Depletion interaction between two plates

A theoretical description of the depletion interaction between two plates caused by ideal polymer chains with a finite width of a Schulz-Zimm distribution was published by Tuinier and Petukhov. They derived an exaa expression for the potential... 

In this chapter we consider the depletion interaction between two flat plates and between two spherical colloidal particles for different depletants (polymers, small colloidal spheres, rods and plates). First of all we focus on the depletion interaction due to a somewhat hypothetical model depletant, the penetrable hard sphere (phs), to mimic a (ideal) polymer molecule. This model, implicitly introduced by Asakura and Oosawa [1] and considered in detail by Vrij [2], is characterized by the fact that the spheres freely overlap each other but act as hard spheres with diameter a when interacting with a wall or a colloidal particle. The thermodynamic properties of a system of hard spheres plus added penetrable hard spheres have been considered by Widom and Rowlinson [3] and provided much of the inspiration for the theory of phase behavior developed in Chap. 3. 

Depletion Interaction Due to Ideal Polymers 2.2.1 Depletion Interaction Between Two Flat Plates... 

Depletion Interaction. When the distance between two plates is smaller than the diameter l of the small particles (micelles), which, in the present case, are uncharged, the depletion force /deP acting between two plates is given by7 20 21... 

Attempts to measure depletion forces were made by Luckham and Klein [122, 123] who eould not measure a depletion force with the surface force apparatus. They measured the interaction between two mica plates in the presence of non-adsorbing polystyrene in toluene. Pashley and Ninham [124] did succeed in measuring the depletion potential between mica plates as induced by CTAB micelles. 

The polymer density profile of ideal chains next to a hard sphere for arbitrary size ratio q was first ealeulated by Taniguchi et al. [125] and later independently by Eisenriegler et al. [126]. Eisenriegler also considered the pair interaction between two colloids for Rg< R [127] and for Rg R [128], as well as the interaction between a sphere and a flat wall due to ideal chains [129]. Depletion of excluded volume polymer chains at a wall and near a sphere was considered by Hanke et al. [130]. One of their results is that the ratio /Rg at a flat plate, which is 1.13 for ideal chains [118, 119], is slightly smaller (1.07) for excluded-volume chains. 

H. Huang, E. Ruckenstein Interaction Force between Two Charged Plates Immersed in a Solution of Charged Particles. Coupling between Double Layer and Depletion Forces, LANGMUIR 20 (2004) 5412-5417. 

The interaction between the two plates is repulsive at small distances and becomes attractive at large distances. At small distances, the electrostatic interactions between the two plates dominate and the net force is repulsive. As the distance increases but remains smaller than the diameter of the particles, the electrostatic repulsion between the plates decreases but, because the attractive depletion force remains almost constant, the net force can become attractive. As soon as the distance between the two plates becomes larger than the particle diameter, the electrostatic and depletion contributions become comparable and the net force becomes small. The above considerations are valid when D is sufficiently large for the double layer repulsion at the distance L = D to become... 

An early theoretical depletion interaction study with polyelectrolytes as depleting agents was made by Bohmer et al. [78] who used the self-consistent field method of Scheutjens and Heer. For high salt concentrations, the polymer concentration dependence of the depletion layer thickness matches with that of an uncharged polymer in solution. Below a salt concentration of 1 mol/L the depletion layer thickness starts to decrease with increasing polyelectrolyte concentration at lower polymer concentration. At low salt concentrations a significant repulsive barrier in the potential between two uncharged parallel flat plates was found. 

In 1954, Asakura and Oosawa [1430] realized that dissolved polymers can influence the interaction between particles in a dispersion, even if they do not interact at all with the particle surfaces. Asakura and Oosawa themselves describe the interaction as follows Let us consider two parallel and large plates of the area A immersed in a solution of rigid spherical macromolecules. If the distance between the plates x is smaller than the diameter of solute molecules, none of these molecules can enter between the plates. Then this region becomes a phase of the pure solvent, while the solution outside the plates is little affected by them. Therefore, a force equivalent to the osmotic pressure of the solution of macromolecules acts inwards on eacii plane. Another way of looking at depletion forces is as follows particles aggregate because in this way the total free volume available to the dissolved macromolecules increases. It increases so much that the gain in translational entropy of the macromolecules is higher than the loss of entropy of the particles. 

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