Parallel Hard Walls Research Articles

Simulation of the macroscopic pitch of a chiral nematic phase of a model chiral mesogen

We examine the effect of molecular chirality on the cholesteric phase of hard spherocylinders with a chiral dispersion potential. Monte Carlo simulations are performed under standard periodic boundary conditions (PBCs), and under confinement between two parallel hard walls. The use of PBCs constrains the helical pitch to be an integer fraction of the box dimension, while the pitch of the confined system decreases as the strength of the chiral interaction is increased. For a chiral interaction which is of the order of thermal energy, a pitch of a few hundred nanometers (much greater than the sample dimension) is observed.

Wetting and capillary nematization of binary hard-platelet and hard-rod fluids.

Density-functional theory is used to investigate the phase behavior of colloidal binary hard-platelet and hard-rod fluids near a single hard wall or confined in a slit pore. The Zwanzig model, in which the orientations of the particles of rectangular shape are restricted to three orthogonal orientations, is analyzed by numerical minimization of the grand potential functional. The density and orientational profiles as well as the surface contributions to the grand potential are determined. The calculations exhibit a wall-induced continuous surface transition from uniaxial to biaxial symmetry for the hard-rod fluid. Complete wetting of the wall-isotropic liquid interface by a biaxial nematic film for rods and a uniaxial nematic film for platelets is found. For the fluids confined by two parallel hard walls, we determine a first-order capillary nematization transition for large slit widths, which terminates in a capillary critical point upon decreasing the slit width.

Density functional theory for inhomogeneous mixtures of polymeric fluids

A new density functional theory is developed for inhomogeneous mixtures of polymeric fluids by combining Rosenfeld’s fundamental-measure theory for excluded volume effects with Wertheim’s first-order thermodynamic perturbation theory for chain connectivity. With no adjustable parameters, theoretical predictions are in excellent agreement with Monte Carlo simulation data for the density distributions and for the adsorption isotherms of hard-sphere chains near hard walls or in slit-like pores. This theory is applied to calculate the force between two parallel hard walls separated by hard-sphere chains at different densities. Calculated results indicate that the chain-mediated force is attractive and decays monotonically with separation at low chain densities, it oscillates at high chain densities and in between, it is attractive at small separation and repulsive at large separation. This new density functional theory is simpler than similar theories in the literature and is directly applicable to mixtures.

Effect of compression on the molecular shape of polymer mushrooms with variable stiffness

Under confinement, the average shape of a polymer chain is modified in interesting ways. In this work, we discuss how confinement affects the mean geometrical properties of wormlike polymers with variable flexibility and monomer–monomer interaction. Here, we consider a polymer mushroom, i.e., a single chain that is permanently anchored to a flat surface by an end point. Compression is introduced by confining the chains inside an infinite slab with parallel hard walls. Regarding polymer shape, we focus on two large-scale geometrical properties that are not correlated a priori: the chain’s size and its entanglement complexity. Using Monte Carlo simulations, we have analyzed the behavior of these two properties under confinement for a range of potential energy functions. A recurrent pattern of shape transitions emerges, as indicated by changes in the correlation between mean size and entanglements. Our results show that, whereas a flexible polymer with strong self-attraction sustains high compression without deforming, polymers that are either too rigid or too weakly self-attracting are “flattened” by slight compression. Furthermore, we find a general relation between molecular size and entanglements that is valid over a range of polymer models and levels of confinement. We conclude that chain stiffness influences less the compressive behavior of a polymer than chain self-interactions.

Wetting and capillary nematization of a hard-rod fluid: a simulation study.

