Effect of polymer size and chain length on depletion interactions between two colloids

A density functional theory based on the weighted density has been developed to investigate the depletion interactions between two colloids immersed in a bath of the binary polymer mixtures, where the colloids are modeled as hard spheres and the polymers as freely jointed tangent hard-sphere chain mixtures. The theoretical calculations for the depletion forces between two colloids induced by the polymer are in good agreement with the computer simulations. The effects of polymer packing fraction, degree of polymerization, polymer/polymer size ratio, colloid/polymer size ratio on the depletion interactions, and colloid-colloid second virial coefficient B2 due to polymer-mediated interactions have been studied. With increasing the polymer packing fraction, the depletion interaction becomes more long ranged and the attractive interaction near the colloid becomes deeper. The effect of degree polymerization shows that the long chain gives a more stable dispersion for colloids rather than the short chain. The strong effective colloid-colloid attraction appears for the large colloid/polymer and polymer/polymer size ratio. The location of maximum repulsion Rmax is found to appear Rmax approximately sigmac+Rg2 for the low polymer packing fraction and this is shifted to smaller separation Rmax approximately sigmac+sigmap2 with increasing the polymer packing fraction, where sigmap2 and Rg2 are the small-particle diameter and the radius of gyration of the polymer with the small-particle diameter, respectively.     

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.     

Density functional theory for the recognition of polymer at nanopatterned surface

The recognition of homopolymer at nanopatterned surface has been investigated by density functional theory (DFT). Chain conformation and pattern transfer parameter predicted from the DFT are in good agreement with Monte Carlo simulation results. The theory describes satisfactorily the transition from depletion at low packing fractions to adsorption and double-layer adsorption at high packing fractions and also accounts for the crucial effect of the segment-wall interaction. It is found that homopolymer is better recognized at a low bulk density and a stronger interaction with the surface. The polymer can not only recognize the surface but also invert the surface at high bulk densities. The chain in the solution-wall interface exhibits a typical "brush" conformation with a length approximated by half the length of polymer chain.     

Demixing in athermal mixtures of colloids and excluded-volume polymers from density functional theory

We study the structure and interfacial properties of model athermal mixtures of colloids and excluded volume polymers. The colloid particles are modeled as hard spheres whereas the polymer coils are modeled as chains formed from tangentially bonded hard spheres. Within the framework of the nonlocal density functional theory we study the influence of the chain length on the surface tension and the interfacial width. We find that the interfacial tension of the colloid-interacting polymer mixtures increases with the chain length and is significantly smaller than that of the ideal polymers. For certain parameters we find oscillations on the colloid-rich parts of the density profiles of both colloids and polymers with the oscillation period of the order of the colloid diameter. The interfacial width is few colloid diameters wide and also increases with the chain length. We find the interfacial width for the end segments to be larger than that for the middle segments and this effect is more pronounced for longer chains.     

Multiple dynamic regimes in colloid‐polymer dispersions: New insight using X‐ray photon correlation spectroscopy

We present an X‐ray photon correlation spectroscopy (XPCS) study of dynamic transitions in an anisotropic colloid‐polymer dispersion with multiple arrested states. The results provide insight into the mechanism for formation of repulsive glasses, attractive glasses, and networked gels of colloids with weakly adsorbing polymer chains. In the presence of adsorbing polymer chains, we observe three distinct regimes: a state with slow dynamics consisting of finite particles and clusters, for which interparticle interactions are predominantly repulsive; a second dynamic regime occurring above the saturation concentration of added polymer, in which small clusters of nanoparticles form via a short‐range depletion attraction; and a third regime above the overlap concentration in which dynamics of clusters are independent of polymer chain length. The observed complex dynamic state diagram is primarily governed by the structural reorganization of a nanoparticle cluster and polymer chains at the nanoparticle‐polymer surface and in the concentrated medium, which in turn controls the dynamics of the dispersion. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 752–760     

The interaction between triton X series surfactants and poly (ethylene glycol) in aqueous solutions

 A series of Triton X surfactants with different ethylene oxide chain length and poly(ethylene glycols) with different molecular weight were used, to find the effects of polymer chain length and size of the micelles on the cloud point of the surfactants. Two possible models are considered on the basis of cloud point changes of the solutions, to describe the polymer–surfactant interactions. One model considers that intra-chain micelles of polysoap are formed among the surfactant monomers and long polymer chains. The bridging attraction between two intra-chain micelles in such structures can enhance the collisions among the micelles, due to the exchange of amphiphilic monomers among the neighboring micelles. The other model suggests that flocculation depletion for the polymer chains exists between two regular micelles. This provides the driving force for the neighboring micelles to approach each other and destabilize the colloidal system. The flocculation effect is more significant for polymer with a long chain. Polymers with a shorter chain block the approach of the micelles, since there is no typical polymer–surfactant association formed but just simple small molecule associations in which the steric and solvation effects of the polymer chains make the inter-micelle interactions repulsive. Received: 19 August 1997 Accepted: 11 December 1997     

