Surface forces between telechelic brushes revisited: the origin of a weak attraction

Telechelic polymers are useful for surface protection and stabilization of colloidal dispersions by the formation of polymer brushes. A number of theoretical investigations have been reported on a weak attraction between two telechelic brushes when they are at the classical contact, i.e., when the surface separation is approximately equal to the summation of the brush thicknesses. While recent experiments have confirmed the weak attraction between telechelic brushes, its origin remains elusive because of conflicting approximations used in the previous theoretical calculations. In this paper, we have investigated the telechelic polymer-mediated surface forces by using a polymer density functional theory (PDFT) that accounts for both the surface-adhesive energy and segment-level interactions specifically. Within a single theoretical framework, the PDFT is able to capture both the depletion-induced attraction in the presence of weakly adhesive polymers and the steric repulsion between compressed polymer brushes. In comparison of the solvation forces between telechelic brushes with those between brushes formed by surfactant-like polymers and with those between two asymmetric surfaces mediated by telechelic polymers, we conclude that the weak attraction between telechelic brushes is primarily caused by the bridging effect. Although both the surfactant-like and telechelic polymers exhibit a similar scaling behavior for the brush thickness, a significant difference has been observed in terms of the brush microstructures, in particular, the segment densities near the edges of the polymer brushes.     

Theoretical and experimental studies on the surface structures of conjugated rod-coil block copolymer brushes

A combined theoretical and experimental investigation of conjugated rod-coil block copolymer brushes is reported. The theoretical study for the surface structures of rod-coil block copolymer brushes was established based on the simulation method of dissipative particle dynamics. The effects of solvent stimuli, grafting density, and rod-coil block ratio of the polymer brushes on the surface structures were examined. The rod blocks of polymer brushes were found to be well-dispersed on the surface in their good solvents. On the other hand, aggregative domains of the rod blocks were formed in their poor solvents with the conformations of isolated islands or worm-like structures depending on the grafting density of the polymer brushes. The aggregative domains tend to stay on top of the coil blocks for small rod-to-coil block ratio. However, the submergence of the aggregative domains into the coil blocks is thermodynamically preferred for large enough rod-to-coil block ratio. New multifunctional amphiphilic rod-coil block copolymers, poly-[2,7-(9,9-di-n-hexylfluorene)]-block-poly-[poly(ethylene glycol) methyl ether methacrylate]-block-poly-[3(tripropoxysilyl)propyl methacrylate] (PF-b-PPEGMA-b-PPOPS), with two different block ratios were synthesized and used to prepare the corresponding polymer brushes via the grafting- method. The effects of stimuli factors on the surface structures characterized by the atomic force microscopy images were consistent with the theoretical results. Furthermore, the photophysical properties of PF-b-PPEGMA-b-PPOPS brushes were significantly varied by the solvent stimuli. The emission peaks originated from the aggregation and/or excimer formation of PF blocks were observed after methanol treatment. The photoluminescence intensity and its efficiency were well correlated to the surface structure and the methanol content in mixed solvents. Our study demonstrates how the surface structures and photophysical properties of rod-coil block copolymer brushes response to environmental stimuli.     

双峰聚合物分子刷的层化机理

建立了用于模拟双峰聚合物分子刷相结构的自洽场理论. 模拟结果表明, 良溶剂条件能够促使双峰聚合物分子刷裂分为内外两个亚分子层, 其中短链居于内分子层, 而长链伸展到外分子层. 体系溶解性的加强不仅使聚合物的密度分布逐渐趋近强分凝理论的解析结果, 而且加大了分子链的伸展和链段的局部取向程度. 分子链接枝密度的增加能够促使分子刷的层化, 并且在良溶剂区域, 不同接枝密度的分子链密度分布可以回归到同一条主线. 在良溶剂条件下, 长链的聚合度对短链的密度分布影响不大, 但能够导致长链向外分子层扩展.     

