Compressible or incompressible blend of interacting monodisperse linear polymers near a surface

We consider a lattice model of a mixture of repulsive, attractive, or neutral monodisperse linear polymers of two species, A and B, with a third monomeric species C, which may be taken to represent free volume. The mixture is confined between two hard, parallel plates of variable separation whose interactions with A and C may be attractive, repulsive, or neutral, and may be different from each other. The interactions with A and C are all that are required to completely specify the effect of each surface on all three components. We numerically study various density profiles as we move away from the surface, by using the recursive method of Gujrati and Chhajer [J. Chem. Phys. 106, 5599 (1997)] that has already been previously applied to study polydisperse solutions and blends next to surfaces. The resulting density profiles show the oscillations that are seen in Monte Carlo simulations and the enrichment of the smaller species at a neutral surface. The method is computationally ultrafast and can be carried out on a personal computer (PC), even in the incompressible case, when Monte Carlo simulations are not feasible. The calculations of density profiles usually take less than 20 min on a PC.     

Structure of inhomogeneous attractive and repulsive hard-core yukawa fluid: grand canonical Monte Carlo simulation and density functional theory study

A density functional theory is proposed for an inhomogeneous hard-core Yukawa (HCY) fluid based on Rosenfeld's perturbative method. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-core repulsion and a quadratic functional Taylor expansion for the long-ranged attractive or repulsive interactions. To test the established theory, grand canonical ensemble Monte Carlo simulations are carried out to simulate the density profiles of attractive and repulsive HCY fluid near a wall. Comparison with the results from the Monte Carlo simulations shows that the present density functional theory gives accurate density profiles for both attractive and repulsive HCY fluid near a wall. Both the present theory and simulations suggest that there is depletion for attractive HCY fluid at low temperature, but no depletion is found for repulsive HCY fluid. The calculated results indicate that the present density functional theory is better than those of the modified version of the Lovett-Mou-Buff-Wertheim and other density functional theories. The present theory is simple in form and computationally efficient. It predicts accurate radial distribution functions of both attractive and repulsive HCY fluid except for the repulsive case at high density, where the theory overestimates the radial distribution function in the vicinity of contact.     

Structures and Surface States of Polymer Brushes in Good Solvents: Effects of Surface Interactions

The influence of the surface interaction on the mesoscopic structure of grafted polymers in good solvents has been examined. At high surface coverage, tethered polymers are in the brush state and the parabolic segment density profile is confirmed by self-consistent field theory (SCFT) calculations. It is found that this is a universal behavior for a whole range of surface interactions from complete repulsion to strong attraction. More interestingly, finite surface repulsion may lead to the maximum in the proximal layer of its segment density profile, which is significantly different from both the depletion layer of pure repulsion and the adsorbing layer of attraction. In addition to the brush state on both repulsive and attractive surfaces, three additional surface states were identified by analyzing the scaling behavior of the layer thickness of polymer brushes: the mushroom state on repulsive substrates, the dilute and the semidilute surface states on attractive substrates.     

Surface tension of polystyrene blends: Theory and experiment

Surface tension of linear–linear and star/linear polystyrene blends were measured using a modified Wilhelmy method. Our results show that for both polystyrene blend systems, the surface tension‐composition profile is convex, indicating a strong surface excess of the component with lower surface energy. Star/linear blends display more convex surface tension profiles than their linear–linear counterparts, indicative of stronger surface segregation of the branched‐component relative to linear chains. As a first step toward understanding the physical origin of enhanced‐surface segregation of star polymers, self‐consistent field (SCF) lattice simulations (both incompressible and compressible models) and Cahn‐Hilliard theory were used to predict surface tension‐composition profiles. Results from the lattice simulations indicate that the highly convex surface tension profiles observed in the star/linear blend systems are only possible if an architecture‐dependent, Flory interaction parameter (χ = 0.004) is assumed. This conclusion is inconsistent with results from bulk differential scanning calorimetry (DSC) measurements, which indicate sharp glass transitions in both the star/linear and linear/linear homopolymer blends and a simple linear relationship between the bulk glass transition temperature and blend composition. To implement the Cahn‐Hilliard theory, pressure‐volume‐temperature (PVT) data for each of the pure components in the blends were first measured and the data used as input for the theory. Consistent with the experimental data, Cahn‐Hilliard theory predicts a larger surface excess of star molecules in linear hosts over a wide composition range. Significantly, this result is obtained assuming a nearly neutral interaction parameter between the linear and star components, indicating that the surface enrichment of the stars is not a consequence of complex phase behavior in the bulk. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1666–1685, 2009     

