Application of perturbation theory to the calculation of the dielectric constant of a dipolar hard sphere fluid

Linear and Nonlinear Dielectric Response of Intrinsically Disordered Proteins

Linear and nonlinear dielectric responses of solutions of intrinsically disordered proteins (IDPs) were analyzed by combining molecular dynamics simulations with formal theories. A large increment of the linear dielectric function over that of the solvent is found and related to large dipole moments of IDPs. The nonlinear dielectric effect (NDE) of the IDP far exceeds that of the bulk electrolyte, offering a route to interrogate protein conformational and rotational statistics and dynamics. Conformational flexibility of the IDP makes the dipole moment statistics consistent with the gamma/log-normal distributions and contributes to the NDE through the dipole moment's non-Gaussian parameter. The intrinsic non-Gaussian parameter of the dipole moment combines with the protein osmotic compressibility in the nonlinear dielectric susceptibility when dipolar correlations are screened by the electrolyte. The NDE is dominated by dipolar correlations when electrolyte screening is reduced.

Molecular theory of the static dielectric constant of dipolar fluids

The link between the static dielectric constant and the microscopic intermolecular interactions is the Kirkwood g₁ factor, which depends on the orientational structure of the fluid. Over the years, there have been several attempts to provide an accurate description of the orientational structure of dipolar fluids using molecular theories. However, these approaches were either limited to mean-field approximations for the pair correlation function or, more recently, limited to adjusting the orientational dependence to simulation data. Here, we derive a theory for the dielectric constant of dipolar hard-sphere fluids using the augmented modified mean-field approximation. Qualitative agreement is achieved throughout all relevant thermodynamic states, as demonstrated by a comparison with simulation data from the literature. Excellent quantitative agreement can be obtained using a single empirical scaling factor, the physical origin of which is analyzed and accounted for. In order to predict the dielectric constant of the Stockmayer fluid (Lennard-Jones plus dipole potential), we use an adjusted version of the expression for the dipolar hard-sphere fluid. Comparing theoretical predictions with newly generated simulation data, we show that it is possible to obtain excellent agreement with simulation by performing the calculations at a corresponding state using the same scaling factor. Finally, we compare the theoretical orientational structure of the Stockmayer fluid with that obtained from simulations. The simulated structure is calculated following a post-processing methodology that we introduce by deriving an original expression that relates the proposed theory to the histogram of relative dipole angles.

Kinetic Yvon-Born-Green theory of the linear dielectric constant and complex permittivity of isotropic polar fluids

The theory of the linear static dielectric constant and linear complex permittivity of isotropic polar fluids is formulated starting from the coupled Langevin equations describing the rototranslational dynamics of long-range interacting molecules with thermal agitation and subjected to external forces and torques. To this aim, adequate reduced densities are introduced and equations governing their dynamics derived. In the equilibrium zero frequency limit, integral expressions for the Kirkwood correlation factor g_{K} are given, transparently showing that the popular method consisting in comparing g_{K} with 1 in order to deduce pair dipolar ordering has no serious theoretical grounding. In the dynamical situation, the complex permittivity spectrum of a simple liquid is shown to exhibit an infinite discrete set of relaxation times, some of which may have thermally activated behavior. The theory is also shown to contain all previous results derived in the area provided molecular inertial effects are ignored, so restricting the range of validity of the theory to frequencies much below the far-infrared region. Finally, the theory can be adapted without much effort to relaxation of interacting magnetic nanoparticles for which macroscopic magnetic anisotropy arising from the assembly of nanoparticles is neglected.

Perturbation approaches for describing dipolar fluids and electrolyte solutions

This work proposes perturbation approaches for describing dipolar fluids as well as model and aqueous electrolyte solutions. The electrostatic pair potentials are split into short- and long-ranged contributions, whereas a third order perturbation expansion is applied for the short-ranged potentials. This circumvents the problem of divergent correlation integrals. The dipolar perturbation terms are represented through a [2,1]-Padé approximation to resum the poorly convergent series. For the remaining charge-charge and charge-dipole contributions, we present a new approximant, which provides a (quasi)linear dependence of the Helmholtz energy. The underlying correlation integrals are adjusted to results from molecular simulations. The long-ranged contribution to the electrostatic interactions is treated through an analytic expression developed by Rodgers and Weeks [J. Chem. Phys. 131, 244108 (2010)]. Theoretical predictions of our perturbation theory are compared to results from a widely used integral equation theory, namely, the mean spherical approximation, and we find that our perturbation theory provides much more accurate results. Furthermore, the theory shows some quantities in rather good agreement with reference data, namely, Helmholtz energies, internal energies, and densities at higher densities of solutions. Limitations of the approach, however, are observed for several other partial molar quantities, such as the mean activity coefficient.

