Effect of solvent quality on the dispersibility of polymer-grafted spherical nanoparticles in polymer solutions

In this work, lattice-based self consistent field theory is used to study the structural properties of individual polymer-grafted spherical nanopartices and particle-particle interactions in polymer melts and solutions under variable solvent conditions. Our study has focused on the depth of the minimum in the potential of mean force between the two brush-coated nanoparticles, if such a minimum occurs, and we have also addressed the corresponding radial density profiles of free and grafted chains around a single nanoparticle, in an attempt to clarify the extent of correlation between the depth of the minimum, W(min), and the parameter δ characterizing the interpenetration between the profiles of free and grafted chains. Although one cannot establish a simple one-to-one correspondence between W(min) and δ, we do find common trends, in particular, if the solvent conditions for free and grafted chains differ: varying the volume fraction of the free chains, δ typically exhibits a broad minimum, corresponding to a region where the magnitude of W(min) exceeds thermal energy k(B)T, leading to particle aggregation.     

Bending moduli of dendritic polymer brushes in a good solvent

The effect of branching on the Helfrich mean k _C and Gaussian k _G bending moduli of polymer brushes consisting of dendrons grafted to both sides of a thin impermeable surface (membrane) is studied theoretically. The case of an athermal solvent is considered. The moduli are calculated from a change in the free energy of a brush upon cylindrical and spherical bending of the grafting surface, respectively. The grafting density σ, the total number of monomer units N, and the number of generations g in tethered dendrons are varied. Two variants of the self-consistent field method are applied: the analytical approach and the numerical Scheutjens-Fleer method. The first method is applied at small values of σ, when the density profile of monomer units of grafted chains is parabolic in shape. The second method is free of these restrictions. The universal ratio between moduli is found: k _G =?64/105k _C . Both methods predict that the values of moduli decrease with increasing g at constant N and σ. The scaling dependence N ³ remains valid for the moduli of dendritic brushes with different generation numbers g at all of the considered values of σ. The analytical approach also gives the universal scaling dependence k _C ～ k _G ～ σ^7/3; however, the numerical method predicts that the dependences of moduli on σ become stronger with increasing degree of branching of tethered dendrons.     

Consistent and transferable coarse-grained model for semidilute polymer solutions in good solvent

We present a coarse-grained model for linear polymers with a tunable number of effective atoms (blobs) per chain interacting by intra- and intermolecular potentials obtained at zero density. We show how this model is able to accurately reproduce the universal properties of the underlying solution of athermal linear chains at various levels of coarse-graining and in a range of chain densities which can be widened by increasing the spatial resolution of the multiblob representation, i.e., the number of blobs per chain. The present model is unique in its ability to quantitatively predict thermodynamic and large scale structural properties of polymer solutions deep in the semidilute regime with a very limited computational effort, overcoming most of the problems related to the simulations of semidilute polymer solutions in good solvent conditions.     

Gel chromatography: Interactions between gel matrix, solvent and solute

The partitioning behaviour of homologous series of low-molecular-weight polar and non-polar compounds has been studied on gels of cellulose and various derivative forms in dimethylformamide. The nature of the functional groups present in the gel matrix, solute and solvent markedly affects the solute partitioning. The observed partitioning is discussed in terms of the structures of the components.     

Interaction between two star polymers in a good solvent

An off-lattice bead model with a hard-spheres potential is used to characterize the two-body properties of star polymers of functionalities f=4–18 in good solvent conditions through Monte Carlo simulations. The second virial results complement a previous study performed with a Lennard-Jones potential. Some intrinsic viscosity numerical data are also obtained. The second virial coefficient and viscosity data are combined in terms of a single parameter, with apparently anomalous features in terms of the star functionalities which are also observed from existing experimental data. The effective intermolecular potential is compared with a global potential recently proposed.     

Interactions between inorganic nanoparticles and cellulose nanofibrils

Nanofibrillated cellulose (NFC) is increasingly utilized in materials and biomedical applications consequently increasing interest in the modification of its surface properties. Besides modification using polyelectrolytes and polysaccharides, NFC can be combined with solid particles enabling formation of fibril network loaded with particles. Use of particles enabling easy functionalization could be beneficial for the development of hybrid structures, and lead to preparation of nanocomposites and functional materials. In order to explore interactions related to preparation of such structures, the interactions between nanosized precipitated calcium carbonate (nanoPCC) and nanoclay particles and NFC were examined by observing adsorption of the particles on NFC substrate using a quartz crystal microbalance with dissipation monitoring (QCM-D) and atomic force microscopy (AFM) imaging. By a treatment with carboxymethylated cellulose (CMC), the anionicity of the NFC substrate could be increased, providing an additional tool to affect the interplay between NFC and the inorganic particles. For slightly cationic nanoPCC particles an increase in the anionicity of the NFC by the CMC treatment increased the affinity, while the opposite was true for anionic nanoclay. Additionally, for interactions between nanoclay and NFC, dispersion stability was an important factor. QCM-D was successfully used to examine the adsorption characteristics of nanoparticles although the technique is commonly used to study the adsorption of thin polymer layers. Distinct adsorption characteristics were observed depending on the nanoparticle used; nanoclay particles deposited as a thin layer, whereas nanoPCC particles formed clusters.     

