Attractive Wall Research Articles

Confined Polymer Chains in a ϑ Solvent: A Model with Polymer−Solvent Interactions

Thermodynamics of polymer chains in the ϑ condition confined to a space between two parallel walls was studied by using lattice Monte Carlo simulations. The ϑ state was realized by allocating positive interaction to nearest-neighbor pairs of a polymer segment and a solvent molecule that is now explicitly included, rather than giving attractive interaction between polymer segments with no explicit solvent molecules present. The two models can be equivalent when used to specify the ϑ state in unconfined solutions, but missing segment−solvent contacts at the wall make the two models different for confined solutions. The effectively attractive wall facilitates entry of polymer chains into narrow slits in the corrected model and lifts the segment density at sites adjacent to the walls. The dependence of the segment density near the wall on the distance from the wall follows a power law different from the one that holds for the conventional model of the ϑ state. In particular, when the wall has explicit interaction with the polymer segments, our model makes the profile highly sensitive to the solvent quality. The corrected model explains enhanced adsorption in a poorer solvent reported in experiments.

Wetting behavior of associating binary mixtures at attractive walls: A lattice Monte Carlo study

The lattice gas model is used to study the effects of molecular association on the wettability of surfaces with attractive walls by binary symmetric associating mixtures. The model assumes that the adsorbate particles occupy a regular cubic lattice of sites and that the interactions between adsorbate particles involve only the first nearest neighbors. The energies of interaction between the pairs of like particles are the same, while the only interaction between a pair of unlike particles is due to association. Only the formation of dimers is allowed and the energy of association is finite. The particles are subject to the surface, van der Waals-like potential, assumed to be the same for both components. The model is studied with the help of the Monte Carlo simulation method in the grand canonical ensemble. Only the ground state properties are treated analytically. It is demonstrated that, in general, molecular association hinders wetting. In particular, in the systems with nonzero wetting temperature, the increase of the association energy leads to the increase of the wetting temperature and for sufficiently high energy of association the mixture does not wet the surface at all. When the system is expected to exhibit complete wetting at the ground state, the film formed by strongly associating mixtures wets the surface only at sufficiently low temperatures, below the dewetting temperature. It is demonstrated that the dewetting temperature increases with the strength of the surface potential as well as with the increase of the association energy.

Wetting of Planar Surfaces by a Gay-Berne Liquid Crystal

Molecular simulation of the wetting of an unstructured attractive wall by Gay-Berne liquid crystals are reported. Simulations are performed in the grand canonical ensemble on a wide pore at constant temperatures of T *=0.53 and 0.56, corresponding to temperatures below and above the nematic-isotropic-vapor triple point. Close to the coexistence chemical potential, a thick liquid film wets the solid surface. The film is composed of stratified layers of molecules parallel to the solid surface, which follow to a nematic domain at the lower temperature and an isotropic one at the higher temperature. In both cases, the film is in equilibrium with the corresponding vapor phase. Close to the liquid-vapor interface there is a manifest tendency for the molecules to orient themselves parallel to the interface. The adsorption on the wall varies continuously with the thermodynamic parameters considered and no evidence of a first order prewetting transition is observed.

The statistical mechanics of semiflexible equilibrium polymers

We give an overview of studies of models for semiflexible, equilibrium polymers with special emphasis on our work on both lattice and continuum models for such systems. We show, principally by Monte Carlo simulations, that, once monomers self assemble to form polymers, their semiflexibility leads to nematic phases at low temperatures. Attractive wall potentials encourage the adsorption of these equilibrium polymers on surfaces. Rapid cooling leads to the formation of glasses with entangled polymers. Shear promotes nematic ordering, but, at high shear rates, this tendency decreases since the equilibrium polymers are torn apart. A version of our model in which the polymers are directed shows the polymer analog of bosonic Mott-insulating, mass-density-wave, and supersolid phases. We give a brief comparison of our work with other studies and also explore the experimental implications of our study.

Micromagnetic simulation of domain wall pinning and domain wall motion

Domain wall pinning is the coercivity mechanism of permanent magnets used in high temperature applications. In SmCo based magnets domain walls get trapped at the cellular precipitation structure causing a high coercive field. The motion of domain walls and their propagation velocity are important in soft magnets as used in sensor applications. A finite element micromagnetic algorithm was developed to study the motion of domain walls in complex microstructures. The cellular microstructure of SmCo magnets or the cylindrical soft wires can be easily built using tetrahedral finite elements. The pinning of the domain walls has been studied for different material compositions. Attractive and repulsive domain wall pinning are observed and their behaviour for increasing thickness of the precipitation structure is explained. The motion of domains in magnetic nanowires was calculated using adaptive mesh refinement. The wall velocity strongly depends on the domain wall structure. Transverse and vortex walls have been observed and their velocity in wires of different thickness has been studied.

