[Show abstract][Hide abstract] ABSTRACT: We use molecular dynamics simulations with a dissipative particle dynamics thermostat to study the behavior of nanosized inclusions (colloids) in a polymer brush under shear whereby the solvent is explicitly included in the simulation. 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 soft spheres whose diameter is about three times larger than that of the chain segments and the solvent. We find that the brush number density profile, as well as the density profiles of the nanoinclusions and the solvent, remains insensitive to strong shear although the grafted chains tilt in direction of the flow. The thickness of the penetration layer of nanoinclusions, as well as their average concentration in the brush, stays largely unaffected even at the strongest shear. Our result manifests the remarkable robustness of polymer brushes with embedded nanoparticles under high shear which could be of importance for technological applications.
[Show abstract][Hide abstract] ABSTRACT: 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.
The Journal of Chemical Physics 05/2010; 132(20):204902. DOI:10.1063/1.3427245 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We demonstrate an efficient and reliable method for wettability characterization by determining the contact angle theta which a liquid-vapor interface makes with a solid wall. The purpose is to overcome the difficulties, related to the curvature of the liquid-vapor interface, which make measurements of theta rather uncertain, especially on the micro- and nanoscale. The method employs a specially designed slitlike channel in contact with a reservoir whereby the wettability of one of the slit walls is to be examined whereas the other (auxiliary) wall is separated by half into a lyophilic and a lyophobic part so as to pin the incoming fluid and fix the one end of the liquid-vapor interface. In the present work, the physical background of the method is elucidated theoretically while the method's applicability is demonstrated by molecular-dynamics simulation of a typical Lennard-Jones fluid, in contact with an atomistic wall. The wettability of the latter, as described by the corresponding contact angle theta, is accurately determined by variation of the liquid-wall interaction in a very broad interval.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: A flexible polymer chain under good solvent conditions, end-grafted on a flat repulsive substrate surface and compressed by a piston of circular cross-section with radius L may undergo the so-called "escape transition" when the height of the piston D above the substrate and the chain length N are in a suitable range. In this transition, the chain conformation changes from a quasi-two-dimensional self-avoiding walk of "blobs" of diameter D to an inhomogeneous "flower" state, consisting of a "stem" (stretched string of blobs extending from the grafting site to the piston border) and a "crown" outside of the confining piston. The theory of this transition is developed using a Landau free-energy approach, based on a suitably defined (global) order parameter and taking also effects due to the finite chain length N into account. The parameters of the theory are determined in terms of known properties of limiting cases (unconfined mushroom, chain confined between infinite parallel walls). Due to the non-existence of a local order parameter density, the transition has very unconventional properties (negative compressibility in equilibrium, non-equivalence between statistical ensembles in the thermodynamic limit, etc.). The reasons for this very unusual behavior are discussed in detail. Using Molecular Dynamics (MD) simulation for a simple bead-spring model, with N in the range 50<or=N<or=300, a comprehensive study of both static and dynamic properties of the polymer chain was performed. Even though for the considered rather short chains the escape transition is still strongly rounded, the order parameter distribution does reveal the emerging transition clearly. Time autocorrelation functions of the order parameter and first passage times and their distribution indicate clearly the strong slowing down associated with the chain escape. The theory developed here is in good agreement with all these simulation results.
The European Physical Journal E 05/2009; 29(1):9-25. DOI:10.1140/epje/i2008-10442-0 · 1.76 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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.
Journal of Colloid and Interface Science 05/2009; 336(1):51-8. DOI:10.1016/j.jcis.2009.03.062 · 3.37 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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.
Annals of the New York Academy of Sciences 03/2009; 1161(1):537 - 548. DOI:10.1111/j.1749-6632.2008.04335.x · 4.38 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We report on simulations of capillary filling of high-wetting fluids in nano-channels with and without obstacles. We use atomistic (molecular dynamics) and hydrokinetic (lattice-Boltzmann) approaches which point out 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 as the main capillary front, z^2(t) ~ t, 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 Lattice-Boltzmann (LB) method and opens the possibility of using hydrokinetic methods to explore space-time scales and complex geometries of direct experimental relevance. Then, LB approach is used to study the fluid behaviour in a nano-channel 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. Comment: 16 pages, 8 figures; To be published on JSTAT: Journal of statistical mechanics: Theory and experiments
Journal of Statistical Mechanics Theory and Experiment 01/2009; 2009(06). DOI:10.1088/1742-5468/2009/06/P06007 · 2.40 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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.
The Journal of Chemical Physics 11/2008; 129(15):154908. DOI:10.1063/1.2993136 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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 spontaneous imbibition decreases only moderately. Thus we demonstrate that one may transport the fluid in vertical brush-coated capillaries to a much larger height than in an equivalent capillary with bare walls. Eventually, we also study the spreading of tracer particles transported by the uptaking fluid in brush-coated capillaries with regard to the grafting density of the brush and the length of the polymers. The observed characteristic asymmetric concentration profiles of the tracers and their evolution with elapsed time are interpreted in terms of a drift-diffusion equation with a reflecting boundary that moves with the fluid front. The resulting theoretical density profiles of the tracer particles are found to be in good agreement with those observed in the computer experiment.
Physics of Fluids 09/2008; 20(9). DOI:10.1063/1.2975840 · 2.03 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: When fluids are confined in slit pores between parallel walls, their static structures and their dynamical properties exhibit inhomogeneity in the z-direction perpendicular to the wall. Of particular interest are local bulk viscosity eta(b)(z) and shear viscosity eta(s)(z). Here, we discuss an algorithm to estimate these quantities from Green-Kubo relations using equilibrium molecular dynamics. As an application example, a. polymer brush (macromolecules end-grafted to a substrate at z = 0) interacting with a solvent formed from point-like particles is given.
