Theory of solvation in polar nematics

We develop a linear response theory of solvation of ionic and dipolar solutes in anisotropic, axially symmetric polar solvents. The theory is applied to solvation in polar nematic liquid crystals. The formal theory constructs the solvation response function from projections of the solvent dipolar susceptibility on rotational invariants. These projections are obtained from Monte Carlo simulations of a fluid of dipolar spherocylinders which can exist both in the isotropic and nematic phases. Based on the properties of the solvent susceptibility from simulations and the formal solution, we have obtained a formula for the solvation free energy which incorporates the experimentally available properties of nematics and the length of correlation between the dipoles in the liquid crystal. The theory provides a quantitative framework for analyzing the steady-state and time-resolved optical spectra and makes several experimentally testable predictions. The equilibrium free energy of solvation, anisotropic in the nematic phase, is given by a quadratic function of cosine of the angle between the solute dipole and the solvent nematic director. The sign of solvation anisotropy is determined by the sign of dielectric anisotropy of the solvent: solvation anisotropy is negative in solvents with positive dielectric anisotropy and vice versa. The solvation free energy is discontinuous at the point of isotropic-nematic phase transition. The amplitude of this discontinuity is strongly affected by the size of the solute becoming less pronounced for larger solutes. The discontinuity itself and the magnitude of the splitting of the solvation free energy in the nematic phase are mostly affected by microscopic dipolar correlations in the nematic solvent. Illustrative calculations are presented for the equilibrium Stokes shift and the Stokes shift time correlation function of coumarin-153 in 4-n-pentyl-4'-cyanobiphenyl and 4,4-n-heptyl-cyanopiphenyl solvents as a function of temperature in both the nematic and isotropic phases.     

Solvation and ion-pairing properties of the aqueous sulfate anion: explicit versus effective electronic polarization

We assessed the relative merits of two approaches for including polarization effects in classical force fields for the sulfate anion. One of the approaches is the explicit shell model for atomic polarization and the other is an implicit dielectric continuum representation of the electronic polarization, wherein the polarizability density is spatially uniform. Both the solvation and ion association properties of sulfate were considered. We carried out an ab initio molecular dynamics simulation for a single sulfate anion in aqueous solution to obtain a benchmark for the solvation structure. For the ion-pairing properties, the models were compared to experimental thermodynamic data through Kirkwood-Buff theory, which relates the integrals of the pair correlation functions to measurable properties. While deficiencies were found for both of the approaches, the continuum polarization model was not systematically worse than the shell model. The shell model was found to give a more structured solution than the continuum polarization model, both with respect to solvation and ion pairing.     

On the microscopic theory of polar solvation dynamics

A microscopic model of the time-resolved Stokes shift is developed. The model calculates the solvation dynamics by combining the atomic resolution of the solute structure with dipolar dynamics from the polarization structure factors of the homogeneous solvent. Calculations are made for coumarin 153 and quinoxaline optical dyes with atomic geometries and charge distributions taken from quantum calculations. Stokes shift dynamics is calculated and compared to experiment in high-temperature acetonitrile and methanol and in low-temperature 2-methyl-tetrahydrofurane using dielectric relaxation data from experiment.     

Dielectric polarization and non-linear dielectric effects in pivalonitrile solutions

Dielectric polarization and non-linear dielectric studies of solutions of pivalonitrile (CH₃)₃CN in carbon tetrachloride, cylohexane and n-hexane are presented. The contributions of Langevin orientation, dipolar coupling and pretransitional fluctuations have been separated from the observed dielectric non-linear effect.     

Dipolar response of hydrated proteins

The paper presents an analytical theory and numerical simulations of the dipolar response of hydrated proteins in solution. We calculate the effective dielectric constant representing the average dipole moment induced at the protein by a uniform external field. The dielectric constant shows a remarkable variation among the proteins, changing from 0.5 for ubiquitin to 640 for cytochrome c. The former value implies a negative dipolar susceptibility, that is a dia-electric dipolar response and negative dielectrophoresis. It means that ubiquitin, carrying an average dipole of ?240 D, is expected to repel from the region of a stronger electric field. This outcome is the result of a negative cross-correlation between the protein and water dipoles, compensating for the positive variance of the intrinsic protein dipole in the overall dipolar susceptibility. In contrast to the neutral ubiquitin, charged proteins studied here show para-electric dipolar response and positive dielectrophoresis. The study suggests that the dipolar response of proteins in solution is strongly affected by the coupling of the protein surface charge to the hydration water. The protein-water dipolar cross-correlations are long-ranged, extending ~2 nm from the protein surface into the bulk. A similar correlation length of about 1 nm is seen for the electrostatic potential produced by the hydration water inside the protein. The analysis of numerical simulations suggests that the polarization of the protein-water interface is highly heterogeneous and does not follow the standard dielectric results for cavities carved in dielectrics. The polarization of the water shell gains in importance, relative to the intrinsic protein dipole, at high frequencies, above the protein Debye peak. The induced interfacial dipole can be either parallel or antiparallel to the protein dipole, depending on the distribution of the protein surface charge. As a result, the high-frequency absorption of the protein solution can be either higher or lower than the absorption of water. Both scenarios have been experimentally observed in the THz window of radiation.     

