Simulation of interaction forces between nanoparticles in the presence of Lennard-Jones polymers: freely adsorbing homopolymer modifiers

The force between two nanoscale colloidal particles dispersed in a solution of freely adsorbing Lennard-Jones homopolymer modifiers is calculated using the expanded grand canonical Monte Carlo simulation method. We investigate the effect of polymer chain length (N), nanoparticle diameter (sigma(c)), and colloid-polymer interaction energy (epsilon(cp)) on polymer adsorption (Gamma) and polymer-induced forces (F(P)(r)) between nanoparticles in the full thermodynamic equilibrium condition. There is a strong correlation between polymer adsorption and the polymer-mediated nanoparticle forces. When the polymer adsorption is weak, as in the case of smaller diameters and short polymer chain lengths (sigma(c) = 5, N = 10), the polymers do not have any significant effect on the bare nanoparticle interactions. The adsorbed amount increases with increasing particle diameter, polymer chain length, and colloid-polymer interaction energy. In general, for strong polymer-particle adsorption the polymer-governed force profiles between nanoparticles show short-range repulsion and long-ranged attraction, suggesting that homopolymers would not be ideal for achieving stabilization in nanoparticle dispersions. The attraction is likely due to bridging, as well as polymer segment-segment interactions. The location and magnitude of attractive minimum in the force profile can be controlled by varying N and epsilon(cp). The results show partial agreement and some marked differences with previous theoretical and experimental studies of forces in the limit of flat walls in an adsorbing polymer solution. The difference could be attributed to incorporation of long-ranged colloid-polymer potential in our simulations and the influence of the curvature of the nanoparticles.     

Structure and Dynamics of Confined Polymer Melts from Attractive Interaction to Repulsive Interaction Between Polymer and Smooth Wall

We studied the static and dynamic properties of unentangled polymer chains which have a variable strength of interaction with the confining smooth walls by means of the lattice Monte Carlo simulation based on the bond-fluctuation model, that is, investigated the wall-polymer interactions which systematically vary from attraction to repulsion. A critical value of attractive potential(ε_wc) is found to be -0.6k_BT, and only below it can the adsorption layer of monomers be formed near the wall. At the critical point of attraction ε_wc, attractive interaction counterba- lances the wall-polymer excluded volume effect, which minimizes the confinement effects on both chain dimension and mobility. Influences on both chain dimension and mobility increase with the increasing of either attraction or repulsion imposed by the walls. Despite of the nature and strength of the wall-polymer interaction, with the decrease of film thickness, configurations more parallelly aligned and flattened are adopted by confined chains, and a systematic trend of deceleration is found. Variations of chain dynamics with both film thickness and wall-polymer interaction can be well explained by the corresponding changes in the confinement of the nearest-neighboring particles that surround the chains. Besides, the thickness of the interfacial layer inside polymer films, where chains adopt a flattened “pancake” shape, is about two times the bulk radius of gyration and independent of the wall-polymer interaction.     

Effect of fluid-solid interactions on symmetry breaking in closed nanoslits

The possibility of symmetry breaking of the fluid (argon) density distribution across a long closed slit with identical walls composed of solid carbon dioxide was noted in previous papers by the authors. The main conclusion was that there is a range of average densities in which symmetry breaking occurs and that outside that range the fluid density profile is symmetrical. A critical temperature T(sb) was also identified below which symmetry breaking can occur. In this paper, symmetry breaking is examined for walls made of other materials and it is shown that it occurs only when the energy parameter epsilon(fw) of the fluid-wall interaction in the Lennard-Jones potential satisfies the inequalities epsilon(fw1) < or = epsilon(fw) < or = epsilon(fw2), where epsilon(fw1) and epsilon(fw2) are temperature-dependent critical values of epsilon(fw). The value of epsilon(fw1) increases and that of epsilon(fw2) decreases with increasing temperature. The comparison of the theory with Monte Carlo simulations confirms the existence of symmetry breaking across the slit. The possibility of symmetry breaking along the slit is also noted.     

