Monte Carlo study of dipolar and quadrupolar hard prolate spherocylinders

Monte Carlo simulations of hard prolate spherocylinders (HPSs) with embedded dipole or quadrupole moment are reported for two elongations (L?=?0.5 and 1) and several values of the packing fraction. The MC values of the residual internal and Helmholtz energy and compressibility factor were determined. Our work represents the first simulation study of dipolar HPSs focused on the determination of the thermodynamic properties. In the case of quadrupolar HPSs, our results enlarge the range of state conditions for which the simulation data are available. The obtained MC data were used for a test of the perturbation theory of polar non-spherical molecule fluids. In order to evaluate the perturbation contributions containing the two-particle integrals, the values of the shape integrals (evaluated recently for dipolar and quadrupolar hard prolate spherocylinders) were employed and we were allowed to avoid the use of the similarity between Kihara and Gaussian overlap models. Fair agreement between the simulation data and the theoretical predictions was reached.     

Liquid–vapour equilibrium of multipolar square-well fluids.Gibbs ensemble simulations and equation of state

Simulation results for a system comprising a square well plus either a point dipole or a point quadrupole are presented. The properties obtained are the vapour–liquid equilibrium densities and the critical properties. Critical densities are not very sensitive to the values of dipole or quadrupole, while critical temperatures increase significantly when the multipole strength rises. A comparison with a perturbation theory for multipolar square-well systems is presented. Overall agreement between simulated and theoretical values is good when comparison is restricted to quadrupoles or dipoles corresponding to the most relevant real polar substances but is only moderate for the largest multipolar strengths considered.     

Thermodynamics of mixtures of non-spherical molecules

Thermodynamic properties of liquid mixtures in which strong anisotropic intermolecular forces exist are studied using the Padé approximant method used by Stell et al. for pure fluids. Equations for the third-order perturbation term are derived for a general intermolecular potential of multipolar type. Using a mixture of Lennard-Jones molecules as the reference system, the effects of adding point dipole, quadrupole and anisotropic overlap potentials are calculated. Numerical results are presented (at low pressures) for the effect of these forces on the excess functions, and on the vapor-liquid equilibrium curves. These anisotropic forces lead to positive deviations from Raoult's law. Strong polar and quadrupolar forces may cause liquid-liquid immiscibility to occur. Numerical calculations are presented to illustrate such behaviour; these systems have upper critical solution points.     

On the difference between a point multipole and an equivalent linear arrangement of point charges in force field models for vapour–liquid equilibria; partial charge based models for 59 real fluids

The replacement of a point dipole and a point quadrupole by a corresponding linear arrangement of two point charges (+q, ?q) and accordingly three point charges (+q, ?2q, +q) is studied with respect to vapour–liquid equilibria. The dependence of saturated liquid density, vapour pressure and heat of vaporization on the choice of the distance d between the charges in the point charge arrangement is analysed. For the studied dipolar two-centre Lennard-Jones (2CLJD) and quadrupolar two-centre Lennard-Jones (2CLJQ) models, d/σ between 1/15 and 1/20 is a reasonable compromise between numerical and physical accuracy, where σ is the Lennard-Jones size parameter. The results are used to derive validated partial charge based models of 59 real fluids from previously published point dipole and point quadrupole based models.     

The statistical mechanics of ion-dipole-tetrahedral quadrupole mixtures

We examine the solution of the Ornstein-Zernike equations for the correlation functions of a fluid mixture in which the molecular interactions consist of a hard sphere plus a multipolar potential that contains coulombic, dipolar as well as quadrupolar terms. In particular we consider the case in which the molecule has a dipole moment in the z direction of the molecular axis system and a non-linear tetrahedral quadrupole tensor of the form Θ _xx = - Θ _yy , Θ _zz = 0 = Θ_αβ, α ≠ β in the molecular frame. This model is a good representation of the dipolar and quadrupolar properties of water and our analysis will form the basis for constructing a Civilized Model electrolyte in which ions are dissolved in a solvent whose molecules possess water-like multipole moments. One of our main results is that for any theory which retains only the subset of rotational invariants that either appear in the interaction potentials or are generated by angular convolution from those appearing in the interaction potentials, e.g. the linearized hypernetted chain (LHNC) or mean spherical approximations (MSA), the equations for an ion-dipole-tetrahedral quadrupolar mixture only differ from those for an ion-dipole-linear quadrupole mixture (Θ _xx = Θ _yy = - 1/2Θ _zz , Θ_αβ = 0, α ≠ β) in minor details. We have investigated the thermodynamic properties of a fluid of hard spheres with the dipole and tetrahedral moments of water using thermodynamic perturbation theory. We find that contributions to the thermodynamic properties from dipole-quadrupole interaction are very important. For a pure hard sphere tetrahedral quadrupolar fluid there is considerable difference between the results from perturbation theory and from the MSA, for which we have obtained an analytic solution.     

