Polymers depletion layers

There are, however, important differences between the phase behavior of sticky spheres and that of small molecules, which arise from differences in the relative ranges of the attractive potentials. These differences have been explored in a wonderful set of calculations and experiments by Cast et al. (1983) and Pusey and coworkers (Uett et al. 1995) for suspensions of spheres that are made to attract each other by the polymer-depletion mechanism. In such systems, the range of the attractive potential relative to the sphere size can be varied by controlling the ratio = Aj fa of the polymer depletion-layer thickness to the sphere radius. For 0 the potential is short-ranged, like that of sticky hard spheres,... 

FIGURE 16.6 Polymer depleted layers around particles. 

A plausible mechanism for the erosion of devices that contain Mg(OH)2 is shown in Fig. 14 (2). According to this mechanism, the base stabilizes the interior of the device and erosion can only occur in the surface layers where the base has been eluted or neutralized. This is believed to occur by water intrusion into the matrix and diffusion of the slightly water-soluble basic excipient out of the device where it is neutralized by the external buffer. Polymer erosion then occurs in the base-depleted layer. 

The principle of depletion is illustrated in Figure 1. If a surface is in contact with a polymer solution of volume fraction , there is a depletion zone near the surface where the segment concentration is lower than in the bulk of the solution due to conformational entropy restrictions that are, for nonadsorbing polymers, not compensated by an adsorption energy. The effective thickness of the depletion layer is A. Below we will give a more precise definition for A. 

C. Allain, D. Ausserre, and F. Rondelez, Direct optical observation of interfacial depletion layers in polymer solutions, Phys. Rev. Lett. 49, 1694-1697 (1982). 

Here, A is the depletion layer thickness (assumed equal to the radius of gyration of the polymer, RG). H = r - 2a is the surface-to-surface particle separation, V ° is the molar volume of the solvent, and ji and ji are the solvent chemical potentials for the polymer solution and the pure solvent. It appears that the assumption A = RG is generally acceptable providing that the polymer solution is in the dilute concentration regime. At higher polymer concentrations, however, the value of A is reduced according to the relationship (Vincent, 1990) ... 

Vincent, B. (1990). The calculation of depletion layer thickness as a function of bulk polymer concentration. Colloids and Surfaces, 50, 241-249. 

Because of restrictions on the number of possible configurations, non-adsorbing polymers tend to stay out of a region near the surfaces of the particles, known as the depletion layer. As two particles approach, the polymers in the solution are repelled from the gap between the surfaces of the particles. In effect the polymer concentration in the gap is decreased and is increased in the solution. As a result, an osmotic pressure difference is created which tends to push the particles together. The resulting attractive force is the reason for depletion flocculation. In contrast to this, depletion stabilisation has been mentioned above. 

In the basic model, put forward by Asakura and Oosawa (5), the hard spherical particles immersed in a solution of macromolecules are considered to be surrounded by depletion layers from which the polymer molecules are excluded. When two particles are far apart with no overlap of the depletion zones, the thermal force acting over the entire particle surface is uniform. However, when the particles come closer, such that their depletion zones begin to overlap, there is a region in which the polymer concentration is zero and the force exerted over the surfaces facing this region is smaller compared to that exerted over the rest of the surface. This gives rise to an attractive force between the two particles which is proportional to the osmotic pressure of the polymer solution. 

The consequences for suspended particles can be understood from either a mechanical or a thermodynamic standpoint. A particle immersed in a polymer solution experiences an osmotic pressure acting normal to its surface. For an isolated particle, the integral of the pressure over the entire surface nets zero force. But when the depletion layers of two particles overlap, polymer will be excluded from a portion of the gap (Fig. 30). Consequently, the pressure due to the polymer solution becomes unbalanced, resulting in an attraction. The same conclusion follows from consideration of the Helmholtz free-energy. Overlap of the depletion layers reduces the total volume depleted of polymer, thereby diluting the bulk solution and decreasing the free energy. 

Fig. 3. Preferential protein hydration in the presence of precipitating agents used in crystallization experiments. When high concentrations of salts are used as precipitants, a precipitant-poor layer forms near the protein (P) surface due to a higher affinity of the protein for water than for the precipitant. Other precipitants (e.g., polyethylene glycol polymers) induce formation of a similar precipitant-depleted region near the protein by solvent exclusion effects. In either case formation of the precipitant-depleted layer is energetically unfavorable. Consequently, the overall effect of precipitants is to promote molecular associations that decrease the total protein surface area exposed to solvent. After Timasheff and Arakawa (1988).

Figure 5.9. Typical Interfaclal concentration profile of a nonadsorbing polymer. The correlation length which is a measure of the depletion layer thickness, is indicated.

Numerical results for a 10% solution of polymer [N - 1000) in Its own monomer are given in fig. 5.15 (solid curves). It is clear that long chains try to avoid the surface region because of the incurred loss of conformational entropy. The available space Is occupied by the monomer which does not suffer from these entroplcal restrictions. Hence, the polymer is depleted. It can be shown that at low (p (below coil overlap) the thickness of the depletion zone is proportional to Vw, see sec. 5.3e. At higher (as in fig. 5.15), the osmotic pressure pushes the chains closer to the surface, making the depletion layer thinner and its thickness more weakly dependent on chain length. 

A second method of local planarization involves spinning photoresist onto the SiOj ILD to obtain local planarity. The resist is then hard baked and etched with an RIE etch tailored to remove SiOz (or ILD) at the same rate as the photoresist. Because the etch rate of the two materials is equal, the planarity of the resist film transfers into the SiOz film. However, a precise match in SiOj and photoresist etch rates is difficult to maintain because the relative ratio of SiOj to photoresist exposed increases as the etch back proceeds. Loading effects then result in a decrease in the Si02 etch rate and increase in the photoresist etch rate. Furthermore, polymer deposits build up on the etch reactor chamber walls over time etching of this polymer depletes the chemicals used to etch the photoresist, which slows the photoresist etch rate. If the etch rates are not matched, the planarity of the photoresist layer will not transfer well to the SiOz. 

A study of paint technology reveals other interactions. The layer of paint in immediate contact with the surface of the substrate is depleted of filler. The next layer is enriched with filler. Between the last layer and the bulk of paint there is still polymer-rich layer. This effect is attributed to the affinity of the polymer with the substrate. This affinity leads to polymer migration. It also causes binder orientation... 

Bondy ° observed coagulation of rubber latex in presence of polymer molecules in the disperse medinm. Asaknra and Oosawa published a theory that attributed the observed interparticle attraction to the overlap of the depletion layers at the surfaces of two approaching colloidal particles (Figure 5.28). The centers of the smaller particles, of diameter, d, cannot approach the surface of a bigger particle (of diameter D) at a distance shorter than d 2, which is the thickness of the depletion layer. When the two depletion layers overlap (Fignre 5.28), some volume between the large particles becomes inaccessible for the smaller particles. This gives rise to an osmotic pressnre. 

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