Interactions between colloidal particles in polymer solutions: A density functional theory study

We present a density functional theory study of colloidal interactions in a concentrated polymer solution. The colloids are modeled as hard spheres and polymers are modeled as freely jointed tangent hard sphere chains. Our theoretical results for the polymer-mediated mean force between two dilute colloids are compared with recent simulation data for this model. Theory is shown to be in good agreement with simulation. We compute the colloid-colloid potential of mean force and the second virial coefficient, and analyze the behavior of these quantities as a function of the polymer solution density, the polymer chain length, and the colloid/polymer bead size ratio.     

环状高分子对胶体稳定性影响的理论研究

将改进的基本度量理论与热力学微扰理论相结合,提出了胶体/高分子系统排空相互作用的IRDFT理论。该理论解释了在实际胶体系统中起重要作用的排斥体积效应和高分子链内相关性的竞争机制。应用该IRDFT,分别以线性链状和环状结构的高分子及其单体为排空元,计算了不同排空元条件下的胶体间排空相互作用。研究表明:对于絮凝破坏,自由环状高分子具有更大的优势。     

端基附壁模型聚合物环形链的构象统计理论

环形链定义为两个端基均附壁的线形聚合物链所得的环 .采用精确计数和蒙特卡罗模拟方法 ,研究了自回避行走 (SAW)模型表示的环形链的构象 ,求得构象数和均方回转半径随链长的变化 .对于二维和三维SAW环形链 ,精确计数的最大链长分别为N =2 9和 1 9.用标度理论处理了数值结果 ,所得的标度指数和其他参数与理论预示值进行了比较 .模拟结果表明 ,SAW环形链限制壁平行方向的尺寸大于垂直方向的尺寸 ,与SAW尾形链尺寸的变化正好相反 .     

Polymer vesicles with a colloidal armor of nanoparticles

The fabrication of polymer vesicles with a colloidal armor made from a variety of nanoparticles is demonstrated. In addition, it is shown that the armored supracolloidal structure can be postmodified through film-formation of soft polymer latex particles on the surface of the polymersome, hereby effectively wrapping the polymersome in a plastic bag, as well as through formation of a hydrogel by disintegrating an assembled polymer latex made from poly(ethyl acrylate-co-methacrylic acid) upon increasing the pH. Furthermore, ordering and packing patterns are briefly addressed with the aid of Monte Carlo simulations, including patterns observed when polymersomes are exposed to a binary mixture of colloids of different size.     

Aggregation of amphiphilic polymers in the presence of adhesive small colloidal particles

The interaction of amphiphilic polymers with small colloids, capable to reversibly stick onto the chains, is studied. Adhesive small colloids in solution are able to dynamically bind two polymer segments. This association leads to topological changes in the polymer network configurations, such as looping and cross-linking, although the reversible adhesion permits the colloid to slide along the chain backbone. Previous analyses only consider static topologies in the chain network. We show that the sliding degree of freedom ensures the dominance of small loops, over other structures, giving rise to a new perspective in the analysis of the problem. The results are applied to the analysis of the equilibrium between colloidal particles and star polymers, as well as to block copolymer micelles. The results are relevant for the reversible adsorption of silica particles onto hydrophilic polymers, used in the process of formation of mesoporous materials of the type SBA or MCM, cross-linked cyclodextrin molecules threading on the polymers and forming the structures known as polyrotaxanes. Adhesion of colloids on the corona of the latter induce micellization and growth of larger micelles as the number of colloids increase, in agreement with experimental data.     

Structure, surface excess and effective interactions in polymer nanocomposite melts and concentrated solutions

The Polymer Reference Interaction Site Model (PRISM) theory is employed to investigate structure, effective forces, and thermodynamics in dense polymer-particle mixtures in the one and two particle limit. The influence of particle size, degree of polymerization, and polymer reduced density is established. In the athermal limit, the surface excess is negative implying an entropic dewetting interface. Polymer induced depletion interactions are quantified via the particle-particle pair correlation function and potential of mean force. A transition from (nearly) monotonic decaying, attractive depletion interactions to much stronger repulsive-attractive oscillatory depletion forces occurs at roughly the semidilute-concentrated solution boundary. Under melt conditions, the depletion force is extremely large and attractive at contact, but is proceeded by a high repulsive barrier. For particle diameters larger than roughly five monomer diameters, division of the force by the particle radius results in a nearly universal collapse of the depletion force for all interparticle separations. Molecular dynamics simulations have been employed to determine the depletion force for nanoparticles of a diameter five times the monomer size over a wide range of polymer densities spanning the semidilute, concentrated, and melt regimes. PRISM calculations based on the spatially nonlocal hypernetted chain closure for particle-particle direct correlations capture all the rich features found in the simulations, with quantitative errors for the amplitude of the depletion forces at the level of a factor of 2 or less. The consequences of monomer-particle attractions are briefly explored. Modification of the polymer-particle pair correlations is relatively small, but much larger effects are found for the surface excess including an energetic driven transition to a wetting polymer-particle interface. The particle-particle potential of mean force exhibits multiple qualitatively different behaviors (contact aggregation, steric stabilization, local bridging attraction) depending on the strength and spatial range of the polymer-particle attraction.     

