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Register a new userGeneralizing The Mean Spherical Approximation as a Multiscale, Nonlinear Boundary Condition at the Solute--Solvent Interface
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In this paper we extend the familiar continuum electrostatic model with a perturbation to the usual macroscopic boundary condition. The perturbation is based on the mean spherical approximation (MSA), to derive a multiscale hydration-shell boundary condition (HSBC). We show that the HSBC/MSA model reproduces MSA predictions for Born ions in a variety of polar solvents, including both protic and aprotic solvents. Importantly, the HSBC/MSA model predicts not only solvation free energies accurately but also solvation entropies, which standard continuum electrostatic models fail to predict. The HSBC/MSA model depends only on the normal electric field at the dielectric boundary, similar to our recent development of an HSBC model for charge-sign hydration asymmetry, and the reformulation of the MSA as a boundary condition enables its straightforward application to complex molecules such as proteins.
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Electrostatic forces play many important roles in molecular biology, but are hard to model due to the complicated interactions between biomolecules and the surrounding solvent, a fluid composed of water and dissolved ions. Continuum model have been surprisingly successful for simple biological questions, but fail for important problems such as understanding the effects of protein mutations. In this paper we highlight the advantages of boundary-integral methods for these problems, and our use of boundary integrals to design and test more accurate theories. Examples include a multiscale model based on nonlocal continuum theory, and a nonlinear boundary condition that captures atomic-scale effects at biomolecular surfaces.
Understanding the behavior of biomolecules such as proteins requires understanding the critical influence of the surrounding fluid (solvent) environment--water with mobile salt ions such as sodium. Unfortunately, for many studies, fully atomistic simulations of biomolecules, surrounded by thousands of water molecules and ions are too computationally slow. Continuum solvent models based on macroscopic dielectric theory (e.g. the Poisson equation) are popular alternatives, but their simplicity fails to capture well-known phenomena of functional significance. For example, standard theories predict that electrostatic response is symmetric with respect to the sign of an atomic charge, even though response is in fact strongly asymmetric if the charge is near the biomolecule surface. In this work, we present an asymmetric continuum theory that captures the essential physical mechanism--the finite size of solvent atoms--using a nonlinear boundary condition (NLBC) at the dielectric interface between the biomolecule and solvent. Numerical calculations using boundary-integral methods demonstrate that the new NLBC model reproduces a wide range of results computed by more realistic, and expensive, all-atom molecular-dynamics (MD) simulations in explicit water. We discuss model extensions such as modeling dilute-electrolyte solvents with Debye-Huckel theory (the linearized Poisson-Boltzmann equation) and opportunities for the electromagnetics community to contribute to research in this important area of molecular nanoscience and engineering.
The process of rapid solidification of a binary mixture is considered in the framework of local nonequilibrium model (LNM) based on the assumption that there is no local equilibrium in solute diffusion in the bulk liquid and at the solid-liquid interface. According to LNM the transition to complete solute trapping and diffusionless solidification occurs at a finite interface velocity $V=V_D$, where $V_D$ is the diffusion speed in bulk liquid. In the present work, the boundary conditions at the phase interface moving with the velocity $V$ close to $V_D$ ($V lesssim V_D$) have been derived to find the non-equilibrium solute partition coefficient. In the high-speed region, its comparison with the partition coefficient from the work [Phys. Rev. E 76 (2007) 031606] is given.
Nonlinear elastic models are widely used to describe the elastic response of crystalline solids, for example, the well-known Cauchy-Born model. While the Cauchy-Born model only depends on the strain, effects of higher order strain gradients are significant and higher order continuum models are preferred, in various applications such as defect dynamics and modeling of carbon nanotubes. In this paper, we rigorously derive a higher order nonlinear elasticity model for crystals from its atomistic description in one dimension. We show that, compared to the second order accuracy of the Cauchy-Born model, the higher order continuum model in this paper is of fourth oder accuracy with respect to the interatomic spacing in the thermal dynamic limit. In addition, we discuss the key issues for the derivation of higher order continuum models in more general cases. The theoretical convergence results are demonstrated by numerical experiments.
A method for study of charge-transfer interactions between solute molecules and solvent based on the comparison of the ratios of spectral shifts of different electronic transitions in solute molecules in chemically inert solvent is proposed. The method is applicable to molecules that do not change their dipole moment on excitation. As an example, a presence of charge transfer interactions in higher electronic states of aromatic hydrocarbons (benzene, phenanthrene, and naphthalene) dissolved in water and alcohols was demonstrated.
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