D. I. Dimitrov

Capillary rise in nanopores : Molecular dynamics evidence for the lucas-washburn equation

When a capillary is inserted into a liquid, the liquid will rapidly flow into it. This phenomenon, well studied and understood on the macroscale, is investigated by molecular dynamics simulations for coarse-grained models of nanotubes. Both a simple Lennard-Jones fluid and a model for a polymer melt are considered. In both cases after a transient period (of a few nanoseconds) the meniscus rises according to a (time)1/2 law. For the polymer melt, however, we find that the capillary flow exhibits a slip length delta, comparable in size with the nanotube radius R. We show that a consistent description of the imbibition process in nanotubes is only possible upon modification of the Lucas-Washburn law which takes explicitly into account the slip length delta. We also demonstrate that the velocity field of the rising fluid close to the interface is not a simple diffusive spreading.

Capillary filling in microchannels with wall corrugations: a comparative study of the Concus-Finn criterion by continuum, kinetic, and atomistic approaches.

We study the impact of wall corrugations in microchannels on the process of capillary filling by means of three broadly used methods: computational fluid dynamics (CFD), lattice Boltzmann equations (LBE), and molecular dynamics (MD). The numerical results of these approaches are compared and tested against the Concus-Finn (CF) criterion, which predicts pinning of the contact line at rectangular ridges perpendicular to flow for contact angles of theta > 45 degrees . Whereas for theta = 30, 40 (no flow), and 60 degrees (flow) all methods are found to produce data consistent with the CF criterion, at theta = 50 degrees the numerical experiments provide different results. Whereas the pinning of the liquid front is observed both in the LB and CFD simulations, MD simulations show that molecular fluctuations allow front propagation even above the critical value predicted by the deterministic CF criterion, thereby introducing a sensitivity to the obstacle height.

Nanoinclusions in polymer brushes with explicit solvent – A molecular dynamics investigation

We use molecular dynamics simulations with a dissipative particle dynamics (DPD) thermostat to study the behavior of nanosized inclusions (colloids) in a polymer brush which is in contact with an explicit solvent in the NPT ensemble. The brush is described by a bead-spring model for flexible polymer chains, grafted on a solid substrate, while the polymer-soluble nanoparticles in the solution are taken as hard spheres. By varying the chain length N, the grafting density of the brush, sigma(g), and the size of the nanoparticles b, we determine the equilibrium particle penetration depth delta and the average concentration of nanoinclusions phi(nano) in the penetration layer delta at constant pressure. In agreement with a recent theoretical prediction, we demonstrate that for nanoinclusions of size bb(*) the thickness of this layer delta is proportional to h(b(*)/b)(3) where h is brush height and b(*) is proportional to sigma(g)(-2/3) is a typical size below which smaller particles are uniformly distributed in the brush. We also observe that particles, larger than some threshold value b(max) do not mix with the brush. The mean density of nanoinclusions is found to scale as phi(nano) is proportional to (b(*)/b)(3) within the whole range of parameter variation. The diffusivity of nanoparticles, embedded in the polymer brush, in direction perpendicular to the grafting plane is found to be up to 20% higher than parallel to the plane. The variation of the respective diffusion coefficients D(perpendicular)(nano) and D(parallel)(nano) changes with growing volume fraction of the nanoparticles in agreement with theoretical predictions.

Universal properties of a single polymer chain in slit: Scaling versus molecular dynamics simulations.

We revisit the classical problem of a polymer confined in a slit in both of its static and dynamic aspects. We confirm a number of well known scaling predictions and analyze their range of validity by means of comprehensive molecular dynamics simulations using a coarse-grained bead-spring model of a flexible polymer chain. The normal and parallel components of the average end-to-end distance, mean radius of gyration and their distributions, the density profile, the force exerted on the slit walls, and the local bond orientation characteristics are obtained in slits of width D=4/10 (in units of the bead diameter) and for chain lengths N=50/300. We demonstrate that a wide range of static chain properties in normal direction can be described quantitatively by analytic model-independent expressions in perfect agreement with computer experiment. In particular, the observed profile of confinement-induced bond orientation is shown to closely match theory predictions. The anisotropy of confinement is found to be manifested most dramatically in the dynamic behavior of the polymer chain. We examine the relation between characteristic times for translational diffusion and lateral relaxation. It is demonstrated that the scaling predictions for lateral and normal relaxation times are in good agreement with our observations. A novel feature is the observed coupling of normal and lateral modes with two vastly different relaxation times. We show that the impact of grafting on lateral relaxation is equivalent to doubling the chain length.

Flow and transport in brush-coated capillaries: A molecular dynamics simulation

We apply an efficient method of forced imbibition to (nano-)capillaries, coated internally with a polymer brush, to derive the change in permeability and suction force, corresponding to different grafting densities and lengths of the polymer chains. While the fluid is modeled by simple point particles interacting with Lennard-Jones forces, the (end-grafted, fully flexible) polymers, which form the brush coating, are described by a standard bead-spring model. Our computer experiments reveal a significant increase in the suction force (by a factor of 4, as compared to the case of a capillary with bare walls) when the brush width approaches the tube radius. A similar growth in the suction force is found when the grafting density of the brush is systematically increased. Even though the permeability of the tube is found to decline with both growing brush width and grafting density, the combined effect on the overall fluid influx into the capillary turns out to be weak, i.e., the total fluid uptake under spont...