We present results of a simulation study of a fluid of hard spherocylinders with a length-to-diameter ratio of 15 in contact with a planar hard wall and confined by two parallel hard walls. A Monte Carlo method is developed for simulating fluids in contact with a single wall. Using this method, we find a transition from a uniaxial to a biaxial surface phase, followed, at larger bulk densities, by the formation of a thick nematic film, with the director parallel to the wall, at the wall-isotropic fluid interface. As the density far from the wall cb approaches the value at bulk isotropic-nematic coexistence cI, the thickness of the nematic film appears to increase as -ln(cI-cb). For a fluid confined by two parallel hard walls, a first-order capillary nematization transition is found. The phase equilibria are determined by Gibbs ensemble Monte Carlo simulations for several wall separations. The difference in the coexisting densities of the capillary condensed nematic and isotropic phases becomes smaller upon decreasing the wall separation, and no capillary nematization transition is found when the wall separation is smaller than about twice the length of the spherocylinders. These features imply that the capillary nematization transition ends in a capillary critical point at a critical wall separation. Our simulation results are fully consistent with the findings of our recent theoretical study of the Zwanzig model for a hard-rod fluid.

Calculation of the compressibilities of hard-sphere fluids from the radial free space distribution function and its application to sound velocity

The relation between the compressibility and the radial free space distribution function (RFSDF) has been derived. This method for calculating the compressibility employing RFSDF is useful because the compressibility of any system is obtainable in a single Monte Carlo simulation without obtaining the equation of state. The compressibilities from the newly derived relation using RFSDF of hard-sphere fluids have been compared with those obtained from the equation of state and they are in good agreement. This method has been used to calculate the velocity of sound for hard spheres confined in parallel hard walls with the results showing that the velocity of sound in parallel direction to the wall is faster than that in normal direction.

Interfaces, wetting, and capillary nematization of a hard-rod fluid: Theory for the Zwanzig model

We investigate interfacial and capillary phenomena in a simple model for a fluid of hard rods, viz. the Zwanzig model, in which the orientations of rectangular blocks are restricted to three orthogonal directions. The theory, which is based on an Onsager-like free energy functional, predicts local biaxial ordering at the “free” interface between the coexisting isotropic and nematic phases. For an isotropic bulk fluid in contact with a single planar hard wall, we find a continuous surface phase transition from uniaxial to biaxial local symmetry, followed by complete wetting of the wall–isotropic fluid interface by a nematic film with director parallel to the wall, as the reservoir density approaches its value at bulk coexistence. For a fluid confined by two parallel hard walls we determine a first-order capillary nematization transition at large wall separation, which terminates in a capillary critical point when the wall separation is about twice the length of the rods. This transition is the analog of the capillary condensation observed for simple fluids confined by attractive walls but is purely entropy driven here.

A Monte-Carlo study of equilibrium polymers in a shear flow

We use an off-lattice microscopic model for solutions of equilibrium polymers (EP) in a lamellar shear flow generated by means of a self-consistent external field between parallel hard walls. The individual conformations of the chains are found to elongate in flow direction and shrink perpendicular to it while the average polymer length decreases with increasing shear rate. The Molecular Weight Distribution of the chain lengths retains largely its exponential form in dense solutions whereas in dilute solutions it changes from a power-exponential Schwartz distribution to a purely exponential one upon an increase of the shear rate. With growing shear rate the system becomes increasingly inhomogeneous so that a characteristic variation of the total monomer density, the diffusion coefficient, and the center-of-mass distribution of polymer chains of different contour length with the velocity of flow is observed. At higher temperature, as the average chain length decreases significantly, the system is shown to undergo an order-disorder transition into a state of nematic liquid crystalline order with an easy direction parallel to the hard walls. The influence of shear flow on this state is briefly examined.

Microphase separation in thin films of the symmetric diblock-copolymer melt

By means of Monte Carlo simulations of a lattice model, microphase separation transition of symmetric diblock-copolymer melts confined in the thin-film geometry between parallel hard walls is studied. We impose a surface field which acts repulsively only on one of the two species, to stabilize lamellar order parallel to the surfaces. However, interplay between two characteristic lengths, that is, the natural thickness of the lamellar l and the thickness of the film D, causes complicated behavior. In case that the two lengths are compatible with each other, clear lamellar order parallel to the surfaces is observed at temperatures lower than the bulk transition temperature, as expected. On the other hand, tilted or deformed lamellar structure, or even coexistence of lamellae in different orientations are found in cases of strong conflict. In both cases, lamellae are fully established. Even at temperature higher than the bulk transition temperature, weak order is induced by the surface field, and a gradual transition between such surface-induced order and bulklike order is observed. Film thickness and temperature dependence of the ordered structure is discussed, as well as a density reduction near the walls and in the interfaces between the segregated regions.

