Similarity of percolation thresholds on the hcp and fcc lattices

Extensive Monte-Carlo simulations were performed in order to determine the precise values of the critical thresholds for site ($p^{hcp}_{c,S} = 0.199 255 5 \pm 0.000 001 0$) and bond ($p^{hcp}_{c,B} = 0.120 164 0 \pm 0.000 001 0$) percolation on the hcp lattice to compare with previous precise measuremens on the fcc lattice. Also, exact enumeration of the hcp and fcc lattices was performed and yielded generating functions and series for the zeroth, first, and second moments of both lattices. When these series and the values of $p_c$ are compared to those for the fcc lattice, it is apparent that the site percolation thresholds are different; however, the bond percolation thresholds are equal within error bars, and the series only differ slightly in the higher order terms, suggesting the actual values are very close to each other, if not identical.Comment: 10 pages, 4 figures, submitted to J. Stat. Phy

Charge Inversion of Divalent Ionic Solutions in Silica Channels

Recent experiments (F.H.J. Van Der Heyden et al., PRL 96, 224502 (2006)) of streaming currents in silica nanochannels with divalent ions report charge inversion, i.e. interfacial charges attracting counterions in excess of their own nominal charge, in conflict with existing theoretical and simulation results. We reveal the mechanism of charge inversion by using all-atomic molecular dynamics simulations. Our results show excellent agreement with experiments, both qualitatively and quantitatively. We further discuss the implications of our study for the general problem of ionic correlations in solutions as well as in regards of the properties of silica-water interfaces.Comment: 5 pages, 5 figure

Precise determination of the critical percolation threshold for the three-dimensional “Swiss cheese” model using a growth algorithm

Precise values for the critical threshold for the three-dimensional “Swiss cheese” continuum percolation model have been calculated using extensive Monte Carlo simulations. These simulations used a growth algorithm and memory blocking scheme similar to what we used previously in three-dimensional lattice percolation. The simulations yield a value for the critical number density nc = 0.652 960±0.000 005,nc=0.652960±0.000005, which confirms recent work but extends the precision by two significant figures. © 2001 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70114/2/JCPSA6-114-8-3659-1.pd

Forces between functionalized silica nanoparticles in solution

To prevent the flocculation and phase separation of nanoparticles in solution, nanoparticles are often functionalized with short chain surfactants. Here we present fully-atomistic molecular dynamics simulations which characterize how these functional coatings affect the interactions between nanoparticles and with the surrounding solvent. For 5 nm diameter silica nanoparticles coated with poly(ethylene oxide) (PEO) oligomers in water, we determined the hydrodynamic drag on two approaching nanoparticles moving through solvent and on a single nanoparticle as it approaches a planar surface. In most circumstances, acroscale fluid theory accurately predicts the drag on these nano-scale particles. Good agreement is seen with Brenner's analytical solutions for wall separations larger than the soft nanoparticle radius. For two approaching coated nanoparticles, the solvent-mediated (velocity-independent) and lubrication (velocity-dependent) forces are purely repulsive and do not exhibit force oscillations that are typical of uncoated rigid spheres.Comment: 4 pages, 3 fig

Shape-dependent universality in percolation

The shape-dependent universality of the excess percolation cluster number and cross-configuration probability on a torus is discussed. Besides the aspect ratio of the torus, the universality class depends upon the twist in the periodic boundary conditions, which for example are generally introduced when triangular lattices are used in simulations.Comment: 11 pages, 3 figures, to be published in Physica

Excess number of percolation clusters on the surface of a sphere

Monte Carlo simulations were performed in order to determine the excess number of clusters b and the average density of clusters n_c for the two-dimensional "Swiss cheese" continuum percolation model on a planar L x L system and on the surface of a sphere. The excess number of clusters for the L x L system was confirmed to be a universal quantity with a value b = 0.8841 as previously predicted and verified only for lattice percolation. The excess number of clusters on the surface of a sphere was found to have the value b = 1.215(1) for discs with the same coverage as the flat critical system. Finally, the average critical density of clusters was calculated for continuum systems n_c = 0.0408(1).Comment: 13 pages, 2 figure

Minor chemistry changes alter surface hydration to control fibronectin adsorption and assembly into nanofibrils

