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

## Overview

- [1] 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

Liang *et al.* write a review article summarizing the major findings and contributions of 158 publications. Most of the major contributions to this field were made since 1940. This review article includes information on the theories of colloidal interaction forces, experiments testing the theories, and the historical development of the field.

**Timeline of events compiled from article:**

1936-1937 de Boer and Hamaker publish papers on theoretical aspects of "dispersion forces acting between colloidal objects (p. 152)."

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 publishes "The Theory of Molecular Attractive Forces between Solids"

1964 Derjaguin *et. al.* make experimental discovery of one of the first non-DLVO forces

1978 First accurate macroscopic surface measurements in aqueous solution carried out by Israelachivili and Adams (using surface forces apparatus)

1991 Atomic force microscopy adapted for measuring interactions of a colloidal particle and a solid surface

This article separates the interaction forces into five groups:

**1) van der Waals Forces**

Dispersion forces between colloidal spheres yielding an attractive interaction energy of the form (equation 1 from [1]):

<math>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)</math>

<math>A_H</math>= Hamaker Constant, <math>a</math>= Sphere Radius, <math>D=</math> Interparticle Distance

**2) Electric Double Layer Forces**

Repulsive forces between colloidal spheres with like charge with an interaction energy of the form (for <math>\kappa a>5</math> and <math>h<<a</math> (equation 5 from [1]):

<math>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)}</math>

<math>a_1, a_2</math>= Particle Radii, <math>n_\infty</math>= Bulk Density of Ions, <math>h=</math> Interparticle Distance, <math>\kappa</math>= Reciprocal Debye-Huckel Length, <math>\gamma_1, \gamma_2</math>= Measure of Surface Potentials (see article equation 6 for details)

**3) Solvation Forces**

When surfaces are only a few nanometers apart, the molecular, discrete nature of a solvent becomes important. DLVO theory based on continuum theories cannot describe short-range interparticle forces. Solvation forces arise when only a few layers of solvent molecueles remain in between surfaces. The solvent molecules become ordered into layers and create a force which oscillates between attractive and repulsive as the separation distance varies. If the solvent is water, these forces are called hydration forces.

**4) Hydrophobic Forces**

Hydrophobic forces are attractive forces between two hydrophobic surfaces in water. Water molecules trapped between the two surfaces are not free to orient themselves as they would naturally and are expelled from the gap between the surfaces. The range of this force is accepted to extend out to separation distances greater than 10nm. “Unfortunately, so far no generally accepted theory has been developed for these forces... (p.157)”.

**5) Steric Forces**

Steric forces arise when polymer-coated surfaces come close enough for the polymers to overlap. The overlapping of the polymers leads to an entropy-driven repulsive force. The magnitude of the force depends on many parameters such as polymer packing density on the surfaces and polymer solubility in the solvent of the system. “There is no simple, comprehensive theory available as steric forces are complicated and difficult to describe (p. 157)”.

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 and room for further experiments to distinguish between proposed mechanisms.

## Soft Matter Details

**Surface Properties:**

The topic of this review article falls within the major field of colloidal science within soft matter. The forces between colloidal particles are due to surface properties and solvent properties which are important in both 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 using the surface forces apparatus. Both tools measure very small forces between two surfaces only nanometers apart.

**History:**

How much does knowing the historical development of science help us in doing current research? 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 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 within the same time period.