Hard-body Systems Research Articles

Theoretical Study of Non-additive Hard Convex Body Fluid Mixtures

The structure of a dense fluid or liquid is largely determined by the repulsive intermolecular forces, so the hard core potential has been extensively employed to model real fluids and fluid mixtures. The properties of two dimensional hard body fluids and fluids mixtures have aroused a considerably interest in recent years. This is because they are treated as models of real fluids or fluid mixtures absorbed onto surfaces. The 2D hard-body fluids and fluid mixtures like their three-dimensional counter part are useful reference system in framing a perturbation theory for 2D real fluids and fluid mixtures of non-spherical molecules. The 2D hard-body systems are convex body (HCB) systems such as ellipse (HE) and hard discorectangles (HDR) and hard non-convex body systems i.e., fused hard discs (FHD) and planar hard dumbbell (HDB) systems. The equation of state of hard convex body fluid mixtures (HCB) is studied. Analytic expressions are given for the equation of state of the fluid mixture of the non-additive HCB. The numerical results are discussed for the non-additive hard dumbbell (HDB) fluid mixtures under different conditions for different values of non-additivity \(\Delta\). They depend on the conditions, shape parameters \(L^*_{11}\) and \(L^*_{22}\) , mole fractions \(x_1\) and \(x_2\) and \(\Delta\) in general and increase with the increase of packing fraction \(\Delta\).

Liquid crystal phase diagram of soft repulsive rods and its mapping on the hard repulsive reference fluid

The liquid crystal phase diagram of the soft repulsive Kihara fluid has been characterised by means of Monte Carlo simulations, for a selection of elongations of the rod-like particles (L*= 2–7) and over a broad range of temperatures (T *= 1–50). Three qualitatively different regimes of liquid crystalline behaviour are described that are related to the emergence of isotropic–nematic–smectic and isotropic–smectic–solid triple points above specific rod elongations. A mapping of the soft repulsive fluids on hardrepulsive fluids of effective elongation depending on L* and T * is evaluated. Such mapping provides a correct qualitative description of the role of temperature on the liquid crystal phases, and provides a fairly accurate prediction of equations of states and radial functions within the isotropic, nematic and smectic phases. Nevertheless, in comparison to the simulation results, the mapping underestimates the temperature of the isotropic–nematic–smectic triple point, while it overestimates that of the isotropic–smectic–solid one. These results should guide the use of reference hard-body systems to describe the behaviour of soft liquid crystalline materials.

Helmholtz energies from equations of state and their relative deviations

Extension of the hard-sphere equations of state to non spherical hard-body systems represents a formidable task. For an equation of state that is applicable to liquid and vapor states (and explicit for pressures), the corresponding characteristic function is the residual energy. The equations of state of Carnahan Starling, Boublik and R J Sadus are used to derive an expression for residual Helmholtz energies. Relative deviations of residual Helmholtz energies for these equations of state have been reviewed. The deviations of compressibility factor against packing fraction have been plotted for these equations of state. The agreement of these plots is found to be good for lower n-alkanes but not for longer n-alkanes. Thus it becomes obvious that the compressibility factor depends considerably on the shape of the studied molecules.

Brownian dynamics simulation of polydisperse hard spheres

Standard algorithms used for the numerical integration of the Langevin equation require that interactions should slowly vary during the integration time-step. This in not the case for hard-body systems, where there is no clear-cut between the correlation time of the noise and the time-scale of the interactions. Starting with a short time approximation of the Smoluchowski equation, we introduce an algorithm for the simulation of the over-damped Brownian dynamics of polydisperse hard-spheres in absence of hydrodynamic interactions and briefly discuss the extension to the case of external drifts.

Event-driven Langevin simulations of hard spheres

The blossoming of interest in colloids and nanoparticles has given renewed impulse to the study of hard-body systems. In particular, hard spheres have become a real test system for theories and experiments. It is therefore necessary to study the complex dynamics of such systems in presence of a solvent; disregarding hydrodynamic interactions, the simplest model is the Langevin equation. Unfortunately, standard algorithms for the numerical integration of the Langevin equation require that interactions are slowly varying during an integration time step. This is not the case for hard-body systems, where there is no clear-cut distinction between the correlation time of the noise and the time scale of the interactions. Starting first from a splitting of the Fokker-Plank operator associated with the Langevin dynamics, and then from an approximation of the two-body Green's function, we introduce and test two algorithms for the simulation of the Langevin dynamics of hard spheres.

