Depletion attraction

The adliesion and fiision mechanisms between bilayers have also been studied with the SEA [M, 100]. Kuhl et al [17] found that solutions of short-chained polymers (PEG) could produce a short-range depletion attraction between lipid bilayers, which clearly depends on the polymer concentration (fignre Bl.20.1 It. This depletion attraction was found to mduce a membrane fusion widiin 10 minutes that was observed, in real-time, using PECO fringes. There has been considerable progress in the preparation of fluid membranes to mimic natural conditions in the SEA [ ], which promises even more exciting discoveries in biologically relevant areas. 

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],...

The second case involves non-adsorbing polymer chains in solution. It was realized by Asakura aird Oosawa (AO) [50] aird separately by Vrij [51] tlrat tlrese chains will give rise to air effective attraction between colloidal particles. This is kirowir as depletion attraction (see figure C2.6.4. We will summarize tire AO tlreory to explain tlris. 

In section C2.6.4.3 it was shown how tlie addition of non-adsorbing polymer chains induces a depletion attraction between colloidal particles. If sufficient polymer is added, tliese attractions can be strong enough to induce a phase separation of tire colloidal particles. An early application of tliis was tire creaming of mbber latex [93]. 

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.)...

FIG. 13.17 Depletion attraction between two surfaces immersed in a polymer solution. 

Figure 9b shows a schematic of the DNA bundle phase observed at MVLBisG2 > 0.5. The bundling phase requires the presence of salt (as found in the cell culture medium used for all our experiments) and is formed by the interplay of the salt-induced screening of the electrostatic interactions and the depletion-attraction [59,60] caused by the lipid micelles. While depletion-attraction has previously been reported for like-charged or neutral objects, the screening of the electrostatic interactions also... 

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... 

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). 

The existence of short-range attractive interactions between particles leads to a much richer phase behavior, as illustrated in Fig. 3. This situation can be achieved by adding a nonadsorbing polymer to the suspensions, which induces an effective depletion attraction between the particles [105]. Such polymer-colloid mixtures can be viewed as model systems of complex fluids and are involved in many practical... 

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],... 

Interesting effects are observed when a dispersion contains both larger and smaller particles the latter are usually polymer coils, spherical or cylindrical surfactant micelles, or microemulsion droplets. The presence of the smaller particles may induce clustering of the larger particles due to the depletion attraction (see Section 5.4.S.3.3, above) such effects are described in the works on surfactant-flocculated and polymer-flocculated emulsions. Other effects can be observed in dispersions representing mixtures of liquid and solid particles. Yuhua et al. ° have established that if the size of the solid particles is larger than three times the size of the emulsion drops, the emulsion can be treated as a continuous medium (of its own average viscosity), in which the solid particles are dispersed such treattnent is not possible when the solid particles are smaller. 

Kuhl T ef a/1996 Direct measurement of polyethylene glycol induced depletion attraction between lipid bilayers Langmuir 12 3003-14... 

Depletion attraction Non-adsorbing Intermediate polymer concentration... 

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. 

Oscillatory structural forces appear in thin films of pure solvent between two smooth solid surfaces and in thin liquid films containing colloidal particles including macromolecules and surfactant micelles (Israelachvili 1992). In the first case, the oscillatory forces are called the solvation forces and they are important for the short-range interactions between solid particles and dispersions. In the second case, the structural forces affect the stability of foam and emulsion films as well as the flocculation processes in various colloids. At lower particle concentrations, the structural forces degenerate into the so-called depletion attraction, which is found to destabilize various dispersions. 

For the colloid/amine-PEP mixture, one can view it eis a two-solute system consisting of the colloid-polymer micelles and the free polymer chains. Equation (3) can still be used except one has to replace fi by f + asolid line in Fig. 4 is a fit to the linear function 3.7(1 — 27.4p2) The effective slope of the linear function is 27.4/(l — ao) = 34.7, which is a factor of 0.68 smaller than that for the colloid/PEP mixture. The smaller slope in PiP2)/ u ) indicates that the polymer adsorption greatly reduces the depletion attraction between the colloidal particles. However, there is still some attraction between the colloid-polymer micelles due to the un-adsorbed... 

The range over which depletion attraction operates equals 2R. In particular, for highly swollen polymers, R may reach values of some tens of nanometer and, hence, the depletion forces may be effective over separation distances between particles that exceed the range of dispersion and double layer forces (cf Section 16.1). On the other hand, the osmotic forces are relatively weak. Depletion flocculation occurs when the molar polymer concentration is sufficiently high, which is more readily achieved by using polymers of a relatively low degree of polymerization. 

We note that in the original paper of Asakura and Oosawa [54], where expression (1.21) was first derived, the polymers were regarded as pure hard spheres. Vrij [40, 56] arrived at the same result by describing the polymer chains as penetrable hard spheres, see Sect. 2.1. Inspection of (1.21) and (1.22) reveals that the range of the depletion attraction is determined by the size 2S of the... 

In Fig. 1.9 we sketch the influence of a combined depletion attraction and a brush repulsion on the total interaction. The presence of bmshes reduces the attraction and the minimum value of the attraction is found at > 0 [57]. 

Thin colloidal disks provide another example of an anisometrie eoUoidal particle as an efficient depletion agent. This problem was first eonsidered by Pieeh and Walz [61]. At the end of this seetion, where we compare spheres, rods and disks as depletion agents, we will see that the disk is intermediate in effieieney to induce depletion attraction between spheres and rods. Here we consider disks of diameter D and thickness L, see Rg. 2.30. Notiee that for the simplest ease, i.e., infinitely thin hard disks, the exeluded volume of the disks with respect to each other is nonzero and only in limit of the concentration going to zero will the disks behave thermodynamically ideal. We restrict ourselves to this limiting case. 

We present a simple theoretical treatment of the hard sphere fluid-crystal transition that will also serve as a reference framework for our treatment of phase transitions in a system of colloids with depletion attraction. 

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