Depletion zone solution

A non-adsorbing polymer in solution can also destabilise a dispersion through a mechanism called depletion flocculation. When polymer molecules do not interact favourably with the particle surfaces from an enthal-pic perspective, they are repelled from the surface regions due to entropic reasons. A depletion zone around the particles is created which has a lower average polymer concentration than the bulk solution. The osmotic... 

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. 

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. 

Aluminum brasses Precipitation of CuA12 at grain boundaries and formation of Cu depleted zones adjacent to grain boundaries results in a potential difference of 200 mV between the boundary and the grain and results in intergranular cracking resistance or immunity to SCC can be achieved by quenching from solution heat-treatment temperature... 

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. 

The magnitude of the depletion attraction free energy, is proportional to the osmotic pressure of the polymer solution, which in turn is determined by

molecular weight M. The range of depletion attraction is proportional to the thickness of the depletion zone. A, which is roughly equal to the radius of gyration, Rq, of the free polymer. A simple expression for Gdep is [7],... 

Fig. 7.52 Interface profile of intergranular corrosion when solute-depleted zone is anodic to precipitate and undepleted matrix, (a) Intergranular attack when precipitateand solute-depleted zone iscontinuous. (b) Intergranular attack when precipitate and depleted zones are discontinuous...

For diffusion-controlled processes the faradaic or electrolysis current grows during the drop lifetime I = ktb (Fig. 1.5d). This growth is the resultant of two opposing processes. The first is the increase in the size of the growing mercury drop causing an increase in the current. The second is the depletion of the electroactive species from the solution and growth of a depletion zone around the electrode, due to electrolysis. The latter produces a decrease in the current Fig. 3.2a shows this decrease in current for an electrode of fixed size. 

Semiconductor nanowires provide very sensitive detectors, where adsorbate-induced charge separation can convert an entire silicon nanowire into an accumulation or depletion zone. The same adsorbate on a macroscale silicon surface would induce only a surface layer but leave the bulk unaffected. The main problems to date with nanowires and their assembly are quality control a number of research endeavors are currently aimed at exploiting nanowires for detection and overcoming these technical challenges. Groups at Caltech and the Naval Research Laboratory have independently been pursuing innovative technical solutions to these problems. ... 

Fig. 21 Pitting potentials as a function of heat-treatment time for grain matrix and solute-depleted zone associated with grain boundary in AI-4 wt. % Cu alloy. The region of ICC (and also IGSCC) susceptibility is indicated. (After Ref. [80].)...

Alloy phase transformation and associated solute depleted zones... 

The phase at the aUoy s grain boundary controls ahoy reactivity or enhances reactivity of the associated solute depleted zone (SDZ) [45]. The aerospace ahoy Al-Zn-Mg (7000) series exhibits SCC susceptibility when ahoyed with Cu. Cu segregation and grain... 

Fig. 1.16 Electron microscopy images and EDX profiles around grain boundaries of the Al-Cu alloy aged at 433 K for 7.2 ks. (a) under-aged, (b) 90 k (peak-aged), and (c) 1728 ks (over-aged). The average widths of precipitate free zone (PFZ) and solute depletion zone (SDZ) are indicated by arrow [46].

T. Ramgopal, P.I. Gouma, G.S. Frankel, Role of grain-boundary precipitates and solute-depleted zone on the intergranular corrosion of aluminum alloy 7150, Corrosion 58 (2002) 687—697. 

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