Convergence of dissolving and melting at the nanoscale.

Phase transitions of water and its mixtures are of fundamental importance in physical chemistry, the pharmaceutical industry, materials sciences, and atmospheric sciences. However, current understanding remains elusive to explain relevant observations, especially at the nanoscale. Here, by using molecular dynamics simulations, we investigate the dissolution of sodium chloride (NaCl) nanocrystals with volume-equivalent diameters from 0.51 to 1.75 nm. Our results show that the dissolution of NaCl in aqueous nanodroplets show a strong size dependence, and its solubility can be predicted by the Ostwald-Freundlich equation and Gibbs-Duhem equation after considering a size-dependent solid-liquid surface tension. We find that the structure of dissolved ions in the saturated aqueous nanodropplet resembles the structure of a molten NaCl nanoparticle. With decreasing nanodroplet size, this similarity grows and the average potential energy of NaCl in solution, the molten phase and the crystal phase converges.

In-situ X-ray monitoring of solidification and related processes of metal alloys.

X-ray radioscopy enables the in-situ monitoring of metal alloy processes and then gives access to crucial information on the dynamics of the underlying phenomena. In the last decade, the utilisation of this powerful imaging technique has been adapted to microgravity platforms such as sounding rockets and parabolic flights. The combination of microgravity experimentation with X-ray radioscopy has resulted in a leap in the understanding of fundamental science and has opened new paths in the fields of materials science. The present review focuses on the short history of this research, which includes facility developments, microgravity experiments and results obtained by partners of the XRMON (In-situ X-Ray MONitoring of advanced metallurgical processes under microgravity and terrestrial conditions) research project in the framework of the MAP (Microgravity Application Promotion) programme of the European Space Agency. Three illustrative research topics that were advanced significantly through the use of X-ray radioscopy will be detailed: solidification of metal alloys, metallic foam formation and diffusion in melts.

Adsorption of Semiflexible Polymers in Cylindrical Tubes.

Conformations of wormlike chains in cylindrical pores with attractive walls are explored for varying pore radius and strength of the attractive wall potential by molecular dynamics simulations of a coarse-grained model. Local quantities such as the fraction of monomeric units bound to the surface and the bond-orientational order parameter as well as the radial density distribution are studied, as well as the global chain extensions parallel to the cylinder axis and perpendicular to the cylinder surface. A nonmonotonic convergence of these properties to their counterparts for adsorption on a planar substrate is observed due to the conflict between pore surface curvature and chain stiffness. Also the interpretation of partially adsorbed chains in terms of trains, loops, and tails is discussed.

How does stiffness of polymer chains affect their adsorption transition?

The adsorption transition and the structure of semiflexible adsorbed macromolecules are studied by a molecular dynamics simulation of a coarse-grained, bead-spring type model. Varying chain length N and stiffness κ (which is proportional to the persistence length ℓp in d = 3 dimensions) as well as the strength ϵwall of the adsorption potential, the adsorbed monomer fraction, orientational bond order parameter, and chain linear dimensions are studied. In the simulations, excluded volume interactions normally are included but can be "switched off," and thus, the influence of excluded volume (leading to deviations from predictions of the wormlike chain model) can be identified. It is shown that the variation in the adsorption threshold ϵwall cr with ℓp is compatible with the predicted law ϵwall cr∝ℓp -1/3. In the vicinity of the adsorption threshold, the coils are still three-dimensional, and for large ℓp, the effect of the excluded volume is almost negligible, while for strongly adsorbed chains it is always felt. Near the transition, the decay length of orientational correlations along the chain contour increases gradually from ℓp to 2ℓp. While the latter value is expected for strictly two-dimensional chains from the Kratky-Porod model, this model is inaccurate for the description of lateral chain dimensions of long, strongly adsorbed, semiflexible polymers due to its neglect of excluded volume. The significance of these findings for the interpretation of pertinent experiments is briefly discussed.

Probing predictions due to the nonlocal interface Hamiltonian: Monte Carlo simulations of interfacial fluctuations in Ising films.

