Colloidal particles modulus

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-... 

The elastic modulus theory of Jacket Jacket (1964) has proposed that protective layers around a colloidal particle can be considered to be similar to a cross-linked gel network and that the mechanical properties of these gel layers determine their protective action, rather than their physicochemical properties. If the modulus of the layers is sufficiently large, deformation in a Brownian collision (see Fig. 10.4) is such as to prevent the van der Waals attraction from coming into play. Any viscous drainage losses of molecules of the dispersion medium from the gel layer would weaken its elastic response and so reduce the repulsion, as would any viscous processes in the layer that dissipate collisional energy as heat 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... 

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. 

We have also conducted adhesion measurements between real CMP abrasive particles (not model particles) and various surfaces as well as particle hardness and elastic modulus measurements, using colloidal AFM and nanoindentation AFM, respectively, in an attempt to correlate CMP defectivity with mechanical and adhesion properties of CMP abrasives [77,78]. For example, in a carefully designed experiment, we have been able to demonstrate that softer particles, indeed, result in fewer scratches [78]. 

Probably this equation remains valid for small deviations from equilibrium ). For colloid scientists, [4.5.30] is not unfamiliar, because in three dimensions the modulus is related to the derivative of the disjoining pressure /7(h) with respect to the distance h between interacting particles and where /7(h) is, in turn, the derivative of the Gibbs or Helmholtz energy of interaction. There is a formed difference... 

The MCT-ITT approach thus provides a microscopic route to calculate the generalized shear modulus g t, y) and other quantities characteristic of the quiescent and the stationary state under shear flow. While MCT has been reviewed thoroughly, see, e.g., [2, 38, 39], the MCT-ITT approach shall be reviewed here, including its recent tests by experiments in model colloidal dispersions and by computer simulations. The recent developments of microscopy techniques to study the motion of individual particles under flow and the improvements in rheometry and preparation of model systems, provide detailed information to scrutinize the theoretical description, and to discover the molecular origins of viscoelasticity in dense colloidal dispersions even far away from thermal equilibrium. 

The importance of the amorphous glassy microstructure of soft particle dispersions is reflected by the great influence that the particle elastic modulus has on yielding and flow. The yield stresses of colloidal pastes and of emulsions scales like the shear modulus [13, 133, 134]. In Sect. 5, the flow curves of soft particle glasses will be shown to exhibit a remarkable universal behavior in terms ofa unique microscopic time scale tliat involves the shear modulus [13]. In Sect.4, the slip velocity... 

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