Depletion attractive force

For the non-adsorbing polymer case, the depletion force w ill be generated. The depletion mechanism was first theoretically addressed in ref. [23] using the excluded volume concept. Other approaches such as the density ftmctional theory [24] and the virial expansion [25] were developed for deriving the exact expression for the depletion force. Simply, the interaction potential due to the depletion force can be expressed [15] 

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Fig. 9 (a) Schematics of the molecular structure of DL/DOPC-DNA complexes assembled in slightly disordered HjC. (b) DNA bundles surrounded by a cloud of micelles. The depletion-attraction force caused by micelles and the screening of the electrostatic interaction in the system enables the formation of the DNA bundles. Reprinted with permission from [46], Copyright 2009 American Chemical Society... 

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. 

Depletion attractive force Smaller particle or free polymer or weakly adsorbed polymer... 

Figure Bl.20.11. Force curves of DMPC/DPPE (dimyristoyl phosphatidylcholine and dipalmitoyl phosphatidylethanolainine) bilayers across a solution of PEG at different concentrations. Clearly visible is a concentration-dependent depletion attraction, with pennission from [17],...

Experimental support for the suggestion that depleted surface layers result in attractive forces (at T 0) has come from recent experiments (J.K. and Y.A., submitted) where mica surfaces partially covered by polystyrene in cyclopentane above the 0-temper-ature show a clear mutual attraction, which disappears when full surface coverage by the polymer is attained. 

Figure 2.7. Force-distance profiles at different CTAB surfactant concentrations. Droplet radius = 98 nm. The continuous fines are the best fits obtained with Eqs. (2.14), (2.15) (for double-layer repulsion), and (2.17) (for depletion attraction). (Adapted from [22].)...

Figure 2.9. Measured force F (normalized by the mean radius of curvature R of the surfaces) as a function of the surface separation between crossed mica cylinders coated with an adsorbed bUayer of CTAB and immersed in a micellar solution of CTAB (volume fraction of 0.073). In addition to the depletion attractive minimum, two oscillations due to structural forces turn up. (Reproduced from [21], with permission.)...

The flocculation of dispersed species induced by nonadsorbing polymer molecules due to depletion forces. When solutes such as polymer molecules do not, for some reason, enter the gap between adjacent surfaces an attractive force is created between the surfaces. This depletion force arises out of the solute s ability to influence osmotic pressure in bulk but not in the gap between the surfaces. 

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. 

However, the dispersion interactions (between ions and the whole system) generate repulsive forces between the water/air interface and the highly polarizable ions (Cl-, Br, I") and attractive forces between the interface and the less polarizable ions (Na+, Li+, K+).3 Some recent experimental results5 also challenged the traditional Langmuir picture of a surface layer depleted of ions they revealed, however, the opposite, namely that the more polarizable anions are positively adsorbed on the interface.5 The conclusion of Hu et al.5 was supported by the numerical simulations of Jungwirth and Tobias,6 which demonstrated that the polarizability of halogen anions (Cl , Br-, I ) is directly related to their propensity for the surface. The less-polarizable ions (Na+ and F ), however, preferred the bulk water.6 These results are opposite to the predictions of the ion dispersion theories.3... 

Figure 10.18 is a schematic representation of depletion stabilization in which the polymer is prevented from the zone of close approach between two particles. As a result of this low polymer concentration between the particles due to size exclusion, there is a lower osmotic pressure, which results in (1) an attractive force for greater than theta solvents and (2) a repulsive force for less than theta solvents. Theta solvents will be discussed in the section on the thermodynamics of polymer solutions, but first a discussion of pol3naaer properties. 

In essence, the ability to maximize entropy by sorting different-sized objects creates a kind of attractive force, called a depletion, or excluded-volume, force. These entropic forces operate for objects in the size range of approximately 10-8 to approximately 10 6 m. For entropy-induced ordering to occur, the particles must be constantly jostling each other and must be constantly agitated by solvent molecules, thus making gravity unimportant. 

It has been postulated [10] that silicate minerals as feldspar exposed to atmospheric agents undergo hydration and decay through the polarization and the ensuing dissociation of the water dipole into and OH due to the attractive forces of the free valencies. In this interaction the oxygens are converted to hydroxyl groups and part of the potassium is removed in solution. A partial or total cationic (K, Na, Ca ) depletion decomposes the feldspar. Since the neutral water now reaches an increased pH, introduction of acids neutralizes these alkali and facilitates a further decay of these minerals. 

Increased depletion attraction. The presence of nonadsorbing colloidal particles, such as biopolymers or surfactant micelles, in the continuous phase of an emulsion causes an increase in the attractive force between the droplets due to an osmotic effect associated with the exclusion of colloidal particles from a narrow region surrounding each droplet. This attractive force increases as the concentration of colloidal particles increases, until eventually, it may become large enough to overcome the repulsive interactions between the droplets and cause them to flocculate (68-72). This type of droplet aggregation is usually referred to as depletion flocculation (17, 18). 

In other words, at small separations Oos, is negative (attractive). Equation 5.215 holds for both solvation forces and coUoid structural forces. In the latter case. Equation 5.215 represents the osmotic pressure of the colloid particles and the resulting attractive force is known as the depletion force (see Section 5.4.5.3.3 below). 

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. 

Note A stable dispersion of small solid or liquid particles may also show a kind of phase separation when conditions in the liquid are changed in such a way that attractive forces between the particles become dominant. A separation into a condensed phase (high volume fraction of particles) and a very dilute dispersion would then result. The interfacial tension between these phases is very small, e.g., a few pN m 1. Conditions for this to occur are (a) that the particles are about monodiperse and of identical shape and (b) that the attractive forces do not become large (because that would lead to fractal aggregation see Section 13.2.3). Since these conditions are rarely met in food systems, we will not further discuss the phenomenon. Nevertheless, phenomena like depletion flocculation (Section 12.3.3) show some resemblance to a phase separation. 

Figure 9.7 Origin of depletion flocculation. Polymer molecules are excluded from a volume V and an area A between the particles at a separation of H. In this region there is a negative adsorption given by —r,K. As H decreases, the adsorption becomes less negative (i.e. increases) and an attractive force results.

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