The critical adsorption point of self-avoiding walks: a finite-size scaling approach

The critical adsorption of self-avoiding polymer chain in a simple cubic lattice onto a flat surface is studied with Monte Carlo simulations. The dependence of number of surface contacts M on chain length N and polymer-surface interaction epsilon is investigated by a finite-size scaling approach. We estimate the critical adsorption point epsilon(c)=0.291+/-0.002 and the exponent phi=0.54+/-0.01. The asymptotic behaviors M proportional variant N for epsilon>epsilon(c) and M proportional variant N(0) for epsilon相似文献   

高分子链在球内表面上的吸附/排空转变

应用自洽场理论(SCFT)研究了受限于球内的高分子溶液的结构,重点关注高分子链在受限壁附近的行为.根据自洽场理论数值计算结果,讨论了球半径、高分子与球限制壁的相互作用、高分子平均浓度等因素对球内高分子浓度分布的影响.从高分子浓度分布和吸附/排空层厚度可以发现,在一定的条件下,受限的高分子在受限壁上会发生吸附/排空转变.吸附/排空转变与受限球大小、高分子链长和平均浓度,以及高分子链与受限壁之间相互作用都有关系.理论预测发生吸附/排空转变时的高分子与球限制壁的临界相互作用参数与链长的倒数成线性关系,且斜率与球半径有关.限制球越小,要发生吸附/排空转变,需要高分子与球之间有更大的临界吸引能.     

Adsorption of water molecules in slit pores

We report molecular dynamics (MD) simulations on the adsorption of water in attractive and repulsive slit pores, where the slit and a bulk region are in contact with each other. Water structure, surface force and adsorption behavior are investigated as a function of the overall density in the bulk region. The gas–liquid transition in both types of pores occurs at similar densities of the bulk region.     

Novel phase behavior in adsorbed film of fluoroalkanol and cationic surfactant mixture

The surface tension of the aqueous solution of the binary mixture of 1H,1H-heptafluoro-1-butanol (FC4OH) and dodecyltrimethylammonium bromide (DTAB) was measured as a function of the total molality of the mixture and the composition (mole fraction in the surfactant mixture) of DTAB at 298.15 K under atmospheric pressure to examine the phase behavior in the adsorbed film. The results of the surface tension measurement were analyzed by the thermodynamic procedure proposed by us and the composition of the mixed adsorbed film in equilibrium with their bulk solution was calculated. Three different phases of the adsorbed film appeared by a subtle balance between the attractive interaction of the polar head groups and weak dispersion interaction of the hydrophobic chains. In the low-concentration regime, FC4OH molecules and DTAB molecules form a gaseous film and mix attractively in the whole composition by the long-range ion–dipole attraction between hydrophilic groups. The effect of the attractive dispersion interaction between CH and CF chains became more influential in the expanded film within a restricted composition region, where it should be noted that the interaction between CH and CF is weaker than that between CH chains or between CF chains alone. Furthermore, the adsorbed films at two specific compositions are stabilized by the stoichiometric arrangements of the molecules, which help ion–dipole attraction, in them.     

Confinement free energy and chain conformations of homopolymers confined between two repulsive walls

Lattice Monte Carlo simulations of polymer solutions confined between two parallel plates were performed. The confinement free energy Deltamicro(conf) per chain and the radius of gyrations of the chains parallel and perpendicular to the plates were obtained. When the concentration of the confined solution is above the overlap concentration, Deltamicro(conf) is found to scale with Na/D in a power law, betaDeltamicro(conf) approximately (Na/D)(m), with an exponent m=1.10+/-0.02 for athermal walls where N is the number of monomers in a chain, D is the slit width, and a is the lattice spacing. The presence of a weak attractive polymer/wall interaction epsilon(w) does not change the scaling variable, but the exponent m increases slightly. Extrapolating the results to melt would suggest that the predictions made by de Gennes [C. R. Acad. Sci. Paris II 305, 1181 (1987)] about the confinement free energy cost per chain in polymer melt is correct as far as the scaling variable is concerned, but is incorrect about the exponent m observed. The implication of this result on the predicted force between plates immersed in polymer melt is discussed. The parallel dimensions of the confined chain is expanded when the slit width D is narrow, however, the expansion is reduced at high concentration. It is conceivable that in melt the chain is not expanded when confined in a repulsive slit.     