Poisson's ratio of simple planar ‘isotropic’ solids in two dimensions

AbstractThe influence of molecular geometry on the Poisson's ratio has been investigated for a few two‐dimensional (2D) hard body systems (hard discs, hard dimers, hard cyclic trimers, and hard cyclic hexamers) forming elastically isotropic solid phases. The Poisson's ratio of the studied periodic and aperiodic solids was determined by Monte Carlo simulations using the analysis of the box fluctuations in the constant pressure ensemble (NpT) with variable box shape. The results obtained for all the studied systems showed that the Poisson's ratio grows when the density is decreased. It has been also found that the Poisson's ratio decreases with increasing number of discs in the molecule and its value for hard trimers is negative near close packing. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Preface: phys. stat. sol. (b) 244/3

The 21st Winterschool on Electronic Properties of Novel Materials (IWEPNM 2007) took place from 10 March to 17 March 2007. It continued the tradition of winterschools of this type in Kirchberg/Tirol in its well-known atmosphere of collegiality and emphasis on scientific exchange between young and experienced scientists. The sessions at the IWEPNM 2007 focused on quantum information, carbon nanostructure synthesis, purification and separation, the characterization and properties of carbon nanostructures, fullerenes, endohedrals, and fullerides, excitons in carbon nanotubes, the chemical treatment of carbon nanotubes, nanotube filling and double-walled nanotubes, graphite and graphene, non-carbonaceous nanostructures, electron and heat transport in carbon nanostructures, composites with carbon nanotubes, and on theory and applications of these materials. This proceedings volume is divided into according sections. The program of the Winterschool was composed of invited oral presentations, poster presentations and mini-workshops. The oral presentations were scheduled in morning and evening sessions, the mini-workshops took place during the afternoons, and the posters were presented and discussed in two late-evening sessions. In 2007 the Winterschool celebrated an anniversary: It had been of taking place for the 20th time at the Hotel Sonnenalp, a hotel ideally suited for the close interactions of international participants from many countries. We are grateful to the manager of Hotel Sonnenalp, Frau Edith Mayer, and her staff for the local arrangements as well as for her patience with many special requests during the meeting. We owe special thanks to the hotel staff for their careful organization of the celebration. The event benefited substantially from support of the Universitat Wien and the Verein zur Forderung der Winterschulen in Kirchberg, as well as from numerous industrial sponsors. We greatly appreciate their financial contribution without which the meeting would have hardly become possible. Finally, special acknowledgments go to all contributors of the IWEPNM 2007 and to the authors of this volume, the proceedings of the Winterschool. Viera Skakalova was instrumental in compiling and editing the proceedings. In the name of all participants who have enjoyed the Winterschools since 1985 we express special thanks to Hans Kuzmany for his outstanding engagement in organizing the IWEP for so many years. His experience and advice will be needed for future Winterschools. The next Winterschool in this series will take place from 1 March to 8 March 2008, again in Kirchberg/Tirol, and will be organized by Christian Thomsen from Berlin. Wien, Darmstadt, Stuttgart, Berlin, 2007

Monte Carlo simulation of two‐dimensional hard body systems with extreme values of the Poisson's ratio

