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.

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.

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.

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.

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.

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.

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) → ∞).

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.

Positive Tolman length in a lattice gas with three-body interactions.

We present a new method to determine the curvature dependence of the interface tension between coexisting phases in a finite volume from free energies obtained by Monte Carlo simulations. For the example of a lattice gas on a 3D fcc lattice with nearest neighbor three-body interactions, we demonstrate how to calculate the equimolar radius R(e) as well as the radius R(s) of the surface of tension and thus the Tolman length δ(R(s))=R(e)-R(s). Within the physically relevant range of radii, δ(R(s)) shows a pronounced R(s) dependence, such that the simple Tolman parametrization for the interface tension is refutable. For the present model, extrapolation of δ(R(s)) to R(s)→∞ by various methods clearly indicates a positive limiting value.

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.

Analysis of the cluster formation in two-component cylindrical bottle-brush polymers under poor solvent conditions: a simulation study.

Two-component bottle-brush polymers, where flexible side chains containing N = 20, 35 and 50 effective monomers are grafted alternatingly to a rigid backbone, are studied by Molecular Dynamics simulations, varying the grafting density [Formula: see text] and the solvent quality. Whereas for poor solvents and large enough [Formula: see text] the molecular brush is a cylindrical object with monomers of different type occupying locally the two different halves of the cylinder, for intermediate values of [Formula: see text] an axially inhomogeneous structure of "pearl-necklace" type is formed, where microphase separation between monomers of different type within a cluster takes place. These "pearls" have a strongly non-spherical ellipsoidal shape, due to the fact that several side chains cluster together in one "pearl". We discuss the resulting structures in detail and we present a comparison with the single-component bottle-brush case.

Polymer-brush lubrication in the limit of strong compression.

By means of molecular dynamics simulations we demonstrate power laws for macroscopic transport properties of strongly compressed polymer-brush bilayers to stationary shear motion beyond the Newtonian response. The corresponding exponents are derived from a recently developed scaling theory, where the interpenetration between the brushes is taken as the relevant length scale. This allows to predict the dependence of the critical shear rate, which separates linear and non-linear behavior, on compression and molecular parameters of the bilayer. We present scaling plots for chain extension (R), viscosity (η) , and shear force (F over a wide range of Weissenberg numbers, W . In agreement with our theory, the simulation reveals simple power laws, R ∼ W (0.53), η ∼ W (-0.46), and F ∼ W (0.54), for the non-Newtonian regime.

Probe molecules in polymer melts near the glass transition: A molecular dynamics study of chain length effects.

Molecular dynamics simulations of a dense melt of short bead-spring polymer chains containing N=5, 10, or 25 effective monomers are presented and analyzed. Parts of our simulations include also a single dumbbell (N=2) of the same type, which is interpreted to represent a coarse-grained model for a fluorescent probe molecule as used in corresponding experiments. We obtain the mean-square displacements of monomers and chains center of mass, and intermediate incoherent scattering functions of both monomers in the chains and particles in the dumbbells as function of time for a broad regime of temperatures above the critical temperature T(c) of mode-coupling theory. For both the chains and the dumbbell, also orientational autocorrelation functions are calculated and for the dumbbell time series for the time evolution of linear dichroism and its autocorrelation function are studied. From both sets of data we find that both the mode-coupling critical temperature T(c) (representing the "cage effect") and the Vogel-Fulcher temperature T(0) (representing the caloric glass transition temperature) systematically increase with chain length. Furthermore, the dumbbell dynamics yields detailed information on the differences in the matrix dynamics that are caused by the chain length variation. Deviations from the Stokes-Einstein relation are discussed, and an outlook to related experiments is given.

Pearl-necklace structures of molecular brushes with rigid backbone under poor solvent conditions: A simulation study.

Bottle-brush polymers, where flexible side chains containing N=20 to 50 effective monomers are grafted to a rigid backbone, are studied by molecular dynamics simulations, varying the grafting density σ and the solvent quality. Whereas for poor solvents and large enough σ the molecular brush is a cylindrical object, homogeneous in axial direction, for intermediate values of σ an axially inhomogeneous structure of "pearl-necklace" type is formed. The "pearls," however, have a strongly nonspherical ellipsoidal shape, due to the fact that several side chains cluster together in one pearl, qualitatively consistent with predictions of Sheiko et al. [Eur. Phys. J. E 13, 125 (2004)] We analyze the structure of these pearls and study both the transition to the axially uniform cylinder at high σ and to the trivial pearl-necklace structure at small σ, where each pearl contains a single collapsed chain only.

