Dielectric spectroscopy on aqueous solutions of some zwitterionic amino acids

The complex (electric) permittivity of aqueous solutions of dipolar solutes has been measured as a function of frequency between 1 MHz and 40 GHz. Solutes are the isomers DL-2-aminobutyric acid, DL-3-aminobutyric acid, and 4-aminobutyric acid, and also 6-aminohexanoic acid. The measured dielectric spectra show two dispersion/dielectric loss regions, one due to the orientational diffusion of the solute molecules the other one due to the dielectric relaxation of the solvent water. A relaxation spectral function based on a model of the solutions has been fitted to the measured frequency dependence of the complex permittivity. The values for the electric dipole moment and reorientation time of the zwitterionic part of the solute particles derived by this analysis from the measurements fairly agree with theoretical predictions. Quite remarkably, the dipole moment in solution of 4-aminobutyric acid and 6-aminohexanoic acid up to remarkably high solute concentrations is nearly constant. A noteworthy result for the hydration water of the amino acids is, that its relaxation time is almost independent of the solute dipole moment.     

Magnetic particles with shifted dipoles

We present simulations and analytical calculations for a system of magnetic nano-particles that possess a dipole moment that is shifted out of the center of mass, towards the surface, leading to a further asymmetry of the dipolar interaction. In our contribution, we discuss the peculiarities of ground state small clusters, both, with and without an external magnetic field. Small clusters help us to get an insight into the inter-particle interactions and form a building block for studies of larger systems. Without external magnetic field, the ground state structure changes from chains and rings with parallel alignment of moments, usually observed in dipolar particles (Prokopieva et al., 2009 [1]), to pairs and triangles with close to anti-parallel orientation of moments, when the shift of the dipole is increased. We also present magnetization properties of larger systems at finite temperature and observe the influence of the shift in particular on the initial slope of the magnetization curve, namely, the initial susceptibility.     

Structure and dielectric properties of polar fluids with extended dipoles: results from numerical simulations

The strengths and shortcomings of the point dipole model for polar fluids of spherical molecules are illustrated by considering the physically more relevant case of extended dipoles formed by two opposite charges ±?q separated by a distance d (dipole moment μ=qd). Extensive molecular dynamics simulations on a high-density dipolar fluid are used to analyse the dependence of the pair structure, dielectric constant ε and dynamics as a function of the ratio d/σ (σ is the molecular diameter), for a fixed dipole moment μ. The point dipole model is found to agree well with the extended dipole model up to d/σ ? 0.3. Beyond that ratio, ε shows a non-trivial variation with d/σ. When d/σ > 0.6, a transition is observed towards a hexagonal columnar phase; the corresponding value of the dipole moment is found to be substantially lower than the value of the point dipole required to drive a similar transition.     

Transport in two dimensional electronic micro-emulsions

In two dimensional electron systems with Coulomb or dipolar interactions, a direct transition, whether first or second order, from a liquid to a crystalline state is forbidden. As a result, between these phases there must be other (micro-emulsion) phases which can be viewed as a meso-scale mixture of the liquid and crystalline phases. We investigate the transport properties of these new electronic phases and present arguments that they are responsible for the various transport anomalies that have been seen in experiments on the strongly correlated 2DEG in high mobility semiconductor devices with low electron densities.     

Molecular dynamics calculation of the dielectric constant without periodic boundary conditions. I

We outline the difficulties in obtaining a reliable value of the dielectric constant of a fluid using molecular dynamics calculations with periodic boundary conditions, and give some explanation of the observed asymptotic behaviour of h_D (r) and hΔ(r) in Monte Carlo simulations of dipolar hard spheres. An alternative method consisting in simulating a dielectric in vacuum is described. This is applied to two dimensional systems. The pertinent theoretical relations for a dielectric disc in vacuum are therefore derived. It is concluded that relations involving MC or MD computation of <m ²> must be carefully handled.     