Macromolecular Theory and Simulations 08/2008; 17(6):313 - 318. DOI:10.1002/mats.200800038 · 1.67 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present an efficient method for direct determination of the excess free energy ΔF of a nanoparticle inserted into a polymer brush. In contrast to Widom's insertion method, the present approach can be efficiently implemented by Monte Carlo or Molecular Dynamics methods also in a dense environment. In the present investigation the method is used to determine the free energy penalty ΔF(R, D) for placing a spherical particle with an arbitrary radius R at different positions D between the grafting plane and the brush surface. Deep inside the brush, or for dense brushes, one finds ΔF∝R3 whereas for shallow nanoclusions ΔF∝R2, regardless of the particle interaction (attractive/repulsive) with the polymer.The pressure and density fields around spherical nanoinclusions in a polymer brush are also investigated. Extensive Monte Carlo simulations show that the force, exerted on the particle by the surrounding brush, depends essentially on the proximity of the nanocolloid particle to the brush surface not only in strength but also with respect to its angular distribution. For shallow nanoinclusions close to the brush surface this angular distribution is shown to result in a growing buoyant force while deep inside the brush this effect is negligible.
[Show abstract][Hide abstract] ABSTRACT: 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.
The Journal of Chemical Physics 07/2008; 128(23):234902. DOI:10.1063/1.2936124 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present hydrokinetic Lattice Boltzmann and Molecular Dynamics simulations of capillary filling of high-wetting fluids in nano-channels, which provide 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 the Lucas-Washburn law as the main capillary front, z2(t) proportional to t, although with a larger prefactor, which we find to take the same value for both geometries under inspection. Both hydrokinetic and Molecular Dynamics approaches indicate a precursor film thickness of the order of one tenth of the capillary diameter. The quantitative agreement between the hydrokinetic and atomistic methods indicates that the formation and propagation of thin precursors can be handled at a mesoscopic/hydrokinetic level, thereby opening the possibility of using hydrokinetic methods to space-time scales and complex geometries of direct experimental relevance. Comment: 11 pages, 6 figures. submitted to PRL
[Show abstract][Hide abstract] ABSTRACT: 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 Darcy's 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.
[Show abstract][Hide abstract] ABSTRACT: The capillary filling of a nanotube coated with a polymer brush is studied by molecular dynamics simulations of a coarse-grained model, assuming various conditions for the fluid-wall and fluid-brush interactions. Whereas the fluid is modeled by simple point particles interacting with Lennard-Jones forces, the (end-grafted, fully flexible) polymers that form the brush coating are described by a standard bead-spring model. Our experiments reveal that capillary filling is observed even for walls that would not be wetted by the fluid, provided the polymer brush coating itself wets. Generally, it is found that the capillary rise always proceeds through a t1/2 law with time t while the underlying molecular mechanism differs for wettable and nonwettable walls. For wettable walls, fluid imbibition is compatible with the Lucas-Washburn mechanism whereby the total influx of matter drops steadily with growing chain length N and the meniscus speed goes through a minimum at intermediate chain lengths. Moreover, because of flow, the polymer brush reorganizes its structure by forming a dense plug of chain segments under the meniscus that follows the meniscus in its motion. When the tube wall does not wet, one observes no meniscus formation for short chains although the fluid seeps through the wet brush. For a brush coating with longer chains, axial segregation between the brush segments and the fluid occurs by a kind of diffusive spreading, reminiscent of invasion percolation transport in a random medium, leading to the formation of a moving meniscus. For even longer chains that reach the tube axis, the rise of a meniscus with vanishing curvature-like imbibition in a porous medium is observed to take place.
[Show abstract][Hide abstract] ABSTRACT: The structure and thermodynamic properties of a system of end-grafted flexible polymer chains grafted to a flat substrate and exposed to a solvent of variable quality are studied by molecular dynamics methods. The macromolecules are described by a coarse-grained bead-spring model, and the solvent molecules by pointlike particles, assuming Lennard-Jones-type interactions between pairs of monomers (epsilon(pp)), solvent molecules (epsilon(ss)), and solvent monomer (epsilon(ps)), respectively. Varying the grafting density sigma(g) and some of these energy parameters, we obtain density profiles of solvent particles and monomers, study structural properties of the chain (gyration radius components, bond orientational parameters, etc.), and examine also the profile of the lateral pressure P( parallel)(z), keeping in the simulation the normal pressure P( perpendicular) constant. From these data, the reduction of the surface tension between solvent and wall as a function of the grafting density of the brush has been obtained. Further results include the stretching force on the monomer adjacent to the grafting site and its variation with solvent quality and grafting density, and dynamic characteristics such as mobility profiles and chain relaxation times. Possible phase transitions (vertical phase separation of the solvent versus lateral segregation of the polymers into "clusters," etc.) are discussed, and a comparison to previous work using implicit solvent models is made. The variation of the brush height and the interfacial width of the transition zone between the pure solvent and the brush agrees qualitatively very well with corresponding experiments.
The Journal of Chemical Physics 09/2007; 127(8):084905. DOI:10.1063/1.2768525 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: 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 typical conditions reachable in either simulation or experiment the data fall in a crossover regime, where no simple power-laws (as derived from the scaling description) hold. Moreover, extensions of the Daoud-Cotton blob picture to the cylinder geometry, implying that each chain in such a cylindrical brush is confined into a conical sector, are invalid; thus, chain ends in densely filled cylinders are not restricted to stay in the “hemicylinder” containing the grafting site of the chain.