Solvent response and dielectric relaxation in supercooled butyronitrile

We have measured the dynamics of solvation of a triplet state probe, quinoxaline, in the glass-forming dipolar liquid butyronitrile near its glass transition temperature T(g)=95 K. The Stokes shift correlation function displays a relaxation time dispersion of considerable magnitude and the optical linewidth changes along the solvation coordinate in a nonmonotonic fashion. These features are characteristic of solvation in viscous solvents and clearly indicate heterogeneous dynamics, i.e., spatially distinct solvent response times. Using the dielectric relaxation data of viscous butyronitrile as input, a microscopic model of dipolar solvation captures the relaxation time, the relaxation dispersion, and the amplitude of the dynamical Stokes shift remarkably well.     

Dipoles-dipole association of mesogenic molecules in solution

The dielectric polarization has been used to study dipolar association of 4-n-pentyl-4'-cyanobiphenyl in benzene solution. The results have been interpreted with the assumption of a monomer-dimer equilibrium. To explain the relatively high effective dipole moment of the dimers, a new structure has been proposed for them.     

Dipolar solvation dynamics in room temperature ionic liquids: an effective medium calculation using dielectric relaxation data

Solvation dynamics in four imidazolium cation based room temperature ionic liquids (RTIL) have been calculated by using the recently measured dielectric relaxation data [ J. Phys. Chem. B 2008, 112, 4854 ] as an input in a molecular hydrodynamic theory developed earlier for studying solvation energy relaxation in polar solvents. Coumarin 153 (C153), 4-aminophthalimide (4-AP), and trans-4-dimethylamino-4'-cyanostilbene (DCS) have been used as probe molecules for this purpose. The medium response to a laser-excited probe molecule in an ionic liquid is approximated by that in an effective dipolar medium. The calculated decays of the solvent response function for these RTILs have been found to be biphasic and the decay time constants agree well with the available experimental and computer simulation results. Also, no probe dependence has been found for the average solvation times in these ionic liquids. In addition, dipolar solvation dynamics have been predicted for two other RTILs for which experimental results are not available yet. These predictions should be tested against experiments and/or simulation studies.     

Glassy protein dynamics and gigantic solvent reorganization energy of plastocyanin

We report the results of molecular dynamics simulations of electron-transfer activation parameters of plastocyanin metalloprotein involved as an electron carrier in natural photosynthesis. We have discovered that slow, non-ergodic conformational fluctuations of the protein, coupled to hydrating water, result in a very broad distribution of donor-acceptor energy gaps far exceeding those observed for commonly studied inorganic and organic donor-acceptor complexes. The Stokes shift is not affected by these fluctuations and can be calculated from solvation models in terms of the linear response of the solvent dipolar polarization. The non-ergodic character of large-amplitude protein/water mobility breaks the strong link between the Stokes shift and the reorganization energy characteristic of equilibrium (ergodic) theories of electron transfer. This mechanism might be responsible for fast electronic transitions in natural electron-transfer proteins characterized by low reaction free energy.     

Redox entropy of plastocyanin: developing a microscopic view of mesoscopic polar solvation

We report applications of analytical formalisms and molecular dynamics (MD) simulations to the calculation of redox entropy of plastocyanin metalloprotein in aqueous solution. The goal of our analysis is to establish critical components of the theory required to describe polar solvation at the mesoscopic scale. The analytical techniques include a microscopic formalism based on structure factors of the solvent dipolar orientations and density and continuum dielectric theories. The microscopic theory employs the atomistic structure of the protein with force-field atomic charges and solvent structure factors obtained from separate MD simulations of the homogeneous solvent. The MD simulations provide linear response solvation free energies and reorganization energies of electron transfer in the temperature range of 280-310 K. We found that continuum models universally underestimate solvation entropies, and a more favorable agreement is reported between the microscopic calculations and MD simulations. The analysis of simulations also suggests that difficulties of extending standard formalisms to protein solvation are related to the inhomogeneous structure of the solvation shell at the protein-water interface combining islands of highly structured water around ionized residues along with partial dewetting of hydrophobic patches. Quantitative theories of electrostatic protein hydration need to incorporate realistic density profile of water at the protein-water interface.     