Adsorption of copolymers in a selective nanoslit: a hybrid density functional theory

A hybrid density functional theory (DFT) is developed for adsorption of copolymers in a selective nanoslit. The DFT incorporates a single-chain simulation for the ideal-gas free energy functional with two weighted density approximations for the residual free energy functional. The theory is found to be insensitive to the width parameter used in the weighted density. Theoretical predictions are in excellent agreement with simulation results in the segment density profiles and the adsorption configurations including tail, loop, and train for copolymers with various sequences over a wide range of surface affinity. The bridge conformation is also observed in multiblock copolymers. Ordered assembly is facilitated in copolymers with longer chain/block and at stronger attraction between segment B and the slit wall. While diblock copolymer shows the longest tail, alternating copolymer has the shortest. As the attraction between segment B and the slit wall increases, the average size and fraction decrease for tail, but increase for loop and train.     

Density-functional theory and Monte Carlo simulation for the surface structure and correlation functions of freely jointed Lennard-Jones polymeric fluids

We present a nonlocal density-functional theory of polymeric fluids consisting of freely jointed Lennard-Jones chains with explicit consideration of the segment size, van der Waals attraction, and structural correlations due to chain connectivity. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the short-ranged repulsion and the first-order thermodynamic perturbation theory for chain connectivity. The contribution of the long-ranged attraction to the Helmholtz energy functional is taken into account using a quadratic density expansion with the direct correlation function obtained from the first-order mean-spherical approximation. The numerical performance of the density-functional theory is compared well with the simulation results from this work as well as those from the literature for the segment-level density profiles and correlation functions of Lennard-Jones chains in slit pores, near isolated nanoparticles, or in bulk.     

Steric stabilization of spherical colloidal particles: Implicit and explicit solvent

We present the results of Monte Carlo simulations and density functional theory treatment of interactions between spherical colloidal brushes both in implicit (good) solvent and in an explicit polymeric solution. Overall, theory is seen to be in good agreement with simulations. We find that interactions between hard-sphere particles grafted with hard-sphere chains are always repulsive in implicit solvent. The range and steepness of the repulsive interaction is sensitive to the grafting density and the length of the grafted chains. When the brushes are immersed in an explicit solvent of hard-sphere chains, a weak mid-range attraction arises, provided the length of the free chains exceeds that of the grafted chains.     

Isotropic-nematic phase transition in athermal solutions of rod-coil diblock copolymers

We present a hybrid method to investigate the isotropic-nematic (I-N) transition in athermal solutions of rod-coil copolymers. This method incorporates the scaled-particle theory for semiflexible chains with two-chain Monte Carlo simulation for the osmotic second virial coefficient and for the angle-dependent excluded volume. We compare the theoretical prediction with Monte Carlo simulations for fused rod-coil copolymers and find good agreement for both the equation of state and the orientational order parameter. The theory is also used to examine the effects of the bond length, the chain length, and the chain composition on orientational ordering in athermal solutions of rod-coil block copolymers. It predicts I-N transition in rod-coil copolymers with fixed rod length but a variable flexible tail in good agreement with experiments.     

Revisiting the dispersion mechanism of grafted nanoparticles in polymer matrix: a detailed molecular dynamics simulation

By focusing on the grafted nanoparticles (NPs) embedded in polymer melts, a detailed coarse-grained molecular dynamics simulation is adopted to investigate the effects of the grafting density, the length of the matrix and grafted chains on the dispersion of the NPs. We have employed visualization snapshots, radial distribution functions (RDFs), the interaction energy between NPs, the number of neighbor NPs, and the conformation of the brush chains to clearly analyze the dispersion state of the grafted NPs. Our simulated results generally indicate that the dispersion of the NPs is controlled by both the excluded volume of the grafted NPs and the interface between the brushes and the matrix. It is found that increasing grafting density or grafted chain length leads to better dispersion, owing to larger excluded volume; however, increasing the length of the matrix chains leads to aggregation of NPs, attributed to both a progressive loss of the interface between the brushes and the matrix and the overlap between brushes of different NPs, intrinsically driven by entropy. Meanwhile, it is found that there exists an optimum grafting density (σ(c)) for the dispersion of the NPs, which roughly obeys the following mathematical relation: σ(c) is proportional to N(m)(K)/N(g)(L), where K, L > 0 and N(m) and N(g) represent the length of the matrix and grafted chain length, respectively. Considering the practical situation that the grafted brushes and the matrix polymer are mostly not chemically identical, we also studied the effect of the compatibility between the brushes and the matrix polymer by taking into account the attraction between the grafted chains and the matrix chains. In general, our comprehensive simulation results are believed to guide the design and preparation of high-performance polymer nanocomposites with good or even tailored dispersion of NPs.     

