Capillary Waves at Liquid/Vapor Interfaces: A Molecular Dynamics Simulation

Evidence for capillary waves at a liquid/vapor interface are presented from extensive molecular dynamics simulations of a system containing up to 1.24 million Lennard-Jones particles. Careful measurements show that the total interfacial width depends logarithmically on $L_\parallel$, the length of the simulation cell parallel to the interface, as predicted theoretically. The strength of the divergence of the interfacial width on $L_\parallel$ depends inversely on the surface tension $\gamma$. This allows us to measure $\gamma$ two ways since $\gamma$ can also be obtained from the difference in the pressure parallel and perpendicular to the interface. These two independent measures of $\gamma$ agree provided that the interfacial order parameter profile is fit to an error function and not a hyperbolic tangent, as often assumed. We explore why these two common fitting functions give different results for $\gamma$

Coating thickness and coverage effects on the forces between silica nanoparticles in water

The structure and interactions of coated silica nanoparticles have been studied in water using molecular dynamics simulations. For 5 nm diameter amorphous silica nanoparticles we studied the effects of varying the chain length and grafting density of polyethylene oxide (PEO) on the nanoparticle coating's shape and on nanoparticle-nanoparticle effective forces. For short ligands of length $n=6$ and $n=20$ repeat units, the coatings are radially symmetric while for longer chains ($n=100$) the coatings are highly anisotropic. This anisotropy appears to be governed primarily by chain length, with coverage playing a secondary role. For the largest chain lengths considered, the strongly anisotropic shape makes fitting to a simple radial force model impossible. For shorter ligands, where the coatings are isotropic, we found that the force between pairs of nanoparticles is purely repulsive and can be fit to the form $(R/2r_\text{core}-1)^{-b}$ where $R$ is the separation between the center of the nanoparticles, $r_\text{core}$ is the radius of the silica core, and $b$ is measured to be between 2.3 and 4.1.Comment: 20 pages, 6 figure

Rheology of Ring Polymer Melts: From Linear Contaminants to Ring/Linear Blends

Ring polymers remain a major challenge to our current understanding of polymer dynamics. Experimental results are difficult to interpret because of the uncertainty in the purity and dispersity of the sample. Using both equilibrium and non-equilibrium molecular dynamics simulations we have systematically investigated the structure, dynamics and rheology of perfectly controlled ring/linear polymer blends with chains of such length and flexibility that the number of entanglements is up to about 14 per chain, which is comparable to experimental systems examined in the literature. The smallest concentration at which linear contaminants increase the zero-shear viscosity of a ring polymer melt of these chain lengths by 10% is approximately one-fifth of their overlap concentration. When the two architectures are present in equal amounts the viscosity of the blend is approximately twice as large as that of the pure linear melt. At this concentration the diffusion coefficient of the rings is found to decrease dramatically, while the static and dynamic properties of the linear polymers are mostly unaffected. Our results are supported by a primitive path analysis.Comment: 5 pages, 4 figures, accepted by PR

Velocity Correlations in Dense Gravity Driven Granular Chute Flow

We report numerical results for velocity correlations in dense, gravity-driven granular flow down an inclined plane. For the grains on the surface layer, our results are consistent with experimental measurements reported by Pouliquen. We show that the correlation structure within planes parallel to the surface persists in the bulk. The two-point velocity correlation function exhibits exponential decay for small to intermediate values of the separation between spheres. The correlation lengths identified by exponential fits to the data show nontrivial dependence on the averaging time \dt used to determine grain velocities. We discuss the correlation length dependence on averaging time, incline angle, pile height, depth of the layer, system size and grain stiffness, and relate the results to other length scales associated with the rheology of the system. We find that correlation lengths are typically quite small, of the order of a particle diameter, and increase approximately logarithmically with a minimum pile height for which flow is possible, \hstop, contrary to the theoretical expectation of a proportional relationship between the two length scales.Comment: 21 pages, 16 figure

Portable implementation of a quantum thermal bath for molecular dynamics simulations

