# Interaction Forces between Colloidal Particles in Liquid: Theory and Experiment

## Overview

•  Yuncheng Liang, Nidal Hilal, Paul Langston, and Victor Starov, Advances in Colloid and Interface Science 134-135, 151-166 (2007).
• Keywords: van der Waals Forces, Electric Double Layer Forces, Solvation Forces, Hydrophobic Forces, Steric Forces, Atomic Force Microscopy, Surface Forces Apparatus

## Summary

This is a review article summarizing the major findings and contributions of 158 publications. Many of the major contributions to this field were made very recently. This review article includes information on the theories of colloidal interaction forces, experiments testing them, and the historical development/breakthroughs in the field.

Timeline: 1941 Derjaguin and Landau publish first big paper leading to DLVO theory 1948 Verwey and Overbeek publish second big paper contributing to DLVO theory 1956 Lifshitz Theory 1964 Derjaguin experimental discovery of an extra repulsive force 1978 First accurate macroscopic surface measurements Israelachivili and Adams (SFA) 1991 AFM adapted for a colloidal particle tapping on a solid surface

5 forces: 1) van der Waals Forces

Equation 1 Interaction energy between two spheres:

$V_A(D)=-\frac{A_H}{6}\left(\frac{2a^2}{D^2+4aD}+\frac{2a^2}{(D+2a)^2}+ln\left(1-\frac{4a^2}{(D+2a)^2}\right)\right)$

$A_H$= Hamaker Constant $a$= Sphere Radius $D=$ Interparticle Distance

2) Electric Double Layer Forces

$V_R=\frac{128\pi a_1 a_2 n_\infty kT}{(a_1+a_2)\kappa^2} \gamma_1 \gamma_2 e^{(-\kappa h)}$

3) Solvation Forces

4) Hydrophobic Forces

5) Steric Forces

The second half of this review article discusses experimental evidence for or against the above five forces. There are still open questions in this field because some of the experimental evidence does not agree with the current theories.

## Soft Matter Details

Surface Properties:

The topic of Liang et. al.'s review article falls under the major field of colloidal science within soft matter. The forces between colloidal particles are due to surface properties and solvent properties that are a mix of applied physics and chemistry. Understanding interparticle forces helps us understand the stability of colloids (when the particles will stay dispersed compared to when they will aggregate and sediment). The small distances between particles which are interesting in colloidal science draw out interesting questions about when the continuum treatment of a solvent breaks down.

Experimental Methods:

The main experimental techniques focused on in this article are atomic force microscopy and surface forces apparatus. Both tools are used to measure very small forces between two surfaces at very small distances.

History:

How much does knowing the historical development help us in doing current science? This review article presents theories in the context of when they were discovered. Particularly in the context of such new work (since 1940), I think it could be very useful to understand how the chronology of the work in the field. Not only does knowing the history help you understand the motivations behind developments, but it also gives a good frame of reference when reading other works from the same time period.