Extensive Monte Carlo simulations have been performed on an Ising ferromagnet under conditions that would lead to complete wetting in a semi-infinite system. We studied an L×L×D slab geometry with oppositely directed surface fields so that a single interface is formed and can undergo a localization-delocalization transition. Under the chosen conditions the interface position is, on average, in the middle of the slab, and its fluctuations allow a sensitive test of predictions that the effective interactions between the interface and the confining surfaces are nonlocal. The decay of distance dependent correlation functions are measured within the surface, in the middle of the slab, and between middle and the surface for slabs of varying thickness D. From Fourier transforms of these correlation functions a nonlinear correlation length is extracted, and its behavior is found to confirm theoretical predictions for D>6 lattice spacings.

Finite-size scaling for a first-order transition where a continuous symmetry is broken: The spin-flop transition in the three-dimensional XXZ Heisenberg antiferromagnet.

Finite-size scaling for a first-order phase transition where a continuous symmetry is broken is developed using an approximation of Gaussian probability distributions with a phenomenological "degeneracy" factor included. Predictions are compared with data from Monte Carlo simulations of the three-dimensional, XXZ Heisenberg antiferromagnet in a field in order to study the finite-size behavior on a L×L×L simple cubic lattice for the first-order "spin-flop" transition between the Ising-like antiferromagnetic state and the canted, XY-like state. Our theory predicts that for large linear dimension L the field dependence of all moments of the order parameters as well as the fourth-order cumulants exhibit universal intersections. Corrections to leading order should scale as the inverse volume. The values of these intersections at the spin-flop transition point can be expressed in terms of a factor q that characterizes the relative degeneracy of the ordered phases. Our theory yields q=π, and we present numerical evidence that is compatible with this prediction. The agreement between the theory and simulation implies a heretofore unknown universality can be invoked for first-order phase transitions.

Relaxation processes and glass transition of confined polymer melts: A molecular dynamics simulation of 1,4-polybutadiene between graphite walls.

Molecular dynamics simulations of a chemically realistic model for 1,4-polybutadiene in a thin film geometry confined by two graphite walls are presented. Previous work on melts in the bulk has shown that the model faithfully reproduces static and dynamic properties of the real material over a wide temperature range. The present work studies how these properties change due to nano-confinement. The focus is on orientational correlations observable in nuclear magnetic resonance experiments and on the local intermediate incoherent neutron scattering function, Fs(qz, z, t), for distances z from the graphite walls in the range of a few nanometers. Temperatures from about 2Tg down to about 1.15Tg, where Tg is the glass transition temperature in the bulk, are studied. It is shown that weakly attractive forces between the wall atoms and the monomers suffice to effectively bind a polymer coil that is near the wall. For a wide regime of temperatures, the Arrhenius-like adsorption/desorption kinetics of the monomers is the slowest process, while very close to Tg the Vogel-Fulcher-Tammann-like α-relaxation takes over. The α-process is modified only for z≤1.2 nm due to the density changes near the walls, less than expected from studies of coarse-grained (bead-spring-type) models. The weakness of the surface effects on the glass transition in this case is attributed to the interplay of density changes near the wall with the torsional potential. A brief discussion of pertinent experiments is given.

Wall-induced orientational order in athermal semidilute solutions of semiflexible polymers: Monte Carlo simulations of a lattice model.

An athermal solution of semiflexible macromolecules with excluded volume interactions has been studied at various concentrations (dilute, semidilute, and concentrated solutions) in a film of thickness D between two hard walls by grand canonical Monte Carlo simulations of the bond fluctuation lattice model. Analyzing profiles of orientational order parameters across the film, we find that for thick films two phase transitions occur at chemical potentials of the polymers (or polymer densities, respectively) where the bulk polymer solution still is in the disordered isotropic phase. At rather small polymer densities, polymers accumulate at the walls due to an entropic attraction and undergo a transition to two-dimensional nematic order. Due to the properties of the lattice model, this order has Ising character, and the simulation results seem to be compatible with a second-order transition. Increasing the polymer density, nematically ordered "wetting" layers form at both walls; the increase of thickness of these layers is compatible with a logarithmic divergence when the chemical potential of the isotropic-nematic transition in the bulk is approached. In a system of finite width, D, between the walls, this leads to capillary nematization, exhibiting a reduction of the transition chemical potential inversely proportional to D. This transition exists only if D exceeds some critical value Dc, while the transition from the isotropic phase to the two-dimensional nematic state is suggested to persist down to ultrathin films.

