Search results for "Scaling"

Island Diffusion on Metal fcc (100) Surfaces

1999

We present Monte Carlo simulations for the size and temperature dependence of the diffusion coefficient of adatom islands on the Cu(100) surface. We show that the scaling exponent for the size dependence is not a constant but a decreasing function of the island size and approaches unity for very large islands. This is due to a crossover from periphery dominated mass transport to a regime where vacancies diffuse inside the island. The effective scaling exponents are in good agreement with theory and experiments.

Does Young's equation hold on the nanoscale? A Monte Carlo test for the binary Lennard-Jones fluid

2010

When a phase-separated binary ($A+B$) mixture is exposed to a wall, that preferentially attracts one of the components, interfaces between A-rich and B-rich domains in general meet the wall making a contact angle $\theta$. Young's equation describes this angle in terms of a balance between the $A-B$ interfacial tension $\gamma_{AB}$ and the surface tensions $\gamma_{wA}$, $\gamma_{wB}$ between, respectively, the $A$- and $B$-rich phases and the wall, $\gamma _{AB} \cos \theta =\gamma_{wA}-\gamma_{wB}$. By Monte Carlo simulations of bridges, formed by one of the components in a binary Lennard-Jones liquid, connecting the two walls of a nanoscopic slit pore, $\theta$ is estimated from the inc…

Bridging scales with thermodynamics: from nano to macro

2014

We have recently developed a method to calculate thermodynamic properties of macroscopic systems by extrapolating properties of systems of molecular dimensions. Appropriate scaling laws for small systems were derived using the method for small systems thermodynamics of Hill, considering surface and nook energies in small systems of varying sizes. Given certain conditions, Hill's method provides the same systematic basis for small systems as conventional thermodynamics does for large systems. We show how the method can be used to compute thermodynamic data for the macroscopic limit from knowledge of fluctuations in the small system. The rapid and precise method offers an alternative to curre…

A new boundary-controlled phase transition: Phase separation in an Ising bi-pyramid with competing surface fields

2005

We study phase coexistence of an Ising ferromagnet in a bi-pyramid geometry with a square basal plane of linear extension 2L + 1. Antisymmetric surface fields act on the pyramid surfaces above and below the basal plane. In the limit L → ∞, the magnetisation stays zero at the bulk critical temperature, but becomes discontinuously non-zero at the cone filling critical temperature associated with a single pyramid. Monte Carlo simulations and scaling considerations show that this transition is described by a Landau theory with size-dependent coefficients that give rise to singular critical amplitudes.

Kirkwood–Buff Integrals Using Molecular Simulation: Estimation of Surface Effects

2020

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Polymer Brushes on Flat and Curved Substrates: Scaling Concepts and Computer Simulations

2007

The scaling concepts for isolated flexible macromolecules in good solvent grafted with one chain end to a flat surface (polymer mushrooms) as well as for layers of many overlapping end-grafted chain molecules (polymer brushes) are introduced. Monte Carlo attempts to test these concepts are briefly reviewed. Then the extension of these concepts to polymer brushes grafted to the interior of a cylinder surface is discussed. Molecular Dynamics results on chain average linear dimensions in the direction normal to the grafting surface and in axial direction are described, as well as distribution functions for the density of end monomers and of all monomers of the chains. It is argued that under t…

Controlling the Interactions between Soft Colloids via Surface Adsorption

2013

By employing monomer-resolved computer simulations and analytical considerations based on polymer scaling theory, we analyze the conformations and interactions of multiarm star polymers strongly adsorbed on a smooth, two-dimensional plane. We find a stronger stretching of the arms as well as a stronger repulsive, effective interaction than in the three dimensional case. In particular, the star size scales with the number of arms $f$ as $\sim f^{1/4}$ and the effective interaction as $\sim f^{2}$, as opposed to $\sim f^{1/5}$ and $\sim f^{3/2}$, respectively, in three dimensions. Our results demonstrate the dramatic effect that geometric confinement can have on the effective interactions and…

Comment on “Finite-size scaling behavior of the tracer surface diffusion coefficient near a second-order phase transition” by F. Nieto et al.

2000

Universal critical behavior of curvature-dependent interfacial tension.

2011

From the analysis of Monte Carlo simulations of a binary Lennard-Jones mixture in the coexistence region, we provide evidence that the curvature dependence of the interfacial tension can be described by a simple theoretical function σ(R)ξ(2)=C(1)/[1+C(2)(ξ/R)(2)], where ξ is the correlation length and R is the droplet radius. The universal constants C(1) and C(2) are estimated. In the model, a Tolman length is strictly absent, but, since its critical behavior is believed to be much weaker than ξ, we argue that it only provides a correction to scaling and does not affect the leading critical behavior, which should be described by the above function for any system in the Ising universality cl…

Monte Carlo studies of anisotropic surface tension and interfacial roughening in the three-dimensional Ising model.

1989

Extensive Monte Carlo simulations of the simple cubic Ising model with nearest-neighbor ferromagnetic interactions with a tilted interface are presented for a wide range of lattice size L, temperature T, and tilt angles \ensuremath{\theta}. The anisotropic interfacial tension is studied in detail. From the small-angle data, we obtain the step free energy density ${f}_{S}$(T,L). Finite-size scaling of the step free energy density is discussed and used to probe the predicted temperature dependence of the correlation length near and above the roughening transition. The square-root temperature dependence predicted by solid-on-solid model calculations is exhibited. Finite-size scaling implies th…