Understanding self-assembly of rod-coil copolymer in nanoslits

Rod-coil diblock copolymers are a special kind of molecule containing a rigid rod and a flexible part. We present a systematic study on self-assembly of the rod-coil copolymers in nanoslits using a hybrid density functional theory. The self-assembly of the rod-coil molecule is driven by the bulk concentration, and there exists a critical bulk concentration beyond which the rod-coil molecule self-assembled into ordered lamellar structures in the slit, otherwise it is in a disordered state. By monitoring the effect of the interaction (epsilon(TT)(*)) of molecular tail on the self-assembly, we found that in the nanoslit of H=13sigma, it is at epsilon(TT)(*)=8 rather than epsilon(TT)(*)=10 or epsilon(TT)(*)=12 that the minimal critical bulk concentration occurs. It may be because the strong tail-tail interaction leads to aggregation of the copolymer molecules in bulk phase, and the resulting supramolecular structures are fairly difficult to enter the slit due to the depletion effect. At a fixed slit, the structural evolution of the self-assembled film with the bulk concentration is observed, including trilayer and five-layer lamellar structures, smectic-A, smectic-C, and a mixture of smectic-A and smectic-C liquid crystal phases and so on. We found that the critical bulk concentration, corresponding to the disordered-ordered phase transition, greatly depends on the separation between two walls, and it changes periodically with the increase of the slit width. In addition, it is also found that the molecular flexibility is one of key factors determining the self-assembled structure in the slit, and the critical bulk density increases with the molecular flexibility.     

Monte Carlo Simulations of Polymers in Nanoslits

Summary: Monte Carlo computer simulations have been performed for model polymers confined in slits of thickness comparable to the transverse diameter of the chains. The density of polymer within the slits is allowed to vary with the slit thickness in such a way that the content of the slits is always in equilibrium with a large reservoir of bulk polymer. The calculations reveal the presence of polymer‐mediated attractive or repulsive interactions between the slit plates, oscillating with the slit thickness in good agreement with experimental results.

The base cell used in the simulations.     

Selective adsorption of biopolymers on zeolites

Zeolites adsorb biopolymers on their surface and may be suitable as a new type of chromatographic carrier material for proteins, nucleic acids, and their conjugates. We report here various parameters that influence the adsorption of biopolymers on synthesized zeolites with regard to the Si/Al2 ratio and three-dimensional structure. There are three physicochemical principles that may underly the adsorption: 1) below the isoelectric point (pI), mainly Coulombic attraction similar to ion-exchange chromatography; 2) at pI, hydrophobic interactions (a kind of van der Waals attraction) plus the three-dimensional mesopore structure; and 3) above pI, the sum of the Coulombic repulsion and attraction forces, such as the hydrophobic interaction, and also substitution reaction of water on the Al molecule with a protein amino-base. At high Si/Al2 ratio in the presence of a small amount of Al and with mesopores between the zeolite particles, maximal adsorption was seen at pI and was suggested to be dependent on the number of hydrophobic interaction points on the mesopores, and their morphology. The application of zeolites to biochemistry and biotechnology is also discussed.     

