stoichiometric models like the steric mass action (SMA) model, discrepancies between experimental data and model results suggest that the conceptually simple stoichiometric description of protein adsorption provides not always an accurate representation of nonlinear adsorption behavior.In this work an alternative colloidal particle adsorption (CPA) model is introduced. Based on the colloidal nature of proteins, the CPA model provides a non-stoichiometric description of electrostatic interactions within IEX columns. Steric hindrance at the adsorber surface is considered by hard-body interactions between proteins using the scaled-particle theory. The model’s capability of describing nonlinear protein adsorption is demonstrated by simulating adsorption isotherms of a monoclonal antibody (mAb) over a wide range of ionic strength and pH. A comparison of the CPA model with the SMA model shows comparable model results in the linear adsorption range, but significant differences in the nonlinear adsorption range due to the different mechanistic interpretation of steric hindrance in both models. The results suggest that nonlinear adsorption effects can be overestimated by the stoichiometric formalism of the SMA model and are generally better reproduced by the CPA model.

Microstructure and rheology of globular protein gels in the presence of gelatin

The microstructure and rheological response of globular protein gels (whey protein isolate (WPI) and soy protein isolate (SPI)) in the presence of gelatin (type A, type B and hydrolyzed type A) was investigated. Microstructural information was obtained using a combination of confocal laser scanning microscopy (CLSM) and spin echo small-angle neutron scattering (SESANS). Addition of gelatin led to a coarsening of the globular protein gel structure and to a reduction in storage modulus of globular protein gels. The presence of hydrolyzed gelatin on the other hand did not induce these changes in the globular protein gels. Results were obtained at conditions where proteins only interact via hard body interactions. For these conditions it was concluded that the ratio of molecular sizes is the most important determinant for the occurrence or absence of rheological and microstructural changes in globular protein gels prepared in the presence of gelatin.

Interactions in protein mixtures. Part II: A virial approach to predict phase behavior

A virial theory was used to relate molecular interactions (in terms of second virial coefficients, B′) and molecular size ratios to liquid–liquid phase separation. Application of the virial theory to binary hard sphere mixtures (additive and non-additive) confirmed the applicability of this simple approach towards predicting phase behavior based on two-particle interactions.Experimentally, second cross virial coefficients were obtained for dextran/gelatin, whey protein isolate (WPI)/gelatin mixtures and whey protein aggregate (WPA)/gelatin mixtures using membrane osmometry at varying ionic strength. From this, solvent conditions where interactions between proteins are dominated by electrostatics and solvent conditions where interactions are dominated by hard body interactions could be determined.Using experimentally obtained second virial coefficients, the liquid–liquid phase separation for gelatin/dextran mixtures was successfully predicted. Second cross virial coefficients for gelatin/whey protein isolate and for gelatin/whey protein aggregate could be related to the absence of phase separation in these mixtures. This could be related to a similar size of the proteins and their non-additive behavior at conditions where they mainly interact via hard body interactions.

Dynamics of a suspension of interacting yolk-shell particles

In this work we study the self-diffusion properties of a liquid of hollow spherical particles (shells) bearing a smaller solid sphere in their interior (yolks). We model this system using purely repulsive hard-body interactions between all (shell and yolk) particles, but assume the presence of a background ideal solvent such that all the particles execute free Brownian motion between collisions, characterized by short-time self-diffusion coefficients for the shells and for the yolks. Using a softened version of these interparticle potentials we perform Brownian dynamics simulations to determine the mean squared displacement and intermediate scattering function of the yolk-shell complex. These results can be understood in terms of a set of effective Langevin equations for the N interacting shell particles, pre-averaged over the yolks' degrees of freedom, from which an approximate self-consistent description of the simulated self-diffusion properties can be derived. Here we compare the theoretical and simulated results between them, and with the results for the same system in the absence of yolks. We find that the yolks, which have no effect on the shell-shell static structure, influence the dynamic properties in a predictable manner, fully captured by the theory.

Monte Carlo simulation of flexible trimers: From square well chains to amphiphilic primitive models

In this work, we present Monte Carlo computer simulation results of a primitive model of self-assembling system based on a flexible 3-mer chain interacting via square-well interactions. The effect of switching off the attractive interaction in an extreme sphere is analyzed, since the anisotropy in the molecular potential promotes self-organization. Before addressing studies on self-organization it is necessary to know the vapor liquid equilibrium of the system to avoid to confuse self-organization with phase separation. The range of the attractive potential of the model, λ, is kept constant and equal to 1.5σ, where σ is the diameter of a monomer sphere, while the attractive interaction in one of the monomers was gradually turned off until a pure hard body interaction was obtained. We present the vapor-liquid coexistence curves for the different models studied, their critical properties, and the comparison with the SAFT-VR theory prediction [A. Gil-Villegas, A. Galindo, P. J. Whitehead, S. J. Mills, G. Jackson, and A. N. Burgess, J. Chem. Phys. 106, 4168 (1997)]. Evidence of self-assembly for this system is discussed.