Free energy and entropy of a dipolar liquid by computer simulations

Thermodynamic properties for a system composed of dipolar molecules are computed. Free energy is evaluated by means of the thermodynamic integration technique, and it is also estimated by using a perturbation theory approach, in which every molecule is modeled as a hard sphere within a square well, with an electric dipole at its center. The hard sphere diameter, the range and depth of the well, and the dipole moment have been calculated from properties easily obtained in molecular dynamics simulations. Connection between entropy and dynamical properties is explored in the liquid and supercooled states by using instantaneous normal mode calculations. A model is proposed in order to analyze translation and rotation contributions to entropy separately. Both contributions decrease upon cooling, and a logarithmic correlation between excess entropy associated with translation and the corresponding proportion of imaginary frequency modes is encountered. Rosenfeld scaling law between reduced diffusion and excess entropy is tested, and the origin of its failure at low temperatures is investigated.

Linear and nonlinear magnetic properties of ferrofluids

Within a high-magnetic-field approximation, employing Ruelle's algebraic perturbation theory, a field-dependent free-energy expression is proposed which allows one to determine the magnetic properties of ferrofluids modeled as dipolar hard-sphere systems. We compare the ensuing magnetization curves, following from this free energy, with those obtained by Ivanov and Kuznetsova [Phys. Rev. E 64, 041405 (2001)] as well as with new corresponding Monte Carlo simulation data. Based on the power-series expansion of the magnetization, a closed expression for the magnetization is also proposed, which is a high-density extension of the corresponding equation of Ivanov and Kuznetsova. From both magnetization equations the zero-field susceptibility expression due to Tani et al. [Mol. Phys. 48, 863 (1983)] can be obtained, which is in good agreement with our MC simulation results. From the closed expression for the magnetization the second-order nonlinear magnetic susceptibility is also derived, which shows fair agreement with the corresponding MC simulation data.

BEHAVIOR OF THE CONFINED HARD-SPHERE FLUID WITHIN NANOSLITS: A FUNDAMENTAL-MEASURE DENSITY-FUNCTIONAL THEORY STUDY

A property of central interest for theoretical study of nanoconfined fluids is the density distribution of molecules. The density profile of the hard-sphere fluids confined within nanoslit pores is a key quantity for understanding the configurational behavior of confined real molecules. In this report, we produce the density profile of the hard-sphere fluid confined within nanoslit pores using the fundamental-measure density-functional theory (FM-DFT). FM-DFT is a powerful approach to studying the structure and the phase behavior of nanoconfined fluids. We report the computational procedure and the calculated data for nanoslits with different widths and for a wide range of hard-sphere fluid densities. The high accuracy of the resulting density profiles and optimum grid-size values in numerical integration are verified. The data reveal a number of interesting features of hard spheres in nanoslits, which are different from the bulk hard-sphere systems. These data are also useful for a variety of purposes, including obtaining the shear stress, thermal conductivity, adsorption, solvation forces, free volume and prediction of phase transitions.

Dielectric constants of simple liquids: stockmayer and ellipsoidal fluids

Coarse-grained models of molecular interactions are of interest because they convey the essence of molecular interactions in simple and easy to understand form. However, coarse-grained models fail to adequately predict some material properties, such as the failure of the Stockmayer model to reproduce the dielectric behavior of highly polar liquids. We examine the behavior of the Stockmayer fluid over a range of dipole densities that covers known organic solvents, as well as that of an ellipsoidal Stockmayer-like fluid, using NVT rigid-body Monte Carlo simulations. Both fluids are examined under different electrostatic boundary conditions and ensemble sizes. While the Stockmayer model predicts that liquids of similar dipole density to acetonitrile would be ferroelectric and have a dielectric constant far higher than shown by experiment, the ellipsoidal model provides a better accounting of dielectric behavior. This result bodes well for the use of coarse-grained solvent models for large-scale simulations.

Exp6-polar thermodynamics of dense supercritical water

We introduce a simple polar fluid model for the thermodynamics of dense supercritical water based on a Buckingham (exp-6) core and point dipole representation of the water molecule. The proposed exp6-polar thermodynamics, which is based on ideas originally applied to dipolar hard spheres, performs very well when tested against molecular dynamics simulations. Comparisons of the model predictions with experimental data available for supercritical water yield excellent agreement for the shock Hugoniot, isotherms, and sound speeds, and are also quite good for the self-diffusion constant and relative dielectric constant.

The dielectric virial expansion and the models of dipolar hard-sphere fluid

The virial expansion technique to determine the dielectric constant epsilon of dipolar hard-sphere fluid is developed. It is shown that the formalism allows to bring into agreement the results of Debye's, Onsager's, and Langevin's to the problem. The third virial coefficient of epsilon is considered as a series over dipolar parameter lambda=m(2)d(3)kT. The terms up to O(lambda(11)) are calculated analytically providing a correct description of the third virial coefficient for small and intermediate values of lambda (0<or=lambda<or=4). The results of the dielectric virial series are compared with the Monte Carlo data for epsilon found by Matyushov and Ladanyi [J. Chem. Phys. 110, 994 (1999)]. The theory is in agreement with simulations only at small values of lambda<or=2. At higher polarities, the virial series diverges. Realization of the renormalization procedure permits to enlarge the range of applicability of the virial series. In this way, the new expression for the dielectric constant as a function of two dipolar parameters, lambda and y=4 pi nm(2)9kT, has been found explicitly. The expression gives a perfect upper bound of the dielectric constant and is more reliable for determination of epsilon than the previously known ones.

