Depletion interaction in colloid/polymer mixtures: application of density functional theory

Investigation of Ring and Star Polymers in Confined Geometries: Theory and Simulations

The calculations of the dimensionless layer monomer density profiles for a dilute solution of phantom ideal ring polymer chains and star polymers with f=4 arms in a Θ-solvent confined in a slit geometry of two parallel walls with repulsive surfaces and for the mixed case of one repulsive and the other inert surface were performed. Furthermore, taking into account the Derjaguin approximation, the dimensionless layer monomer density profiles for phantom ideal ring polymer chains and star polymers immersed in a solution of big colloidal particles with different adsorbing or repelling properties with respect to polymers were calculated. The density-force relation for the above-mentioned cases was analyzed, and the universal amplitude ratio B was obtained. Taking into account the small sphere expansion allowed obtaining the monomer density profiles for a dilute solution of phantom ideal ring polymers immersed in a solution of small spherical particles, or nano-particles of finite size, which are much smaller than the polymer size and the other characteristic mesoscopic length of the system. We performed molecular dynamics simulations of a dilute solution of linear, ring, and star-shaped polymers with N=300, 300 (360), and 1201 (4 × 300 + 1-star polymer with four arms) beads accordingly. The obtained analytical and numerical results for phantom ring and star polymers are compared with the results for linear polymer chains in confined geometries.

Modulating transparency and colour of cellulose nanocrystal composite films by varying polymer molecular weight

HYPOTHESIS

Cellulose nanocrystals (CNC) can produce photonic composite films that selectively reflect light based on their periodic cholesteric structure. The hypothesis of this research is that by incorporating water-soluble polymer, photonic properties of CNC composite film can be designed by manipulating the polymer molecular weight.

EXPERIMENTAL

Flexible free-standing composite films of five different poly (ethylene glycol) (PEG) molecular weights were prepared via air drying under a controlled environment, and characterised by reflectance UV-vis spectrometer, atomic force microscopy (AFM) and scanning electron microscopy (SEM). Films with each molecular weight were investigated over a concentration range.

FINDINGS

The colour and transmission haze of the composite films was modified by varying both the PEG molecular weight and concentration. Depending on the molecular weight, the films were able to reflect light from the UV region (242 nm) across the visible spectrum to the near-infrared region (832 nm). Different trends in variation of the reflected light based on the molecular weight was found with increasing PEG concentration and was explained by weak depletion interactions occurring between CNC and PEG, which was reduced with increasing PEG molecular weight.

Efficient Molecular Approach to Quantifying Solvent-Mediated Interactions

The solvent-mediated interaction, or equivalently the depletion force, play a pivotal role in the processes, by which two objects in solution such as lock and key particles, antibody and antigen, macromolecule and substrate, are attracted to each other. The quantification of this interaction is important yet challenging since it depends on the microscopic solvent structure in the surrounding. Here, we report an efficient molecular approach for predicting the solvent-mediated interaction by combining the classical density functional theory with a reversible solvation thermodynamic circle. For demonstration, the solvent-mediated interactions between two nanoparticles and between a nanoparticle and a rough wall are examined, and good agreements compared with the simulation results are illustrated. This approach is thereafter employed to interpret the reported self-assembly phenomena of lock and key colloidal particles. We show that the binding probability between the lock and key colloids can be successfully characterized at different depletant concentrations and system temperatures. This approach provides a potential route for identifying the coarse-graining interaction between two objects in fluid systems.

Potential distribution theorem for the polymer-induced depletion between colloidal particles

The authors investigated the polymer-mediated colloidal interactions in a good solvent wherein the particle size varies from that much smaller than the polymer radius of gyration up to macroscopic and the polymer concentration varies from that corresponding to a dilute solution to that close to a melt. At conditions directly accessible to molecular simulations, the theoretical predictions agree favorably with the simulation results for the distributions of polymer segments and for the polymer-mediated colloidal interactions. The theoretical methods were then exploited to examine the polymer structure and colloidal interactions when the particle/polymer size ratio changes from the "protein" limit to the "colloid" limit at different regimes of the polymer concentration (i.e., dilute, semidilute, and concentrated). The authors found that the surface curvature plays a significant role on the distribution of polymer segments near the particle surface at low polymer concentration, but this effect diminishes as the polymer concentration increases. The Derjaguin approximation works reasonably well at high polymer concentration even in the protein limit, but it may fail qualitatively at low polymer concentration where the polymer-induced colloidal force becomes long range.