The dipole moment distribution on water is improved by using large flexibility and large bending angle

A highly flexible model of water with fixed charges is used to study properties of water. The bending angle of an isolated molecule is 125^○ that was chosen to match the experimental dipole moment. The geometry of water in the liquid phase is made closer to that of the rigid SPC/E model by decreasing the bending angle spring constant, k _Θ. The new model, called SPCE-FHΘ, is a modified version of the recently proposed SPCE-FH [J. Alejandre, G.A. Chapela, F. Bresme and J.-P. Hansen, J. Chem. Phys. 130, 174505 (2009)] to simulate ionic solutions which includes short ranged interactions on the hydrogen atoms. By increasing angle flexibility it is possible to obtain, in the liquid phase at ambient conditions, bending angles ?Θ(HOH)? ～ 109^○, dipole moment ?μ? ～ 2.5 D and dielectric constant ?ε? ～ 80. The dipole moment distribution at room temperature goes from 1.5 to 3.5 D due to large fluctuations in bending angle and has the same trend found in ab initio simulations of liquid water. The dipole moment profile at the interface of water varies from 1.9 D in the vapour phase to 2.5 D in the liquid region at 400 K. The SPCE-FHΘ gives dipole moment, dielectric constant, coexisting densities and surface tension along the liquid–vapour coexistence line closer to the experimental values than those obtained for the SPC/E force field.     

On the calculation of dielectric properties from computer simulations

We report a reaction field calculation for Stockmayer particles at reduced density $\text{?}{}^1\text{= 0.8}$, reduced temperature $\text{T}{}^1\text{= 1.35}$ and reduced dipole moment $\text{μ}{}^1\text{= 1.64}$ using a relatively large cutoff distance for the dipolar interaction. The dipole-dipole correlation function is compared with corresponding simulations using truly periodic boundary conditions. The mean square fluctuation of the total dipole moment are shown to exhibit a long period oscillation, precluding a determination of the dielectric constant with an accuracy better than 15%, in a Monte-Carlo calculation of the order of 5 × 10⁶ configurations.     

A systematic Monte Carlo simulation and renormalized perturbation theoretical study of the dielectric constant of the polarizable Stockmayer fluid

A systematic Monte Carlo (MC) simulation and perturbation theory (PT) study is reported for the dielectric constant of the polarizable Stockmayer fluid. Our MC simulations apply the ‘pair approximation for polarization interaction’ procedure suggested by P?edota et al. The theoretical approach is based on our newly introduced equation (Valiskó et al., 2002, Molec. Phys., 100, 559) which is a density expansion for the dielectric constant using Wertheim's renormalized PT method. The agreement between our MC and PT results is excellent for low to moderate dipole moments and polarizabilities. At stronger dipolar interactions ergodicity problems and anisotropic behaviour appear where simulation results become uncertain and the theoretical approach becomes invalid.     

Metal-insulator transition in two- and three-dimensional logarithmic plasmas

We consider the scaling of the mean square dipole moment in a plasma with logarithmic interactions in a two- and three-dimensional systems. In both cases, we establish the existence of a low-temperature regime where the mean square dipole moment does not scale with system size and a high-temperature regime where it does scale with system size. Thus, there is a nonanalytic change in the polarizability of the system as a function of temperature and hence a metal-insulator transition in both cases. The relevance of this transition in three dimensions to quantum phase transitions in (2+1)-dimensional systems is briefly discussed.     

Static dielectric properties of Stockmayer fluids

Dielectric constants for the Stockmayer fluid are computed both from the equilibrium fluctuations of the polarization and from the polarization response to an applied field in a molecular dynamics simulation with periodic boundary conditions and with the dipole interactions treated by the Ewald method. The dielectric constant at finite wavelength is obtained from a Kirkwood-like expression, while for uniform polarization fluctuations a different expression applies due to the absence of surface effects in the Ewald calculation. The results are nearly independent of the number (up to 500) of particles investigated, even at large values of the dipole moment. The dielectric constants obtained from the approximate solution of the hypernetted chain integral equation are considerably larger than the molecular dynamics results except at low dielectric constants. The external field simulation permits study of the non-linear dependence of the dielectric constant on the magnitude of the applied electric field.     

