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In this work we report on molecular dynamics simulations of the embedding process of a nano-particle into a polymeric film as a function of temperature. This process has been employed experimentally in recent years to test for a shift of the glass transition of a material due to the confined film geometry and to test for the existence of a liquid-like layer on top of a glassy polymer film. The embedding process is governed thermodynamically by the prewetting properties of the polymer on the nano-particle. We show that the dynamics of the process depends on the Brownian motion characteristics of the nano-particle in and on the polymer film. It displays large sample to sample variations, suggesting that it is an activated process. On the timescales of the simulation an embedding of the nano-particle is only observed for temperatures above the bulk glass transition temperature of the polymer, agreeing with experimental observations on noble metal clusters of comparable size.

A two-dimensional magnetic Ising system confined in an L × D geometry () in the presence of competing magnetic fields (h) acting at opposite walls along the D-direction exhibits an interface between domains of different orientation that runs parallel to the walls. In the limit of infinite film thickness () this interface undergoes a wetting transition that occurs at the critical curve Tw(h), so that for T

The structure of a polymer nanodroplet adsorbed on a flat lyophobic substrate chemically decorated with a lyophilic stripe of width 2RD is studied by molecular dynamics simulation of a coarse-grained bead–spring model of short macromolecules (containing N = 20 effective monomers). Varying the stripe width, the strength of the monomer–wall attraction and the temperature, the equilibrium morphology of the resulting droplets is studied and discussed in terms of current phenomenological theories. In the second part, the behaviour of a liquid bridge connecting two such lyophilic stripes a distance L apart is analysed. It is shown that for large enough L such free-standing films are unstable and rupture, after a hole has nucleated and grown into an elongated cavity in the lateral direction leaving only a cylindrical bridge between the stripes immediately before break-up. The forces acting between the two walls of the slit pore in equilibrium due to the thin film forming the liquid bridge are also estimated as a function of distance between the walls.

We present extensive Monte Carlo simulations of the Ising film confined in an L × M geometry () in the presence of long-range competing magnetic fields h(n) = h1/n3(n = 1,2,...,L) which are applied at opposite walls along the M-direction. Due to the fields, an interface between domains of different orientations that runs parallel to the walls forms and can be located close to one of the two surfaces or fluctuate in the centre of the film (localization–delocalization transition). This transition is the precursor of the wetting phase transition that occurs in the limit of infinite film thickness () at the critical curve Tw(h1). For T

By confining a binary mixture, one can profoundly alter its miscibility behaviour. The qualitative features of miscibility in confined geometry are rather universal and are shared by polymer mixtures as well as small molecules, but the unmixing transition in the bulk and the wetting transition are typically well separated in polymer blends. We study the interplay between wetting and miscibility of a symmetric polymer mixture via large scale Monte Carlo simulations in the framework of the bond fluctuation model and via numerical self-consistent field calculations. The film surfaces interact with the monomers via short-ranged potentials, and the wetting transition of the semi-infinite system is of first order. It can be accurately located in the simulations by measuring the surface and interface tensions and using Young's equation. If both surfaces in a film attract the same component, capillary condensation occurs and the critical point is close to the critical point of the bulk. If surfaces attract different components, an interface localization/delocalization occurs which gives rise to phase diagrams with two critical points in the vicinity of the pre-wetting critical point of the semi-infinite system. The crossover between these two types of phase diagrams as a function of the surface field asymmetry is studied. We investigate the dependence of the phase diagram on the film width Δ for antisymmetric surface fields. Upon decreasing the film width the two critical points approach the symmetry axis of the phase diagram, and below a certain width, Δtri, there remains only a single critical point at symmetric composition. This corresponds to a second order interface localization/delocalization transition even though the wetting transition is of first order. At a specific film width, Δtri, tricritical behaviour is found. The behaviour of antisymmetric films is compared with the phase behaviour in an antisymmetric double wedge. While the former is the analogy of the wetting transition of a planar surface, the latter is the analogy of the filling behaviour of a single wedge. We present evidence for a second order interface localization/delocalization transition in an antisymmetric double wedge and relate its unconventional critical behaviour to the predictions of Parry et al (1999 Phys. Rev. Lett. 83 5535) for wedge filling. The critical behaviour differs from the Ising universality class and is characterized by strong anisotropic fluctuations. We present evidence that the transition in large double wedges can be of second order although there is a first order wetting transition on a planar substrate.

