# Universal Features of the Fluid to Solid Transition for Attractive Colloidal Particles

Original Entry by Holly McIlwee, AP225 Fall 09

## Overview

Universal Features of the Fluid to Solid Transition for Attractive Colloidal Particles V. Prasad, V. Trappe, A.D. Dinsmore, P.N. Segre, L. Cipelletti, and D.A. Weitz. Faraday Discussions, 123, 1-12 (2003)

## Abstract

Attractive colloidal particles can exhibit a fluid to solid transition under these 3 conditions: If the attraction is large, if the volume fraction is large, and if the applied stress is small. Applications of colloidal suspensions are highly dependent on the its rheological properties. In colloidal suspensions these properties vary widely. They are determined primarily by: size, concentration, particle energy and interactions, volume fraction.

Two aspects of colloidal particles are well understood: The regime in which volume fraction, <math>\phi</math>, is low, and interparticle attraction, U, is high, and oppositely when <math>\phi</math> is high and U is low. Transitions between these well understood regimes have been widely studied, but are poorly understood. Weitz et al. presents a discussion on the methods and concepts being employed to gain an understanding of these regimes.

## Keywords

## Soft Matter

Attractive colloidal particles can exhibit a fluid to solid transition under these 3 conditions: If the attraction is large, if the volume fraction is large, and if the applied stress is small. Two aspects of colloidal particles are well understood: The situation when volume fraction, <math>\phi</math>, is low, and attraction, U, is high, and oppositely when <math>\phi</math> is high and U is low.

In systems of low <math>\phi</math> and high U, diffusion cluster aggregation dominates (DLCA), and the network that forms during the fluid to solid transition is continuous but tenuous, resulting in a solid that can bear stress.

In systems of high <math>\phi</math> and low U, particles act as hard spheres, crowding leads to a colloidal gas at <math>\phi</math>=0.58. Also, the particles are caged and cannot diffuse freely. Here the suspension acts as an elastic solid. At <math>\phi</math>-0.63, the particles exhibit random packing and come in contact with each other for optimum efficiency.

Between these two phase transitiopsn there are many transitions which have been widely studied yet are still poorly understood. But it is known that all transitions have some things in common: • Fluid to solid transitions involve crowding of aggregates, leading to an arrest of their kinetics. • There is a well defined <math>\phi</math> for transitions which is dependent on interparticle interactions. • They can bear stress and also be transformed into a fluid at high stress

Weitz et al. introduces an extension of the concept of jamming phase transition. This unifies behavior as a function of particle volume fraction, energy interparticle interactions, and applied stress. Herein the applicability of a jamming state diagram is discussed, although it is noted that not all transitions are fully understood. The jamming transition was originally introduced by Liu and Nagel[1]. Describing the bahavior of repulsive systems in molecular glasses to granular systems. They suggested that the system could be described in a 3D phase diagram. With the axes: 1/density, T, and applied load. Increasing any of these results in a phase transition from fluid to solid.

This concept can also be applied to attractive colloidal particles and this allows these previously poorly understood transitions to be described in a single framework. In this treatment, for attractive particles, density is replaced by <math>\phi</math>. The solvent is treated as background. Assumptions of jamming: <math>\phi</math>, U, and applied stress all play a similar role in arrest kinetics. If 1/<math>\phi</math>, 1/U, or applied stress are decreased a jamming transition occurs. A jamming transition focuses on stress-bearing features of the solid. The author aims to reassess the status of jamming as applied to attractive colloidal particles, clearly delineate regimes of behavior that are understood, and to identify key issues remaining to be resolved.

*Scaling of viscoelasticity of colloidal gels*
An accurate method to determine <math>\phi</math>, and U of transitions is needed. The onset of the elastic modulus finds a phase boundary although this is difficult at low <math>\phi</math> and high U. Scaling behavior at large U makes it possible.

A good measure of the approach to the phase boundary is provided by light scattering, probing the structure, and dynamics of the colloidal suspension. As <math>\phi</math> approaches <math>\phi</math>C from below, low angle static light scattering from polymer systems exhibits a peak in the scattering intensity at small scattering wave vectors, q. This reflects separation clusters which are equal in size. The size here is consistent with DLCA mechanism for aggregation. Fluid to Solid transitions have many featurs in common over ranges of U and <math>\phi</math>, as well as colloid materials.

*In conclusion:*
In jamming phase behavior, some features are well understood, some are not. Behavior in the two limiting regimes discussed above without stress are well understood. High <math>\phi</math>, low U, Fluid to solid is a colloidal glass transition. In he low <math>\phi</math>, high U regime, the fluid to solid transition results from irreversible aggregation forming fractal clusters which gel. Transitions in between these regimes are not well understood. Some of the features in the intermediate regimes are universal. In all fluid to solid transitions, the transition is caused by crowding of the system leading to kinetic arrest and formation of stress bearing paths. Stress bearing paths are transient in region of glass transiton, therefore higher volume fraction is required for fluid to solid transition. Paths are more permanent at low <math>\phi</math>, requiring a high interparticle interaction.

Weitz et al. has given a clear description of what is currently known about fluid to solid phase transitions, as well as conclusions that have been drawn about all regimes, and the difficulties associated with determining with exactness the <math>\phi</math> and U of specific transitions.

## References

[1] A.J. Liu, and S. R. Nagel, *Nature*, 1998, **396**, 21.