The structure of inhomogeneous molecular fluids: a restricted orientation model

It is suggested that the structural properties of an inhomogeneous fluid of very anisotropic molecules can be studied through a theoretical model in which the orientations of the molecules are restricted to certain discrete values. The general basis of the model is explained and then for illustrative purposes, it is applied to a fluid of cylindrical molecule confined between parallel planar hard structureless walls. Density functional theory and the analogue of the PY equation are used to obtain equations for the density profiles of the fluid which depend on the direct correlation function of the bulk fluid. As this function is unknown, it is approximated by a linear combination of geometrical functions. The equations are solved and the results presented for various values of the packing fraction of the fluid, the separation of the walls and the length to diameter ratio (l/d) of the molecules. A comparison with a recent Monte Carlo simulation of the fluid indicates that the approximations provide as good ...

Fluctuations of a polymerized membrane between walls

Abstract. Thefluctuationsof a self-avoiding,polymer12ed(ortethered) membranewhichis re- stdcted by the presenceof two parallel hard walls are studied using MonteCarlosimulations and scaling arguments. tilebehaviorofthe area,the pressure, normalvector susceptibility, as well as the mean curvature suceptibility are investigated. lAhcalculatethe scaling functions andshow that the critical behavior follows predictedscaling lawsvith an exponent q = 0.55 + 0.10. 1.Iutloductiou.OrRofthe major current challenges intheoretical physics b to understandthe statbtical me- chanicsofsurfacesand membranes (see, e.g.Refs. [1,2], references therein). This field hasattractedconsiderableattention recently becauseofits importance in understanding such diversqproblems as the structure oflamellar liquid crystals,microemulsions, block copolymers andother self-assembling structures [3,4], cellmembraneinteractionsin biology [5] andbiomimetic systems, andworld-sheet dynamics in stringtheory [6]. Themembranesof physical

Liquids at interfaces: what can a theorist contribute?

Reviews some recent theoretical and computer simulation studies of simple atomic fluids adsorbed at structureless substrates. Emphasis is placed on phase transitions, especially the various types of wetting transition. Criticality is associated with capillary-wave-like fluctuations in a continuously growing wetting film. This is of a subtle nature, which is best understood in terms of the pairwise correlation function of the fluid. Other surface phase transitions, such as prewetting and layering, occur out of bulk coexistence. Theory suggests that for sufficiently attractive substrates a sequence of first-order transitions, corresponding to the growth of new adsorbed liquid layers, should occur as the pressure of the bulk gas increases towards saturation at temperatures not too far above the bulk triple point. The extent to which such behaviour is found in adsorption experiments is discussed. The authors also argue that a simple fluid confined between two parallel hard-walls can exhibit surprisingly rich equilibria.

ChemInform Abstract: Molecular Arrangements and Conformations of Liquid n‐Tridecane Chains Confined Between Two Hard Walls.

Monte Carlo simulations based on united CH2 atoms linked with fixed bond lengths and angles, and continuously varying torsional angles subject to appropriate interaction energies, were used to study liquid n-tridecane chains confined between two parallel hard walls with 5 mm separation. The molecules located in the central region are noted to be in very close agreement with ideal unperturbed chains. Nearly all the chain units in the first segmental layer adjacent to the walls belong to two-dimensional chains, and exhibit considerable orientational correlations between neighboring segments of different chains.