Control of the geometry of the adsorbed thin layer by the depletion interaction

The depletion interaction was reported to drive the mixtures of rodlike colloids and polymer coils into a variety of phase transitions such as isotropic-nematic, nematic-smectic, and so forth. We describe in this Communication a convenient preparation of the self-assembled monolayer of the platelike porphyrin molecules by the depletion interaction between the absorbent and the metal substrates. After the depletant, low molecular weight poly(ethylene oxide) (PEO), was added into the porphyrin/ethanol solution, random oriented porphyrin was then regulated to lie parallel to the adjacent metal substrates, forming the self-assembled monolayer.     

Optimization of functionalized polymer layers for specific targeting of mobile receptors on cell surfaces

The reversible binding between a planar polymer layer functionalized by ligands and a planar cell surface containing different densities of mobile receptors has been studied by Monte Carlo simulations. Using the acceptance-ratio method, the distance-dependent profiles for the average number of ligands bound to receptors, the total free energy for the polymer layer-cell surface interaction and the interaction force were obtained. Four main design parameters for the polymer layer were considered: the degree of functionalization, chain degree of polymerization, polymer grafting density and the binding energy for the ligand-receptor interaction. We found that an increase in the degree of functionalization or in the absolute energy of ligand-receptor binding results in a larger number of ligands bound to the receptors, lower free energy, and stronger attractive force. Polymer layers composed of shorter chains were found to exhibit a deeper and narrower free energy profile and a larger attractive force, while longer tethers can interact with the cell surface at a larger and broader range of separation distances, in agreement with experimental observations. Our simulation results show that the increase in polymer grafting density from the mushroom to brush regime enhances the ligand availability and results in a stronger attractive force, increases the maximum binding distance, but exhibits a shallower free energy minimum due to the smaller tolerance to compression for polymer layers with high grafting density. We used two measures of the polymer layer binding affinity to the cell surface: the free energy minimum, related to the equilibrium binding constant and the fraction of bound ligands. We found that the polymer layers with a smaller chain length and grafting density, larger degree of functionalization, and larger absolute binding energy exhibit both a larger equilibrium binding constant to the cell surface and a larger average number of bound ligands, except for high binding energies when the maximum level of binding is reached independently of polymer length and grafting density. We showed that high binding specificity can be achieved by the polymer layers with intermediate ligand-receptor binding energies or an intermediate number of ligands, as a larger binding energy or number of ligands ensures a high binding affinity but lacks specificity while a smaller binding energy or number of ligands provides inadequate affinity. We found that the results for polymer layers with different properties follow a similar pattern when both high binding affinity to cells with high receptor density and high binding specificity are considered. As a result, the optimal design of the polymer layers can be achieved by using several different strategies, which are discussed.     

Why surfaces modified by flexible polymers often have a finite contact angle for good solvents

Polymers adsorbing from a dilute solution onto the solvent-vapor interface generate a nonzero surface pressure. When the same polymers are end-grafted onto a surface such that a so-called polymer brush is formed, one will find that the solvent wets this compound interface partially. The partial wetting and the finite surface pressure are intimately linked properties of the polymer-solvent-vapor combination. It is shown that the spreading parameter in the wetting problem is proportional to the surface pressure in the adsorption case. Complete wetting is only possible when this surface pressure is nonpositive. The wetting characteristics are hardly influenced by the grafting density and chain length characterizing the brush. We argue that the grafted polymer chains can bridge to the solvent-vapor interface, thereby preventing the wetting film to become macroscopically thick. We present experimental data underpinning our self-consistent field analysis. Indeed, finite contact angles should be expected in various systems in which bridging attraction contributes to the disjoining pressure in wetting films.     

