# Difference between revisions of "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, $\phi$, is low, and interparticle attraction, U, is high, and oppositely when $\phi$ 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.

## 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. 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. Colloidal particles are metastable. Two aspects of colloidal particles are well understood: The situation when volume fraction is low, and attraction is high, and oppositely when volume fraction is high and attraction is low. In systems of low VF and high A, Diffusion cluster aggregation dominates, and the netowkr that forms during the fluid to solid transition is continuous but tenuous, resulting in a solid that can bear stress. In systems of high VF and low A, particles act as hard spheres, crowding leads to a colloidal gas at VF=0.58. Also, the particles are caged and cannot diffuse freely. Here the suspension acts as an elastic solid. At VF-0.63, the particles exhibit random packing and touch each other for optimium efficiency. Between these two phase transitiopsn there are many transitions which have been widely studied yet are still poorly understood. It is known that all transitions have some things in common: • Fluid to solis transitions involve crowding of aggregates, leading to an arrest of their kinetics. • There is a well defined VF 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 ineteractions, and applied stress. Herein the applicability of a jamming stat ediagram is discussed, although it is noted that not all transitions are fully understood. The jamming transition was originall introduced by Liu and Nagel (9). Describing the bahvior 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 undersood transitions to be described in a single framework. In this treatment, for attractive particles, density is replaced by VF. The solvent is treated as background. Assumptions of jamming: VF, attractive energy, and applied stress all play a similar role in arrest kinetics. If 1/VF, 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 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.

Further in the article: New data that explores details of the transition in the absence of applied stress, highlight still not understood issue. Scaling of viscoelasticity of colloidal gels An accurate method to determine phi, and U of transitions is needed. The onset of the elastic modulus finds a phase boundary although this is difficult at low phi and high U. Scaling behavior at large U makes it possible. The origin of the scaling behavior Depletion Gels 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 VF approaches phi C from belo, 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 phi, 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 VF, low U, Fluid to solid is a colloidal glass transition. In he low VF, high U regime, the fluid to solid transition results from irreversibily 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 VF, requiring a high interparticle interaction.