Molecular dynamics simulation study of the structure of poly(ethylene oxide) brushes on nonpolar surfaces in aqueous solution

The structure of poly(ethylene oxide) (PEO, M(w) = 526) brushes of various grafting density (sigma) on nonpolar graphite and hydrophobic (oily) surfaces in aqueous solution has been studied using atomistic molecular dynamics simulations. Additionally, the influence of PEO-surface interactions on the brush structure was investigated by systematically reducing the strength of the (dispersion) attraction between PEO and the surfaces. PEO chains were found to adsorb strongly to the graphite surface due primarily to the relative strength of dispersion interactions between PEO and the atomically dense graphite compared to those between water and graphite. For the oily surface, PEO-surface and water-surface dispersion interactions are much weaker, greatly reducing the energetic driving force for PEO adsorption. This reduction is mediated to some extent by a hydrophobic driving force for PEO adsorption on the oily surface. Reduction in the strength of PEO-surface attraction results in reduced adsorption of PEO for both surfaces, with the effect being much greater for the graphite surface where the strong PEO-surface dispersion interactions dominate. At high grafting density (sigma approximately 1/R(g)(2)), the PEO density profiles exhibited classical brush behavior and were largely independent of the strength of the PEO-surface interaction. With decreasing grafting density (sigma < 1/R(g)(2)), coverage of the surface by PEO requires an increasingly large fraction of PEO segments resulting in a strong dependence of the PEO density profile on the nature of the PEO-surface interaction.     

Density profiles and solvation forces for a Yukawa fluid in a slit pore

The effect of varying wall-particle and particle-particle interactions on the density profiles near a single wall and the solvation forces between two walls immersed in a fluid of particles is investigated by grand canonical Monte Carlo simulations. Attractive and repulsive particle-particle and particle-wall interactions are modeled by a versatile hard-core Yukawa form. These simulation results are compared to theoretical calculations using the hypernetted chain integral equation technique, as well as with fundamental measure density functional theory (DFT), where particle-particle interactions are either treated as a first order perturbation using the radial distribution function or else with a DFT based on the direct-correlation function. All three theoretical approaches reproduce the main trends fairly well, but exhibit inconsistent accuracy, particularly for attractive particle-particle interactions. We show that the wall-particle and particle-particle attractions can couple together to induce a nonlinear enhancement of the adsorption and a related "repulsion through attraction" effect for the effective wall-wall forces. We also investigate the phenomenon of bridging, where an attractive wall-particle interaction induces strongly attractive solvation forces.     

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.     

Density functional theory study on the structure and capillary phase transition of a polymer melt in a slitlike pore: effect of attraction

A density functional theory is proposed to investigate the effects of polymer monomer-monomer and monomer-wall attractions on the density profile, chain configuration, and equilibrium capillary phase transition of a freely jointed multi-Yukawa fluid confined in a slitlike pore. The excess Helmholtz energy functional is constructed by using the modified fundamental measure theory, Wertheim's first-order thermodynamic perturbation theory, and Rosenfeld's perturbative method, in which the bulk radial distribution function and direct correlation function of hard-core multi-Yukawa monomers are obtained from the first-order mean spherical approximation. Comparisons of density profiles and bond orientation correlation functions of inhomogeneous chain fluids predicted from the present theory with the simulation data show that the present theory is very accurate, superior to the previous theory. The present theory predicts that the polymer monomer-monomer attraction lowers the strength of oscillations for density profiles and bond orientation correlation functions and makes the excess adsorption more negative. It is interesting to find that the equilibrium capillary phase transition of the polymeric fluid in the hard slitlike pore occurs at a higher chemical potential than in bulk condition, but as the attraction of the pore wall is increased sufficiently, the chemical potential for equilibrium capillary phase transition becomes lower than that for bulk vapor-liquid equilibrium.     

