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  • 3640 Phys. Chem. Chem. Phys., 2012, 14, 3640–3650 This journal is c the Owner Societies 2012

    Cite this: Phys. Chem. Chem. Phys., 2012, 14, 3640–3650

    Determination of the distance-dependent viscosity of mixtures in parallel slabs using non-equilibrium molecular dynamics

    Stanislav Pařeza and Milan Předota*b

    Received 30th June 2011, Accepted 9th January 2012

    DOI: 10.1039/c2cp22136e

    We generalize a technique for determination of the shear viscosity of mixtures in planar slabs

    using non-equilibrium computer simulations by applying an external force parallel to the surface

    generating Poiseuille flow. The distance-dependent viscosity of the mixture, given as a function of

    the distance from the surface, is determined by analysis of the resulting velocity profiles of all

    species. We present results for a highly non-ideal water + methanol mixture in the whole

    concentration range between rutile (TiO2) walls. The bulk results are compared to the existing

    equilibrium molecular dynamics and experimental data while the inhomogeneous viscosity profiles

    at the interface are interpreted using the structural data and information on hydrogen bonding.

    1. Introduction

    The growing interest in nanostructured materials requires

    detailed knowledge of the properties of the fluids in nano-

    confinement for understanding processes on this scale, leading

    to better design of nanodevices.1 While there is significant

    advance in the capabilities of experimental techniques in

    probing the interfacial properties of fluids adsorbed on solid

    materials, computer simulations offer an alternative approach

    to provide pieces of information on the structure and dynamics

    of such interfaces. The structural information of the inhomo-

    geneous region formed at the solid–liquid interface, including

    both relaxation of the solid and structure of interfacial liquid,

    is more readily available e.g. from X-ray diffraction,2,3

    nonlinear optics,4 and neutron scattering.5–7 The pieces of

    information on the dynamics of the interfacial molecules

    typically include the residence times of ions or molecules in

    adsorption layers,8–10 translational diffusivity (either averaged

    over the whole volume of the nanopore11 or calculated

    bin-wise to yield the distance-dependent diffusivity,12–14

    streaming velocity15) or more rarely rotation diffusivity and/or

    orientation relaxation times.12

    Motivated by the applications in microfluidic devices, mole-

    cular sieves and flow through porous and nanostructured

    materials in general, we explore in detail a method for

    determination of distance-dependent shear viscosity of mixtures

    in parallel slabs. While our simulations employ, for simplicity

    of both the derivation and simulations, planar 2D-periodic

    systems, the key message is the information on the viscosity

    profile of a mixture as a function of the distance from the

    surface, as the properties of the planar interface represent a

    limiting case of surface of (infinitely) a large sphere or cylinder

    or generally any surface with small enough curvature.

    Methods for determination of shear viscosity from simula-

    tions employ equilibrium molecular dynamics16–19 (EMD) as

    well as non-equilibrium molecular dynamics (NEMD). The

    latter use various approaches, such as e.g. 3D-periodic simula-

    tions using oscillatory elongational flow,20–24 planar shear flow

    described by SLLOD equations,25–27,29 momentum impulse

    relaxation28 or Poiseuille flow between immobile surfaces.14,30,31

    Obviously, only the latter example features interactions with

    surfaces and thus leads to inhomogeneous profiles of structural

    and dynamic properties as a function of the distance from the

    surface. The potential models used in homogeneous simulations

    range from simple atomic potentials, such as e.g. short ranged

    WCA potential,21 argon studied using the Barker–Fisher–Watts

    and three-body Axilrod–Teller potentials,29 to molecular systems

    such as e.g. n-alkanes17 or ionic liquids.24

    The determination of distance-dependent viscosity has been

    implemented mostly for atomic fluids based on Lennard-Jones

    potential31 or its modifications, e.g. short ranged WCA

    potential.30,32 Dynamics of two-site and four-site chain

    WCA molecules undergoing planar Poiseuille flow was also

    studied,33 including velocity and shear profiles, but viscosity

    was not determined. Travis et al.34 determined shear viscosity

    by the Poiseuille flow of either atoms or rigid diatomic

    molecules between two atomistic walls.