Light scattering from reacting polymer systems. Associating polymers in a good solvent

The forward scattering of light allows determination of the osmotic modulus (=inverse osmotic compressibility), which in good solvents is a measure of repulsive forces among the particles in solution but also depends on the molar mass of the particle. The osmotic modulus increases with concentration if the particle weight remains constant. The increase differs for particles of different architecture and can for c < 3c* be described by structure specific g-factors, where g is defined through A₃=gA₂² M_w with A₂ and A₃ being the 2nd and 3rd virial coefficients. For associating systems in a good solvent also the particle weight increases with c. A procedure is suggested which allows within limits a correction of the measured apparent molar mass M̄_app (c) for the true molar mass M̄_w (c) at the concentration c. Three examples are discussed in detail.     

Spherical polymer brushes under good solvent conditions: molecular dynamics results compared to density functional theory

A coarse grained model for flexible polymers end-grafted to repulsive spherical nanoparticles is studied for various chain lengths and grafting densities under good solvent conditions by molecular dynamics methods and density functional theory. With increasing chain length, the monomer density profile exhibits a crossover to the star polymer limit. The distribution of polymer ends and the linear dimensions of individual polymer chains are obtained, while the inhomogeneous stretching of the chains is characterized by the local persistence lengths. The results on the structure factor of both single chain and full spherical brush as well as the range of applicability of the different theoretical tools are presented. Finally, a brief discussion of the experiment is given.     

Interactions between surfactant capped CdS nanocrystals and organic solvent

The dispersibility of organic capped nanocrystals (NCs) in diverse solvents is one of the key factor of the success of such a class of nanostructured materials. In this work the α-cyclodextrins, mediated phase transfer has been considered as an effective procedure to direct the NC transfer from the organic solvent to water. The effect of the original organic solvent, namely hexane and chloroform, and of the ligand molecule coordinating CdS nanocrystal surface has been investigated by optical (UV-Vis, Photoluminescence, FTIR, Dynamic Light Scattering) and calorimetric techniques. The calorimetric investigation has been carried out by performing dilution experiments and the correlation between thermal effects and dilution ratio has been evaluated using the McMillan approach. The obtained results have provided relevant insight on the parameters driving the phase transfer process and on the NC mutual interaction, thus resulting valuable on the effectiveness of the phase transfer procedure.     

Phase separation of symmetric polymer mixtures in a common good solvent in the semidilute concentration regime

Monte Carlo simulations of lattice models of binary (AB) symmetric polymer mixtures (chain lengthsN _A=N _B=N) in a common good solvent are carried out and the phase diagrams and critical properties of the unmixing transitions are estimated and interpreted in terms of recent theories. Polymers are modeled by self-avoiding walks of lengthN=16, 32 and 64 on the simple cubic lattice. Data for vacancy concentrations of _V=0.6, 0.8 and 0.85 are analyzed. It is shown that forN=16, _V=0.85 no phase separation occurs, down to the lowest temperature, while forN=32, _V=0.85 still phase separation occurs but no longer is complete. Our results are compatible with a scaling theory based on a renormalization of the Flory-Huggins -parameter due to blob effects.Dedicated to Prof. Fischer on the occasion of his 65th birthday.Both of the authors are deeply indebted to Prof. E. W. Fischer, not only for help, support, and enlightening discussions, but even for bringing them together and suggesting to them to collaborate! By this catalytic action he actually played a decisive role in creating a longstanding and successful collaboration, the latest results of which are presented below.     

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.     

Interactions between nanocolloidal particles in polymer solutions: effect of attractive interactions

We present a density-functional theory study of nanoparticle interactions in a concentrated polymer solution. The polymers are modeled as freely jointed tangent chains; all nonbonded interactions between polymer segments and nanoparticles are described by Lennard-Jones potentials. We test several recently proposed methods of treating attractive interactions within the density-functional theory framework by comparing theoretical results with recent simulation data. We find that the simple van der Waals approach provides the most accurate results for the polymer-mediated potential of mean force between two dilute nanoparticles. We employ this approach to study nanoparticle interactions as a function of nanoparticle-segment interaction strength and polymer solution density and temperature.     

