Repulsion - Steric(entropic)

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"When a sol of gelatin, for instance, is added to a gold sol prepared by the reduction of a gold salt in an alkaline medium, it appears that the gold sol is strongly protected against the flocculating action of electrolytes."

H.R. Kruyt, Colloids: A textbook; H.S. van Klooster*, Translator; John Wiley & Sons: London; 1927; p. 87. (*Who I met in the late 1960's)

It had been known for a long time that electrolytes would flocculate many sols; gold sols were a common example. These were call lyophobic colloids. The colloids insensitive to electrolyte were, in hindsight, polymeric. They were call lyophilic colloids. Kruyt reports here that some combinations of the lyophilic colloids could "protect" the lyophobic colloids from salt addition. This lyophilic colloids were also called "protective" colloids.

We now know this mechanism to be polymer adsorption; and in the present context, examples of steric stabilization.

From the very beginning, the stability of polymer-stabilized sols has been understood primarily in terms of the solution solubility behavior of the polymer. Polymer-coated sols are stable when the polymer is both adsorbed and soluble; and unstable even when the polymer is adsorbed if it is no longer soluble.

Stability of a thin film or a dispersion requires a repulsive force. In this case a "steric" or "entropic" barrier.

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Simple model of steric stabilization

The dispersion energy for two spheres increases as two spheres near each other by Brownian motion.

<math>\Delta G_{121}=\frac{-A_{121}d}{24H}</math>

For the kinetic energy to remain greater than the attractive energy, the distance must be kept greater than H. <math>kT>\frac{A_{121}d}{24H}</math>
If polymer layers of thickness 't' around each particle just touch at this distance, 'H': <math>kT>\frac{A_{121}d}{48t}</math>
or <math>t>\frac{A_{121}}{48kT}d</math>
For example:
Polymer thickness for stabilization as a function of particle diameter:

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Polymer Size

A polymer increases the viscosity of the solution in a manner dependent on molecular size.

This polymer size can be calculated from the intrinsic viscosity: <math>\left[ \eta \right]=\underset{c\to 0}{\mathop{\lim }}\,\frac{1}{c}\left( \frac{\eta _{solution}}{\eta _{solvent}}-1 \right)</math>
<math>\left\langle r^{2} \right\rangle ^{1/2}=\left( \frac{2}{5}\frac{MW}{N_{0}}\left[ \eta \right] \right)^{1/3}</math> Where MW is molecular weight and N0 is Avogadro’s number.
Or from c* where c* is the concentration where the viscosity is not linear in concentration. <math>\left[ \eta \right]=\frac{1}{c*}</math>
Or from a theory where l is the “Kuhn” length. <math>R_{g}=\frac{l\sqrt{n}}{\sqrt{6}}</math>

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A slightly better model

Take into account the compressibility of the outer reaches of the polymer chain:

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Configurations of adsorbed polymers

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