Polymer depletion interaction

H. Huang, E. Ruckenstein Effect of Steric, Double Layer, and Depletion Interactions on the Stability of Colloids in Systems Containing a Polymer and an Electrolyte, LANGMUIR 22 (2006) 4541 1546. 

In the present paper, calculations are carried out to explain the restabilization followed sometimes by destabilization, as the electrolyte concentration increases, observed by Stenkamp et al. In these calculations, double-layer, steric, and depletion interactions are taken into account. The steric interaction at various electrolyte concentrations is calculated using the scaling theory. The surface density of the polymer chain was evaluated by using the Sechenov equation for the polymer solubility as a function of electrolyte concentration. 

Most food systems are of a colloidal as well as a polymeric nature. The presence of a nonadsorbing polymer in a skim milk dispersion induces an effective attraction between the casein particles, called depletion interaction, resulting in phase separation at sufficiently high polymer concentration. Tuinier et al. (2003) discussed the influence of colloid-polymer size ratio, polymer concentration regime, size, poly-dispersity and charges in colloid/biopolymer mixtures, demonstrating the challenging complexity of the subject. 

We have seen that the rheological properties of weakly flocculated gels can be predicted at least qualitatively using reasonable particle-particle interaction potentials derived from van der Waals and polymer depletion forces. Can a similar approach succeed in predicting the mechanical properties of strongly flocculated gels ... 

Polymer-grafted silica (SiO2) particles represent one of the most popular colloidal systems with tunable interactions. Ilie chains of choice were mainly polystyrene, poly(dimethyl siloxane), poly(butyl methacrylate), and n-octadecyl or stearyl alcohol. Chain grafting provided the means to tailor the colloidal particle behavior from hard to soft, as well as introduce attractions in a controlled way by varying the temperature or adding non-absorbing polymer depletant [44,95-112]. 

Polymers can strongly affect colloid stability. Many polymers can adsorb onto particles and then cause steric interaction (Section 12.3.1), which is often repulsive and thereby stabilizing, although attractive interaction can also occur. If polymer molecules adsorb on two particles at the same time, they cause bridging (Section 12.3.2), hence aggregation. Polymers in solution can also cause aggregation via depletion interaction (Section 12.3.3), or they can stabilize a dispersion by immobilizing the particles in a gel network. 

Complications. In practice, precise calculation of the interaction free energy is not always easy. Eq. (12.12) applies to a pair of identical hard spheres, and even in that case the result may differ from the prediction. The relation <5 = rg is not exact, even if the polymer is monodisperse, because some chains will protrude beyond rg. If the particles are somewhat deformable, because they are very soft or because they have a deformable adsorption layer, the depletion interaction forcing them together may cause local flattening, by which Fdepi becomes even larger. Particle shape has a large effect, and for platelets the depletion interaction is far stronger than for spheres of equal volume (can you explain this ). 

On the other hand, dissolved polymers may cause depletion interaction. This is because the polymer molecules cannot come very close to the particle surface, which amounts to polymer being depleted from part of the solvent. Hence, polymer concentration, and thereby osmotic pressure, is increased. If particles aggregate, the depletion layer decreases in volume due to overlapping, and the polymer concentration decreases, hence the osmotic pressure decreases. This means that an attractive force acts between the particles. It increases with concentration and radius of gyration of the polymer. 

Especially useful are Vol. I, Chapter 4, for van der Waals forces, and Vol. II, Chapter 3, for electric double layers. A comprehensive monograph on adsorbed and grafted polymer layers, including treatment of steric interaction and depletion interaction, is... 

Aggregation. The interactions involved are treated in Chapter 12. It follows that the main cause is often van der Waals attraction (Section 12.2), as given by the Hamaker equations. Another important cause is depletion interaction, where the driving force is increase in mixing entropy of polymer molecules or other small species present in solution (Section 12.3.3). 

There are three main modes of interaction between a polymer solution and a solid surface. The first interaction mode is depletion [2,3]. If the monomers are repelled by the surface (or in other words if the attractive interaction between the solvent molecules and the surface is larger than the interaction between the monomers and the surface), the polymer concentration in solution decreases as the surface is approached and a region depleted in polymer exists in the vicinity of the surface. The size of this region is the size of the polymer chain if the solution is dilute and the size of the correlation length of the solution if the solution is semidilute (if the polymer chains overlap). When two surfaces are brought in close contact, the density in the gap between the surfaces is smaller than the bulk concentration and the osmotic pressure in the gap is smaller than the bulk osmotic pressure. This osmotic pressure difference induces an attraction between the surfaces. The depletion interaction is not specific to polymers and exists with any particle with a size in the colloidal range [4]. It has sometimes been used to induce adhesion between particles of mesoscopic size such as red blood cells. The only limitation to this qualitative description of the depletion force is that at equilibrium the polymer chains (or any other particles) must leave the gap as the surfaces get closer. There is no attractive depletion force if they remain trapped in the gap. We will not consider further the depletion interaction. 

Non-adsorbing polymers generate attractive interactions and depletion attractions, thus causing the system to phase-separate into one polymer-depleted and one particle-depleted solution. Typical polymers that could cause this behaviour are large non-adsorbing polysaccharides, such as xanthan or starch. This effect is usually observed as an increased creaming or a coarsening of the system. 

I he development of experimental methods of determining the spinodal, the interaction parameter x (or g), and other critical parameters has promoted the appearance of the third approximation of h lory-IIuggins lattice theory where the dependence of the interaction parameter g on the polymer molecular weight (or MWD) and the peculiar features of dilute polymer solutions or of polymer-depleted phetse at phase separation arc taken into account. 

---