Vapour pressure of non-polar fluids and their repulsive and attractive contributions

Using a simple equation of state, based on the Weeks-Chandler-Andersen separation of the intermolecular potential, we have obtained the contributions of repulsive and attractive intermolecular forces to the thermodynamic properties of coexisting vapour and liquid phases of a Lennard-Jones (LJ) fluid.

In order to obtain the vapour pressure of real non-polar fluids, we take the LJ fluid as a reference model, and propose a new perturbative contribution, which is dependant on the temperature and on the acentric factor of the substance. Using the complete perturbed equation, we determine the corresponding repulsive and attractive contributions to the vapour pressure of non-polar fluids. The results show that the attractive vapour pressure of non-polar fluids increases with increasing acentric factor, i.e., larger deviation of the molecular shape from spherical symmetry.

This procedure could be extended to separate the repulsive and attractive contributions of the intermolecular forces to other thermodynamic properties of non-polar fluids as well as of polar fluids and fluid mixtures.     

Dipolar Order in Molecular Fluids: II. Molecular Influence

The influence on the short-range packing in dipolar fluids by molecular shape and by additional higher order electrostatic moments has been investigated by molecular dynamic simulations. The dipole polarization was found to decrease as the particles were elongated parallel to the dipole and to increase for elongation perpendicular to the dipole, eventually forming a nematic order. The addition of a quadrupole lead to a reduction of the polarization, and the influence of an axial octupole was weaker and more complex. Both a decrease and an increase of the polarization is possible depending on the relative dipole–dipole and octupole–octupole interaction strengths and the relative direction of the symmetry axes of the moments. These observations were attributed to the different parity of a dipole and a quadrupole and the same parity of a dipole and an axial octupole under reflection. In addition, further insights into the formation of dipole polarization were obtained. Short polar and long equatorial radii and strong dipole–dipole interaction are particle properties that promote a fluid with a high dipole polarization.     

The use of a non-spherical reference potential in statistical mechanical perturbation theory

A statistical mechanical perturbation theory for the pair correlation function and thermodynamic properties of molecular fluids is presented in which the reference potential function is non-spherical. With this choice the short-range molecular repulsive forces can be properly taken into consideration and attractive forces, such as those resulting from electric moments, treated as the perturbation. Calculations are presented for the first-order perturbation term to the Helmholtz free energy due to quadrupolar forces in models of liquid nitrogen and chlorine, and due to dipolar forces in liquid hydrogen chloride. For these calculations the rigid diatomic model and its modification appropriate to heteronuclear molecules were used for the reference potentials. It is found that the lowest-order perturbation terms here are proportional to the second power of the dipole or quadrupole moments, and not the fourth power as had been found previously using a spherical reference potential function. This second-order dependence on the electric moment is especially important in the case of mixtures, where it leads to an explanation for the occurrence of negative azeotropes in binary mixtures of species with quadrupole moments of opposite sign.     

Electric field dependence of phase equilibria of binary Stockmayer fluid mixtures

A perturbation theory based study of the effect of an external electric field on the phase equilibrium properties of binary Stockmayer fluids is presented. The dipole–dipole interaction and the applied field are treated as independent perturbations to a Lennard–Jones mixture, and the reference fluid is treated by the van der Waals one-fluid approximation. A third-order free energy expression in the electric field strength is established, and the dielectric constant is calculated for a needle-shaped sample parallel to the field direction. We present and discuss vapour–liquid and liquid–liquid equilibrium curves at a given temperature for some dipolar mixtures exposed to an electric field, including chlorodifluoromethane +?difluoromethane and acetonitrile +?methanol. A sufficiently high electric field may result in massive shifts of vapour pressures and critical or azeotropic points, and can considerably alter the properties of coexisting phases. The vapour pressure decreases with increasing field strength.     