Concentration Effects in Partitioning of Macromolecules into Pores with Attractive Walls

The influence of polymer concentration on the partitioning of flexible macromolecules into adsorptive pores was examined by simulations in an open system under good solvent conditions. In dilute solutions, the partition coefficient K(ε,φ) is sensitive to small variations of both polymer−pore attraction strength ε and concentration φ, whereas in semidilute solutions both influences level off. At weak attraction below critical adsorption energy εc, the coefficient K increases with φ in a fashion that resembles the weak-to-strong penetration transition found for purely steric exclusion (ε = 0) but modified as if the width of pores effectively increased. At moderate attraction above the critical condition the increasing concentration brings about a dramatic drop in the value of K. Additionally, the K(φ) dependences in attractive pores were calculated by an approximate method based on expressions for chemical potentials, and the results were in good agreement with the simulation data. The critical adsorption energy εc for excluded volume chains was found to depend on concentration; the compensation point K = 1 was located at about φ = 0.012 irrespective of the pore width. The energy and entropy contributions to the free energy of confinement were calculated and the compensation of their values at the critical condition was demonstrated. Furthermore, it was shown that the effect of concentration in polymer partitioning with adsorptive pores can alternatively be regarded as a confined adsorption and two alternatives of the adsorbed amount Γ were calculated. The adsorption and depletion concentration profiles φI(x) in the pore in equilibrium with the bulk solution were presented and their variation with concentration φ and attraction ε was analyzed.

Asymmetric Diblock Copolymer Thin Film Confined in a Slit: Microphase Separation and Morphology

Microphase separation and morphology of asymmetric diblock copolymer (f = 0.4) thin films confined in a slit with surfaces neutral or attractive towards block A or block B were studied by the cell dynamic system method (CDS). The size effect in CDS calculations was carefully investigated. For asymmetric copolymers, the size effect is important even in the case of attractive walls. Not only must we use boxes with larger sizes in the X- and Y-directions, the size is also dependent on the film thickness. In contrast, for symmetric copolymers, the size effect is not serious when we adopt attractive plates. Various microdomain morphologies including regular lamellae adjacent to the surfaces, mesh-like layers with nanosized spheres dispersed in a matrix of block A, and flexuous cylindrical phases are found in this work. A series of conditions we can control, such as the chemical composition of the copolymer, the thickness of the film, the selective interactions between plates and blocks as well as their strength, all make the potential technology more adaptable. To test the reliability of the CDS method, the results are compared with those from dynamical density functional theory and Monte Carlo simulation.

Adsorption and collapse transitions in a linear polymer chain near an attractive wall.

We deduce the qualitative phase diagram of a long flexible neutral polymer chain immersed in a poor solvent near an attracting surface using phenomenological arguments. The actual positions of the phase boundaries are estimated numerically from series expansion up to 19 sites of a self-attracting self-avoiding walk in three dimensions. In two dimensions, we calculate phase boundaries analytically in some cases for a partially directed model. Both the numerical and analytical results corroborate the proposed qualitative phase diagram.

Phase behavior of Lennard-Jones fluids in pores formed between two cylindrical walls

Abstract We study structure and phase behavior of a Lennard-Jones (12, 6) fluid adsorbed in pores with curved walls that are made of two uniaxial cylinders by using a density functional approach. The attractive wall-particle potential is an analogue of the Lennard-Jones (9, 3) potential that has been developed to model interaction of a particle with a flat wall. We also compare the results obtained for attractive pore walls with those evaluated for hard cylindrical walls. We have found that in both cases, i.e. in the case of the attractive, as well as, hard walls, the increase of the radius of curvature of the walls while keeping the distance between them constant, decreases the critical temperature of the liquid–vapor transition in the confined fluid. However, the shift of the chemical potential at the transition point is different for the pores with attractive walls and for the pores with hard walls. In the case of the walls exerting an attractive adsorbing potential, the increase of the radius of the curvature causes decrease of the chemical potential at the capillary condensation point. In the case of hard walls the increase of the radius of the curvature leads to an increase of the chemical potential at the capillary evaporation point.

How do droplets on a surface depend on the system size?

Abstract We investigate the thermodynamics of inhomogeneous polymer melts in the framework of a coarse grained off-lattice model. Properties of the liquid–vapour interface and the packing of the melt in contact with an attractive wall are considered. We employ Monte Carlo simulations in the grand canonical ensemble to determine excess free energies, the wetting temperature and the pre-wetting line, as well as the pre-wetting critical point. Having determined the wetting properties and the phase diagram of the model polymer, we perform canonical Monte Carlo simulations of small droplets on a surface. This allows us to study the dependence of droplet size on the wetting properties. It is found that the contact angles of small droplets may be very much larger than those observed for macroscopic drops.