SEGMENT DENSITY PROFILES OF COMPACT POLYMER CHAINS CONFINED BETWEEN TWO PARALLEL PLANE WALLS

We use the pruned-enriched Rosenbluth method to investigate systematically the segment density profiles of compact polymer chains confined between two parallel plane walls.The non-adsorption case of adsorption interaction energyε=0 and the weak adsorption case ofε=-1 are considered for the compact polymer chains with different chain lengths N and different separation distances between two walls D.Several special entropy effects on the confined compact polymer chains,such as a damped oscillation in the segment density profile for the large separation distance D,are observed and discussed for different separation distances D in the non-adsorption case.In the weak adsorption case,investigations on the segment density profiles indicate that the competition between the entropy and adsorption effects results in an obvious depletion layer.Moreover,the scaling laws of the damped oscillation period T_d and the depletion layer width L_d are obtained for the confined compact chains.Most of these results are obtained for the first time so far as we know,which are expected to understand the properties of the confined compact polymer chains more completely.     

Brownian dynamics simulations of polyelectrolyte adsorption in shear flow with hydrodynamic interaction

The adsorption of single polyelectrolyte molecules in shear flow is studied using Brownian dynamics simulations with hydrodynamic interaction (HI). Simulations are performed with bead-rod and bead-spring chains, and electrostatic interactions are incorporated through a screened Coulombic potential with excluded volume accounted for by the repulsive part of a Lennard-Jones potential. A correction to the Rotne-Prager-Yamakawa tensor is derived that accounts for the presence of a planar wall. The simulations show that migration away from an uncharged wall, which is due to bead-wall HI, is enhanced by increases in the strength of flow and intrachain electrostatic repulsion, consistent with kinetic theory predictions. When the wall and polyelectrolyte are oppositely charged, chain behavior depends on the strength of electrostatic screening. For strong screening, chains get depleted from a region close to the wall and the thickness of this depletion layer scales as N(1/3)Wi(2/3) at high Wi, where N is the chain length and Wi is the Weissenberg number. At intermediate screening, bead-wall electrostatic attraction competes with bead-wall HI, and it is found that there is a critical Weissenberg number for desorption which scales as N(-1/2)kappa(-3)(l(B)|sigmaq|)(3/2), where kappa is the inverse screening length, l(B) is the Bjerrum length, sigma is the surface charge density, and q is the bead charge. When the screening is weak, adsorbed chains are observed to align in the vorticity direction at low shear rates due to the effects of repulsive intramolecular interactions. At higher shear rates, the chains align in the flow direction. The simulation method and results of this work are expected to be useful for a number of applications in biophysics and materials science in which polyelectrolyte adsorption plays a key role.     

A hybrid approach for microscopic properties and self-assembly of dendrimers between two hard walls

Dendrimers are of interest in a number of applications and theoretical studies due to their interesting and complex architectures. We use a hybrid approach to investigate the microstructure of hard dendrimers and self-assembly of diblock dendrimers confined between two hard walls. In the hybrid approach, a single-chain Monte Carlo simulation is used to evaluate the ideal-gas contribution of the Helmholtz energy and a density functional theory is employed to calculate the excess Helmholtz energy. In our calculations, a coarse-grained model is used to represent the dendrimers of generations 1-4. The effects of generation and bulk packing fraction on the microscopic properties of the hard dendrimers are explored. With the increase of generations, the complexity of the dendritic architecture increases. Accordingly, the depletion effect becomes stronger with the generation at etabulk = 0.1. Furthermore, it is found that the more complex the molecular architecture and the higher the molecular stiffness, the smaller is the partitioning coefficient of confined dendrimers. In addition, we also investigate the effects of the width of the slit and the interaction (epsilon*AA) between hydrophilic segments on the self-assembly of diblock dendrimers in the slit. With the increase of epsilon*AA, we observe that the curves of average packing fraction of the dendrimers in the slit exist an abrupt jump, which corresponds to the first-order phase transition from a disordered state to a lamellar ordered structure. In the slit of H = 11sigma, it is at epsilon*AA = 8 rather than epsilon*AA = 10 or epsilon*AA = 12 that the minimum critical bulk packing fraction appears. This observation is distinctively different from the case of self-assembly of rod-like molecules in the slit, where the critical bulk concentration increases with the decrease of the head-head interaction linearly.     