Analytic model for surface-induced molecular weight segregation in thermoplastic composites

An analytic model based on a random-walk formulation for absorbing barriers is presented. The range of applicability of the model is established from results derived from Monte Carlo simulations. The model takes into account the influences of neutral, repulsive, and attractive polymer-surface interactions on the spatial variation of species concentrations in the vicinity of a surface. The model predicts that the lower molecular weight species of a polydisperse mixture will accumulate in the vicinity of a surface to create an interphase region. The extent of this surface-perturbed interphase region is on the order of three times the radius of gyration of the longest species of the mixture. The degree of molecular weight segregation is dependent upon the breadth of the molecular weight distribution. © 1994 John Wiley & Sons. Inc.     

Comparison of random-walk density functional theory to simulation for bead-spring homopolymer melts

Density profiles for a homopolymer melt near a surface are calculated using a random-walk polymeric density functional theory, and compared to results from molecular dynamics simulations. All interactions are of a Lennard-Jones form, for both monomer-monomer interactions and surface-monomer interactions, rather than the hard core interactions which have been most investigated in the literature. For repulsive systems, the theory somewhat overpredicts the density oscillations near a surface. Nevertheless, near quantitative agreement with simulation can be obtained with an empirical scaling of the direct correlation function. Use of the random phase approximation to treat attractive interactions between polymer chains gives reasonable agreement with simulation of dense liquids near neutral and attractive surfaces.     

Hybrid density functional theory for homopolymer mixtures confined in a selective nanoslit

By integrating polymer density function theory (DFT) and single-chain molecular simulation, a hybrid DFT is developed for homopolymer mixtures confined in a selective nanoslit. Two weighting functions are adopted separately in the polymer DFT for repulsive and attractive contributions to the excess free energy functional. The theoretical results agree well with simulation data for the density profiles, configurations (tail, loop and train), adsorption amounts, layer thicknesses, and partition coefficients. The polymer-slit interaction is found to have a large effect on the density profiles and partition coefficients but is found to have a small effect on the average sizes and percentages of the configurations. Nearly half of the polymer segments form tails, and the other half form trains. In addition, bridges are observed to form for sufficiently long polymer chains. As the length difference between two polymers increases, the effect of chain connectivity becomes increasingly important.     

Density functional theory of homopolymer mixtures confined in a slit

A density functional theory (DFT) is developed for polymer mixtures with shorted-ranged attractive interparticle interactions confined in a slit. Different weighting functions are used separately for the repulsive part and the attractive part of the excess free energy functional by applying the weighted density approximation. The predicted results by DFT are in good agreement with the corresponding simulation data indicating the reliability of the theory. Furthermore, the center-of-mass profiles and the end-to-end distance distributions are obtained by the single chain simulation; the predictions also agree well with simulation data. The results reveal that both the attraction of the slit wall and the temperature has stronger effect on longer chains than on shorter ones because the intrasegment correlation of chains increases with increasing chain length.     

Friction and normal interaction forces between irreversibly attached weakly charged polymer brushes

Polyelectrolyte brushes were built on mica by anchoring polystyrene-poly(acrylic acid) (PS-b-PAA) diblock copolymers at a controlled surface density in a polystyrene monolayer covalently attached to OH-activated mica surfaces. Compared to physisorbed polymer brushes, these irreversibly attached charged brushes allow the polymer grafting density to remain constant upon changes in environmental conditions (e.g., pH, salt concentration, compression, and shear). The normal interaction and friction forces as a function of surface separation distance and at different concentrations of added salt (NaCl) were investigated using a surface forces apparatus. The interaction force profiles were completely reversible both on loading and receding and were purely repulsive. For a constant polymer grafting density, the influence of the polyelectrolyte charges and the Debye screening effect on the overall interaction forces was investigated. The experimental interaction force profiles agree very well with scaling models developed for neutral and charged polymer brushes. The variation of the friction force between two PAA brushes in motion with respect to each other as a function of surface separation distance appeared to be similar to that observed with neutral brushes. This similarity suggests that the increase in friction is associated with an increase in mutual interpenetration upon compression as observed with neutral polymers. The effect of the PAA charges and added ions was more significant on the repulsive normal forces than on the friction forces. The reversible characteristics of the normal force profiles and friction measurements confirmed the strong attachment of the PAA brushes to the mica substrate. High friction coefficients (ca 0.3) were measured at relatively high pressures (40 atm) with no surface damage or polymer removal.     