Light scattering from spherical plasmonic nanoantennas: effects of nanoscale roughness

We have investigated the light scattering properties of smooth and roughened nanoshells with dipolar and quadrupolar plasmon resonances tuned to 830 nm. In the dipole resonant case small but measurable variations in the angle dependent light scattering (ADLS) due to the introduction of surface roughness are observed. In the quadrupole case, the distinctive side lobe scattering characteristic of quadrupolar emission is strongly quenched for roughened nanoshells. PACS 81.07.-b; 78.67.-n     

Theoretical investigations of the vapour-liquid equilibrium and dielectric properties of dipolar Yukawa fluids in an external field

In a low field approximation, using the dipolar Yukawa fluid model (in mean spherical approximation as a reference system) a consistent field-dependent free energy expression is proposed for the calculation of the vapour-liquid equilibrium of polar fluids in an applied electric field. A perturbation theory high field approximation expression of the free energy is also proposed to study the field-dependent properties of fluids. In the high field approximation, equations for the field-dependent polarization and for the nonlinear dielectric constant (or Piekara constant) are also predicted. It has been discussed that our approximations are appropriate to describe the vapour-liquid-like phase equilibria and the magnetization curves of magnetic fluids.     

Surface lattice dynamics and inelastic He scattering in Cu(111)

Summary We present a calculation of the Cu(111) surface dynamics in the framework of the multipole model. The electronic degrees of freedom include dipole and quadrupole deformabilities of the conduction electron density, the multipole expansion points being located at the midpoints between nearest-neighbour ions. The model accounts for the anomalous longitudinal resonance by an increase of dipolar deformability at the surface. Moreover the model explains in a straight-forward way the intense He scattering from the longitudinal resonance via the dipolar and quadrupolar modulations of the surface electron density. The surface dipolar contribution also explains the intense electron scattering from the optical surface resonance localized on the second layer.     

Generalized Debye-Falkenhagen energy in condensed matter

The thermodynamic perturbation theory of Stell, Rasaiah and Narang is generalized to the case of multi-component Stockmayer fluids. The effects of polarization by the permanent dipoles is included to first order and the perturbation series is summed approximately to all orders in the dipole moments by means of two Padé approximants. The two-body and triplet terms in the expansion have been evaluated by Monte Carlo integration for a specific choice of the reference Lennard-Jones mixture and the results are used to study systematically the effect of dipolar interactions on excess thermodynamic properties. The utility of a one-fluid theory based on the van der Waals model is investigated and it is shown that the approach is useful for obtaining semi-quantitative information on mixtures of weakly polar fluids. The special case of mixtures of hydrogen chloride and xenon is considered and it is shown that the potential model used is inadequate to account for the large deviations from ideality which are observed for this system.     

The role of higher-order terms in perturbation approaches to the monomer and bonding contributions in a SAFT-type equation of state for square-well chain fluids

A perturbation theory for square-well chain fluids is developed within the scheme of the (generalised) Wertheim thermodynamic perturbation theory. The theory is based on the Pavlyukhin parametrisations [Y. T. Pavlyukhin, J. Struct. Chem. 53, 476 (2012)] of their simulation data for the first four perturbation terms in the high temperature expansion of the Helmholtz free energy of square-well monomer fluids combined with a second-order perturbation theory for the contact value of the radial distribution function of the square-well monomer fluid that enters into bonding contribution. To obtain the latter perturbation terms, we have performed computer simulations in the hard-sphere reference system. The importance of the perturbation terms beyond the second-order one for the monomer fluid and of the approximations of different orders in the bonding contribution for the chain fluids in the predicted equation of state, excess energy and liquid–vapour coexistence densities is analysed.     

