Simulations and integral-equation theories for dipolar density interacting disks.

Integral equation theories (IETs) based on the Ornstein-Zernike (OZ) relation can be used as an analytical tool to predict structural and thermodynamic properties and phase behavior of fluids with low numerical cost. However, there are no studies of the IETs for the dipolar density interaction potential in two-dimensional systems, a relevant interdomain interaction in lipid monolayers with phase coexistence. This repulsive interaction arises due to the excess dipole density of the domains, which are aligned perpendicular to the interface. This work studies the performance of three closures of the OZ equation for this novel system: Rogers-Young (RY), modified hypernetted chain (MHNC), and variational modified hypernetted chain (VMHNC). For the last two closures the bridge function of a reference system is required, with the hard disk being the most convenient reference system. Given that in two dimensions there is no analytical expressions for the hard disk correlation functions, two different approximations are proposed: one based on the Percus-Yevick (PY) approximation, and the other based on an extension of the hard spheres Verlet-Weis-Henderson-Grundke (LB) parametrization. The accuracy of the five approaches is evaluated by comparison of the pair correlation function and the structure factor with Monte Carlo simulation data. The results show that RY closure is satisfactory only for low-structured regimes. MHNC and VMHNC closures perform globally well, and there are no significant differences between them. However, the reference system in some cases affects their performance; when the pair correlation function serves as the measure, the LB-based closures quantitatively outperform the PY ones. From the point of view of its applicability, LB-based closures do not have a solution for all studied interaction strength parameters, and, in general, PY-based closures are numerically preferable.

Hitting the wall: Human sperm velocity recovery under ultra-confined conditions.

Infertility is a common medical condition encountered by health systems throughout the world. Despite the development of complex in vitro fertilization techniques, only one-third of these procedures are successful. New lab-on-a-chip systems that focus on spermatozoa selection require a better understanding of sperm behavior under ultra-confined conditions in order to improve outcomes. Experimental studies combined with models and simulations allow the evaluation of the efficiency of different lab-on-a-chip devices during the design process. In this work, we provide experimental evidence of the dynamics of sperm interacting with a lateral wall in a shallow chamber. We observe a decrease in average sperm velocity during initial wall interaction and partial recovery after the alignment of the trajectory of the cell. To describe this phenomenon, we propose a simple model for the sperm alignment process with a single free parameter. By incorporating experimental motility characterization into the model, we achieve an accurate description of the average velocity behavior of the sperm population close to walls. These results will contribute to the design of more efficient lab-on-a-chip devices for the treatment of human infertility.

Short- and long-time diffusion and dynamic scaling in suspensions of charged colloidal particles.

We report on a comprehensive theory-simulation-experimental study of collective and self-diffusion in concentrated suspensions of charge-stabilized colloidal spheres. In theory and simulation, the spheres are assumed to interact directly by a hard-core plus screened Coulomb effective pair potential. The intermediate scattering function, fc(q, t), is calculated by elaborate accelerated Stokesian dynamics (ASD) simulations for Brownian systems where many-particle hydrodynamic interactions (HIs) are fully accounted for, using a novel extrapolation scheme to a macroscopically large system size valid for all correlation times. The study spans the correlation time range from the colloidal short-time to the long-time regime. Additionally, Brownian Dynamics (BD) simulation and mode-coupling theory (MCT) results of fc(q, t) are generated where HIs are neglected. Using these results, the influence of HIs on collective and self-diffusion and the accuracy of the MCT method are quantified. It is shown that HIs enhance collective and self-diffusion at intermediate and long times. At short times self-diffusion, and for wavenumbers outside the structure factor peak region also collective diffusion, are slowed down by HIs. MCT significantly overestimates the slowing influence of dynamic particle caging. The dynamic scattering functions obtained in the ASD simulations are in overall good agreement with our dynamic light scattering (DLS) results for a concentration series of charged silica spheres in an organic solvent mixture, in the experimental time window and wavenumber range. From the simulation data for the time derivative of the width function associated with fc(q, t), there is indication of long-time exponential decay of fc(q, t), for wavenumbers around the location of the static structure factor principal peak. The experimental scattering functions in the probed time range are consistent with a time-wavenumber factorization scaling behavior of fc(q, t) that was first reported by Segrè and Pusey [Phys. Rev. Lett. 77, 771 (1996)] for suspensions of hard spheres. Our BD simulation and MCT results predict a significant violation of exact factorization scaling which, however, is approximately restored according to the ASD results when HIs are accounted for, consistent with the experimental findings for fc(q, t). Our study of collective diffusion is amended by simulation and theoretical results for the self-intermediate scattering function, fs(q, t), and its non-Gaussian parameter α2(t) and for the particle mean squared displacement W(t) and its time derivative. Since self-diffusion properties are not assessed in standard DLS measurements, a method to deduce W(t) approximately from fc(q, t) is theoretically validated.