Brownian dynamics simulations with hard-body interactions: Spherical particles

A novel approach to account for hard-body interactions in (overdamped) Brownian dynamics simulations is proposed for systems with non-vanishing force fields. The scheme exploits the analytically known transition probability for a Brownian particle on a one-dimensional half-line. The motion of a Brownian particle is decomposed into a component that is affected by hard-body interactions and into components that are unaffected. The hard-body interactions are incorporated by replacing the "affected" component of motion by the evolution on a half-line. It is discussed under which circumstances this approach is justified. In particular, the algorithm is developed and formulated for systems with space-fixed obstacles and for systems comprising spherical particles. The validity and justification of the algorithm is investigated numerically by looking at exemplary model systems of soft matter, namely at colloids in flow fields and at protein interactions. Furthermore, a thorough discussion of properties of other heuristic algorithms is carried out.

Crystallization of Deformable Spherical Colloids

We introduce and characterize a first-order model for a generic class of colloidal particles that have a preferred spherical shape but can undergo deformations while always maintaining hard-body interactions. The model consists of hard spheres that can continuously change shape at fixed volume into prolate or oblate ellipsoids of revolution, subject to an energetic penalty. The severity of this penalty is specified by a single parameter that determines the flexibility of the particles. The deformable hard spheres crystallize at higher packing fractions than rigid hard spheres, have a narrower solid-fluid coexistence region and can reach high densities by a second transition to an orientationally ordered crystal.

Event-driven Brownian dynamics for hard spheres

Brownian dynamics algorithms integrate Langevin equations numerically and allow to probe long time scales in simulations. A common requirement for such algorithms is that interactions in the system should vary little during an integration time step; therefore, computational efficiency worsens as the interactions become steeper. In the extreme case of hard-body interactions, standard numerical integrators become ill defined. Several approximate schemes have been invented to handle such cases, but little emphasis has been placed on testing the correctness of the integration scheme. Starting from the two-body Smoluchowski equation, the authors discuss a general method for the overdamped Brownian dynamics of hard spheres, recently developed by one of the authors. They test the accuracy of the algorithm and demonstrate its convergence for a number of analytically tractable test cases.

Monte Carlo simulations of conformations of chain molecules in a cylindrical pore

Off-lattice Monte Carlo simulations are employed to study the behavior of chain molecules confined in a long cylindrical pore under the condition of hard-body interaction. The emphasis is placed on the chain and bead distributions as well as the location dependence of the chain conformation and anisotropy. The simulation results show that the chains very near the pore surface tend to wrap around the surface in various configurations. This behavior is qualitatively similar to that of the chains near but outside a cylindrical rod. Moreover, the bead concentration near the pore surface increases with increasing surface curvature.

Revised Equation of State for Two-Center Lennard-Jones Fluids

The equation of state for two-center Lennard-Jones fluids originally proposed by Mecke et al. [Int. J. Thermophys.18:683–698 (1997); Erratum, Int. J. Thermophys.19:1495 (1998)] has been revised to extend its applicability to large molecular elongations. The equation of state is written in the form of a generalized augmented van der Waals equation for the Helmholtz energy, F=FH+FA, where FH accounts for the hard-body interaction and FA for the attractive dispersion forces. The revised EOS is constructed on the basis of previously published simulation data for 2CLJ fluids with reduced elongations L=0.0, 0.22, 0.3292, 0.505, and 0.67 and results from new extensive simulations for two-center Lennard-Jones fluids with L=0.8 and 1.0. The revised equation of state provides a very good description of the fluid state behavior over a wide range of temperatures and pressures as well as of the vapor-liquid equilibrium phase behavior for the two-center Lennard-Jones fluids with L ranging from 0.0 to 1.0.

Accurate method for the Brownian dynamics simulation of spherical particles with hard-body interactions

In Brownian Dynamics simulations, the diffusive motion of the particles is simulated by adding random displacements, proportional to the square root of the chosen time step. When computing average quantities, these Brownian contributions usually average out, and the overall simulation error becomes proportional to the time step. A special situation arises if the particles undergo hard-body interactions that instantaneously change their properties, as in absorption or association processes, chemical reactions, etc. The common “naı̈ve simulation method” accounts for these interactions by checking for hard-body overlaps after every time step. Due to the simplification of the diffusive motion, a substantial part of the actual hard-body interactions is not detected by this method, resulting in an overall simulation error proportional to the square root of the time step. In this paper we take the hard-body interactions during the time step interval into account, using the relative positions of the particles at the beginning and at the end of the time step, as provided by the naı̈ve method, and the analytical solution for the diffusion of a point particle around an absorbing sphere. Öttinger used a similar approach for the one-dimensional case [Stochastic Processes in Polymeric Fluids (Springer, Berlin, 1996), p. 270]. We applied the “corrected simulation method” to the case of a simple, second-order chemical reaction. The results agree with recent theoretical predictions [K. Hyojoon and Joe S. Kook, Phys. Rev. E 61, 3426 (2000)]. The obtained simulation error is proportional to the time step, instead of its square root. The new method needs substantially less simulation time to obtain the same accuracy. Finally, we briefly discuss a straightforward way to extend the method for simulations of systems with additional (deterministic) forces.