AbstractMonte Carlo computer simulations with variable shape of the periodic box were performed for a few two‐dimensional, hard‐body models showing elastically isotropic solid phases. Two examples of homo‐molecular (i.e. consisting of identical molecules) systems of anisotropic molecules are discussed which form unusual solid phases, showing negative Poisson's ratio and know as auxetic ones, at densities and pressures higher than the elastically isotropic solid phases. Sharp extremes of the Poisson's ratio were observed for both systems at freezing of the orientational degrees of freedom of the molecules: a minimum was observed for the system for which the auxetic phase with frozen rotation is isotropic and a maximum was found for the other system. This indicates that isotropic auxetic phases can have auxetic precursors with much more negative Poisson's ratios than those characterizing the auxetic phases themselves. An example of a hetero‐molecular (i.e. mixture consisting of different molecules), elastically isotropic system is also discussed – the polydisperse hard disc system. The simulations revealed a maximum of the Poisson's ratio in the close packing limit at any nonzero polydispersity. Although no manifestation of any auxetic behaviour has been found in this system, the obtained results indicate other unusual effect – a jump (discontinuity) of the Poisson's ratio at close packing when the polydispersity tends to zero. The results obtained in this work demonstrate that the Poisson's ratio can play the role of a sensitive indicator of (at least) some structural changes in solids. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Calculation of elementary diagrams using a Metropolis-like simulation method

A method for the evaluation of higher order elementary diagrams is proposed. It utilizes symbolic algebra programming and automatic code generation. The method is used to calculate elementary diagrams for hard spheres up to the fifth. The obtained values are fitted to suitable functions of interparticle distance. The resulting truncated density expansion is compared with recent values of the bridge function calculated directly from the simulated pair distribution function. The method can be straightforwardly extended to hard-body systems and their mixtures.

Orientational phasetransition between hexagonal solids in planar systems of hardcyclic pentamers and heptamers

Two-dimensional, hard-body systems of cyclic multimers(pentamers and heptamers) are studied by Monte Carlosimulations. Elastic properties (the elastic constants and thePoisson ratio) are computed for hexagonal solid phases withmolecular rotation by using an algorithm based on thestrain-fluctuation method. In both systems a minimum of thePoisson ratio is observed at the same density at which aqualitative change of the orientational singlet distributionfunction occurs. This result confirms that, in each of thestudied systems, a phase transition occurs between twoelastically isotropic solid phases exhibiting orientationaldisorder: a higher-density phase with (strongly) hinderedrotation and a lower-density phase with (almost) free rotation.The study also suggests that it is worth paying moreattention to the dependence of the Poisson ratio on thethermodynamic variables (volume, pressure or temperature) insolids because this quantity can play the role of a sensitiveindicator of (at least some) structural phase transitions.

GENERALIZED IMPULSE AND MOMENTUM APPLIED TO MULTIBODY IMPACT WITH FRICTION1*

A mechanism composed of rigid bodies joined by ideal nondissipative pinned joints has a configuration that can be described in terms of generalized coordinates q i and time t; the system has a kinetic energy . The generalized momentum of the system is defined as a vector, . If the system is subject to a set of time-dependent external forces F j that act at locations r j , these forces result in differential impulses dp j = F j dt. The generalized impulse vector Πι associated with these impulses has a differential d, where are velocities of the points at which the impulses are applied. If the forces act impulsively (i.e., there is a negligibly small period of force application), the differentials of generalized momentum and generalized impulse are equal, and if the forces are proportional during the “period” of application, then integration of this equation gives a change of state . When applied to impact between systems of hard bodies for which there is friction and slip that changes direction during contact, the differential relation is required. If the direction of slip is constant, however, it is more convenient to use the integrated form of this generalized impulse-momentum relation. In either case, at the point of external impact, the terminal impulse is obtained from the energetic coefficient of restitution. *Communicated by B. Gilmore.

The evolution of multicomponent systems at high pressures. Part IV. The genesis of optical activity in high-density, abiotic fluids