Ions in a binary asymmetric dipolar mixture: mole fraction dependent Born energy of solvation and partial solvent polarization structure

Mean spherical approximation (MSA) for electrolyte solution has been extended to investigate the role of partial solvent polarization densities around an ion in a completely asymmetric binary dipolar mixture. The differences in solvent diameters, dipole moments, and ionic size are incorporated systematically within the MSA framework in the present theory for the first time. In addition to the contributions due to difference in dipole moments, the solvent-solvent and ion-solvent size ratios are found to significantly affect the nonideality in binary dipolar mixtures. Subsequently, the theory is used to investigate the role of ion-solvent and solvent-solvent size ratios in determining the nonideality in Born free energy of solvation of a unipositive rigid ion in alcohol-water and dimethyl sulfoxide-acetonitrile mixtures, where the solvent components are represented only by their molecular diameters and dipole moments. Nonideality in Born free energy of solvation in such simplified mixtures is found to be stronger for smaller ions. The slope of the nonideality for smaller alkali metal ions in methanol-water mixture is found to be opposite to that for larger ion, such as quaternary tertiary butyl ammonium ion. For ethanol-water mixtures, the slopes are in the same direction for all the ions studied here. These results are in qualitative agreement with experiments, which is surprising as the present MSA approach does not include the hydrogen bonding and hydrophobic interactions present in the real mixtures. The calculated partial polarization densities around a unipositive ion also show the characteristic deviation from ideality and reveal the microscopic origin of the ion and solvent size dependent preferential solvation. Also, the excess free energy of mixing (in the absence of any ion) for these binary mixtures has been calculated and a good agreement between theory and experiment has been found.     

Structural Anisotropy in Polar Fluids Subjected to Periodic Boundary Conditions

A heuristic model based on dielectric continuum theory for the long-range solvation free energy of a dipolar system possessing periodic boundary conditions (PBCs) is presented. The predictions of the model are compared to simulation results for Stockmayer fluids simulated using three different cell geometries. The boundary effects induced by the PBCs are shown to lead to anisotropies in the apparent dielectric constant and the long-range solvation free energy of as much as 50%. However, the sum of all of the anisotropic energy contributions yields a value that is very close to the isotropic one derived from dielectric continuum theory, leading to a total system energy close to the dielectric value. It is finally shown that the leading-order contribution to the energetic and structural anisotropy is significantly smaller in the noncubic simulation cell geometries compared to when using a cubic simulation cell.     

New formulation and implementation for volume polarization in dielectric continuum theory

In the use of dielectric continuum theory to model bulk solvation effects on the electronic structure and properties of a solute, volume polarization contributions due to quantum mechanical penetration of the solute charge density outside the cavity nominally enclosing it are known to be significant. This work provides a new formulation and implementation of methods for solution of the requisite Poisson equation. In previous formulations the determination of the surface polarization contribution required evaluation of the difficult to calculate electric field generated by the volume polarization. It is shown that this problematic quantity can be eliminated in favor of other more easily evaluated quantities. That formal advance also opens the way for a more efficient apparatus to be implemented for calculation of the direct contribution of volume polarization to the solvation energy. The new formulation and its practical implementation are described, and illustrative numerical results are given for several neutral and ionic solutes to study the convergence and precision in practice.     

Free energy landscape analysis of two-dimensional dipolar solvent model at temperatures below and above the rotational freezing point

Ionic solvation in a polar solvent is modeled by a central charge surrounded by dipolar molecules posted on two-dimensional distorted lattice sites with simple rotational dynamics. Density of states is calculated by applying the Wang-Landau algorithm to both the energy and polarization states. The free energy landscapes of solvent molecules as a function of polarization are depicted to explore the competition between the thermal fluctuation and solvation energy. Without a central charge, for temperatures higher than the energy scale of the dipole-dipole interactions, the energy landscape for the small polarization region exhibits a parabolic shape as predicted by Marcus [Rev. Mod. Phys. 65, 599 (1993)] for electron transfer reaction, while there is an additional quartic contribution to the landscape for the large polarization region. When the temperature drops, the simulated free energy landscapes are no longer smooth due to the presence of multiple local minima arising from the frustrated interaction among the dipoles. The parabolic contribution becomes negligible and the energy landscape becomes quartic in shape. For a strong central charge, the energy landscape exhibits an asymmetric profile due to the contributions of linear and cubic terms that arise from the charge-dipole interactions.     