Domain size polydispersity effects on the structural and dynamical properties in lipid monolayers with phase coexistence.

In lipid monolayers with phase coexistence, domains of the liquid-condensed phase always present size polydispersity. However, very few theoretical works consider size distribution effects on the monolayer properties. Because of the difference in surface densities, domains have excess dipolar density with respect to the surrounding liquid expanded phase, originating a dipolar inter-domain interaction. This interaction depends on the domain area, and hence the presence of a domain size distribution is associated with interaction polydispersity. Inter-domain interactions are fundamental to understanding the structure and dynamics of the monolayer. For this reason, it is expected that polydispersity significantly alters monolayer properties. By means of Brownian dynamics simulations, we study the radial distribution function (RDF), the average mean square displacement and the average time-dependent self-diffusion coefficient, D(t), of lipid monolayers with normally distributed size domains. For this purpose, we vary the relevant system parameters, polydispersity and interaction strength, within a range of experimental interest. We also analyze the consequences of using a monodisperse model to determine the interaction strength from an experimental RDF. We find that polydispersity strongly affects the value of the interaction strength, which is greatly underestimated if polydispersity is not considered. However, within a certain range of parameters, the RDF obtained from a polydisperse model can be well approximated by that of a monodisperse model, by suitably fitting the interaction strength, even for 40% polydispersities. For small interaction strengths or small polydispersities, the polydisperse systems obtained from fitting the experimental RDF have an average mean square displacement and D(t) in good agreement with that of the monodisperse system.

Dipolar interactions between domains in lipid monolayers at the air-water interface.

A great variety of biologically relevant monolayers present phase coexistence characterized by domains formed by lipids in an ordered phase state dispersed in a continuous, disordered phase. From the difference in surface densities between these phases, inter-domain dipolar interactions arise. These interactions are relevant for the determination of the spacial distribution of domains as well as their dynamics. In this work, we propose a novel way of estimating the dipolar repulsion using a passive method that involves the analysis of images of the monolayer with phase coexistence. This method is based on the comparison of the pair correlation function obtained from experiments with that obtained from Brownian dynamics simulations of a model system. As an example, we determined the difference in dipolar density of a binary monolayer of DSPC/DMPC at the air-water interface from the analysis of the radial distribution of domains, and the results are compared with those obtained by surface potential determinations. A systematic analysis for the experimentally relevant parameter range is given, which may be used as a working curve for obtaining the dipolar repulsion in different systems.

Short-time rheology and diffusion in suspensions of Yukawa-type colloidal particles.