The role of fluid wall association on adsorption of chain molecules at functionalized surfaces: a density functional approach

We present a density functional theory to describe adsorption in systems where selected segments of chain molecules of fluids can bond (or associate) with functional groups attached to the surfaces. Association of active segments with the surface is modeled within the framework of the first-order thermodynamic perturbation theory. We discuss the influence of several parameters such as the density of surface active sites, the energy of association, the chain length, and the number of the active segment in the chain molecule on the structure of the fluid adjacent to the wall. The proposed model can be considered as a first step towards developing a density functional theory of molecular brushes chemically bonded to solid surfaces.     

Density functional theory for copolymers confined in a nanoslit

A density functional theory is developed for copolymers confined in a nanoslit on the basis of our previous work for homopolymers. The theory accurately captures the structural characteristics for diblock and alternating copolymers composed of hard-sphere or square-well segments. Satisfactory agreement is obtained between the theoretical predictions and simulation results in segment density profiles, segment fractions, and partition coefficients. Structures under confinement strongly depend on the substituent segment sizes for the hard-sphere copolymers and also on the segment-wall attractions for the square-well copolymers. Alternating copolymers are found to behave as homopolymers with effective segment size, and effective segment-segment and segment-wall interactions.     

Microstructure and depletion forces in polymer-colloid mixtures from an interfacial statistical associating fluid theory

By using a classical density functional theory (interfacial statistical associating fluid theory), we investigate the structure and effective forces in nonadsorbing polymer-colloid mixtures. The theory is tested under a wide range of conditions and performs very well in comparison to simulation data. A comprehensive study is conducted characterizing the role of polymer concentration, particle/polymer-segment size ratio, and polymer chain length on the structure, polymer induced depletion forces, and the colloid-colloid osmotic second virial coefficient. The theory correctly captures a depletion layer on two different length scales, one on the order of the segment diameter (semidilute regime) and the other on the order of the polymer radius of gyration (dilute regime). The particle/polymer-segment size ratio is demonstrated to play a significant role on the polymer structure near the particle surface at low polymer concentrations, but this effect diminishes at higher polymer concentrations. Results for the polymer-mediated mean force between colloidal particles show that increasing the concentration of the polymer solution encourages particle-particle attraction, while decreasing the range of depletion attraction. At intermediate to high concentrations, depletion attraction can be coupled to a midrange repulsion, especially for colloids in solutions of short chains. Colloid-colloid second virial coefficient calculations indicate that the net repulsion between colloids at low polymer densities gives way to net attraction at higher densities, in agreement with available simulation data. Furthermore, the results indicate a higher tendency toward colloidal aggregation for larger colloids in solutions of longer chains.     

Elastic behavior of adsorbed polymer chains

Elastic behaviors of single polymer chains adsorbed on the attractive surface are first investigated using Monte Carlo simulation method based on the bond fluctuation model. We investigate the chain size and shape of adsorbed chains, such as mean-square radius of gyration S2, mean-square bond length b2, shape factors sf(i) and delta*, and the orientation of chain segments P2, to illuminate how the shape of polymer chains changes during the process of tensile elongation. There are some special behaviors of the chain size and shape at the beginning of elongation, especially for strong attraction interaction. For example, mean fraction of adsorbed segments decreases abruptly in the region of small elongation ratio and then decreases slowly with increasing elongation ratio. In fact, the chain size and shape also changes abruptly for small elongation ratio with strong attraction interaction. Some thermodynamics properties are also investigated here. Average Helmholtz free energy increases fast for elongation ratio lambda<1.15, especially with strong attraction, and increases slowly for lambda>1.15. Similar behaviors are obtained for average energy per bond. Elastic force (f ) and energy contribution to force (f(U)) are also studied, and we find that elastic force decreases abruptly for lambda<1.15, and there is a minimum of elastic force for strong attraction interaction, then increases very slowly with increasing elongation ratio. However, there are different behaviors for weak attraction interaction. For energy contribution to force (f(U)), there is a maximum value for strong attraction interaction in the region of lambda<1.15. Some comparisons with the atomic force microscopy experiments are also made. These investigations may provide some insights into the elastic behaviors of adsorbed polymer chains.     