Adsorption of a cationic dye molecule on polystyrene microspheres in colloids: effect of surface charge and composition probed by second harmonic generation

Nonlinear optical probe, second harmonic generation (SHG), of the adsorption of the dye molecule malachite green (MG), in cationic form at pH < or = 5, on polystyrene microspheres in aqueous solution is used to study the effect of surface charge and composition on molecular adsorption. Three types of polystyrene microspheres with different surface composition are investigated: (1) a sulfate terminated, anionic surface, (2) a neutral surface without any functional group termination, and (3) an amine terminated, cationic surface. The cationic dye was found to adsorb at all three surfaces, regardless of surface charge. The adsorption free energies, DeltaG's, measured for the three surfaces are -12.67, -12.39, and -10.46 kcal/mol, respectively, with the trend as expected from the charge interactions. The adsorption density on the anionic surface, where attractive charge-charge interaction dominates, is determined by the surface negative charge density. The adsorption densities on the neutral and cationic surfaces are on the other hand higher, perhaps as a result of a balance between minimizing repulsive charge interaction and maximizing attractive molecule-substrate and intermolecular interactions. The relative strength of the SH intensity per molecule, in combination of a model calculation, reveals that the C(2) axis of the MG molecule is nearly perpendicular to the surface on the anionic surface and tilts away from the surface norm when the surface is neutral and further away when cationic. Changing the pH of the solution may alter the surface charge and subsequently affect the adsorption configuration and SH intensity.     

Surface-induced morphologies of ABC star triblock copolymer in spherical cavities

The morphologies and phase diagrams exhibited by symmetric ABC star triblock copolymer nanoparticles are investigated on the basis of real-space self-consistent field theory. The ABC star triblock copolymers were chosen to be tiling-forming with fixed polymer parameter and the spherical boundaries were modeled using the masking technique. We first study a number of examples where the ABC triblock copolymers confined in spherical cavities with neutral surface. Then, two types of spherical cavity distinct preferential surfaces are considered, including both A-block attractive and repulsive preferential surfaces. We aim at the effects due to various spherical cavity diameters and the degree of interactions between the polymer and the spherical surface. A variety of morphologies, such as ring-like structures, concentric sphere, and irregular cylinder, were identified in phase diagrams. The results show that both the degree of interactions and spherical diameters can influence the formation of morphologies so that ring-like structures and other novel structures could be obtained.     

Attractive bridging interactions in dense polymer brushes in good solvent measured by atomic force microscopy

Using an atomic force microscope (AFM), we have investigated the interaction forces exerted by latex particles bearing densely grafted polymer brushes consisting of poly(N,N-dimethylacrylamide) (PDMA), poly(methoxyethylacrylamide) (PMEA), poly(N-isopropylacrylamide) (PNIPAM), and PMEA-b-PNIPAM in aqueous media (good solvent). The brushes were prepared by controlled surface-initiated atom transfer radical polymerization, and the hydrodynamic thicknesses were measured by dynamic light scattering. The molecular weight (Mn), grafting density (sigma), and polydispersity (PDI) of the brushes were determined by gel permeation chromatography and multiangle laser light scattering after cleaving the polymer from the latex surface by hydrolysis. Force profiles of PDMA (0.017 nm(-2) < or = sigma < or = 0.17 nm-2) and PMEA (sigma = 0.054 nm-2) brushes were purely repulsive upon compression, with forces increasing with Mn and a, as expected, due to excluded volume interactions. At a sufficiently low grafting density (sigma = 0.012 nm-2), PDMA exhibited a long-range exponentially increasing attractive force followed by repulsion upon further compression. The long-range attractive force is believed to be due to bridging between the free chain ends and the AFM tip. The PNIPAM brush exhibited a bridging force at a grafting density of 0.037 nm(-2), a value lower than the sigma needed to induce bridging in the PDMA brush. Bridging was therefore found to depend on grafting density as well as on the nature of the monomer. The grafting densities of these polymers were larger than those typically associated with bridging. Bridging interactions were used to confirm the presence of PNIPAM in a block copolymer PMEA-b-PNIPAMA brush given that the original PMEA homopolymer brush produced a purely repulsive force. The attractive force was first detected in the block copolymer brush at a separation that increased with the length of the PNIPAM block.     