Recently, Dammak and coworkers (H. Dammak, Y. Chalopin, M. Laroche, M. Hayoun, and J.J. Greffet. Quantumthermal bath for molecular dynamics simulation. Phys. Rev. Lett., 103:190601, 2009.) proposed that the quantum statistics of vibrations in condensed systems at low temperature could be simulated by running molecular dynamics simulations in the presence of a colored noise with an appropriate power spectral density. In the present contribution, we show how this method can be implemented in a flexible manner and at a low computational cost by synthesizing the corresponding noise 'on the fly'. The proposed algorithm is tested for a simple harmonic chain as well as for a more realistic model of aluminium crystal. The energy and Debye-Waller factor are shown to be in good agreement with those obtained from harmonic approximations based on the phonon spectrum of the systems. The limitations of the method associated with anharmonic effects are also briefly discussed. Some perspectives for disordered materials and heat transfer are considered.Comment: Accepted for publication in Journal of Statistical Physic

Dynamic surface decoupling in a sheared polymer melt

We propose that several mechanisms contribute to friction in a polymer melt adsorbed at a structured surface. The first one is the well known disentanglement of bulk polymer chains from the surface layer. However, if the surface is ideal at the atomic scale, the adsorbed parts of polymer chains can move along the equipotential lines of the surface potential. This gives rise to a strong slippage of the melt. For high shear rates chains partially desorb. However, the friction force on adsorbed chains increases, resulting in quasi-stick boundary conditions. We propose that the adsorbed layers can be efficiently used to adjust the friction force between the polymer melt and the surface

Scaling of Selfavoiding Tethered Membranes: 2-Loop Renormalization Group Results

The scaling properties of selfavoiding polymerized membranes are studied using renormalization group methods. The scaling exponent \nu is calculated for the first time at two loop order. \nu is found to agree with the Gaussian variational estimate for large space dimension d and to be close to the Flory estimate for d=3.Comment: 4 pages, RevTeX + 20 .eps file

Stress Relaxation in Entangled Polymer Melts

We present an extensive set of simulation results for the stress relaxation in equilibrium and step-strained bead-spring polymer melts. The data allow us to explore the chain dynamics and the shear relaxation modulus, $G(t)$, into the plateau regime for chains with $Z=40$ entanglements and into the terminal relaxation regime for $Z=10$. Using the known (Rouse) mobility of unentangled chains and the melt entanglement length determined via the primitive path analysis of the microscopic topological state of our systems, we have performed parameter -free tests of several different tube models. We find excellent agreement for the Likhtman-McLeish theory using the double reptation approximation for constraint release, if we remove the contribution of high-frequency modes to contour length fluctuations of the primitive chain.Comment: 5 pages, 3 figure

Molecular Dynamics Simulation Study of Nonconcatenated Ring Polymers in a Melt: I. Statics

Molecular dynamics simulations were conducted to investigate the structural properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N=1600 monomers per chain which corresponds to roughly 57 entanglement lengths for comparable linear polymers. For the rings, the radius of gyration squared was found to scale as N to the 4/5 power for an intermediate regime and N to the 2/3 power for the larger rings indicating an overall conformation of a crumpled globule. However, almost all beads of the rings are "surface beads" interacting with beads of other rings, a result also in agreement with a primitive path analysis performed in the following paper (DOI: 10.1063/1.3587138). Details of the internal conformational properties of the ring and linear polymers as well as their packing are analyzed and compared to current theoretical models.Comment: 15 pages, 14 figure

Structure Function of Polymer Nematic Liquid Crystals: A Monte Carlo Simulation

We present a Monte Carlo simulation of a polymer nematic for varying volume fractions, concentrating on the structure function of the sample. We achieve nematic ordering with stiff polymers made of spherical monomers that would otherwise not form a nematic state. Our results are in good qualitative agreement with theoretical and experimental predictions, most notably the bowtie pattern in the static structure function.Comment: 10 pages, plain TeX, macros included, 3 figures available from archive. Published versio