Wetting of a symmetrical binary fluid mixture on a wall

Abstract We study the wetting behavior of a symmetrical binary fluid below the demixing temperature at a non-selective attractive wall. Although it demixes in the bulk, a sufficiently thin liquid film remains mixed. On approaching liquid/vapor coexistence, however, the thickness of the liquid film increases and it may demix and then wet the substrate. We show that the wetting properties are determined by an interplay of the two length scales related to the density and the composition fluctuations. The problem is analyzed within the framework of a generic two component Ginzburg–Landau functional (appropriate for systems with short-ranged interactions). This functional is minimized both numerically and analytically within a piecewise parabolic potential approximation. A number of novel surface transitions are found, including first order demixing and prewetting, continuous demixing, a tricritical point connecting the two regimes, or a critical end point beyond which the prewetting line separates a strongly and a weakly demixed film. Our results are supported by detailed Monte Carlo simulations of a symmetrical binary Lennard–Jones fluid at an attractive wall.

Wetting of a symmetrical binary fluid mixture on a wall.

We study the wetting behavior of a symmetrical binary fluid below the demixing temperature at a nonselective attractive wall. Although it demixes in the bulk, a sufficiently thin liquid film remains mixed. On approaching liquid vapor coexistence, however, the thickness of the liquid film increases and it may demix and then wet the substrate. We show that the wetting properties are determined by an interplay of the two length scales related to the density and the composition fluctuations. The problem is analyzed within the framework of a generic two component Ginzburg-Landau functional (appropriate for systems with short-ranged interactions). This functional is minimized both numerically and analytically within a piecewise parabolic potential approximation. A number of surface transitions are found, including first-order demixing and prewetting, continuous demixing, a tricritical point connecting the two regimes, or a critical end point beyond which the prewetting line separates a strongly and a weakly demixed film. Our results are supported by detailed Monte Carlo simulations of a symmetrical binary Lennard-Jones fluid at an attractive wall.

Dielectric studies of freezing behavior in porous materials: Water and methanol in activated carbon fibres

We report both experimental measurements and molecular simulations of the melting and freezing behavior of two dipolar fluids, water and methanol, in activated carbon fibres. Differential scanning calorimetry (DSC) and dielectric relaxation spectroscopy (DS) were used to determine the melting point in these porous materials. The melting point was found to be very sensitive to the relative strength of the fluid–wall interaction compared to the fluid–fluid interaction. Monte Carlo simulations and the Landau free energy formalism were used to determine the shift in the melting point, Tm, for simple fluids in pores having weakly attractive and strongly attractive walls. The strength of the interaction of the fluid with the pore wall is shown to have a large effect on the shift in Tm, with Tm being reduced for weakly attracting walls and elevated for strongly attracting walls.

Interfaces, wetting, and capillary nematization of a hard-rod fluid: Theory for the Zwanzig model

We investigate interfacial and capillary phenomena in a simple model for a fluid of hard rods, viz. the Zwanzig model, in which the orientations of rectangular blocks are restricted to three orthogonal directions. The theory, which is based on an Onsager-like free energy functional, predicts local biaxial ordering at the “free” interface between the coexisting isotropic and nematic phases. For an isotropic bulk fluid in contact with a single planar hard wall, we find a continuous surface phase transition from uniaxial to biaxial local symmetry, followed by complete wetting of the wall–isotropic fluid interface by a nematic film with director parallel to the wall, as the reservoir density approaches its value at bulk coexistence. For a fluid confined by two parallel hard walls we determine a first-order capillary nematization transition at large wall separation, which terminates in a capillary critical point when the wall separation is about twice the length of the rods. This transition is the analog of the capillary condensation observed for simple fluids confined by attractive walls but is purely entropy driven here.

Forces between like-charged walls in an electrolyte solution: A comparison of McMillan–Mayer results for several models

The interaction of like-charged walls immersed in aqueous solutions with monovalent counterions is investigated at the McMillan–Mayer (MM) level of description. The net pressure acting between the walls is obtained by applying the anisotropic hypernetted-chain theory. The MM approach requires solvent-averaged ion–ion potentials of mean force as input. Results based on “realistic” models for Na+ and Cl− in water are available in the literature and these are used in the present calculations. The wall–wall interactions obtained can differ dramatically from the primitive model (dielectric continuum solvent) case. For some models attractive wall–wall forces are observed at small separations. The MM theory is found to be rather sensitive to details of the counterion–counterion potential of mean force, and different models for the same counterion can give qualitatively different results. At present it is difficult to evaluate the relative accuracy of the different models that have been proposed. However, the results presented here give at least an idea of the interesting possibilities that lie in the physically realistic range.