Controlling the wetting properties of the Asakura-Oosawa model and applications to spherical confinement.

We demonstrate for the Asakura-Oosawa model and an extension of this model that uses continuous rather than hard potentials, how wetting properties at walls can be easily controlled. By increasing the interaction range of the repulsive wall potential acting on the colloids (while keeping the polymer-wall interactions constant) polymers begin to substitute colloids at walls and the system can be driven from complete wetting of colloids via partial wetting to complete wetting of polymers. As an application, we discuss the morphology and wetting behavior of colloid-polymer mixtures in spherical confinement. We apply the recently developed 'ensemble switch method' where the Hamiltonian is extended to a combination of a system with walls and of a system without walls to calculate the surface excess free energies of colloid-rich and polymer-rich phases. The contact angle then is inferred from Young's equation.

Effects of confinement and external fields on structure and transport in colloidal dispersions in reduced dimensionality.

In this work, we focus on low-dimensional colloidal model systems, via simulation studies and also some complementary experiments, in order to elucidate the interplay between phase behavior, geometric structures and transport properties. In particular, we try to investigate the (nonlinear!) response of these very soft colloidal systems to various perturbations: uniform and uniaxial pressure, laser fields, shear due to moving boundaries and randomly quenched disorder. We study ordering phenomena on surfaces or in monolayers by Monte Carlo computer simulations of binary hard-disk mixtures, the influence of a substrate being modeled by an external potential. Weak external fields allow a controlled tuning of the miscibility of the mixture. We discuss the laser induced de-mixing for the three different possible couplings to the external potential. The structural behavior of hard spheres interacting with repulsive screened Coulomb or dipolar interaction in 2D and 3D narrow constrictions is investigated using Brownian dynamics simulations. Due to misfits between multiples of the lattice parameter and the channel widths, a variety of ordered and disordered lattice structures have been observed. The resulting local lattice structures and defect probabilities are studied for various cross sections. The influence of a self-organized order within the system is reflected in the velocity of the particles and their diffusive behavior. Additionally, in an experimental system of dipolar colloidal particles confined by gravity on a solid substrate we investigate the effect of pinning on the dynamics of a two-dimensional colloidal liquid. This work contains sections reviewing previous work by the authors as well as new, unpublished results. Among the latter are detailed studies of the phase boundaries of the de-mixing regime in binary systems in external light fields, configurations for shear induced effects at structured walls, studies on the effect of confinement on the structures and defect densities in three-dimensional systems, the effect of confinement and barriers on two-dimensional flow and diffusion, and the effect of pinning sites on the diffusion.

Effect of solvent quality on the dispersibility of polymer-grafted spherical nanoparticles in polymer solutions.

In this work, lattice-based self consistent field theory is used to study the structural properties of individual polymer-grafted spherical nanopartices and particle-particle interactions in polymer melts and solutions under variable solvent conditions. Our study has focused on the depth of the minimum in the potential of mean force between the two brush-coated nanoparticles, if such a minimum occurs, and we have also addressed the corresponding radial density profiles of free and grafted chains around a single nanoparticle, in an attempt to clarify the extent of correlation between the depth of the minimum, W(min), and the parameter δ characterizing the interpenetration between the profiles of free and grafted chains. Although one cannot establish a simple one-to-one correspondence between W(min) and δ, we do find common trends, in particular, if the solvent conditions for free and grafted chains differ: varying the volume fraction of the free chains, δ typically exhibits a broad minimum, corresponding to a region where the magnitude of W(min) exceeds thermal energy k(B)T, leading to particle aggregation.

Langevin dynamics simulations of a two-dimensional colloidal crystal under confinement and shear.

