# Repulsion - Steric(entropic)

## 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.

## Simple model of steric stabilization

 The dispersion energy for two spheres increases as two spheres near each other by Brownian motion. $\Delta G_{121}=\frac{-A_{121}d}{24H}$ For the kinetic energy to remain greater than the attractive energy, the distance must be kept greater than H. $kT>\frac{A_{121}d}{24H}$ If polymer layers of thickness 't' around each particle just touch at this distance, 'H': $kT>\frac{A_{121}d}{48t}$ or $t>\frac{A_{121}}{48kT}d$ For example: Reference Polymer thickness for stabilization as a function of particle diameter: Reference

## 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: $\left[ \eta \right]=\underset{c\to 0}{\mathop{\lim }}\,\frac{1}{c}\left( \frac{\eta _{solution}}{\eta _{solvent}}-1 \right)$ $\left\langle r^{2} \right\rangle ^{1/2}=\left( \frac{2}{5}\frac{MW}{N_{0}}\left[ \eta \right] \right)^{1/3}$ 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. $\left[ \eta \right]=\frac{1}{c*}$ Or from a theory where l is the “Kuhn” length. $R_{g}=\frac{l\sqrt{n}}{\sqrt{6}}$

## A slightly better model

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

## 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!) 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. Dejin and Zhao, Langmuir, 2001, 23, 2208

## Steric Effects and steric repulsion

### Steric Effects

Steric effects arise from the fact that each atom within a molecule occupies a certain amount of space. If atoms are brought too close together, there is an associated cost in energy due to overlapping electron clouds (Pauli or Born repulsion), and this may affect the molecule's preferred shape (conformation) and reactivity.

Chemisorbed long-chain thiol can still be physisorbed as well. While S-As bond acting as a lever and steric repulsion of the first CH2 unit acts as a pivot, the NH2 endgroup of the molecule still feels quite strong attraction to the surface.

There are a few types of steric effects:

Steric hindrance or steric resistance occurs when the size of groups within a molecule prevents chemical reactions that are observed in related smaller molecules. Although steric hindrance is sometimes a problem, it can also be a very useful tool, and is often exploited by chemists to change the reactivity pattern of a molecule by stopping unwanted side-reactions (steric protection). Steric hindrance between adjacent groups can also restrict torsional bond angles. However, hyperconjugation has been suggested as an explanation for the preference of the staggered conformation of ethane because the steric hindrance of the small hydrogen atom is far too small.

Steric shielding occurs when a charged group on a molecule is seemingly weakened or spatially shielded by less charged (or oppositely charged) atoms, including counterions in solution (Debye shielding). In some cases, for an atom to interact with sterically shielded atoms, it would have to approach from a vicinity where there is less shielding, thus controlling where and from what direction a molecular interaction can take place.

Steric attraction occurs when molecules have shapes or geometries that are optimized for interaction with one another. In these cases molecules will react with each other most often in specific arrangements.

Chain crossing — A random coil can't change from one conformation to a closely related shape by a small displacement if it would require one polymer chain to pass through another, or through itself.

### Steric Repulsion

The origins of steric or electrosteric repulsion lie in both volume restriction and interpenetration effects, although it is unlikely that either effect would occur in isolation to provide a repulsive force. In many industrial processes where the coagulation of colloidal particles would naturally occur, steric repulsion between particles can be induced by the addition of a polymer, to prevent the approach of the particle cores to a separation where their mutual van der Waals attraction would cause flocculation to occur. Complete particle surface coverage by absorbed or anchored polymer at high concentration can produce a steric layer that prevents close approach of the particles. The steric layer also acts as a lubricant to reduce the high frictional forces that occur between particles with large attractive interactions. The time-dependent, displaceable and slow-forming hydrolyzed inorganic layers which lead to repulsive electrosteric forces between mica surfaces in 0.1M Cr(NO3)3 electrolyte have been reported.

The magnitude of the repulsion resulting from steric forces is dependent upon the surface rare of the particle that the polymer occupies and whether the polymer is reversibly or irreversibly attached to the particle’s surface.

Adsorbed and nonadsorbing surfactants and polymers are widely used to induce steric stabilization. The principal advantages of steric stabilization over charge stabilization are:

• 1. Provision of stability in nonpolar media where weak electrical effects occur
• 2. Use of higher levels of electrolyte in aqueous media without causing flocculation
• 3. Reduction of electroviscous effects arising from particle charge by the addition of electrolyte without flocculation.
• 4. Dispersion stabilization can be achieved at higher particle concentrations

Graft or block copolymers commonly used as steric stabilizers are designed to have two groups of different functionality, A and B. A is chosen to be insoluble in the dispersion medium and has strong affinity for the particle surface while B is selected to be soluble but have little or no affinity for the particle surface. Other steric interactions, which give rise to short-range repulsion in aqueous dispersions due to bare size of ions present at the particle solution interface at high ion concentrations, have been observed.