Interface and Surface Properties of Short Polymers in Solution: Monte Carlo Simulations and Self-Consistent Field Theory

We investigate the structure and thermodynamics of inhomogeneous polymer solutions in the framework of a coarse-grained off-lattice model. Properties of the liquidvapor interface and the packing of the solution in contact with an attractive wall are considered. The wall interacts with the monomers via a long-range interaction. We employ Monte Carlo simulations in the grand canonical ensemble and self-consistent field calculations to study segment profiles, excess free energies, and the wetting behavior. The self-consistent field calculations incorporate the detailed chain structure via a partial enumeration scheme and use a weighteddensity functional ansatz for the monomeric interactions. Quantitative agreement between the Monte Carlo simulations and the self-consistent field calculations is achieved for the conformational arrangements at the wall. Only qualitative agreement is obtained for the excess free energies of interfaces and surfaces. Possible sources for the quantitative deviations are discussed. Using the Young equation, we accurately locate the first-order wetting transition. In the Monte Carlo simulations and the self-consistent field calculations, we find a strong first-order wetting transition and locate the concomitant prewetting line. The behavior of the prewetting line close to the bulk coexistence yields a compatible estimate for locating the wetting transition. The location of the prewetting critical point is estimated in the simulations.

Phase transitions in an associating, network-forming, Lennard-Jones fluid in slit-like pores. II. Extension of the density functional method

We study adsorption of hydrogen-bonded fluids in slit-like pores with strongly attractive walls, in the framework of the four-site associating Lennard-Jones model. The density profiles, as well as the phase behavior, are obtained by using a density functional method. We have found that, at temperatures lower than the critical temperature of the bulk fluid, the confined fluid undergoes one or more layering transitions dependent on the pore width, followed by capillary condensation. Each of the transitions is localized by analyzing the grand thermodynamic potential. The density profiles of nonbonded and differently bonded particles demonstrating changes of the structure of the fluid in the pore along the coexistence are discussed briefly. The critical temperature for capillary condensation is lower for confined fluid, compared with that for the bulk liquid–vapor transition, as expected. However, an increase of the energy of association between fluid species increases the critical temperatures for layering transitions and for capillary condensation. The envelope of the capillary condensation is narrower than the bulk liquid–vapor phase diagram. The ratio between the critical temperatures for layering transitions and capillary condensation depends on the pore width. The critical temperature for the second layering is always lower than for the first one. The triple point temperature between either the second layering transition and the capillary condensation (in wider pores) or the first layering transition and the capillary condensation (in narrower pores) increases with decreasing pore width. The triple point temperature between the layering transitions is much lower than the relevant temperature between the second layering transition and the capillary condensation. The triple point temperatures also depend on the association energy. We have shown that highly bonded fluid species prevail at triple point temperatures.

Characteristics of driven polymer surfaces: Growth and roughness

Using a Monte Carlo simulation, the growth and roughness characteristics of polymer surfaces are studied in 2+1 dimensions. Kink-jump and reptation dynamics are used to move polymer chains under a driving field where they deposit onto an impenetrable attractive wall. Effects of field (E), chain length (L(c)), and the substrate size (L) on the growing surfaces are studied. In low field, the interface width (W) shows a crossover from one power-law growth in time (W approximately t(beta(1))) to another (W approximately t(beta(2))), before reaching its asymptotic value (W(s)), with beta(1)( approximately 0.5+/-0.1)<beta(2)( approximately 0.6-1.0). For short chain lengths (L(c)=4), the saturated width (W(s)) is independent of the substrate length (L), while for long chain lengths, W(s) decays with L before becoming independent at large L. W(s) depends strongly on the magnitude of the field: for short chains, W(s) approximately E-delta with delta approximately 0.4, while for long chains, it varies nonmonotonically with E.

Statics and dynamics of adsorbed uniform star chains

In this paper, we investigate the static and dynamic properties of uniform star chains with F=3, 6, and 9 branches of length N adsorbed on the attractive wall ( xy-plane) using the bond-fluctuation model. Chain dimensions, fraction of segments adsorbed and maximum thickness of adsorbed layer are measured for systems with a different branch number of star chains over a range of temperatures. Adsorbed layers begin to form at the more adsorption transition temperature as the number of branches increases. The diffusion constants decrease with increasing number of branches. At the same time, some comparisons with linear chains are made.

Statics and dynamics of adsorbed ring polymer chains

Monte Carlo calculations of the statics and dynamics behavior of ring polymers adsorbed on a short-range attractive wall ( xy-plane) are described using the bond-fluctuation model. Chain conformation, fraction of segment adsorbed and chain dimensions are measured over a wide range of temperatures. An adsorbed layer begins to form at the larger adsorption transition temperature T a than a single linear polymer chain. For the dynamics, the mean square displacements and the diffusion coefficients parallel and perpendicular to the z-axis are also calculated. Some comparisons with linear chains are made.