# Difference between revisions of "The Role of Polymer Polydispersity in Phase Separation and Gelation in Colloid−Polymer Mixtures"

Entry by Emily Redston, AP 225, Fall 2011

Work in progress

## Reference

The Role of Polymer Polydispersity in Phase Separation and Gelation in Colloid−Polymer Mixtures by J. J. Lietor-Santos, C. Kim, M. L. Lynch, A. Fernandez-Nieves, and D. A. Weitz. Langmuir 26 3174–3178 (2010)

## Introduction

Mixtures of non-adsorbing polymer and colloidal particles exhibit a very rich range of morphologies. These microstructures depend on the particle and polymer concentrations as well as the relative size of the particles and polymer. The addition of the polymer to a colloidal suspension leads to a depletion attraction that is capable of inducing a fluid-solid transition (i.e. forming a gel). A gel is defined as a connected network that spans space and can support weak stresses. Gels are extensively used in commercial applications, such as personal care or food products, where they are able to help stabilize the system against sedimentation. In this manner, gels can reduce phase separation, which will increase product shelf life. The nature of the fluid-solid transition depends on the range of the depletion attraction, which, in turn, depends on the ratio of the size of the polymer to the colloidal particle. For short-range interactions, gelation is induced by spinodal decomposition. A gel is formed because, when the system undergoes a gas-liquid phase separation, it is interrupted by the dynamical arrest of the particles in the colloid-rich region. By contrast, for larger ranges of the attraction, phase separation can proceed to completion, without being interrupted by dynamic arrest.

However, in the presence of gravitational effects, the structure may no longer be capable of sustaining its own weight; instead it collapses, disrupting the phase separation process or rupturing the gel that was previously formed. This is obviously an undesirable effect as it can dramatically shorten the shelf life of a commercial product. This suggests that the use of shorter polymers at sufficiently high concentration is of greatest practical interest. However, technological polymers are very rarely monodisperse, and thus the microstructures and their behavior may be drastically modified. However, despite the practical importance, the gravitational behavior of colloid-polymer mixtures using polydisperse polymers has never been investigated. It is not known how the polydispersity of polymers effects the phase behavior of the mixture.

In this paper, the authors investigate the behavior of model colloidal particles mixed with nonadsorbing polymer with a polydisperse size distribution, similar to that often found in commercial samples. Ultimately they find that the presence of even a small amount of large polymer in a distribution of nominally much smaller polymer can drastically modify the behavior.

## Sample Preparation

The authors use an aqueous dispersion of polystyrene particles with a density $\rho = 1.057 g/cm^3$ and an average radius $a = 1.5 \mu m$. They use polyethyleneglycol (PEG) with an average molecular weight $M_w = 475500 g/mol$, polydispersity index $M_w/ M_n = 2.63$, and mean radius of gyration $\bar r_g = 40 nm$. Here, $M_w$ and $M_n$ are the mass- and number-averaged molecular weights, respectively. Salt was also added to reduce electrostatic interactions.