Capillary condensation in cylindrical pores: Monte Carlo study of the interplay of surface and finite size effects.

When a fluid that undergoes a vapor to liquid transition in the bulk is confined to a long cylindrical pore, the phase transition is shifted (mostly due to surface effects at the walls of the pore) and rounded (due to finite size effects). The nature of the phase coexistence at the transition depends on the length of the pore: for very long pores, the system is axially homogeneous at low temperatures. At the chemical potential where the transition takes place, fluctuations occur between vapor- and liquidlike states of the cylinder as a whole. At somewhat higher temperatures (but still far below bulk criticality), the system at phase coexistence is in an axially inhomogeneous multidomain state, where long cylindrical liquid- and vaporlike domains alternate. Using Monte Carlo simulations for the Ising/lattice gas model and the Asakura-Oosawa model of colloid-polymer mixtures, the transition between these two different scenarios is characterized. It is shown that the density distribution changes gradually from a double-peak structure to a triple-peak shape, and the correlation length in the axial direction (measuring the equilibrium domain length) becomes much smaller than the cylinder length. The (rounded) transition to the disordered phase of the fluid occurs when the axial correlation length has decreased to a value comparable to the cylinder diameter. It is also suggested that adsorption hysteresis vanishes when the transition from the simple domain state to the multidomain state of the cylindrical pore occurs. We predict that the difference between the pore critical temperature and the hysteresis critical temperature should increase logarithmically with the length of the pore.

Monte Carlo simulations of the solid-liquid transition in hard spheres and colloid-polymer mixtures.

Monte Carlo simulations at constant pressure are performed to study coexistence and interfacial properties of the liquid-solid transition in hard spheres and in colloid-polymer mixtures. The latter system is described as a one-component Asakura-Oosawa (AO) model where the polymer's degrees of freedom are incorporated via an attractive part in the effective potential for the colloid-colloid interactions. For the considered AO model, the polymer reservoir packing fraction is eta(p) (r)=0.1 and the colloid-polymer size ratio is q[triple bond]sigma(p)/sigma=0.15 (with sigma(p) and sigma as the diameter of polymers and colloids, respectively). Inhomogeneous solid-liquid systems are prepared by placing the solid fcc phase in the middle of a rectangular simulation box, creating two interfaces with the adjoined bulk liquid. By analyzing the growth of the crystalline region at various pressures and for different system sizes, the coexistence pressure p(co) is obtained, yielding p(co)=11.576 k(B)T/sigma(3) for the hard-sphere system and p(co)=8.00 k(B)T/sigma(3) for the AO model (with k(B) as the Boltzmann constant and T as the temperature). Several order parameters are introduced to distinguish between solid and liquid phases and to describe the interfacial properties. From the capillary-wave broadening of the solid-liquid interface, the interfacial stiffness is obtained for the (100) crystalline plane, giving the values gamma approximately 0.49 k(B)T/sigma(2) for the hard-sphere system and gamma approximately 0.95 k(B)T/sigma(2) for the AO model.

Monte Carlo test of the classical theory for heterogeneous nucleation barriers.

Flat walls facilitate the condensation of a supersaturated vapor: classical theory of heterogeneous nucleation predicts that the free energy barrier DeltaF(het)*, which needs to be overcome for the formation of sphere-cap-shaped nucleation seeds, is smaller than the barrier DeltaF(hom)* for spherical droplets in the bulk by a factor 0 < f(theta) < 1, which only depends on the contact angle theta. In this Letter, we compute both DeltaF(hom)* and DeltaF(het)* from Monte Carlo simulations and test the theory for the lattice gas model (for which theta can be readily controlled). Even though the theory is only based on macroscopic arguments, it is shown to hold for experimentally relevant nanoscopic nucleation seeds (20 < or = DeltaF(hom)*/k(B)T < or = 200) if (independently estimated) line tension effects are considered.