Phase behavior of a blend of polymer-tethered nanoparticles with diblock copolymers

Using the self-consistent field theory (SCFT), we investigate the phase behavior of a mixture of diblock copolymers and nanoparticles with monodisperse polymer chains tethered to their surfaces. We assume the size of the nanoparticles to be much smaller than that of the attached polymer chains and therefore model the particles with their grafted polymer "shell" as star polymers. The polymer chains attached to the particles are of the same species as one of the blocks of the symmetric diblock copolymer. Of primary interest is how to tune the shell of the particle by changing both the length and number of tethered polymers in order to achieve higher loading of nanoparticles within an ordered structure without macrophase separation occurring. We find that the phase behavior of the system is very sensitive to the size of the particle including its tethered shell. The region of microphase separation is increased upon decreasing the star polymer size, which may be achieved by shortening and/or removing tethered polymer chains. To explore the possible structures in these systems we employ SCFT simulations that provide insight into the arrangement of the different species in these complex composites.     

Surface enrichment of branched polymers in linear hosts: effect of asymmetry in intersegmental interactions and density gradients

Variable density lattice treatment of surface enrichment of f-arm star-branched chains in star/linear polymer blends is compared with results of an analytical response theory proposed by Wu and Fredrickson [Macromolecules 29, 7919 (1996)]. We find that differences in treating the intersegmental interactions in the small interfacial region near a free surface lead to significant differences in the potentials by which polymer chain ends are attracted towards the surface. Consideration of an asymmetric relationship between segment potentials and density changes in polystyrene at 450 K and 0.1 MPa, for example, gives typically a threefold to fourfold enhancement in composition of star molecules at a vacuum interface. When contributions from gradients in density are included in the analysis even greater levels of surface enhancement (fivefold to sixfold increases) are observed. By appropriately estimating the attraction of chain ends and repulsion of branch points at a free surface, we show that concentration profiles of branched polymers predicted in the lattice model are consistent with results obtained in the analytical response theory.     

Effect of grafting on nanoparticle segregation in polymer/nanoparticle blends near a substrate

Nanoparticles in polymer films have shown the tendency to migrate to the substrate due to an entropic-based attractive depletion interaction between the particles and the substrate. It is also known that polymer-grafted nanoparticles show better dispersion in a polymer matrix. Here, molecular dynamics simulations are employed to study the effect of grafting on the nanoparticle segregation to the substrate. The nanoparticles were modeled as spheres and the polymers as bead-spring chains. The polymers of the grafts and the matrix are identical in nature. For a purely repulsive system, the nanoparticle density near the surface was found to decrease as the length of grafted chains and the number of grafts increased and in the bulk, the nanoparticles are well-dispersed. Whereas, in case of attractive systems with interparticle interactions on the order of thermal energy, the nanoparticles segregated to the substrate even more strongly, essentially forming clusters on the wall and in the bulk. However, due to the presence of grafted chains on the nanoparticles, the clusters formed in the bulk are structurally anisotropic. The effect of grafts on nanoparticle segregation to the surface was found to be qualitatively similar to the purely repulsive case.     

Attraction-driven disorder in a hard-core colloidal monolayer

Monte Carlo simulation techniques were employed to explore the effect of short-range attraction on the orientational ordering in a two-dimensional assembly of monodisperse spherical particles. We find that if the range of square-well attraction is approximately 15% of the particle diameter, the dense attractive fluid shows the same ordering behavior as the same density fluid composed of purely repulsive hard spheres. Fluids with an attraction range larger than 15% show an enhanced tendency to crystallization, while disorder occurs for fluids with an attractive range shorter than 15% of the particle diameter. A possible link with the existence of "repulsive" and "attractive" states in dense colloidal systems is discussed.     