The nature of the melting transition for a system of hard discs with translational degrees of freedom in two spatial dimensions has been analysed by a combination of computer simulation methods and a finite size scaling technique. The behaviour of the system is consistent with the predictions of the Kosterlitz–Thouless–Halperin–Nelson–Young (KTHNY) theory. The structural and elastic properties of binary colloidal mixtures in two and three spatial dimensions are discussed as well as those of colloidal systems with quenched point impurities. Hard and soft discs in external periodic (light-) fields show rich phase diagrams including freezing and melting transitions when the density of the system is varied. Monte Carlo simulations for detailed finite size scaling analysis of various thermodynamic quantities like the order parameter, its cumulants, etc, have been used in order to map the phase diagram of the system for various values of the density and the amplitude of the external potential. For hard discs we find clear indication of a reentrant liquid phase over a significant region of the parameter space. The simulations therefore show that the system of hard discs behaves in a fashion similar to charge stabilized colloids which are known to undergo an initial freezing, followed by a remelting transition as the amplitude of the imposed modulating field produced by crossed laser beams is steadily increased. Detailed analysis of the simulation data shows several features consistent with a recent dislocation unbinding theory of laser induced melting. The differences and similarities of systems with soft potentials (DLVO, 1/r12, 1/r6) and the relation to experimental data is analysed.

Confined magnetic Ising films in a L ? D geometry (), with short-range competing magnetic fields?(h) acting at opposite walls along the D-direction, exhibit a slightly rounded localization?delocalization transition of the interface between domains of different orientations that runs parallel to the walls. This transition is the precursor of a wetting transition that occurs in the limit of infinite film thickness () at the critical curve Tw(h). For T Tw(h)) such an interface is bounded (unbounded) to the walls, while right at Tw(h) the interface is freely fluctuating around the centre of the film. Starting from disordered configurations, corresponding to , we quench to the wetting critical temperature and study the dynamics of the approach to the stationary regime by means of extensive Monte Carlo simulations. It is found that for all layers parallel to the wall (rows), the row magnetizations exhibit a peak at a time and subsequently relax to the stationary, equilibrium behaviour. The characteristic time for such a relaxation scales as , as expected from theoretical arguments, that are discussed in detail.

We present the results of large-scale computer simulations in order to discuss the structural and dynamic properties of sodium silicate melts with the compositions (Na2O)2(SiO2) (NS2) and (Na2O)20(SiO2) (NS20). We show that, compared to silica (SiO2), these systems exhibit additional intermediate range order on intermediate length scales that stem from the tetrahedral network structure. By means of intermediate-scattering functions, we characterize the dynamics of sodium in the system under consideration. Whereas in NS2 the incoherent scattering functions for Na decay much faster to zero than the coherent ones for Na–Na, in NS20 this different behaviour of the incoherent and coherent functions is not very pronounced. On the other hand, the incoherent functions of the two systems share a very peculiar feature: their long-time decay can be described by a Kohlrausch law with a constant exponent β for q_{th}$>q > qth where qth is significantly below the location of the main peak in the static structure factor for the Na–Na correlations.

