Colloid modulus

Alexander S, Chaikin P M, Grant P, Morales G J, Pincus P and Hone D 1984 Charge renormalisation, osmotic pressure, and bulk modulus of colloidal crystals theory J. Chem. Phys. 80 5776-81... 

Shear modulus, 13 498, 26 777 of dry foams, 12 16 of silicon carbide, 22 526t of vitreous silica, 22 430 of wet foams, 12 17-18 Shear plane, polymer colloid, 20 383, 384 Shear pulverization, of polymer blends, 20 326... 

At high stresses and strains, non-linearity is observed. Strain hardening (an increasing modulus with increasing strain up to fracture) is normally observed with polymeric networks. Strain softening is observed with some metals and colloids until yield is observed. 

What we would like to do is use these thermodynamic properties to calculate an equilibrium elastic moduli. The bulk modulus is by definition the constant of proportionality that links the infinitesimal pressure change resulting from a fractional change in volume (Section 2.2.1). In colloidal terms this becomes... 

The high frequency shear modulus is proportional to the rate of change of force with distance. For colloidal systems this is dominated by the integral expression15... 

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... 

The thermodynamic approach does not make explicit the effects of concentration at the membrane. A good deal of the analysis of concentration polarisation given for ultrafiltration also applies to reverse osmosis. The control of the boundary layer is just as important. The main effects of concentration polarisation in this case are, however, a reduced value of solvent permeation rate as a result of an increased osmotic pressure at the membrane surface given in equation 8.37, and a decrease in solute rejection given in equation 8.38. In many applications it is usual to pretreat feeds in order to remove colloidal material before reverse osmosis. The components which must then be retained by reverse osmosis have higher diffusion coefficients than those encountered in ultrafiltration. Hence, the polarisation modulus given in equation 8.14 is lower, and the concentration of solutes at the membrane seldom results in the formation of a gel. For the case of turbulent flow the Dittus-Boelter correlation may be used, as was the case for ultrafiltration giving a polarisation modulus of ... 

In some case, however, only a flattening of the osmotic modulus curve is observed. Such a case is found with star-branched macromolecules. This observation has rather comprehensively been investigated by Roovers et al. with stars of 64 and 128 arms [172]. The authors give the following explanation. At the point of coil overlap and at somewhat higher concentrations the stars feel the interaction as a quasi colloidal particle. Hence, a steeper increase of the osmotic mod-... 

H.M. Princen and A.D. Kiss Rheology of Foams and Highly Concentrated Emulsions III. Static Shear Modulus. I. Colloid Interface Sci. 112, 427 (1986). 

Equations (5.11), (5.12), and (5.13) allow us to apply some convenient rules of thumb. Eor most hard materials, v 1/3, such that K E and G (3/ )E. Eor elastomers, putties, gels, and colloidal systems, the compressive modulus is much higher than the other moduli, and the system is considered incompressible. In this case, Rs 3G. 

The behaviour and magnitude of the storage and loss moduli and yield stress as a function of applied stress or oscillatory frequency and concentration can be modelled mathematically and leads to conclusions about the structure of the material.3 For supramolecular gels, for example, their structure is not simple and may be described as cellular solids, fractal/colloidal systems or soft glassy materials. In order to be considered as gels (which are solid-like) the elastic modulus (O ) should be invariant with frequency up to a particular yield point, and should exceed G" by at least an order of magnitude (Figure 14.2). 

The final parameter in Equation (4.9) that determines the value of the concentration polarization modulus is the diffusion coefficient A of the solute away from the membrane surface. The size of the solute diffusion coefficient explains why concentration polarization is a greater factor in ultrafiltration than in reverse osmosis. Ultrafiltration membrane fluxes are usually higher than reverse osmosis fluxes, but the difference between the values of the diffusion coefficients of the retained solutes is more important. In reverse osmosis the solutes are dissolved salts, whereas in ultrafiltration the solutes are colloids and macromolecules. The diffusion coefficients of these high-molecular-weight components are about 100 times smaller than those of salts. 

Colloidal boehmite nanorods have been included in a PA-6 matrix to yield a homogeneous dispersion by in situ polymerization.91 At weight fractions up to 9%, improvements in the Young s modulus of the composite and changes in the crystalline morphology of the PA-6 matrix were observed, although fire properties were not reported. 

It should be emphasized that, without any doubt, there are many differences between the double layers formed in LiCl and CsCl electrolytes, particularly at high ionic strengths, which are completely disregarded here. The dissociation constant of Li—AOT is probably different from that of Cs—AOT. In addition, the dependence of the bending modulus on the electrolyte concentration for the two types of electrolytes is unknown. The purpose of this paper was not to provide a set of parameters, which can describe the experiment, but merely to suggest that the DLVO theory, the traditional workhorse of colloid science, still provides reasonable results, when the undulations of the interfeces are taken into account. 

Awad, T.S., Rogers, M.A., Marangoni, A.G. 2004. Scaling behavior of the elastic modulus in colloidal networks of fat crystals. J. Phys. Chem.B. 108, 171-179. 

The stabilising action of the adsorption layers from high molecular substances (protective colloids) is related to the decrease in the forces of molecular attraction. Hence, films from aqueous solution of polyvinyl alcohol obtained between drops of cyclohexane have thickness of 80 nm and respectively, a very low attraction force, in contrast to black films [513]. Along with that the adsorption layers from such compounds possess visco-elasticity properties with modulus of elasticity 104 N m"2, impeding the film thinning and drop coalescence [503]. 

Fig. 5. Schematic illustration of the fluid-to-gel transition observed for colloidal silica inks. The bottom graph is a plot of zeta potential as a function of pH for PEl-coated silica and bare silica microspheres suspended in water. The upper graph is a log-log plot of shear elastic modulus as a function of shear stress for concentrated silica gels of varying strength (o) denotes weak gel pH = 9.5 and ( ) denotes strong gel pH = 9.75 (Ref. 36).

In 1992, Vreeker et al. presented rheological data for aggregated fat networks in the framework of previous fractal theories. These authors indicated that the elastic modulus varied with particle concentration according to a power law, in keeping with the proposed models for the elasticity of colloidal gels. 

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