Langevin dynamics simulations are used to study the effect of shear on a two-dimensional colloidal crystal (with implicit solvent) confined by structured parallel walls. When walls are sheared very slowly, only two or three crystalline layers next to the walls move along with them, while the inner layers of the crystal are only slightly tilted. At higher shear velocities, this inner part of the crystal breaks into several pieces with different orientations. The velocity profile across the slit is reminiscent of shear banding in flowing soft materials, where liquid and solid regions coexist; the difference, however, is that in the latter case the solid regions are glassy while here they are crystalline. At even higher shear velocities, the effect of the shearing becomes smaller again. Also the effective temperature near the walls (deduced from the velocity distributions of the particles) decreases again when the wall velocity gets very large. When the walls are placed closer together, thereby introducing an incommensurability between the periodicity of the confined crystal and the walls, a structure containing a soliton staircase arises in simulations without shear. Introducing shear increases the disorder in these systems until no solitons are visible anymore. Instead, similar structures like in the case without mismatch result. At high shear rates, configurations where the incommensurability of the crystalline structure is compensated by the creation of holes become relevant.

Mean arterial pressure following prolonged exercise in the heat: influence of training status and fluid replacement.

Prolonged exercise in the heat without fluid replacement represents a significant challenge to the regulation of mean arterial pressure (MAP). It is unknown, however, if MAP is equally challenged during the post-exercise period, and whether regular endurance exercise training can provide any benefit to its regulation. We examined MAP (Finometer) in eight trained (T) and eight untrained (UT) individuals prior to, and following, 120 min of cycling at 42 °C with (HYD) and without (DEHY) fluid replacement. Exercise during DEHY induced significant hyperthermia (T: 39.20 ± 0.52 °C vs UT: 38.70 ± 0.36 °C, P = 0.941) and body weight losses (T: 3.4 ± 1.2% vs UT: 2.7 ± 0.9%, P = 0.332), which did not differ between groups. Although MAP was equally reduced 5 min into the post-exercise period of DEHY (T: -20 ± 11 mmHg vs UT: -22 ± 13 mmHg, P = 0.800), its subsequent recovery was significantly different between groups (P = 0.037). While MAP returned to pre-exercise values in UT (-1 ± 3 mmHg), it remained reduced in T (-9 ± 3 mmHg, P = 0.028). No differences in MAP post-exercise were observed between groups during HYD. These data suggest that trained men exhibit a greater level of post-exercise hypotension following prolonged exercise in the heat without fluid replacement. Furthermore, fluid replacement reverses the sustained post-exercise hypotension observed in trained individuals.

Microcanonical determination of the interface tension of flat and curved interfaces from Monte Carlo simulations.

The investigation of phase coexistence in systems with multi-component order parameters in finite systems is discussed and, as a generic example, Monte Carlo simulations of the two-dimensional q-state Potts model (q = 30) on L × L square lattices (40 ≤ L ≤ 100) are presented. It is shown that the microcanonical ensemble is well suited both to find the precise location of the first-order phase transition and to obtain an accurate estimate for the interfacial free energy between coexisting ordered and disordered phases. For this purpose, a microcanonical version of the heat bath algorithm is implemented. The finite size behaviour of the loop in the curve describing the inverse temperature versus energy density is discussed, emphasizing that the extrema do not have the meaning of van der Waals-like 'spinodal points' separating metastable from unstable states, but rather describe the onset of heterophase states: droplet/bubble evaporation/condensation transitions. Thus all parts of these loops, including the parts that correspond to a negative specific heat, describe phase coexistence in full thermal equilibrium. However, the estimates for the curvature-dependent interface tension of the droplets and bubbles suffer from unexpected and unexplained large finite size effects which need further study.

Numerical approaches to determine the interface tension of curved interfaces from free energy calculations.

A recently proposed method to obtain the surface free energy σ(R) of spherical droplets and bubbles of fluids, using a thermodynamic analysis of two-phase coexistence in finite boxes at fixed total density, is reconsidered and extended. Building on a comprehensive review of the basic thermodynamic theory, it is shown that from this analysis one can extract both the equimolar radius R(e) as well as the radius R(s) of the surface of tension. Hence the free energy barrier that needs to be overcome in nucleation events where critical droplets and bubbles are formed can be reliably estimated for the range of radii that is of physical interest. It is found that the conventional theory of nucleation, where the interface tension of planar liquid-vapor interfaces is used to predict nucleation barriers, leads to a significant overestimation, and this failure is particularly large for bubbles. Furthermore, different routes to estimate the effective radius-dependent Tolman length δ(R(s)) from simulations in the canonical ensemble are discussed. Thus we obtain an instructive exemplification of the basic quantities and relations of the thermodynamic theory of metastable droplets/bubbles using simulations. However, the simulation results for δ(R(s)) employing a truncated Lennard-Jones system suffer to some extent from unexplained finite size effects, while no such finite size effects are found in corresponding density functional calculations. The numerical results are compatible with the expectation that δ(R(s) → ∞) is slightly negative and of the order of one tenth of a Lennard-Jones diameter, but much larger systems need to be simulated to allow more precise estimates of δ(R(s) → ∞).

