Polymer depletion

The thud step gives a polymer-rich phase forming the membrane, and a polymer-depleted phase forming the pores. The ultimate membrane structure results as a combination of phase separation and mass transfer, variation of the production conditions giving membranes with different separation characteristics. Most MF membranes have a systematic pore structure, and they can have porosity as high as 80%.11,12Figure 16.6 shows an atomic force microscope... 

This is a free-radical polymerization with short chain lives. The first molecules formed contain nearly 58 mol% styrene when there is only 50% styrene in the monomer mixture. The relative enrichment of styrene in the polymer depletes the concentration in the monomer mixture, and both the polymer and monomer concentrations drift lower as polymerization proceeds. If the reaction went to completion, the last 5% or so of the polymer would be substantially pure polyacrylonitrile. 

At high polymer concentrations, one may also have what is known as depletion stabilization. The polymer-depleted regions between the particles can only be created by demixing the polymer chains and solvent. In good solvents the demixing process is thermodynamically unfavorable, and under such conditions one can have depletion stabilization. 

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. 

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,... 

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 ... 

The mixing of surfactant and polymer in the porous medium occurs due to both dispersion and the excluded volume effect for the flow of polymer molecules in porous media, which in turn could lead to the phase separation. Figure 16 illustrates the schematic explanation of the surfactant-polymer incompatibility and concomittant phase separation. We propose that around each micelle there is a region of solvent that is excluded to polymer molecules. However, when these micelles approach each other, there is overlapping of this excluded region. Therefore, if all micelles separate out then the excluded region diminishes due to the overlap of the shell and more solvent becomes available for the polymer molecules. This effect is very similar to the polymer depletion stabilization (55). Therefore, this is similar to osmotic effect where the polymer molecule tends to maximize the solvent for all possible configurations. ... 

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]. 

Hanke, A., Eisenriegler, E. and Dietrich, S. (1999) Polymer depletion effects near mesoscopic particles. Phys. Rev. E, 59, 6853-6878. 

When a liquid dispersion contains non-adsorbing polymers, there will be a layer of liquid surrounding each dispersed species that is depleted in polymer compared with the concentration in bulk solution. This causes an increase in osmotic pressure in the system compared with what it would be were the dispersed species absent. If the dispersed species move close to each other, then the volume of solvent depleted is reduced, reducing the overall osmotic pressure, which provides a driving force for flocculation. Xanthan gum, added in low concentrations, can cause depletion flocculation [43]. Polymer depletion can also cause a gel to form [98]. 

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. 

V and Vn are the volum< sof polymer-depleted pha.se I and of polymer-enriched phase II, respectively. 

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. 

FIGURE 16.6 Polymer depleted layers around particles. 

Anderson, T. H., S. H. Donaldson, H. Zeng, and J. N. Israelachvih. 2010. Direct measurement of double-layer, van der Waals, and polymer depletion attraction forces between supported cationic bilayers. Langmuir26, no. 18 14458-14465. doi 10.1021/lal020687. 

Nonadsorbing polymer Depletion stabilization V Depletion flocculation... 

Fig. 3. Phase diagram for poly(NIPAAM) in aqueous solution. The area under the bin-odal curve presents the range of temperatures/polymer concentrations for homogeneous solution. Separation into polymer-enriched and polymer-depleted phases takes place for any polymer concentration/temperature above the binodal curve. Reproduced from Ref. 14 with permission.

Mixing two oppositely charged PELs usually results in the separatimi of a nulky polymer-rich phase from a clear polymer-depleted phase. Given the task of preparing a PEL complex from standard PELs Uke poly(diallyldimethylammonium chloride) (PDADMAC) and polyfstyrenesulfonate) (PSS), one would expect a similar... 

It was found fairly recently that free (non-adsorbing) polymer can affect colloid stability (4-11). Flocculation caused by free polymers is called depletion flocculation (5,6). The first theory for the depletion flocculation was the theory proposed by Asakura and Oosawa (10,11) of Nagoya University in Japan. According to them, when two particles approach each other in a polymer solution to a distance of separation that is less than the diameter of polymer molecules, polymer may be extruded from the inter-particle space. This leads to a polymer-depleted-free zone between two particles. An osmotic force is then exerted from the polymer solution outside the particles and this results in flocculation. 

III.1. Polymer Depletion at the Solid/Solvent Interface (Fig. 5) With... 

Inaccessible pore volume has a beneficial effect on field performance. The bank of connate water and polymer-depleted injection water that precedes the polymer bank will be reduced by the amount of inaccessible pore volume. Polymer response will be seen at production wells sooner than expected for example, a pilot test reported by Jones found polymer in the produced water immediately after breakthrough. Because adsorption is unchanged, the total polymer treatment cannot be reduced, but the income acceleration benefits of earlier response can be substantial. 

The above differential equation can now be solved analytically. We first present the results in more detail for polymer adsorption (y > 0) and then repeat the main findings for polymer depletion (y < 0). 

We highlight the main differenees between the polymer adsorption and polymer depletion. Keeping in mind that y < 0 for depletion, the solution of the same profile equation (24), with the appropriate boundary condition, results in... 

For polymer depletion, similar arguments [36] suggest the following scaling form for the central and mean-field proximal regions, a < z... 

Forces Due to the Presence of Non-adsorbing Polymers— Depletion and Structural Interactions... 

The amount of polymer depleted from the interface region, enriching the bulk of the phases, can be approximated by integrating the total polymer concentration along the distance from the center of the interface. The result for the example of Figure 9.2 is in Figure 9.6. 

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