Computer simulation of the phase behavior of a model membrane protein: Annexin V

The bulk thermodynamic properties of membrane proteins originate from a complex combination of molecular interactions. We propose a simple model based on the pair interactions between a model membrane protein, annexin V. The experimental observations of a honeycomb (p6) and a triangular (p3) phase are successfully reproduced with Monte Carlo computer simulations. Grand canonical simulations and a newly developed “strip”-move constant pressure technique reveal the stability of a dilute fluid phase and a dense solid phase, not observed with the current experimental technology. While this model is extremely simple in that it relies only on hard-body and short-range directional interactions, it nevertheless captures the essential physics of the interactions between the protein molecules and reproduces the phase behavior observed in experiments.

Diffusion into a nanoparticle with first-order surface reaction confined within a sphere

The exact series solution for the reaction rate of a spherical sink confined within a sphere is presented from reaction- to diffusion-limited condition based on the bispherical coordinate method. The reaction rate varies with the particle location and the size ratio of particle to enveloping sphere. The maximum and minimum rates take place when the particle and the confining sphere are at contact and concentric, respectively. A thin-gap analysis is employed to derive the rate expression analytically for a near contact case. While the reaction rate at near contact diverges logarithmically for a purely diffusion-limited condition, it remains finite for a fast surface reaction with finite rate constant. The average reaction rate is then calculated based on a prescribed particle distribution function. It is found that for a uniform distribution, the mean rate is at most 50% higher than that for the concentric case. Other than the hard-body interaction, additional attractive and repulsive interactions will enhance and reduce the mean rate, respectively.

Modeling the Phase Behavior of the Membrane Binding Protein Annexin V

The bulk thermodynamic properties of proteins originate from a varied and complex combination of interactions. We propose a simple model for the formation of ordered two-dimensional aggregates based on the interactions between pairs of annexin V molecules. Simulations of this model are shown to reproduce the experimental observations of a honeycomb (p6) and a triangular (p3) crystalline phase. The simulations indicate that the transition between these two phases is first order. While this model is extremely simple in that it relies only on hard body and short-range directional interactions, it nevertheless captures the essential physics of the interactions between the protein molecules and reproduces the phase behavior observed in electron microscopy and atomic force microscopy experiments.

An equation of state for two-center Lennard-Jones fluids

A new equation of state (EOS) is proposed for the Helmholzt energyF of two-center Lennard-Jones fluids. The EOS is written in the form of a generalized van der Waals equation,F=FH+FA, whereFH accounts for the hard-body interaction andFA for the attractive dispersion forces. The equation is constructed on the basis of previously published data sets and results from new extensive computer simulation studies. It correlates pressures and internal energies over a wide fluid range for two-center model fluids with elongations up to 0.67 in reduced units with a high accuracy and shows an excellent description of the vapor-liquid coexistence properties. Comparisons of results from the new EOS with other data sets and recently published VLE from the NpT plus test particle method show very good agreement.

Shape-Dominated Ordering in Nematic Solvents. A Deuterium NMR Study of Cycloalkane Solutes

We examine a series of closely related, relatively inert, cyclic aliphatic solutescyclohexane, methylcyclohexane, 1,1-dimethylcyclohexane, 1,4-trans-dimethylcyclohexane, 1,4-cis-dimethylcyclohexane, trans-decalin, and cis-decalinin a nematic solvent and demonstrate that their orientational ordering can be accurately described in terms of purely hard-body interactions with the solvent molecules. These interactions are treated explicitly in the context of a statistical mechanical approximation wherein the orientational correlations among the solvent molecules are not taken into account directly. We test the theory by predicting the observed order parameters of the aliphatic solutes as determined with deuterium nuclear magnetic resonance. The utility and limitations of a description of solute ordering derived exclusively from hard-body interactions is discussed.

Molecular dynamics simulation of a needle-sphere binary mixture

This paper investigates the dynamic behaviour of a hard needle-sphere binary system using a novel numerical technique called the Newton homotopy continuation (NHC) method. This mixture is representative of a polymer melt where both long chain molecules and monomers coexist. Since the intermolecular forces are generated from hard body interactions, the consequence of missed collisions or incorrect collision sequences have a significant bearing on the dynamic properties of the fluid. To overcome this problem, in earlier work NHC was chosen over traditional Newton-Raphson methods to solve the hard body dynamics of a needle fluid in random media composed of overlapping spheres. Furthermore, the simplicity of interactions and dynamics allows us to focus our research directly on the effects of particle shape and density on the transport behaviour of the mixture. These studies are also compared with earlier works that examined molecular chains in porous media primarily to understand the differences in molecular ...