Phase behavior of a single polyethylene chain confined between two adsorption walls

The phase behavior of a single polyethylene chain confined between two adsorption walls is investigated by using molecular dynamics simulations. In the free space, it is confirmed in our calculation that the isolated polymer chain exhibits a disordered coil state at high temperatures, and collapses into a condensed state at low temperatures, that is, the coil‐to‐globule transition, and the finite chain length effects are considered since the critical region depends on chain lengths. When the chain is confined between two attractive walls, however, the equilibrium properties not only depend on the chain length but also depend on the adsorption energy and the confinement. Mainly, we focus on the influence of polymer chain length, confinement, and adsorption interaction on the equilibrium thermodynamic properties of the polyethylene chains. Chain lengths of N = 40, 80, and 120 beads, distances between the two walls of D = 10, 20, 30, 50, and 90 Å, and adsorption energies of w = 1.5, 2.5, 3.5, 6.5, and 8.5 kcal/mol are considered here. By considering the confinement–adsorption interactions, some new folding structures are found, that is, the hairpin structure for short chain of N = 40 beads, and the enhanced hairpin or crystal like structures for long chains of N = 80 and 120 beads. The results obtained in our simulations may provide some insights into the phase behaviors of confined polymers, which can not be obtained by previous studies without considering confinement–adsorption interactions. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 370–387, 2008     

Molecular weight distribution effects on the structure of strongly adsorbed polymers by Monte Carlo simulation

Monte Carlo simulations are reported to study the structure of polymers adsorbed from solution onto strongly attractive, perfectly smooth substrates. Six systems spanning a range of molecular weight distributions are investigated with a coarse-grained united atom model for freely rotating chains. By employing a global replica exchange algorithm and topology altering Monte Carlo moves, a range of monomer-surface attraction from weak (0.27kT) to strong (4kT) is simultaneously explored. Thus for the first time ever, equilibrium polymer adsorption on highly attractive surfaces is studied, with all adsorbed molecules displaying similar properties and statistics. The architecture of the adsorbed layers, including density profiles, bond orientation order parameters, radii of gyration, and distribution of the adsorbed chain fractions, is shown to be highly dependent on the polydispersity of the polymer phase. The homology of polymer chains, and the ergodicity of states explored by the molecules is in contrast to the metastable, kinetically constrained paradigm of irreversible adsorption. The structure of more monodisperse systems is qualitatively similar to experimental results and theoretical predictions, but result from very different chain conformations and statistics. The polydispersity-dependent behavior is explained in the context of the competition between polymers to make contact with the surface.     

Star-branched polymers in an adsorbing slit: a Monte Carlo study

A coarse-grained model of star-branched polymer chains confined in a slit was studied. The slit was formed by two parallel impenetrable surfaces, which were attractive for polymer beads. The polymer chains were flexible homopolymers built of identical united atoms whose positions in space were restricted to the vertices of a simple cubic lattice. The chains were regular star polymers consisted of f = 3 branches of equal length. The chains were modeled in good solvent conditions and, thus, there were no long-range specific interactions between the polymer beads-only the excluded volume was present. Monte Carlo simulations were carried out using the algorithm based on a chain's local changes of conformation. The influence of the chain length, the distances between the confining surfaces, and the strength of the adsorption on the properties of the star-branched polymers was studied. It was shown that the universal behavior found previously for the dimension of chains was not valid for some dynamic properties. The strongly adsorbed chains can change their position so that they swap between both surfaces with frequency depending on the size of the slit and on the temperature only.     