Active nonlinear microrheology in a glass-forming Yukawa fluid.

A molecular dynamics computer simulation of a glass-forming Yukawa mixture is used to study the anisotropic dynamics of a single particle pulled by a constant force. Beyond linear response, a scaling regime is found where a force-temperature superposition principle of a Peclet number holds. In the latter regime, the diffusion dynamics perpendicular to the force can be mapped on the equilibrium dynamics in terms of an effective temperature, whereas parallel to the force a superdiffusive behavior is seen in the long-time limit. This behavior is associated with a hopping motion from cage to cage and can be qualitatively understood by a simple trap model.

Phase transitions in thin films with competing surface fields and gradients.

As a generic model for phase equilibria under confinement in a thin-film geometry in the presence of a gradient in the field conjugate to the order parameter, an Ising-lattice gas system is studied by both Monte Carlo simulations and a phenomenological theory. Choosing an L×L×D geometry with L≫D and periodic boundary conditions in the x,y directions, we place competing surface fields on the two L×L surfaces. In addition, a field gradient g is present in the z direction across the film, in competition with the surface fields. At temperatures T exceeding the critical temperature of the interface localization-delocalization transition, one finds a phase coexistence between oppositely oriented domains, aligned parallel to the surface fields and separated by an interface in the center of the film, for small enough g. For a weak gradient, a second-order transition to a monodomain state occurs, but it becomes first order if g exceeds a tricritical threshold. For sufficiently large gradients, another domain state becomes stabilized with domains oriented antiparallel to the surface fields.

Orientational ordering transitions of semiflexible polymers in thin films: a Monte Carlo simulation.

Athermal solutions (from dilute to concentrated) of semiflexible macromolecules confined in a film of thickness D between two hard walls are studied by means of grand-canonical lattice Monte Carlo simulation using the bond fluctuation model. This system exhibits two phase transitions as a function of the thickness of the film and polymer volume fraction. One of them is the bulk isotropic-nematic first-order transition, which ends in a critical point on decreasing the film thickness. The chemical potential at this transition decreases with decreasing film thickness ("capillary nematization"). The other transition is a continuous (or very weakly first-order) transition in the layers adjacent to the hard planar walls from the disordered phase, where the bond vectors of the macromolecules show local ordering (i.e., "preferential orientation" along the x or y axes of the simple cubic lattice, but no long-range orientational order occurs), to a quasi-two-dimensional nematic phase (with the director at each wall being oriented along either the x or y axis), while the bulk of the film is still disordered. When the chemical potential or monomer density increase, respectively, the thickness of these surface-induced nematic layers grows, causing the disappearance of the disordered region in the center of the film.

Simulation evidence for nonlocal interface models: two correlation lengths describe complete wetting.

Monte Carlo simulations of (fluctuating) interfaces in Ising models confined between competing walls at temperatures above the wetting transition are presented and various correlation functions probing the interfacial fluctuation are computed. Evidence for the nonlocal interface Hamiltonian approach of A. O. Parry et al. [Phys. Rev. Lett. 93, 086104 (2004)] is given. In particular, we show that two correlation lengths exist with different dependence on the distance D between the walls.

Polymer-brush lubricated surfaces with colloidal inclusions under shear inversion.

We characterize the response of compressed, sheared polymer-brush bilayers with colloidal inclusions to highly nonstationary inversion processes by means of molecular dynamics simulations and scaling theory. Bilayers with a simple (dimeric) solvent reveal an overshoot for the shear stress, while simulations of dry brushes without explicit solvent molecules fail to display this effect. We demonstrate that mechanical instabilities can be controlled by the inclusion of macromolecular structures, such as colloids of varying softness. Based on a recently developed theory, we suggest a scaling approach to determine a characteristic time for conformational and collective responses.