Fibronectin (FN) is a large glycoprotein which links and transmits signals between the cell's cytoskeleton and the extracellular matrix. FN organization into fibrils and then fibrillogenesis can be induced with the right substrate, such as poly(ethyl acrylate) (PEA), on which FN becomes extended. Interestingly, the almost identical polymer poly(methyl acrylate) (PMA), which has one less methylene bridge (─CH2─), does not cause fibrillogenesis. To investigate the difference in FN behavior on PEA and PMA, the two substrates are modeled using ethyl acrylate (EA) and methyl acrylate (MA) functionalized self‐assembled monolayers (SAMs). It is confirmed experimentally that the EA and MA SAMs exhibit a similar behavior in vitro to the polymers in terms of fibronectin fibrillogenesis, domain exposure, and cell adhesion. All‐atom molecular dynamics simulations of the FNIII 9‐10 domains interacting with each SAM show the adsorption of these two domains on EA SAMs and no adsorption on MA SAMs. Consistently, the experiments show that FN fibrillogenesis takes place on EA SAMs but not on MA SAMs. It is found that the extra methylene group in the EA headgroup leads to more motion within the headgroup that results in a markedly less dense hydration layer, which facilitates FN fibrillogenesis

Universality of the excess number of clusters and the crossing probability function in three-dimensional percolation

Extensive Monte-Carlo simulations were performed to evaluate the excess number of clusters and the crossing probability function for three-dimensional percolation on the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered cubic (b.c.c.) lattices. Systems L x L x L' with L' >> L were studied for both bond (s.c., f.c.c., b.c.c.) and site (f.c.c.) percolation. The excess number of clusters $\tilde {b}$ per unit length was confirmed to be a universal quantity with a value $\tilde {b} \approx 0.412$. Likewise, the critical crossing probability in the L' direction, with periodic boundary conditions in the L x L plane, was found to follow a universal exponential decay as a function of r = L'/L for large r. Simulations were also carried out to find new precise values of the critical thresholds for site percolation on the f.c.c. and b.c.c. lattices, yielding $p_c(f.c.c.)= 0.199 236 5 \pm 0.000 001 0$, $p_c(b.c.c.)= 0.245 961 5\pm 0.000 001 0$.Comment: 14 pages, 7 figures, LaTeX, submitted to J. Phys. A: Math. Gen, added references, corrected typo

Temperature control in molecular dynamic simulations of non-equilibrium processes

Thermostats are often used in various condensed matter problems, e.g. when a biological molecule undergoes a transformation in a solution, a crystal surface is irradiated with energetic particles, a crack propagates in a solid upon applied stress, two surfaces slide with respect to each other, an excited local phonon dissipates its energy into a crystal bulk, and so on. In all of these problems, as well as in many others, there is an energy transfer between different local parts of the entire system kept at a constant temperature. Very often, when modelling such processes using molecular dynamics simulations, thermostatting is done using strictly equilibrium approaches serving to describe the NV T ensemble. In this paper we critically discuss the applicability of such approaches to non-equilibrium problems, including those mentioned above, and stress that the correct temperature control can only be achieved if the method is based on the generalized Langevin equation (GLE). Specifically, we emphasize that a meaningful compromise between computational efficiency and a physically appropriate implementation of the NV T thermostat can be achieved, at least for solid state and surface problems, if the so-called stochastic boundary conditions (SBC), recently derived from the GLE (Kantorovich and Rompotis 2008 Phys. Rev. B 78 094305), are used. For SBC, the Langevin thermostat is only applied to the outer part of the simulated fragment of the entire system which borders the surrounding environment (not considered explicitly) serving as a heat bath. This point is illustrated by comparing the performance of the SBC and some of the equilibrium thermostats in two problems: (i) irradiation of the Si(001) surface with an energetic CaF2 molecule using an ab initio density functional theory based method, and (ii) the tribology of two amorphous SiO2 surfaces coated with self-assembled monolayers of methyl-terminated hydrocarbon alkoxylsilane molecules using a classical atomistic force field. We discuss the differences in behaviour of these systems due to applied thermostatting, and show that in some cases a qualitatively different physical behaviour of the simulated system can be obtained if an equilibrium thermostat is used