Molecular arrangements and conformations of liquid n-tridecane chains confined between two hard walls

Liquid n-tridecane (C13H28) chains confined between two parallel hard walls separated by 5.0 nm have been studied by Monte Carlo simulations, employing united CH2 atoms linked with fixed bond lengths and angles and continuously varying torsional angles subject to appropriate interaction energies. Molecules located in the central region are in remarkable agreement with ideal unperturbed chains. Significant influences of walls persist over a distance of ∼1.5 nm, exhibiting progressively less-dense and less-pronounced segmental layers of ∼0.4 nm thickness. Segmental orientations preferentially aligned along the surface are found only in the first layer, accompanied by little perturbations in the fraction of trans-conformations. Furthermore, nearly all the chain units in the first segmental layer adjacent to the walls belong to two-dimensional chains, and exhibit considerable orientational correlations between neighboring segments of different chains. The terminal portions of some of the molecules in the succeeding layer are also located in the first layer, thus increasing the fraction of methyl chain ends in contact with the walls. These findings match very closely the experimental results of surface forces and viscosities of liquid n-alkanes confined between two mica plates, measured as a function of the plate separation.

The second and third surface virial coefficient for hard dumb-bells in contact with a hard wall

The hard dumb-bell fluid near a hard wall and between two parallel hard walls is investigated by using the virial approach. The exact values of the first two surface virial coefficients are compared with those resulting from the RAM-type perturbational theory and from the scaled particle theory for the surface tension of hard convex molecules.

Phase equilibria of fluid interfaces and confined fluids

Phase transitions at fluid interfaces and in fluids confined in pores have been investigated by means of a density functional approach that treats attractive forces between fluid molecules in mean-field approximation and models repulsive forces by hard-spheres. Two types of approximation were employed for the hard-sphere free energy functional: (a) the well-known local density approximation (LDA) that omits short-ranged correlations and (b) a non-local smoothed density approximation (SDA) that includes such correlations and therefore accounts for the oscillations of the density profile near walls. Three different kinds of phase transition were considered: (i) wetting transition. The transition from partial to complete wetting at a single adsorbing wall is shifted to lower temperatures and tends to become first-order when the more-realistic SDA is employed. Comparison of the results suggests that the LDA overestimates the contact angle γ in a partial wetting situation. (ii) capillary evaporation of a fluid confined between two parallel hard walls. This transition, from dense ‘liquid’ to dilute ‘gas’, occurs in a supersaturated fluid (p > p sat). The lines of capillary coexistence calculated in the LDA and SDA are rather close, suggesting that non-local effects are not especially important in this case. (iii) capillary condensation of fluids confined between two adsorbing walls or in a single cylindrical pore. For a partial wetting situation the condensation pressures p(<p sat) obtained from the SDA are in remarkably good agreement with the macroscopic Laplace (or Kelvin) prediction for wall separations H or pore radii R c ≳ 5σ; σ is a molecular diameter. While, because of different packing, the density profiles of the fluid differ considerably between slits and cylinders this has little effect on the coexistence line until H or R c ∼ σ. In contrast to the LDA the SDA describes two-dimensional-like liquid-gas coexistence for very narrow pores (H < σ) and temperatures below the two-dimensional critical temperature and this has ramifications for the existence of capillary critical points.

A simple separable Hamiltonian having bound states in the continuum

The author discusses a simple separable two-freedom Hamiltonian H describing the motion of a point particle in a plane region (V=0) between two infinite parallel hard walls (V= infinity ) and with a rectangular finite potential well (V=-V0). The quantal spectrum of H is discrete below the continuum limit (ionisation energy) different from the classical escape energy (E=0) by the zero point energy of the transverse motion and has infinitely many bound states embedded in the continuum. The author shows that this spectrum is fragile against perturbations of H: if the hard walls are made diverging, the bound states in the continuum disappear, while if they are converging, the continuum disappears and the spectrum is pure point.

Studies in molecular dynamics. XVI. Fluctuation driven resonance

The natural fluctuations in a system of hard spheres that is placed between closely spaced parallel hard walls lead to resonance for those wavelengths which correspond to the spacing, or integer fractions thereof. The temporal behavior of this resonance is shown to be quantitatively equivalent to the autocorrelation function of the appropriate sum over modes of longitudinal currents which are calculated separately by molecular dynamics for a periodic system at an equivalent density. The decay of this resonance is also analyzed in terms of hydrodynamic and kinetic theory, and the regions of their validity is delineated.