Effects of chain architectures on the surface structures of conjugated rod-coil block copolymer brushes

Rod-coil block copolymers are of unique and interesting characteristics since their physical properties can be reversibly tuned in response to the external stimuli, such as change in solvent quality. In this study, dissipative particle dynamics is used to investigate the surface structures of rod-coil polymer brushes tethered onto a surface. When immersed in the selective solvent for the coil blocks, rod blocks tend to form aggregates. Our results show that linear and Y-shaped polymer brushes exhibit similar aggregative behavior. However, some of the surface structures can be acquired within experimentally attainable surface grafting density only for Y-shaped polymer brushes. On the other hand, comblike polymer brushes are found to possess more diverse aggregative manners than linear brushes. Surface structures with aggregates taking the forms of cones, cylinders, or layers of spheres are found. By controlling the aggregative structures, it is possible for us to adjust the physical properties, such as optical function, of the material.     

Generalized Langevin theory on the dynamics of simple fluids under external fields

A theory on the time development of the density and current fields of simple fluids under an external field is formulated through the generalized Langevin formalism. The theory is applied to the linear solvation dynamics of a fixed solute regarding the solute as the external field on the solvent. The solute-solvent-solvent three-body correlation function is taken into account through the hypernetted-chain integral equation theory, and the time correlation function of the random force is approximated by that in the absence of the solute. The theoretical results are compared with those of molecular-dynamics (MD) simulation and the surrogate theory. As for the transient response of the density field, our theory is shown to be free from the artifact of the surrogate theory that the solvent can penetrate into the repulsive core of the solute during the relaxation. We have also found a large quantitative improvement of the solvation correlation function compared with the surrogate theory. In particular, the short-time part of the solvation correlation function is in almost perfect agreement with that from the MD simulation, reflecting that the short-time expansion of the theoretical solvation correlation function is exact up to t(2) with the exact three-body correlation function. A quantitative improvement is found in the long-time region, too. Our theory is also applied to the force-force time correlation function of a fixed solute, and similar improvement is obtained, which suggests that our present theory can be a basis to improve the mode-coupling theory on the solute diffusion.     

Polymer brushes in nanopores surrounded by silicon-supported tris(trimethylsiloxy)silyl monolayers

A chemically grafted tris(trimethylsiloxy)silyl (tris(TMS)) monolayer on a silicon oxide substrate was used as a template for creating nanoclusters of polymer brushes. Polymer brushes were synthesized by surface-initiated polymerization of 2-methacryloyloxyethyl phosphorylcholine (MPC) and tert-butyl methacrylate (t-BMA) via atom transfer radical polymerization (ATRP) from alpha-bromoester groups tethered to the residual silanol groups on the silicon surface after generating a range of tris(TMS) coverage. CuBr/bpy and CuBr/PMDETA were used as the catalytic system for PMPC and Pt-BMA synthesis, respectively. The percentage of tris(TMS) coverage significantly influenced the thickness and morphology of the polymer brushes. Protrusions representing self-aggregation of PMPC brushes in nanopores as visualized by AFM analysis evidently suggested that PMPC brushes were distributed nanoscopically on the surface. The protrusion size and surface roughness corresponded quite well with the graft density of PMPC brushes. The fact that Pt-BMA brushes grown from nanopores were almost featureless implies that self-aggregation of PMPC brushes is truly a consequence of phase incompatibility between hydrophilic PMPC brushes and hydrophobic tris(TMS). The anti-fouling characteristic of PMPC brushes, inferred from plasma protein adsorption, was subsequently varied by controlling the surface coverage ratio between PMPC brushes and tris(TMS).     

Partition potential for hydrogen bonding in formic acid dimers

The ground-state energy and density of 4 low-energy conformations of the formic acid dimer were calculated via partition density functional theory (PDFT). The differences between isolated and PDFT monomer densities display similar deformation patterns for primary and secondary hydrogen bonds (HBs) among all 4 dimers. In contrast, the partition potential shows no transferable features in the bonding regions. These observations highlight the global character of the partition potential and the cooperative effect that occurs when a dimer is bound via more than 1 HB. We also provide numerical confirmation of the intuitive (but unproven) observation that fragment deformation energies are larger for systems with larger binding energies.