A comprehensive study is presented on the short-time dynamics in suspensions of charged colloidal spheres. The explored parameter space covers the major part of the fluid-state regime, with colloid concentrations extending up to the freezing transition. The particles are assumed to interact directly by a hard-core plus screened Coulomb potential, and indirectly by solvent-mediated hydrodynamic interactions. By comparison with accurate accelerated Stokesian Dynamics (ASD) simulations of the hydrodynamic function H(q), and the high-frequency viscosity η(∞), we investigate the accuracy of two fast and easy-to-implement analytical schemes. The first scheme, referred to as the pairwise additive (PA) scheme, uses exact two-body hydrodynamic mobility tensors. It is in good agreement with the ASD simulations of H(q) and η(∞), for smaller volume fractions up to about 10% and 20%, respectively. The second scheme is a hybrid method combining the virtues of the δγ scheme by Beenakker and Mazur with those of the PA scheme. It leads to predictions in good agreement with the simulation data, for all considered concentrations, combining thus precision with computational efficiency. The hybrid method is used to test the accuracy of a generalized Stokes-Einstein (GSE) relation proposed by Kholodenko and Douglas, showing its severe violation in low salinity systems. For hard spheres, however, this GSE relation applies decently well.

Pair structure of the hard-sphere Yukawa fluid: an improved analytic method versus simulations, Rogers-Young scheme, and experiment.

We present a comprehensive study of the equilibrium pair structure in fluids of nonoverlapping spheres interacting by a repulsive Yukawa-like pair potential, with special focus on suspensions of charged colloidal particles. The accuracy of several integral equation schemes for the static structure factor, S(q), and radial distribution function, g(r), is investigated in comparison to computer simulation results and static light scattering data on charge-stabilized silica spheres. In particular, we show that an improved version of the so-called penetrating-background corrected rescaled mean spherical approximation (PB-RMSA) by Snook and Hayter [Langmuir 8, 2880 (1992)], referred to as the modified PB-RMSA (MPB-RMSA), gives pair structure functions which are in general in very good agreement with Monte Carlo simulations and results from the accurate but nonanalytical and therefore computationally more expensive Rogers-Young integral equation scheme. The MPB-RMSA preserves the analytic simplicity of the standard rescaled mean spherical (RMSA) solution. The combination of high accuracy and fast evaluation makes the MPB-RMSA ideally suited for extensive parameter scans and experimental data evaluation, and for providing the static input to dynamic theories. We discuss the results of extensive parameter scans probing the concentration scaling of the pair structure of strongly correlated Yukawa particles, and we determine the liquid-solid coexistence line using the Hansen-Verlet freezing rule.

Short-time transport properties in dense suspensions: from neutral to charge-stabilized colloidal spheres.

We present a detailed study of short-time dynamic properties in concentrated suspensions of charge-stabilized and of neutral colloidal spheres. The particles in many of these systems are subject to significant many-body hydrodynamic interactions. A recently developed accelerated Stokesian dynamics (ASD) simulation method is used to calculate hydrodynamic functions, wave-number-dependent collective diffusion coefficients, self-diffusion and sedimentation coefficients, and high-frequency limiting viscosities. The dynamic properties are discussed in dependence on the particle concentration and salt content. Our ASD simulation results are compared with existing theoretical predictions, notably those of the renormalized density fluctuation expansion method of Beenakker and Mazur [Physica A 126, 349 (1984)], and earlier simulation data on hard spheres. The range of applicability and the accuracy of various theoretical expressions for short-time properties are explored through comparison with the simulation data. We analyze, in particular, the validity of generalized Stokes-Einstein relations relating short-time diffusion properties to the high-frequency limiting viscosity, and we point to the distinctly different behavior of de-ionized charge-stabilized systems in comparison to hard spheres.

Many-body hydrodynamic interactions in charge-stabilized suspensions.

In this joint experimental-theoretical work we study hydrodynamic interaction effects in dense suspensions of charged colloidal spheres. Using x-ray photon correlation spectroscopy we have determined the hydrodynamic function H(q), for a varying range of electrosteric repulsion. We show that H(q) can be quantitatively described by means of a novel Stokesian dynamics simulation method for charged Brownian spheres, and by a modification of a many-body theory developed originally by Beenakker and Mazur. Very importantly, we can explain the behavior of H(q) for strongly correlated particles without resorting to the controversial concept of hydrodynamic screening, as was attempted in earlier work by Riese [Phys. Rev. Lett. 85, 5460 (2000)].