Theory of polar fluids. I

We examine a classical fluid composed of molecules which contain a polarizable electric dipole with finite permanent moment. The long-ranged dipolar and the short-ranged interactions are treated on a different footing by expanding relative to a reference system characterized by the absence of electrostatic interactions. Extensions of graph theoretical techniques developed in an earlier paper are used to analyse the pair distribution function and the dielectric constant. Reduction of the number of graphs and their complexity is effected by introducing renormalizations of the permanent moment and the polarizability. The analysis leads to the definition of a new function w(12), which is free of terms dependent on the shape of the sample. For polar, polarizable molecules the direct correlation function lacks translational invariance; its role as a basic quantity is ceded to w(12). The pair distribution function and the dielectric constant ε are expressed in terms of w(12) and two closely related functions. Attention is drawn to an unsolved problem in dielectric theory, and an alternative formula for ε is presented in the form of a conjecture. An approximation for ε is formulated for the case in which the short-ranged non-dipolar interactions are independent of the molecular orientations. A simplified version is solved analytically.     

Zur theorie polarer multikomponentsysteme

A fluid mixture consisting of molecules with permanent electric dipole moment and scalar polarizability is described by means of correlation functions. To analyse the two-particle correlation functions we extend the graph-theoretical conception developed by Wertheim in the case of multicomponent systems by using graphs with colored points. In order to carry out a topological reduction of these sets of colored graphs the corresponding functions are found to be matrices or tensors. By the aid of a new connecting formalism the tensor notation preserves the structure of the equations in the analysis of correlation functions. These functions can be separated with respect to the range of interactions involved. Then, in applying the results to the case of a polar multicomponent mixture we can derive equations for the dielectric constant of systems consisting of both rigid and polarizable dipoles. These equations involve a correlation factor matrix which is the multicomponent equivalence of the Kirkwood factor. The dielectric expressions are used to obtain dipolar contributions to the Helmholtz free energy of mixing.     

Fluids of polarizable hard spheres with dipoles and tetrahedral quadrupoles Integral equation results with application to liquid water

The mean spherical, linearized hypernetted chain and quadratic hypernetted chain approximations are solved for a fluid of hard spheres with embedded point dipoles and tetrahedral quadrupoles and this system is shown to be quite similar to the dipole-linear quadrupole case previously studied. However, tetrahedral quadrupoles have a larger influence upon the structural and thermodynamic properties and are slightly more effective in decreasing the dielectric constant from the purely dipolar value. Also we describe a simple self-consistent mean field theory which allows molecular polarizability to be taken into account. This approximation together with the integral equation methods is applied to a polarizable dipole-tetrahedral quadrupole fluid with water-like parameters. The dielectric constant of this system is found to be in good agreement with the experimental results for liquid water for temperatures ranging from 25°C to 300°C. The influence of molecular polarizability is shown to be very large. At 25°C the mean dipole moment is ～2·56 D compared with ～1·85 D in the gas phase and the dielectric constant increases from ～25 for non-polarizable particles to ～80 for the polarizable model.     

The dielectric constant of polarizable fluids from the renormalized perturbation theory

A perturbation theoretical equation for the dielectric constant of polarizable dipolar fluids is proposed. For the fluctuation of the dipole moment, namely for the Kirkwood g-factor, a formula is given on the basis of Wertheim's renormalized perturbation theory. Using this formula, a series expansion for ?(p) is suggested on the basis of the Kirkwood equation, which gives an implicit function for ? as a function of ¶. The same series expansion can be derived from the Clausius-Mosotti equation—thus it proves to be independent of the boundary conditions. The resulting equation gives excellent results for the dielectric constant of the polarizable Stockmayer fluid producing good agreement with computer simulation data. The series expansion gives better results than the Kirkwood equation itself.     

A model phospholipid monolayer: a computer simulation study

A phospholipid monolayer is modelled by quasi two-dimensional hard dipoles. The dipole interactions are three-dimensional and the two continuous phases are characterized by their dielectric constants. A tendency of dipolar chain formation is observed for low temperatures and for equal dielectric constants. This tendency disappears when the two regions are slightly different.     