Square L ? L (L = 24?128) Ising lattices with nearest neighbour ferromagnetic exchange are considered using free boundary conditions at which boundary magnetic fields ? h are applied, i.e., at the two boundary rows ending at the lower left corner a field +h acts, while at the two boundary rows ending at the upper right corner a field ?h acts. For temperatures T less than the critical temperature Tc of the bulk, this boundary condition leads to the formation of two domains with opposite orientations of the magnetization direction, separated by an interface which for T larger than the filling transition temperature Tf (h) runs from the upper left corner to the lower right corner, while for T T > Tf (h) it scales as w ? L. The distribution P (?) of the interface position ? (measured along the z-direction from the corners) decays exponentially for T T > Tf (h). Furthermore, the Monte Carlo data are compatible with ? (Tf (h) ? T)?1 and a finite size scaling of the total magnetization according to M(L, T) = {(1 ? T/Tf (h))?? L} with ?? = 1. Unlike the findings for critical wetting in the thin film geometry of the Ising model, the Monte Carlo results for corner wetting are in very good agreement with the theoretical predictions.

We consider the question of whether a two-dimensional hard-disc fluid has a first-order transition from the liquid state to the solid state as in the three-dimensional melting-crystallization transition or whether one has two subsequent continuous transitions, from the liquid to the hexatic phase and then to the solid phase, as proposed by Kosterlitz, Thouless, Halperin, Nelson and Young (KTHNY). Monte Carlo (MC) simulations of the fluid that study the growth of the bond orientational correlation length, and of the crystal are discussed. The emphasis is on a recent consistency test of the KTHNY renormalization group (RG) scenario, where MC simulations are used to estimate the bare elastic constants and dislocation fugacities in the solid, as a function of density, which then are used as starting values for the RG flow. This approach was validated earlier for the XY model as well.

This paper reports results of molecular dynamics simulations for a glassy polymer melt consisting of short, non-entangled chains. The temperature region studied covers the supercooled state of the melt above the mode-coupling critical temperature. The analysis focuses on the interplay of simple-liquid and polymer-specific effects. One can clearly distinguish two regimes: a regime of small and one of large monomer displacements. The first regime corresponds to motion of a monomer in its local environment. It is dominated by the cage effect and well described by the idealized mode-coupling theory. The second regime is governed by the late-β/early-α process. In this regime the connectivity of the monomers begins to interfere with the cage dynamics and finally becomes dominant. The monomer displacement is compared with simulation results for a binary Lennard-Jones mixture to highlight the differences which are introduced by the connectivity of the particles.

A two-dimensional Ising model with nearest-neighbour ferromagnetic exchange confined in a strip of width L between two parallel boundaries is studied by Monte Carlo simulations. `Free' boundaries are considered with unchanged exchange interactions at the boundary but long-range boundary fields of the form H (n ) = ? h [n -3 - (L - n + 1) -3 ], where n = 1, 2, ... ,L labels the rows across the strip. In the case of competing fields and L , the system exhibits a critical wetting transition of a similar type as in the well studied case of short-range boundary fields. At finite L , this wetting transition is replaced by a (rounded) interface localization-delocalization transition at Tc (h , L ). The order parameter profiles and correlation function G (n , r ), where r is a coordinate parallel to the boundaries of the strip, are analysed in detail. It is argued that for T Tc (h , L ) the order parameter profile is essentially a linear variation across the strip, i.e. the width w varies as w L , unlike the case in d = 3 where w L 1/2 is the short-range case and w lnL in the case of the n -3 boundary potential holds. The parallel correlation length scales as L 2 as for the short-range case. In addition to this case of competing boundary fields, also the case where both boundaries are sources of fields of the same sign is studied, which then compete with a uniform bulk field such that a capillary condensation transition occurs. The data obtained are consistent with the Kelvin equation as in the case of the short-range surface fields.

The semi-infinite axial next-nearest-neighbour Ising (ANNNI) model in the disordered phase is treated within a molecular-field approximation, and the singularities of various response functions characterizing the critical behaviour at the surface are obtained. In previous work (Binder K and Frisch H L 1999 Eur. Phys. J. B 10 71) the axis where a nearest-neighbour ferromagnetic (J 1 ) and next-nearest-neighbour antiferromagnetic (J 2 ) exchange compete was chosen perpendicular to the surface plane. In the present work we consider an orientation of this axis parallel to the surface, allowing also for different values of these exchange interactions (j 1 ,j 2 ) in the surface plane. We derive the conditions for the occurrence of a surface transition, where the surface plane (at a temperature where the bulk is still disordered) orders either ferromagnetically or into a modulated structure. At the ordinary transition of the surface we obtain the mean-field values of the surface critical exponents, including the Lifshitz point of the bulk, where L 1 = 1/2, L 11 = -1/2, L = 0, L = 3. These exponents differ from their counterparts for the case where the axis of competing interactions is oriented perpendicular to the surface, and thus it is shown that for a uniaxial Lifshitz point the surface critical behaviour depends on the surface orientation.