Interactions between sterically stabilized nanoparticles in supercritical fluids: a simulation study

The authors report a simulation study of the interaction between gold nanoparticles stabilized with both linear and branched alkane chains in supercritical ethane. In agreement with experimental and previous theoretical work, the authors find that increasing solvent density and making ligands more branched make the nanoparticle interaction more repulsive. These findings are analyzed in terms of the extent of the chain interdigitation and chain-solvent interaction energy.     

Interactions between macromolecules and metal nanoparticles in aqueous-saline media

The influence of the concentration of low-molecular-mass salt additives in the reaction medium on the size characteristics of copper nanoparticles in sols formed through the reduction of Cu²⁺ ions in the presence of a cationic polyelectrolyte and nonionogenic polymers with hydrophilic (poly(ethylene oxide) and hydrophobic (poly(N-vinylpyrrolidone)) main chains has been studied. Formation of sols with a narrow size (diameter) distribution of metal nanoparticle indicates the pseudomatrix character of formation of the metal phase under the studied conditions. Effects of the neutral salt and its concentration in the reaction medium on the synthesis of copper sols and on the mean size of metal nanoparticles are related to a change in the nature or character (when oppositely charged polyelectrolyte macromolecules and copper nanoparticles are involved in interaction) of noncovalent interactions stabilizing the macromolecule-nanoparticle complex on passage from the salt-free aqueous medium to the aqueous-saline medium with a sufficiently high concentration of the neutral salt.     

Molecular dynamics simulation of the forces between colloidal nanoparticles in n-decane solvent

Molecular dynamics is utilized to simulate solvation forces between two nanoparticles immersed in liquid n-decane. Three types of solvophilic nanoparticles are investigated with sizes in the 1-6 nm range: small and large amorphous spheres and crystalline cubes. We find that the solvation forces are negligible for the small spheres, which have diameters comparable to the end-to-end distance of all-trans decane, and we attribute this to the inability of the small spheres to induce decane ordering in the interparticle gap. The cubic nanoparticles (and to a lesser extent, the large spheres) are able to induce the formation of solidlike, n-decane layers in their gap for certain nanoparticle separations, and the transition between layered and disordered structures leads to solvation forces that oscillate between repulsion and attraction as the nanoparticle separation is varied. We find that the Derjaguin approximation [B. V. Derjaguin, Kolloid-Z. 69, 155 (1934)] is not effective at describing the dependence of the solvation forces on nanoparticle size and shape-contrasting results from a previous study involving these nanoparticles in Lennard-Jones solvent [Y. Qin and K. A. Fichthorn, J. Chem. Phys. 119, 9745 (2003)]. In particular, we find that for decane, the magnitude of the repulsive solvation forces is sensitive to nanoparticle size and shape, a phenomenon we attribute to the size and rigid-rod structure of n-decane, which makes its ordering in the interparticle gap sensitive to the size and the surface roughness of the nanoparticles.     

Interactions between a telechelic polymer and a silica—I: Influence of the polymer concentration-measure of the solvolysis temperature

A study of the interactions between a telechelic polybutadiene with isocyanate end-groups and a silica has shown the occurrence of grafting of the elastomer onto the solid surface through a urethane bond. The relationship between the grafting ratios, measured by pyrolysis, and the polymer concentration appeared to be linear but the solvolysis temperature was independent of it.     

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.     

Interactions between colloidal particles induced by polymer brushes grafted onto the substrate

We investigate the interaction energy between two colloidal particles on or immersed in nonadsorbing polymer brushes grafted onto the substrate as a function of the separation of the particles by the use of a self-consistent-field theory calculation. Depending on the colloidal size and the penetration depth, we demonstrate the existence of a repulsive energy barrier of several kBT, which can be interpreted by separating the interaction energy into three parts: colloid-polymer interfacial energy, entropic contribution due to "depletion zone" overlap of colloidal particles, and entropic elastic energy of grafted chains by the compression of particles. The existence of a repulsive barrier which is of entirely entropic origin can lead to kinetic stabilization of the mixture rather than depletion flocculation or phase separation. Therefore, the present result may suggest an approach for controlling the self-assembling behavior of colloids for the formation of target structures, by tuning the colloidal interaction on the grafting substrate under appropriate selection of colloidal size, effective gravity (influencing the penetration depth), and brush coverage density.