Osmotic shrinkage in star/linear polymer mixtures

Abstract

Multiarm star polymers were used as model grafted colloidal particles with long hairs, to study their size variation due to osmotic forces arising from added linear homopolymers of smaller size. This is the origin of the depletion phenomenon that has been exploited in the past as a means to melt soft colloidal glasses by adding linear chains and analyzed using dynamic light scattering experiments and an effective interactions analysis yielding the depletion potential. Shrinkage is a generic phenomenon for hairy particles, which affects macroscopic properties and state transitions at high concentrations. In this work we present a small angle neutron scattering study of star/linear polymer mixtures with different size ratios (varying the linear polymer molar mass) and confirm the depletion picture, i.e., osmotic star shrinkage. Moreover, we find that as the linear/star polymer size ratio increases for the same effective linear volume fraction (c/c * with c * the overlapping concentration), the star shrinkage is reduced whereas the onset of shrinkage appears to take place at higher linear polymer volume fractions. A theoretical description of the force balance on a star polymer in solution, accounting for the classic Flory contributions, i.e. elastic and excluded volume, as well as the osmotic force due to the linear chains, accurately predicts the experimental findings of reduced star size as function of linear polymer concentration. This is done in a parameter-free fashion, in which the size of the cavity created by the star, and from which the chains are excluded, is related to the radius of the former from first principles.

Depletion gels from dense soft colloids: Rheology and thermoreversible melting

“…At equilibrium, the size of a single star polymer in a linear polymer chains solution, with a degree of polymerization N c , can be calculated by solving the following equation for the equilibrium of forces on the star [Wilk et al (2010)…”

“…is a function of the osmotic pressure Pðw L Þ exerted by the chains on the star and can be computed as [Wilk et al (2010)]…”

Ultrasoft Colloid-Polymer Mixtures: Structure and Phase Diagram

“…In particular, mixtures of star polymers of different sizes and functionalities have been recently investigated in a joint theoretical and experimental effort, revealing the existence of multiple glassy states [15]. On the other hand, the paradigmatic case of a mixture of star polymers and linear chains (the direct soft counterpart of the AO model) has been investigated theoretically [14,16] and experimentally by (mainly) macroscopic rheology [11,12,17]; however, detailed structural information is still missing. Recently a microscopic theory [14,16], capable to appropriately coarse-grain stars and chains, has been developed, but an accurate comparison between theoretical predictions and experimental results for the structural correlations for starchains mixtures has not been attempted so far.…”

Coherent X-ray scattering reveals nature of dynamical transitions in nanoparticle–polymer suspensions

“…For the mixtures with x ¼ 0.14, the addition of minimum fraction of polymers will break/melt the structure (indicated by the increase in the interparticle separation shown in Fig. 2) formed by PGNPs due to the osmotic shrinkage of the grafted polymers [55]. As a result, a decrease in the relaxation time of PGNPs has been observed (refer Fig.…”

“…For the mixtures with large polymers (x ¼ 0.14), the stretching energy required to accommodate the linear polymers with in the structure formed from PGNPs will be larger than the energy gained due to interpenetration. As a consequence, the presence of 382 kDa PS will exert an osmotic pressure on the grafted polymers resulting in the shrinkage of grafted polymers [55], which results in the decrease of the overall hydrodynamic radius of the PGNPs. With the addition of smaller polymers (x ¼ 2.76), we have observed almost an increase of~50% in the R h of the PGNPs.…”