The three-state Potts model with nearest ferromagnetic interaction J on the simple cubic lattice, exposed to a field which randomly favours one of the states, is studied by finite size scaling analysis of Monte Carlo simulations. The consequences of the hyperscaling violations for the finite size scaling description are worked out, and it is shown that at criticality the order parameter distribution develops a trivial character (superposition of three delta functions), unlike the nontrivial distributions in models where hyperscaling holds. The numerical data are compatible with this interpretation, and are also compatible with a description in terms of only two independent static critical exponents, as proposed by Schwartz et al. Slow relaxation and the need of averaging over a large number of random field samples restricts the range of linear dimensions L to , and in view of crossover problems only rough estimates of critical exponents are obtained.

A model molecular fluid with two-dimensional classical degrees of freedom and two internal quantum states is studied by path integral Monte Carlo simulations. The temperature-density phase diagram is obtained to a high degree of precision using finite-size scaling techniques and local structure analysis methods. We locate the phase boundaries of gas, liquid, square and hexagonal lattice solid phases together with a preferred internal quantum state resulting in tricritical and triple points. The simulation results for the liquid-solid transitions are compared with recent density functional theory calculations.

The authors propose a simple model for (CO)1-x(N2)x mixtures adsorbed on graphite where a lattice site carries a spin Si=+or-1 representing the orientations of the CO electric dipole moment if the site is occupied by a CO molecule, while the spin Si=0 if the site is taken by an N2 molecule, which has a quadrupole moment only. Assuming a bilinear dipole-quadrupole coupling, randomly quenched N2 impurities then act as random fields would act on an Ising antiferromagnet. For simplicity, a square lattice is treated and the range of all interactions is restricted to nearest neighbours. Monte Carlo studies are performed for a range of lattice linear dimensions L from L=24 to L=50, and the specific heat order parameter and susceptibility, as well as the fourth-order cumulant, are studied, applying finite-size scaling concepts where appropriate. The specific heat results display a striking qualitative similarity to the experimental data of Wiechert and Arlt, and provide evidence that the transition is already rounded by arbitrarily small dilution, consistent with theoretical predictions for the two-dimensional random field Ising model. While the experiments needed to rely on the specific heat only, the data for the (strongly rounded) ordering susceptibility and the cumulant (where the common intersection point disappears, consistent with the absence of a transition) provide compelling evidence for this picture. The crossover scaling analysis first proposed by Ferreira et al. for dilute antiferromagnets in a field also works out reasonably well for the present model.

The glass transition in a lattice model (bond-fluctuation model) of a dense two-dimensional polymer melt has been studied using the Monte Carlo technique. Temperature is introduced in this model by associating energies with the bonds connecting the monomers in the chains. This creates competition between the energetic and geometric constraints within the system at low temperatures and the system becomes frozen. The frozen monomers and the persistence of such states are investigated in terms of an appropriately defined autocorrelation function. Attention has been paid to the various relaxation processes at different length scales. In particular, the global relaxation by the diffusion of the polymers, the Rouse relaxation at the scale of the chain length and the relaxation of the above-mentioned autocorrelation function involving the frozen monomers have been studied. The system is equilibrated at various temperatures down to T=0.22 K and the results thus correspond to those in the limit of an infinitely slow cooling rate. No phase transition is observed in the temperature range studied. On all length scales the relaxation times exhibit a crossover from an Arrhenius behaviour at high temperatures to a behaviour closely fitted to the form tau approximately exp(A/T2) at low temperatures, where A is constant independent of the relaxation processes. The increase of the relaxation times does not seem to be fast enough to explain a finite-temperature transition observed on quenching the system.