Dipolar response and hydrogen-bond kinetics in liquid water in square-wave time-varying electric fields

Non-equilibrium molecular dynamics simulations of liquid water have been performed at 298 K in the presence of external time-varying electric fields, approximating a square wave, of varying peak intensity (0.005–0.1 V/Å) in the microwave to far-infrared frequency range (20–500 GHz). Significant non-thermal field effects were noted in terms of dipolar response and acceleration of hydrogen-bond kinetics. The coupling between the total dipole moment and the external field has been investigated and autocorrelation functions (ACFs) of both the total dipole moment and the average of the individual molecular dipole moment along the laboratory axis of the applied fields exhibited coupling, with the former showing a stronger coupling and the latter showing coupling to lower magnitude fields. The maximum alignment achieved has been computed as a function of field intensities and frequencies: the lower frequencies show a greater maximum alignment as the system had more time within each field cycle to respond. The normalised probability distribution and the hydrogen-bond ACFs have been computed: the ACF showed a clear effect over shortening the hydrogen-bond relaxation time. The field effects over the molecules’ transitions from four to five hydrogen bonds have been computed. There was an enhancement of fewer molecules undergoing transitions and a dampening for a larger proportion of molecules, depending on the external fields’ periods.     

Small divisors with spatial structure in infinite dimensional Hamiltonian systems

A general perturbation theory of the Kolmogorov-Arnold-Moser type is described concerning the existence of infinite dimensional invariant tori in nearly integrable hamiltonian systems. The key idea is to consider hamiltonians with aspatial structure and to express all quantitative aspects of the theory in terms of rather general weight functions on such structures. This approach combines great flexibility with an effective control of the vrious interactions in infinite dimensional systems.Supported by Sonderforschungsbereich 256 at the University of Bonn     

Effect of Fabry‐Perot resonances in disordered one‐dimensional array of alternating dielectric bi‐layers

We study numerically and analytically the role of Fabry‐Perot resonances in the transmission through a one‐dimensional finite array formed by two alternating dielectric slabs. The disorder consists in varying randomly the width of one type of layers while keeping constant the width of the other type. Our numerical simulations show that localization is strongly inhibited in a wide neighborhood of the Fabry‐Perot resonances. Comparison of our numerical results with an analytical expression for the average transmission, derived for weak disorder and finite number of cells, reveals that such expression works well even for medium disorder up to a certain frequency. Our results are valid for photonic and phononic one‐dimensional disordered crystals, as well as for semiconductor superlattices.     

Finite size effect of ions and dipoles close to charged interfaces

The modified dipolar Poisson-Boltzmann(MDPB) equation,where the electrostatics of the dipolar interactions of solvent molecules and also the finite size effects of ions and dipolar solvent molecules are explicitly taken into account on a mean-field level,is studied numerically for a two-plate system with oppositely charged surfaces.The MDPB equation is solved numerically,using the nonlinear Multigrid method,for one-dimensional finite volume meshes.For a high enough surface charge density,numerical results of the MDPB equation reveal that the effective dielectric constant decreases with the increase of the surface charge density.Furthermore,increasing the salt concentration leads to the decrease of the effective dielectric constant close to the charged surfaces.This decrease of the effective dielectric constant with the surface charge density is opposite to the trend from the dipolar Poisson-Boltzmann(DPB) equation.This seemingly inconsistent result is due to the fact that the mean-field approach breaks down in such highly charged systems where the counterions and dipoles are strongly attracted to the charged surfaces and form a quasi two-dimensional layer.In the weak-coupling regime with the electrostatic coupling parameter(the ratio of Bjerrum length to Gouy-Chapman length) Ξ 1,where the MDPB equation works,the effective dielectric constant is independent of the distance from the charged surfaces and there is no accumulation of dipoles near the charged surfaces.Therefore,there are no physical and computational advantages for the MDPB equation over the modified Poisson-Boltzmann(MPB) equation where the effect of dipolar interactions of solvent dipoles is implicitly taken into account in the renormalised dielectric constant.