Magnetic properties in monolayers of a model polydisperse ferrofluid

The influence of polydispersity on the equilibrium properties of monolayers of three-dimensional dipolar spheres with short-range repulsive interactions is studied by means of Monte Carlo simulations and a high field approximation perturbation theory. The particle distribution in the simulations is realized in the semigrand ensemble by tuning appropriately the underlying particle distribution density. The magnetization curves are calculated as functions of density and temperature, and the obtained results are compared with the data determined in a monodisperse equivalent of the system. In-plane and out-of-plane initial magnetic susceptibilities are determined using external fields applied parallel or normal to the monolayer plane. Susceptibility data for the true two- and three-dimensional counterparts of the system are also calculated for comparison. Our findings for the magnetic properties can partly be explained by the structural characteristics obtained from the simulations.

The ferroelectric transition of dipolar hard spheres

We investigate by Monte Carlo simulation the size dependence of the variation of the polarization and the dielectric constant with temperature for dipolar hard spheres at the two densities rho sigma3=0.80 and 0.88. From the crossing of the fourth-order cumulant for different system sizes first more precise estimates of the ferroelectric transition temperatures are obtained. Theoretical approaches, when predicting an ordering transition, are shown to generally overestimate the critical temperature.

Relative Permittivity of Polar Liquids. Comparison of Theory, Experiment, and Simulation

A molecular-based second-order perturbation theory is applied to calculate the relative permittivity of polar liquids. Our basic model is the dipolar hard sphere fluid. The main purpose of this work is to propose various approaches to take into account the molecular polarizability. In the continuum approach, we apply the Kirkwood-Fröhlich equation and use the high-frequency relative permittivity. The Kirkwood g-factor representing molecular correlations is calculated by a perturbation theory. In the molecular approach, the molecular polarizability is built into the model on the molecular level (the polarizable dipolar hard sphere fluid). To calculate the relative permittivity of this system, an equation obtained from a renormalization procedure is used. In both approaches, we apply a series expansion for the relative permittivity and show that these series expansions give results in better agreement with simulation data than the original equations. After testing our theoretical equations against our own Monte Carlo simulation results, we compare the results obtained from our theoretical equations and simulations to experimental data for amines, ethers, and halogenated, sulfur, and hydroxy compounds. We propose a procedure to calculate potential parameters (hard sphere diameter, reduced polarizability, and reduced dipole moment) from experimental data such as the permanent dipole moment, refractive index, density, and temperature. We show that for compounds of low relative permittivity the polarizable dipolar hard sphere (PDHS) model and the continuum approach give reasonable results. For nonassociative liquids of higher relative permittivity, the PDHS model overestimates experimental data due to unsatisfactory representation of the shape of the molecules. In the case of associative liquids, the PDHS model works well, and in some cases it underestimates the experimental values due to the unsatisfactory treatment of electrostatic interactions.

Solvent reorganization energy of electron-transfer reactions in polar solvents

A microscopic theory of solvent reorganization energy in polar molecular solvents is developed. The theory represents the solvent response as a combination of the density and polarization fluctuations of the solvent given in terms of the density and polarization structure factors. A fully analytical formulation of the theory is provided for a solute of arbitrary shape with an arbitrary distribution of charge. A good agreement between the analytical procedure and the results of Monte Carlo simulations of model systems is achieved. The reorganization energy splits into the contributions from density fluctuations and polarization fluctuations. The polarization part is dominated by longitudinal polarization response. The density part is inversely proportional to temperature. The dependence of the solvent reorganization energy on the solvent dipole moment and refractive index is discussed.

Magnetic properties of dense ferrofluids: an influence of interparticle correlations

A statistical model has been developed describing the magnetostatic properties of dense ferrocolloids and the dielectric properties of polar fluids. The model is based on the relation between the magnetization and the pair correlation function of a spatially homogeneous system of dipole particles. This approach allows us to calculate the ferrofluid magnetization (polarization density of polar fluid) in a form of expansion over both the particle concentration and the potential of the interparticle dipole-dipole interaction U(d). The obtained expressions for the ferrocolloid initial magnetic susceptibility, the dielectric constant of polar fluid and the ferrofluid magnetization with the accuracy approximately U(2)(d) describe well the experimental data and the results of computer modeling. The model justifies the validity of the "modified mean-field approach," and the effective field is calculated as a function of the Langevin magnetization.

Comment on "Algebraic perturbation theory for polar fluids: A model for the dielectric constant"

Kalikmanov [Phys. Rev. E 59, 4085 (1999)] proposed a perturbation theory method to calculate the dielectric constant of dipolar hard sphere fluids using an infinitely long cylindrical container to avoid the depolarization. We demonstrate that while the method is very helpful, his theory appears to be incomplete because of the incorrect calculation of the corresponding three-body integrals. It is shown that with the correct consideration of these terms the theory is consistent with the results of earlier work in low-density limit, and at high densities the method yields the equation of Tani et al. [Mol. Phys. 48, 863 (1983)] for the dipolar hard sphere fluid dielectric constant.