Depletion interaction energy

Here, Hq is the shortest distance between the surfaces of the larger particles, and n is the number density of the smaller particles. By integrating Equation 5.222 we can derive an expression for the depletion interaction energy between the two larger particles, U iho). For D> d this expression... 

The pair potential of colloidal particles, i.e. the potential energy of interaction between a pair of colloidal particles as a function of separation distance, is calculated from the linear superposition of the individual energy curves. When this was done using the attractive potential calculated from London dispersion forces, Fa, and electrostatic repulsion, Ve, the theory was called the DLVO Theory (from Derjaguin, Landau, Verwey and Overbeek). Here we will use the term to include other potentials, such as those arising from depletion interactions, Kd, and steric repulsion, Vs, and so we may write the total potential energy of interaction as... 

Figure 3.6 Effect of Ca2+ content on predicted values of osmotic pressure (H, , left axis) of caseinate nanoparticles in emulsion continuous phase and the free energy of the depletion interaction (AGdep, , right axis) between a pair of emulsion droplets (

Cell injury can be initiated by a number of mechanisms, such as inhibition of enzymes, depletion of cofactors or metabolites, depletion of energy (ATP) stores, interaction with receptors, and alteration of cell membranes. In recent years attention has focused on the role of biotransformation of chemicals to highly reactive metabolites that initiate cellular toxicity. Many compounds, including clinically useful drugs, can cause cellular damage through metabolic activation of the chemical to highly reactive compounds, such as free radicals, carbenes, and nitrenes (Chapters 7 and 8). 

If a depletion interaction is present in a colloidal system, it generates a negative free energy change, and, as a result,... 

When the radius of the spherical colloidal particles a is much larger than the shortest distance between the surfaces of two colloidal particles, the free energy between two identical spherical particles, due to double-layer, steric, and depletion interactions, can be calculated using the Derjaguin approximation 2... 

Several theories have been put forward to account for the distributicm of polymer segments in the depletion zone. The theories of Feigin and Napper [48] and Scheutjens and Fleer [49] are qualitatively different from the theory of Asakura and Oosawa and de Cannes and coworkers [50,51] in that they predict not only depletion flocculation but also depletion stabilization. Depletion stabilization has not to date been verified experimentally although depletion fiocculation has been verified experimentally for several systems [52,53]. The effect of an adsorbed poljnner layer [54] and ordered solvent layers [55] on depletion flocculation is also under theoretical attack. The depletion stabilization interaction energy cannot simply be added to the other interaction energy terms to give the total interaction energy. 

We have compared these theoretical predictions of the low-frequency modulus to experimental measurements on compressed emulsions and concentrated dispersions of microgels [121]. The emulsions were dispersions of silicone oil (viscosity 0.5 Pas) in water stabilized by the nonionic surfactant Triton X-100 [102, 121]. The excess surfactant was carefully eliminated by successive washing operations to avoid attractive depletion interactions. The size distribution of the droplets was moderately polydisperse with a mean droplet diameter of 2pin. The interfacial energy F between oil and water was 4mJ/m. The contact modulus for these emulsions was thus F 35 kPa. The volume fraction of the dispersed phase was easily obtained from weight measurements before and after water evaporation. Concentrated emulsions have a plateau modulus that extends to the lowest accessible frequencies, from which the low-frequency modulus Gq was obtained. Figure 11 shows the variations of Gq/E"" with 0 measured for the emulsions against the values calculated in the... 

Complications. In practice, precise calculation of the interaction free energy is not always easy. Eq. (12.12) applies to a pair of identical hard spheres, and even in that case the result may differ from the prediction. The relation <5 = rg is not exact, even if the polymer is monodisperse, because some chains will protrude beyond rg. If the particles are somewhat deformable, because they are very soft or because they have a deformable adsorption layer, the depletion interaction forcing them together may cause local flattening, by which Fdepi becomes even larger. Particle shape has a large effect, and for platelets the depletion interaction is far stronger than for spheres of equal volume (can you explain this ). 

Quantitative prediction of the depletion free energy of interaction. Feigin and Napper (1980b) were unable to predict analytically the free energy of... 

Backdonation of metal electrons into the CO 2it orbital increases the charge on the parallel-oriented CO molecules and depletes the d-valence electron band of electrons. The former increases the direct repulsive interaction, the latter increases metal atom-metal atom interactions, but also decreases electron backdonation. It results in an overall increase of the repulsion of neighbor CO molecules with approximately 10 kJ mol T Shared bonding of CO adsorbed in bridge coordination and atop leads to additional repulsive interactions on the order 10-20 kJ mol . This interaction energy value is very similar to that found for the Rh4 cluster of Figure 10.22. 

Depletion interactions are interactions between two surfaces (particles) in the presence of firee, i.e., non-adsorbed, macromolecules, micelles, or very fine particles. Asakura and Oosawa (1954) first pointed out that if the distance between two surfaces h is smaller than the diameter of solute molecules Jm, this region will contain pure solvent depletion zone, cf. Fig. 3.14, left). Thus, an attractive force corresponding to the osmotic pressure of the bulk solution is acting on the two surfaces. Agglomeration caused by this effect is called depletion flocculation. In a second paper, the authors calculated the potential energy of this interaction for... 

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