Towards a unified view of fluids

It has traditionally been believed that, unlike normal fluids whose structural properties are determined primarily by the intermolecular short-range repulsive interactions, the properties of polar and associating fluids are strongly affected by the long-range Coulombic interactions. In the course of investigations to determine the primary driving forces governing the behaviour of various (non-simple) fluids, and hence to gain a deeper understanding of the molecular mechanisms leading to the development of theoretically based simple models and theory, extensive and systematic computer simulations have been performed on typical quadrupolar (carbon dioxide), dipolar (acetone and acetonitrile), and associating (hydrogen fluoride, methanol, and water) fluids using the available realistic effective pair potentials and their variants involving forces of different ranges. In addition to the main structural characteristics (one- and two-dimensional site–site correlation functions, local g factors, and radial slices through the full pair correlation function), the dielectric constants and the thermodynamic properties (internal energy and pressure) of both the homogeneous liquid and supercritical fluid phases, and vapor–liquid equilibria have also been considered. Furthermore, in the case of water, the diffusion coefficient and viscosity have also been considered along with water at the interface. All the obtained results lead to the unambiguous conclusion that the structure, defined in terms of the complete set of site–site correlation functions, for both polar and associating pure fluids is governed by the same molecular mechanism as for normal fluids, i.e. by the short-range interactions (which, however, may be both repulsive and attractive), whereas the long-range part of the electrostatic forces, regardless of their strength, plays only a marginal role and may be treated as a perturbation only. The consequences of these findings for theory and applications are also discussed.     

Perturbation theory for a mixture of polarizable liquids

Thermodynamic perturbation theory developed for pure polar liquids with significant polarizability is applied to a mixture with polar and nonpolar polarizable components. Expressions for the average and unperturbed dipole moments of the components of the mixture are presented and the dipole and induced contributions to the thermodynamic functions of the mixture are calculated. The equation of state is obtained and used to calculate the excess properties of a binary mixture of particles interacting with a stockmeyer potential. It is shown that the induced dipole moments contribute significantly to the thermodynamic properties of this model solution and that their effects must be taken into account in predicting the properties of real liquid mixtures containing polar components.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 69–73, March, 1985.     

Perturbation theory for a polarizing liquid

The thermodynamic perturbation theory is applied to polar polarizing liquids. A system of rigid dipoles is chosen as a basis, and the magnitude of the dipole moment is determined from the Gibbs-Bogolyubov variational principle. The equation of state obtained within the framework of the variational approach is used for calculating the free energy of a model system of polarizing dipolar solid spheres. Good agreement is obtained with results of computer experiment.     

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.     

瞬态荧光方法研究溶剂诱导的三苯胺衍生物的对称性破缺电荷转移动力学

在缺乏特征红外振动的情况下追踪具有四极或八极对称性分子的激发态对称性破缺电荷转移通常是很困难的.本文以一种具有八极对称性的三苯胺衍生物为研究对象,利用飞秒时间分辨瞬态荧光光谱方法获得发光跃迁偶极矩的演化动力学,进而实时表征了其溶剂诱导对称性破缺电荷转移的动力学过程.当该分子处于弱极性甲苯溶液中时,在激发态弛豫过程中其发射偶极矩变化较小;当处于较强极性的四氢呋喃溶液中时,其发射偶极矩在数皮秒内快速减小.在对比单体偶极分子的荧光动力学后,推断八极分子的发光态在强极性溶剂中经历溶剂诱导的结构变化,由激子耦合的八极对称性降低至激发定域的偶极对称性;而在较弱极性的溶剂中,其八极对称性在溶剂化稳定中得以较大程度的保持.     

From realistic to simple models of fluids. III. Primitive models of carbon dioxide,hydrogen sulphide and acetone,and their properties

Recently developed methodology to construct primitive models of associating fluids as direct descendants of complex realistic intermolecular potential functions [L. Vl?ek, I. Nezbeda. Molec. Phys., 102, 485 (2004).] is extended to polar fluids and applied to three substances of practical importance: quadrupolar carbon dioxide, and dipolar hydrogen sulphide and acetone. It is shown that the structural properties (in terms of the site–site correlation functions) of the primitive models of polar fluids reproduce very well those of their parent realistic models but, nonetheless, they perform worse than in the case of associating fluids. A number of thermodynamic properties of the developed models obtained by computer simulations is also reported (for their later use in theoretical investigation) and discussed.