On the anatomy of the adsorption heat versus loading as a function of temperature and adsorbate for a graphitic surface

In this paper we review and classify the various patterns of isosteric heat versus loading for adsorption of gases on graphitised thermal carbon black at temperatures ranging from below the 3D triple point to temperatures above it, but less than the 3D critical point. We have identified the features of heat curve and highlighted the microscopic origin of these features. The patterns vary with temperature and with the relative strength of the fluid-fluid interaction and solid-fluid interaction. For simple adsorptives (by simple we meant there is no strong association between fluid particles), the heat curve is typified by fluid-fluid attraction and layering phenomena. For adsorptives showing strong association such as water, ammonia and methanol, the heat curve essentially begins below the condensation heat and then approaches it as loading is increased. This is mainly due to the strong hydrogen bonding in these fluids. A third group includes adsorptives such as benzene, where the heat curve is constant in the sub-monolayer coverage region (but is higher than the condensation heat) and then drops off to the condensation heat when higher layers are formed. The constant heat in the sub-monolayer region is due to the balance between the energy factor (from fluid-fluid interaction) and entropy factor (due to re-orientation of adsorbed molecules). Our proposed classification is supported by detailed GCMC simulations of various gases that have been reported in the literature, and we supplement these with new results for the adsorption of xenon on graphite to investigate in more detail the change in heat pattern with temperature. Xenon is chosen because of its high fluid-fluid interaction, allowing us to study the 2D-phase transition in the first as well as higher layers.     

Equilibration of fluid-phase coexistence in polydisperse particle systems with short- and moderate-range depletion attractions

Gibbs ensemble Monte Carlo (GEMC) simulations have been done on polydisperse systems of particles interacting via the Asakura-Oosawa depletion potential. On restricting the range of the depletion attraction particles aggregate forming long-lived, unequilibrated structures and it becomes increasingly difficult to sample phase space. It is found that by simply equilibrating systems sequentially starting at longer ranges of attraction, the equilibrium fluid-fluid phase coexistence can be determined down to polymer-colloid size ratios approaching 10%. For such short ranges of the depletion interaction it becomes difficult to obtain reliable estimates of chemical potentials due to occasional particle insertions resulting in very low energies. The results show that full equilibrium is not reached at a polymer-colloid size ratio of 10% in spite of lengthy simulations due to persistent structures in the dense-fluid phase dominated by particles belonging to the larger size fraction. Free-volume theory with a polydisperse colloid component, modeled as a three-component mixture, is used for qualitative comparison with some of the results of the computer simulations.     

Does water condense in carbon pores?

Using grand canonical Monte Carlo (GCMC) simulations of molecular models, we investigate the nature of water adsorption and desorption in slit pores with graphitelike surfaces. Special emphasis is placed on the question of whether water exhibits capillary condensation (i.e., condensation when the external pressure is below the bulk vapor pressure). Three models of water have been considered. These are the SPC and SPC/E models and a model where the hydrogen bonding is described by tetrahedrally coordinated square-well association sites. The water-carbon interaction was described by the Steele 10-4-3 potential. In addition to determining adsorption/desorption isotherms, we also locate the states where vapor-liquid equilibrium occurs for both the bulk and confined states of the models. We find that for wider pores (widths >1 nm), condensation does not occur in the GCMC simulations until the pressure is higher than the bulk vapor pressure, P0. This is consistent with a physical picture where a lack of hydrogen bonding with the graphite surface destabilizes dense water phases relative to the bulk. For narrow pores where the slit width is comparable to the molecular diameter, strong dispersion interactions with both carbon surfaces can stabilize dense water phases relative to the bulk so that pore condensation can occur for P < P0 in some cases. For the narrowest pores studied--a pore width of 0.6 nm--pore condensation is again shifted to P > P0. The phase-equilibrium calculations indicate vapor-liquid coexistence in the slit pores for P < P0 for all but the narrowest pores. We discuss the implications of our results for interpreting water adsorption/desorption isotherms in porous carbons.