    Studies on distance-dependent viscosity of water in contact

    with surfaces are also scarce.14,31,35 As a pioneering work

    in this direction we identify the work of Freund,35 who

    described the dynamic properties of SPC/E water containing

    Cl� ions adjacent to a smooth, positively charged wall of

    generic Lennard-Jones atoms. We have later applied a similar

    a Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, 165 02 Prague, Czech Republic

    b Faculty of Science, University of South Bohemia, Branisovska 31, Ceske Budejovice, 370 05, Czech Republic. E-mail: predota@prf.jcu.cz

    PCCP Dynamic Article Links

    www.rsc.org/pccp PAPER

    http://dx.doi.org/10.1039/c2cp22136e http://dx.doi.org/10.1039/c2cp22136e

  • This journal is c the Owner Societies 2012 Phys. Chem. Chem. Phys., 2012, 14, 3640–3650 3641

    approach to study viscosity of pure water in contact with

    atomistic rutile (TiO2) surfaces. 14 Here we extend our former

    work14 to a detailed study of the viscosity profiles of highly

    non-ideal aqueous methanol mixtures in contact with the rutile

    surfaces. Doing so we also elaborate the determination

    of distance-dependent viscosity of mixtures in much more

    detail than given by Freund.35 Particularly, we generalize the

    formulas for viscosity calculation to an arbitrary number of

    mixture species and arbitrary combination of external forces

    acting on molecules.

    Regarding the simulation results of the components of the

    water + methanol system studied here, the viscosity of SPC/E

    water was found to be about 10–15% lower than experimental

    viscosity of real water36 earlier,25,35 in part also in ref. 16.

    Nonequilibrium simulations using Lees–Edwards boundary

    conditions of viscosity of water + methanol mixtures (and

    also of mixtures with acetone) were carried out by Wheeler

    and Rowley25 with SPC/E water, methanol model due to van

    Leeuwen and Smit37 and applying a hybrid mixing rule for

    cross-interactions. Wensink et al.22 used a periodic perturbation

    method employing sinusoidal external forces for NEMD

    simulations of diffusion and viscosity of OPLS mixtures of

    methanol, ethanol or 1-propanol with TIP4P water using

    OLPS potentials for alcohols. However, the agreement of

    the viscosities of water + alcohol mixtures with experimental

    data was only qualitative.22 Viscosity of methanol + ethanol

    mixtures, employing the same model of methanol38 as in

    this study, was studied by EMD.18 The recent results of

    Guevara-Carrion et al.19 explore in detail the diffusivity and

    viscosity, as well as other properties, of aqueous methanol

    mixtures using SPC, SPC/E, TIP4P and TIP4P/2005 models

    for water and represent a direct EMD benchmark for our

    NEMD simulations. Moreover, the TIP4P/2005 water model

    and the methanol model used in this study19 offer a qualita-

    tively very good match to experimental data without further

    fitting of binary parameters.

    2. Simulations

    Models

    Rigid nonpolarizable models based on Lennard-Jones (LJ)

    and point charge Coulombic interactions were used for both

    methanol and water. For methanol, a united-atom model by

    Schnabel et al.38 was adopted for its very good agreement with

    experimental data. This model has two LJ sites, one for the

    methyl group and one for the oxygen atom. In addition, it

    contains three point charges, two are located at positions of LJ

    centers and the third is at hydroxyl hydrogen. The interaction

    parameters of this molecule are summarized in Table 1

    (adopted from Schnabel et al.38). Geometry of methanol is

    characterized by bond lengths |CH3–O| = 1.4246 Å, |O–H| =

    0.9451 Å and the angle +CH3–O–H = 108.531. For water, two very common models in molecular simulations, the SPC/E39

    and the TIP4P/2005,40 were employed. The SPC/E model was

    chosen to continue our series of papers on the rutile–aqueous

    solution interface properties.13,14,41,42 The TIP4P/2005 was

    included for its superior dynamic properties in very good

    agreement with experiment. Finally, the viscosity of water +

    methanol mixtures from EMD simulations, employing the

    very same three models (Schnabel model of methanol, SPC/E

    and TIP4/2005 for water), has been recently published,19 and

    offers thus possibility to benchmark our NEMD results both

    in terms of accuracy and efficiency.

    Surfaces

    In our simulations the liquid was confined between two planar

    surfaces (slab geo

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