A thermodynamic argument has been developed which relates the chirality of the constituents of a mixture of enantiomers to the system excess volume, and thereby to its Gibbs free enthalpy. A specific connection is shown between the excess volume and the statistical mechanical partition function. The Kihara–Steiner equations, which describe the geometry of convex hard bodies, have been extended to include also chiral hard bodies. These results have been incorporated into an extension of the Pavlicek–Nezbeda–Boublik equation of state for convex, aspherical, hard-body systems. The Gibbs free enthalpy has been calculated, both for single-component and racemic mixtures, for a wide variety of hard-body systems of diverse volumes and degrees of asphericity, prolateness, and chirality. The results show that a system of chiral enantiomers can evolve to an unbalanced, scalemic mixture, which must manifest optical activity, in many circumstances of density, particle volume, asphericity, and degree of chirality. The real chiral molecules fluorochloroiodomethane, CHFClI, and 4-vinylcyclohexene, C8H12, have been investigated by Monte Carlo simulation, and observed to both manifest positive excess volumes (in their racemic mixtures) which increase with pressure, and thereby the racemic–scalemic transition to unbalanced distributions of enantiomers. The racemic–scalemic transition, responsible for the evolution of an optically active fluid, is shown to be one particular case of the general, complex phase behavior characteristic of “closely-similar ” molecules (either chiral or achiral) at high pressures.

The evolution of multicomponent systems at high pressures Part III. Effects of particle shape upon the Alder–Wainwright transition

The thermodynamic stability of pure, aspherical hard-body fluids has been examined throughout the range of pressure 1–100000 atm, and over a range of temperature extending from 10 to 10000 K, using the equation of state developed from scaled particle theory (SPT) by Boublik for convex, aspherical, hard-body systems (T. Boublik, J. Chem. Phys., 1975, 63, 4084). The scaled particle theory description of the spherical hard-body system is an exact solution in statistical mechanics, as is also its extension to aspherical hard bodies. Therefore, the Boublik solutions share the absolute property of scaled particle theory. Accordingly, the constraints of the third law of thermodynamics have been applied to this analysis of the thermodynamic stability of aspherical hard-body fluids. Aspherical hard-body fluids are shown to undergo the Alder–Wainwright transition at monotonically lower pressures and reduced volumes with increasing degree of asphericity, in consistent agreement with data from computer simulation experiments. The results developed by the Boublik equations are compared with those of the simplified perturbed hard chain theory (SPHCT); and the SPHCT formalism is shown to give acceptably accurate results for the density and Gibbs free enthalpy at pressures less than approximately 50000 atm, and modest degrees of asphericity.

Thermodynamics of complex hard body fluids

An equation of state (EOS) for complex hard body fluids is developed by using as input the virial coefficients: this has been called the CY5 EOS. After comparing with molecular simulation data of complex hard body systems, it is concluded that this is a very accurate route for predicting thermodynamic behaviour of such fluid phases. It corrects well established EOSs, like the Carnaham—Starling type equations for had spheres and non-spherical bodies. In addition, it gives new insight into controversial problems, like the demixing phenomena of hard sphere mixtures, produced by large size ratios or the presence of non-additive interactions.

Liquid crystals of asymmetric hard body molecules

We study the role of molecular asymmetry in the isotropic-nematic phase transition of hard body systems. Our results confirm previous indications that the first-order character of the phase transition is significatively weakened by the molecular asymmetry. A comparative analysis of the theories for soft anisotropic interactions and hard-core repulsions helps the discrepancies to be understood as the result of the molecular shape models.

Density functional approximation for hard-body liquid crystals

We present a density functional approximation for the free energy of a system of hard bodies with arbitrary shape and orientational distribution. For systems with homogeneous density it reduces to existing treatments, which describe the isotropic liquid and the nematic liquid crystal. The treatment of the inhomogeneous density allows the study of smectic and crystal phases. We applied the approximation to a system of parallel hard spherocylinders, for which we compare the nematic to smectic-A phase transition with recent computer simulation data. We also study a system of oblique cylinders and show that smectic-C phase may appear as the result of packing effects in systems of hard bodies.

Monte Carlo simulation of the background correlation function of non-spherical hard body fluids

A new Monte Carlo technique for the calculation of the function y = g exp (βu) is proposed for hard body systems. The method is especially suitable at low and moderate densities and separations below the contact. The y-function was calculated for hard spheres and hard diatomics. For hard spheres surprisingly small deviations from Grundke-Henderson formula were found. For the diatomics at Ls = 0·6 radial slices at four special orientations were determined. The applicability of the proposed method and of the umbrella sampling technique due to Patey and Torrie are compared.