In this Monte Carlo simulation the authors study the glass transition of a dense three-dimensional polymer melt using a lattice model (a bond-fluctuation model on a simple cubic lattice) that was highly optimized for a vector supercomputer. Long bonds are energetically favoured to create a competition between bond energy and packing constraints, which prevents the melt from crystallizing when it freezes. The onset of this freezing can be monitored by the temperature variation of various static quantities that probe both the length scale of a bond vector, such as the mean bond length and mean energy per bond, and that of the whole chain, such as the radius of gyration. As the melt vitrifies, these quantities gradually become independent of temperature in a narrow range around T approximately=0.2 (the temperature is measured in units of an energy parameter, epsilon , introduced in the model Hamiltonian) and their value at low temperatures is strongly influenced by the cooling rate. It is thus possible to infer from these curves the cooling-rate dependence of the freezing temperature Tg. Despite the difference in the detailed dependence of Tg on the cooling rate, the extrapolated value TK coincides with the Vogel-Fulcher temperature T0, obtained from the temperature variation of the diffusion coefficient, within the error bars.

Information from recent X-ray and neutron diffuse scattering investigations of Fe-Al alloys and the resulting effective interaction parameters are used to construct a model in which the lattice configurational degrees of freedom of these alloys are described by Ising spins, and the magnetic moments of iron atoms are described by classical Heisenberg spins. Starting from the exact ground state of the model, information on the phase diagram at non-zero temperature is obtained from both spin wave theory, mean-field approximations and extensive Monte Carlo simulations. It is shown that use of the unrenormalized interaction parameters from the various experiments yields a phase diagram which disagrees severely with experiment even at the qualitative level. However, with a suitable renormalization of the ratio between magnetic and non-magnetic interactions, a qualitatively reasonable phase diagram of the model is obtained. The consequences for the authors' understanding of effective interaction parameters in Fe-Al alloys are spelt out, and the implications for experimental work are discussed.

Monte Carlo simulations of two-dimensional fluids with a truncated Lennard-Jones interaction in the NVT ensemble are analysed with a block density distribution technique, for N=256 and N=576 particles. It is shown that below Tc (critical temperature) the block density function develops a well defined two-peak structure. From the locations of these two peaks the densities of the two coexisting phases can be reliably estimated. In the one-phase region the width of the single-peak is used to extract information on the compressibility, by extrapolating the results for finite block size versus inverse block linear dimension to the thermodynamic limit. Studying the temperature dependence of the fourth-order cumulant of the block density distribution at the critical density for various block sizes, the location of the critical temperature is found from the intersection of the cumulants, just as in the simpler case of Ising models. The authors' results suggest that finite-size scaling techniques can be used to analyse the critical properties of Lennard-Jones fluids and related systems.

While for a slightly supersaturated vapor the free energy barrier ΔF(hom)(*), which needs to be overcome in a homogeneous nucleation event, may be extremely large, nucleation is typically much easier at the walls of the container in which the vapor is located. While no nucleation barrier exists if the walls are wet, for incomplete wetting of the walls, described via a nonzero contact angle Θ, classical theory predicts that nucleation happens through sphere-cap-shaped droplets attracted to the wall, and their formation energy is ΔF(het)(*) = ΔF(hom)(*)f(Θ), with f(Θ) = (1-cosΘ)(2)(2+cosΘ)/4. This prediction is tested through simulations for the simple cubic lattice gas model with nearest-neighbor interactions. The attractive wall is described in terms of a local 'surface field', leading to a critical wetting transition. The variation of the contact angle with the strength of the surface field is determined by using thermodynamic integration methods to obtain the wall free energies which enter Young's equation. Obtaining the chemical potential as a function of the density for a system with periodic boundary conditions (and no walls), the droplet free energy of a spherical droplet in the bulk is obtained for a wide range of droplet radii. Similarly, ΔF(het)(*) is obtained for a system with two parallel walls. We find that the classical theory is fairly accurate if a line tension correction for the contact angle is taken into account.

