Colloidal systems modulus

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... 

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). 

Chem. Descrip. Anionic colloidal system containing a high-modulus copolymer of chloroprene and sulfur... 

Chem. Descrip. Anionic, high solids, colloidal system containing a low-modulus polychloroprene homopolymer CAS 9010-98-4... 

In any given material, the relaxation modulus will reflect the response of the material on different timescales. To make a measurement, materials are deformed under a periodic load with frequency w. Then, G and G are measured across a wide range of frequencies (typically three to four decades). Measurements of G and G" can be used to characterize the mechanical properties of soft materials, including polymer networks and colloidal systems. The technique is also known as mechanical spectroscopy. In a viscoelastic material, the elastic modulus will cross over the viscous modulus at the transition point from viscous to elastic bulk behavior and indicates a possible sol-gel transition or the onset of rubbery behavior in a polymer network. 

Another way to look at this result is to consider the modulus as an energy density in a hard-sphere colloidal system the only energy is k T (on the order of 10 J at room temperature) and the only volume is the volume per particle (on the order of 10 m for densely packed, micrometer-size particles). As an aside the moduH of hard (or more accurately stiff ) materials are on the order of 10 Pa, which corresponds to an energy density of the cohesive energy (on the order of a few electron volts, or 10 J) per atomic volume (on the order of a few cubic angstroms, or 10 ° m ). 

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. 

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