Simple model for grafted polymer brushes

The first theories of grafted polymer brushes assumed a step profile for the monomer density. Later, the real density profile was obtained from Monte Carlo or molecular dynamics simulations and calculated numerically using a self-consistent field theory. The analytical approximations of the solutions of the self-consistent field equations provided a parabolic dependence of the self-consistent field, which in turn led to a parabolic distribution for the monomer density in neutral brushes. As shown by numerical simulations, this model is not accurate for dense polymer brushes, with highly stretched polymers. In addition, the scaling laws obtained from the analytical approximations of the self-consistent field theory are identical to those derived from the earlier step-profile-approximation and predict a vanishing thickness of the brush at low graft densities, and a thickness exceeding the length of the polymer chains at high graft densities. Here a simple model is suggested to calculate the monomer density and the interaction between surfaces with grafted polymer brushes, based on an approximate calculation of the partition function of the polymer chains. The present model can be employed for both good and poor solvents, is compatible with a parabolic-like profile at moderate graft densities, and leads to an almost steplike density for highly stretched brushes. While the thickness of the brush depends strongly on solvent quality, it is a continuous function in the vicinity of the temperature. In good and moderately poor solvents, the interactions between surfaces with grafted polymer brushes are always repulsive, whereas in poor solvents the interactions are repulsive at small separations and become attractive at intermediate separation distances, in agreement with experiment. At large separations, a very weak repulsion is predicted.     

Arm-first method as a simple and general method for synthesis of miktoarm star copolymers

Miktoarm star copolymers containing two or more arm species were synthesized by atom transfer radical polymerization using a simple and general "arm-first" method, that is, one-pot cross-linking a mixture of different linear macroinitiator (MI) species by a divinyl cross-linker, such as divinylbenzene. Using linear MIs with a high degree of bromine chain-end functionality, including polyacrylate, polystyrene, polymethacrylate and poly(ethylene oxide), resulted in high-yield star polymers (>90%). Characterized by liquid adsorption chromatography techniques, which separated star polymers on the basis of the chemical composition of arms, the obtained star product was proved to be miktoarm star copolymers containing two or more arm species in one molecule, instead of mixture of different homoarm star polymers. Within our investigation, the molar ratios of the arms in the miktoarm star copolymers were always in agreement with the composition of the initial MI mixture, indicating the powerful capacity of this arm-first method for synthesis of miktoarm star copolymers with potentially any molar ratios and species of the arms. By using a mixture containing five types of linear MIs with different chemical compositions, miktoarm star copolymers containing five kinds of arms were synthesized for the first time, which significantly expanded the methodologies for synthesis of miktoarm star copolymers by living polymerization techniques.     

Coarse graining of star-polymer--colloid nanocomposites

We consider mixtures of self-avoiding multiarm star polymers with hard colloids that are smaller than the star polymer size. By employing computer simulations, and by extending previous theoretical approaches, developed for the opposite limit of small star polymers [A. Jusufi et al., J. Phys.: Condens. Matter 13, 6177 (2001)], we coarse-grain the mixture by deriving an effective cross-interaction between the unlike species. The excellent agreement between theory and simulation for all size ratios examined demonstrates that the theoretical approaches developed for the colloidal limit can be successfully modified to maintain their validity also for the present case of the protein limit, in contrast to the situation for mixtures of colloids and linear polymers. We further analyze, on the basis of the derived interactions, the non-additivity parameter of the mixture as a function of size ratio and star functionality and delineate the regions in which we expect mixing as opposed to demixing behavior. Our results are relevant for the study of star-colloid nanocomposites and pave the way for further investigations of the structure and thermodynamics of the same.     

Effect of attractions on the structure of polymer solutions confined between surfaces: a density functional approach

A density functional theory is presented to study the effect of attractions on the structure of polymer solutions confined between surfaces. The polymer molecules have been modeled as a pearl necklace of freely jointed hard spheres and the solvent as hard spheres, both having Yukawa-type attractions and the mixture being confined between attractive Yukawa-type surfaces. The present theory treats the ideal gas free energy functional exactly and uses weighted density approximation for the hard chain and hard sphere contributions to the excess free energy functional. The attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions on the density profiles of the polymer and the solvent molecules are found to agree quite well with the Monte Carlo simulation results for varying densities, chain lengths, wall separations, and different sets of interaction potentials.