Repulsion - Steric(entropic)

From Soft-Matter
Revision as of 02:27, 17 November 2008 by Morrison (Talk | contribs) (Polymers in solution - Phase diagrams)

Jump to: navigation, search

Back to Topics.

Introduction

"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.
StericInteraction.png

Top of Page


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>

DispersionAttractionBetweenSpheres.png
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:
Reference
Polymer thickness for stabilization as a function of particle diameter:
Reference


Top of Page


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>

Top of Page


A slightly better model

Take into account the compressibility of the outer reaches of the polymer chain:
SteriStabilizationBetterModel.png


Top of Page


Configurations of adsorbed polymers

ConfigurationsOfAdsorbedPolymers.png


Top of Page


Polymers in solution - Phase diagrams

Sterically stabilized dispersions are stable when the polymer is soluble – the one phase regions. The higher temperature is called the "lower critical temperature" and the lower temperature is called the "upper critical solution temperature. (No kidding!)
PolymerSolutionPhaseDiagrams.png
141 nm silica particles- with grafted polymer.

Pictures were taken at 0 C and 60 C. The particles phase-transfer with the change in polymer solubility. The upper liquid is ethylacetate and the lower, water.

File:ImageFileName
Langmuir, 2001, 23, 2208


Top of Page


Back to Topics.