Colloidal phase separation of concentrated PNIPAm solutions

In the concentration range of 1-6 wt %, solutions of a thermosensitive polymer (poly-N-isopropylacrylamide (PNIPAm), Mw = 1.4 x 10(5) g.mol(-1)) are shown to phase separate in the form of dense stable colloids of nearly pure polymer. Diffuse wave spectroscopy and small-angle neutron scattering both provide consistent measurements of the colloidal size as a function of temperature. Results are in agreement with a Cahn regime of spinodal decomposition blocked at an early stage, prior to a growth that would lead to a macroscopic phase separation. [Early results of this work were presented at the 231st American Chemical Society National Meeting, Symposium on Amphiphilic Polymers, Atlanta, GA, 2006, March 26-30.].     

Relation between packing density and thermal transitions of alkyl chains on layered silicate and metal surfaces

Self-assembled layers of alkyl chains grafted onto the surfaces of layered silicates, metal, and oxidic nanoparticles are utilized to control interactions with external media by tuning the packing density of the chains on the surface, head group functionality, and chain length. Characterization through experiment and simulation shows that the orientation of the alkyl layers and reversible phase transitions on heating are a function of the cross-sectional area of the alkyl chains in relation to the available surface area per alkyl chain. On even surfaces, a packing density less than 0.2 leads to nearly parallel orientation of the alkyl chains on the surface, a high degree of conformational disorder, and no reversible melting transitions. A packing density between 0.2 and 0.75 leads to intermediate inclination angles, semicrystalline order, and reversible melting transitions on heating. A packing density above 0.75 results in nearly vertical alignment of the surfactants on the surface, a high degree of crystalline character, and absence of reversible melting transitions. Curved surfaces can be understood by the same principle, taking into account a local radius of curvature and a distance-dependent packing density on the surface. In good approximation, this simple model is independent from the length of the alkyl chains (a minimum length of C10 is required to form sufficiently distinctive patterns), the chemical nature of the surface, and of the surfactant head group. These structural details primarily determine the functionality of alkyl modified surfaces and the temperature of thermal transitions.     

Alignment of particles in sheared viscoelastic fluids

We investigate the shear-induced structure formation of colloidal particles dissolved in non-Newtonian fluids by means of computer simulations. The two investigated visco-elastic fluids are a semi-dilute polymer solution and a worm-like micellar solution. Both shear-thinning fluids contain long flexible chains whose entanglements appear and disappear continually as a result of Brownian motion and the applied shear flow. To reach sufficiently large time and length scales in three-dimensional simulations with up to 96 spherical colloids, we employ the responsive particle dynamics simulation method of modeling each chain as a single soft Brownian particle with slowly evolving inter-particle degrees of freedom accounting for the entanglements. Parameters in the model are chosen such that the simulated rheological properties of the fluids, i.e., the storage and loss moduli and the shear viscosities, are in reasonable agreement with experimental values. Spherical colloids dispersed in both quiescent fluids mix homogeneously. Under shear flow, however, the colloids in the micellar solution align to form strings in the flow direction, whereas the colloids in the polymer solution remain randomly distributed. These observations agree with recent experimental studies of colloids in the bulk of these two liquids.     

Synthesis and properties of metal poly(butyl methacrylates) 7

Metal butyl methacrylate colloids were obtained by codeposition at 77K of the monomer with several metals such as Au, Pd, Cu, Ag, Zn, Cd, Ga, In, Ge, Sn, Sb and Bi. Au and Pd colloids are stable tor months at room temperature. The colloids were polymerized with different amounts of initiator benzoyl peroxide at 65°C for 25 min and a wide range of viscosity-average molecular weights (10³ <M̄_v < 10⁵) were obtained depending upon the metal used. The particle size of the clusters dispersed in the polymer matrix is around 500 A°. The polymers are stable even at 300°C, being Pd-poly(butyl methacrylate) the most stable with 388.90°C. The metal content is ranging from 0.02 to 1.65 wt% for Sb and Pd, respectively. Polymers with different colors were obtained depending on the metal used.     

Structure and thermodynamics of protein-polymer solutions: effects of spatially distributed hydrophobic surface residues

Protein-polymer association in solution driven by a short-range attraction has been investigated using a simple coarse-grain model solved by Monte Carlo simulations. The effect of the spatial distribution of the hydrophobic surface residues of the protein on the adsorption of weakly hydrophobic polymers at variable polymer concentration, polymer length, and polymer stiffness has been considered. Structural data on the adsorbed polymer layer and thermodynamic properties, such as the free energy, energy, and entropy, related to the protein-polymer interaction were calculated. It was found that a more heterogeneous distribution of the surface residues promotes adsorption and that this also applies for different polymer concentrations, polymer chain lengths, and polymer flexibilities. Furthermore, the polymer adsorption onto proteins with more homogeneous surface distributions displayed larger sensitivity to polymer properties such as chain length and flexibility. Finally, a simple relation between the adsorption probability and the change in the free energy was found and rationalized by a simple two-state adsorption model.