Techniques for the characterization of physical gels - Physical Gels from Biological and Synthetic Polymers - page 52

valuable samples that is a major bene t; potentially, measurements can be made over a

whole range of length scales so, for example, analysis of a gel close to the sample edge
can be made. There is also a good deal of work on both whole-cell assemblies and cellular
components (e.g. actin; see Chapter 9 ) where the technique has been able to probe, and
where classical rheology cannot be used.
The disadvantages of the technique are not to be discounted. For a gelling system, it
cannot be assumed that the local strain close to the bead is small, and at higher modulus
the bead size may not be negligible relative to the mesh size of the network. These two
factors can even lead to the tunnelling effect seen, for example, in earlier magnetic
microsphere experiments. Also, the nominal frequency is often quite high, in the kHz
region for some scattering methods, a thus a long way from the required zero-frequency
limit. Overall, the technique is still developing, and remains in the hands of the devel-
opers rather than being available for general applications.
Attempts have been made to compare these methods and classical rheology, but so far
the results are not clear. Some papers show results in agreement (Dasgupta and Weitz,
2005 ), while others do not (Valentine et al., 2004 ). Perhaps most signi cant of all is that

no study of which we are aware has made both classical rheological and PTM measure-
ments on a physical gel during and through the sol

- gel transition.

2.6 Role of numerical simulations

The relationship between the phase diagram and the physical properties of colloidal
solutions is an area where experimental

findings can be addressed by numerical simu-
lations. Simulations may provide strong support for experimentalists in understanding
the origins of the effects they observe, and may also help to predict what should happen
when experimental conditions are changed. For example, for particulate gels, one
fundamental approach to understanding the gel formation mechanism is provided by
the analogy between a colloidal suspension and a molecular liquid such as argon.
Typically, colloidal particles are arranged in a gas-like state at low concentrations and
in a liquid-like, glassy or crystal-like state at much higher concentrations. Interactions
between colloidal particles can often be treated as the sum of pairwise additive potentials,
as in a molecular liquid. When the attraction between colloidal particles is strong
enough and has a long enough range, this attraction leads to a vapour liquid phase

transition as predicted in the well-known van der Waals equation of state, familiar in
thermodynamics.
Numerical simulations on colloidal suspensions are often performed using molecular
dynamics (Allen and Tildesley, 1989 ) and more recently using the Brownian dynamics
(BD) model invented in 1975 by Ermak ( 1975 ). In this model the particles are treated as
hydrodynamically isolated, interacting with solvent via a simple friction coef

-

cient and
Brownian forces only. Hydrodynamic forces between particles are neglected, an assump-
tion that should be valid at least in the absence of external field (Ansell and Dickinson,

1987 ). This simpli ed description permits relatively large systems to be followed for

long enough times to observe any structural changes.