Colloidal interactions interaction energy

The major difficulty in predicting the viscosity of these systems is due to the interplay between hydrodynamics, the colloid pair interaction energy and the particle microstructure. Whilst predictions for atomic fluids exist for the contribution of the microstructural properties of the system to the rheology, they obviously will not take account of the role of the solvent medium in colloidal systems. Many of these models depend upon the notion that the applied shear field distorts the local microstructure. The mathematical consequence of this is that they rely on the rate of change of the pair distribution function with distance over longer length scales than is the case for the shear modulus. Thus... 

FIGURE 12.1 Hypothetical example (solid curve) of the colloidal interaction free energy V divided by kBT, as a function of interparticle distance h. The insert defines the geometry involved for the case of two spheres of radius R. The broken lines give two other examples of interaction curves. 

Tirado-Miranda, M., A. Schmitt, J. Callejas-Femandez, and A. Femandez-Barbero. 2003. Aggregation of protein-coated colloidal particles Interaction energy, cluster morphology, and aggregation kinetics. Journal of Chemical Physics 119 (17) 9251-9259. 

Figure C2.6.9. Phase diagram of charged colloidal particles. The solid lines are predictions by Robbins et al [85]. Fluid phase (open circles), fee crystal (solid circles) and bee crystal (triangles). is tire interaction energy at tire...

Surface forces measurement directly determines interaction forces between two surfaces as a function of the surface separation (D) using a simple spring balance. Instruments employed are a surface forces apparatus (SFA), developed by Israelachivili and Tabor [17], and a colloidal probe atomic force microscope introduced by Ducker et al. [18] (Fig. 1). The former utilizes crossed cylinder geometry, and the latter uses the sphere-plate geometry. For both geometries, the measured force (F) normalized by the mean radius (R) of cylinders or a sphere, F/R, is known to be proportional to the interaction energy, Gf, between flat plates (Derjaguin approximation). 

Physical model for colloid stability. Net energy of interaction for spheres of constant potential surface for various ionic strengths (1 1 electrolyte) (cf. Verwey and Overbeck). 

Use schematic diagrams to describe the influence of electrolyte concentration, type of electrolyte, magnitude of surface electrostatic potential and strength of the Hamaker constant on the interaction energy between two colloidal-sized spherical particles in aqueous solution. What theory did you use to obtain your description Briefly describe the main features of this theory. 

The total DLVO interaction energy (Vs) between two spherical colloids (each of radius a and separated by distance H) is given by the following approximate equation ... 

This approximate formula contains information concerning what happens when two colloidal particles (the two metal spheres) collide. One has to plot this total interaction energy C/total against the distance apart of the particles. 

Equations for calculating van der Waals interaction forces/energies between macromolecules or colloidal particles are quite well established (Israelachvili, 1992 Dickinson and McClements, 1995 McClements, 2005). (For example, see equations (3.35) and (3.36) in chapter 3). The interactions between nanoparticles are potentially more complicated, however, because the nanoparticle size and interparticle separation are comparable in magnitude, precluding the use of the asymptotic forms of the equations also nanoparticles are commonly anisotropic, and their dielectric properties are often not known (Min et al., 2008). 

TABLE 4.4 Summary of Some Colloidal Interaction Energies and Parameters from Chapters 10-12... 

Fig. 5.9 Representation of the interaction energy E(T) between two colloidal particles [E(R) = repulsion energy E(A) = attraction energy E(T) = E(R) + E(A), r = distance between two particles].

Fig. 31 Overall interaction energy between two DNA-coated colloids, (a) Sketch of the interacting surfaces of two spheres of radius R0 separated by d. The maximum length of hybridized strands is 2L. (b) Total interaction energy as a function of d. It is the sum of the attractive I/DNA from the binding of accessible DNA strands, the repulsive I/rep from electrostatics and/or polymer steric effect, and the van der Waals attraction t/vdw. (c) For weak, short-range I/rep, particles which are unbound at high temperatures are irreversibly trapped in the van der Waals well after DNA hybridization at low temperatures, (d) For strong, medium-range I/rep, DNA binding produces a secondary minimum of reversible aggregation. Reproduced with permission from [138]...

Fig. 32 Unbound particle fraction as a function of temperature for colloids interacting through DNA sticky-end pairing. Experimental data for various sticky end fraction (symbols) are compared with the melting curve for the same sticky end sequence in solution blue line), much broader. The red line shows the hybridization free energy of DNA in solution right axis), while the dashed red line shows the effect of an entropy correction (see discussion in the text). Reproduced with permission from [136]...

The results of such summations predict that the London interaction energy between collections of molecules (e.g. between colloidal particles) decays much less rapidly than that between individual molecules. 

---