Thermal breakage and self-healing of a polymer chain under tensile stress

We consider the thermal breakage of a tethered polymer chain of discrete segments coupled by Morse potentials under constant tensile stress. The chain dynamics at the onset of fracture is studied analytically by Kramers-Langer multidimensional theory and by extensive molecular dynamics simulations in one dimension (1D) and three dimension (3D) space. Comparison with simulation data in one and three dimensions demonstrates that the Kramers-Langer theory provides good qualitative description of the process of bond scission as caused by a collective unstable mode. We derive distributions of the probability for scission over the successive bonds along the chain which reveal the influence of chain ends on rupture in good agreement with theory. The breakage time distribution of an individual bond is found to follow an exponential law as predicted by theory. Special attention is focused on the recombination (self-healing) of broken bonds. Theoretically derived expressions for the recombination time and distance distributions comply with MD observations and indicate that the energy barrier position crossing is not a good criterion for true rupture. It is shown that the fraction of self-healing bonds increases with rising temperature and friction.

Dynamics of a stretched nonlinear polymer chain

We study the relaxation dynamics of a coarse-grained polymer chain at different degrees of stretching by both analytical means and numerical simulations. The macromolecule is modeled as a string of beads, connected by anharmonic springs, subject to a tensile force applied at the end monomer of the chain while the other end is fixed at the origin of coordinates. The impact of bond nonlinearity on the relaxation dynamics of the polymer at different degrees of stretching is treated analytically within the Gaussian self-consistent (GSC) approach and then compared to simulation results derived from two different methods: Monte Carlo (MC) and Molecular Dynamics (MD). At low and medium degrees of chain elongation we find good agreement between GSC predictions and the MC simulations. However, for strongly stretched chains, the MD method, which takes into account inertial effects, reveals two important aspects of the nonlinear interaction between monomers: (i) a coupling and energy transfer between the damped, oscillatory normal modes of the chain and (ii) the appearance of nonvanishing contributions of a continuum of frequencies around the characteristic modes in the power spectrum of the normal mode correlation functions.

Hydrokinetic simulations of nanoscopic precursor films in rough channels

We report on simulations of capillary filling of highly wetting fluids in nanochannels with and without obstacles. We use atomistic (molecular dynamics) and hydrokinetic (lattice Boltzmann; LB) approaches which indicate clear evidence of the formation of thin precursor films, moving ahead of the main capillary front. The dynamics of the precursor films is found to obey a square-root law like that obeyed by the main capillary front, , although with a larger prefactor, which we find to take the same value for the different geometries (2D–3D) under inspection. The two methods show a quantitative agreement which indicates that the formation and propagation of thin precursors can be handled at a mesoscopic/hydrokinetic level. This can be considered as a validation of the LB method and opens the possibility of using hydrokinetic methods to explore space–time scales and complex geometries of direct experimental relevance. Then, the LB approach is used to study the fluid behaviour in a nanochannel when the precursor film encounters a square obstacle. A complete parametric analysis is performed which suggests that thin-film precursors may have an important influence on the efficiency of nanochannel-coating strategies.

Forced imbibition—a tool for separate determination of Laplace pressure and drag force in capillary filling experiments

When a very thin capillary is inserted into a liquid, the liquid is sucked into it: this imbibition process is controlled by a balance of capillary and drag forces which are hard to quantify experimentally, particularly considering flow on the nanoscale. By computer experiments using a generic coarse-grained model, it is shown that an analysis of imbibition forced by a controllable external pressure independently quantifies the Laplace pressure and Darcys permeability as relevant physical parameters governing the imbibition process. From the latter one may then compute the effective pore radius, effective viscosity, dynamic contact angle and slip length of the fluid flowing into the pore. In determining all these parameters independently, the consistency of our analysis of such forced imbibition processes is demonstrated.

Capillary Rise in Nanotubes Coated with Polymer Brushes

The spontaneous rise of a fluid in a brush‐coated nanocapillary is studied by molecular dynamics simulation of a coarse‐grained model. The cases of changing wettability of both the capillary walls and the brush were examined. We also investigated the impact of polymer chain length on the transport of fluid along the nanotube. We found that capillary filling takes place in both lyophilic and lyophobic tubes, provided that the polymer brush coating is wetted by the fluid. In all the cases studied, capillary rise proceeds by a time‐square law, but the mechanisms behind them (Lucas–Washburn or diffusive propagation) differ, depending on the chain length N. For a wettable wall, the speed of fluid imbibition decreases steadily with growing N, whereas the meniscus speed goes through a minimum at intermediate chain lengths. The polymer brush coating reorganizes into “channels” parallel to the tube axis and forms a dense plug of monomers in the vicinity of the meniscus, which moves with the meniscus along the nanotube. For lyophobic capillary walls (covered with a wettable polymer brush), depending on the chain length N, one finds three regimes: (1) short chains—one observes no meniscus motion, but an influx of fluid through the wet brush; (2) intermediate chain lengths—the fluid creates “fluid walls” inside the brush by diffusive spreading, whereby a meniscus is formed and moves up within the fluid walls; and (3) long chains—a “negative curvature” meniscus rises up the capillary by means of diffusive propagation.