Solvation effects in near-critical binary mixtures

A Ginzburg-Landau theory is presented to investigate solvation effects in near-critical polar fluid binary mixtures. Concentration dependence of the dielectric constant gives rise to a shell region around a charged particle within which solvation occurs preferentially. As the critical point is approached, the concentration has a long-range Ornstein-Zernike tail representing strong critical electrostriction. If salt is added, strong coupling arises among the critical fluctuations and the ions. The structure factors of the critical fluctuations and the charge density are calculated and the phase transition behavior is discussed.     

Density functional theory of solvation and its relation to implicit solvent models

We describe a density functional theory approach to solvation in molecular solvents. The solvation free energy of a complex solute can be obtained by direct minimization of a density functional, instead of the thermodynamic integration scheme necessary when using atomistic simulations. In the homogeneous reference fluid approximation, the expression of the free-energy functional relies on the knowledge of the direct correlation function of the pure solvent. After discussing general molecular solvents, we present a generic density functional describing a dipolar solvent and we show how it can be reduced to the conventional implicit solvent models when the solvent microscopic structure is neglected. With respect to those models, the functional includes additional effects such as the microscopic structure of the solvent, the dipolar saturation effect, and the nonlocal character of the dielectric constant. We also show how this functional can be minimized numerically on a three-dimensional grid around a solute of complex shape to provide, in a single shot, both the average solvent structure and the absolute solvation free energy.     

Rotational dynamics and conformational kinetics in liquid crystals

Two particular aspects of solute dynamics in ordered media are analysed on the basis of the solution of multivariate diffusion equations: the effects of the solvation dynamics on the rotational motions of dipolar probes in liquid crystal solvents, and the alteration of reaction pathways in isomerization kinetics caused by the solvent order. The introduction of a suitable solvent coordinate allows the interpretation of high frequency contributions in the rotational correlation functions observed by spectroscopic techniques, namely dielectric dispersion, IR and Raman spectroscopy, ESR lineshapes and optical Kerr effect. For molecular systems undergoing conformational changes, a method is offered to evaluate the modification of the torsional barriers resulting from the anisotropic torques modulated by the molecular shape changes along the reaction coordinate.     

Dielectric relaxation processes in PVDF composite

The present study aims at the detailed elaboration of the dielectric relaxation behavior in PVDF composites using broadband dielectric spectroscopy and the Havriliak – Negami method. The composites with multi-wall nanotube carbon and zirconium dioxide in PVDF is fabricated using a simple melt mixing method. The polarization behavior in PVDF composites are investigated on the different frequency region with various temperature. The complex dielectric constants are calculated with the aid of the Havriliak – Negami equation. The characteristic parameters in Havriliak – Negami equation were in excellent agreement with the experimental complex dielectric constants. The results of utilizing these calculated parameters to analyze the origination of the polarization relaxation are given. The purposes of this work expect to give a deeper insight into the impact of different fillers on the dielectric relaxation behavior, and it could provide the technique for the discrepancy with the dipolar for interfacial polarization and the filler effect on the dielectric relaxation.     

Incorporating the excluded solvent volume and surface charges for computing solvation free energy

Gauss's law or Poisson's equation is conventionally used to calculate solvation free energy. However, the near‐solute dielectric polarization from Gauss's law or Poisson's equation differs from that obtained from molecular dynamics (MD) simulations. To mimic the near‐solute dielectric polarization from MD simulations, the first‐shell water was treated as two layers of surface charges, the densities of which are proportional to the electric field at the solvent molecule that is modeled as a hard sphere. The intermediate water was treated as a bulk solvent. An equation describing the solvation free energy of ions using this solvent scheme was derived using the TIP3P water model. © 2013 Wiley Periodicals, Inc.     

Rotational dynamics and conformational kinetics in liquid crystals

Abstract

Two particular aspects of solute dynamics in ordered media are analysed on the basis of the solution of multivariate diffusion equations: the effects of the solvation dynamics on the rotational motions of dipolar probes in liquid crystal solvents, and the alteration of reaction pathways in isomerization kinetics caused by the solvent order. The introduction of a suitable solvent coordinate allows the interpretation of high frequency contributions in the rotational correlation functions observed by spectroscopic techniques, namely dielectric dispersion, IR and Raman spectroscopy, ESR lineshapes and optical Kerr effect. For molecular systems undergoing conformational changes, a method is offered to evaluate the modification of the torsional barriers resulting from the anisotropic torques modulated by the molecular shape changes along the reaction coordinate.