Using Molecular Dynamics (MD) and Monte Carlo (MC) simulations interfacial properties of crystal-fluid interfaces are investigated for the hard sphere system and the one-component metallic system Ni (the latter modeled by a potential of the embedded atom type). Different local order parameters are considered to obtain order parameter profiles for systems where the crystal phase is in coexistence with the fluid phase, separated by interfaces with (100) orientation of the crystal. From these profiles, the mean-squared interfacial width w^2 is extracted as a function of system size. We rationalize the prediction of capillary wave theory that w^2 diverges logarithmically with the lateral size of the system. We show that one can estimate the interfacial stiffness from the interfacial broadening, obtaining 0.5 k_B T/sigma^2 for hard spheres and 0.18 J/m^2 for Ni., 15 pages, 7 figures

The statistical mechanics of flexible and semiflexible macromolecules is distinct from that of small molecule systems, since the thermodynamic limit can also be approached when the number of (effective) monomers of a single chain (realizable by a polymer solution in the dilute limit) is approaching infinity. One can introduce effective attractive interactions into a simulation model for a single chain such that a swollen coil contracts when the temperature is reduced, until excluded volume interactions are effectively canceled by attractive forces, and the chain conformation becomes almost Gaussian at the theta point. This state corresponds to a tricritical point, as the renormalization group theory shows. Below the theta temperature a fluid globule is predicted (at nonzero concentration then phase separation between dilute and semidilute solutions occurs), while at still lower temperature a transition to a solid phase (crystal or glass) occurs. Monte Carlo simulations have shown, however, that the fluid globule phase may become suppressed, when the range of the effective attractive forces becomes too short, with the result that a direct (ultimately first-order) transition from the swollen coil to the solid occurs. This behavior is analogous to the behavior of colloidal particles with a very short range of attractive forces, where liquid–vapor-type phase separation may be suppressed. Analogous first-order transitions from swollen coils to dense rodlike or toroidal structures occur for semiflexible polymers. Finally, the modifications of the behavior discussed when the polymers are adsorbed at surfaces are also mentioned, and possible relations to wetting behavior of polymer solutions are addressed.

We present a computer simulation study of suspensions of rod-like colloids and a depletant in confinement to a slit-pore. Mixtures of hard spherocylinders and ideal spheres were studied by means of Monte Carlo simulations in the grand canonical ensemble. By use of finite size scaling analysis we determined the critical behaviour. In order to overcome large barriers in the free energy we applied the successive umbrella sampling method (Virnau and Muller 2004 J. Chem. Phys. 120 10925). We find that, under confinement, the critical point of gas–liquid demixing shifts to higher concentrations of rods and smaller concentrations of spheres due to the formation of an orientationally ordered surface film. If the separation between the walls becomes very small, the critical point is shifted back to smaller concentrations of rods because the surface film breaks up. In particular, we present a method for determining the wetting behaviour from an analysis of the distribution of particle concentration. For large wall separations we find wetting near the critical point consistent with the Cahn argument.

Monte Carlo simulation in the grand canonical ensemble, the histogram reweighting technique and finite size scaling are used to study the phase behaviour of dimers in three-dimensional systems. A single molecule is composed of two segments A and B, and the bond between them cannot be broken. The phase diagrams have been estimated for a set of model systems. Different structures formed by heteronuclear dimers have been found. The results show a great variety of vapour–liquid coexistence behaviour depending on the strength of the interactions between segments.

The structure and dynamics of glass forming fluids are accessible in atomistic detail through molecular dynamics simulation. Although for molten silica and its mixtures with oxides of sodium, lithium, aluminium etc only systems at rather high temperatures can be fully equilibrated, since only timescales less than 100 ns are accessible, valuable insight can be gained, including guidance for corresponding experiments. A survey of the state of the art of such simulations and an outlook on open problems will be given.