Linear Rheology

The rheological properties of glassy liquids are dominated by one or more very long relaxation times and a high modulus. The detailed linear viscoelastic response varies somewhat with the type of liquid. Some inorganic glassy liquids, such as zinc alkali 

---

J. F. Berret, J. Appell, G. Porte. Linear rheology of entangled wormlike micelles. Langmuir 9 2851-2854, 1993. 

G. Eleury, G. Schlatter, and R. Muller, Non linear rheology for long branching characterization, comparison of two methodologies Fourier transform rheology and relaxation, Rheol. Acta, 44, 174—187, 2004. 

These two mathematical Equations (4.59) and (4.60) illustrate an important feature about linear viscoelastic measurements, i.e. the central role played by the relaxation function and the compliance. These terms can be used to describe the response of a material to any deformation history. If these can be modelled in terms of the chemistry of the system the complete linear rheological response of our material can be obtained. 

The approximate treatment described above accounts rather well for the linear rheology of star polymer melts. In fact it has been remarked that the case for the tube model draws its real strength from the results for star polymers rather than for linear chains, where the problems of constraint release and breathing modes are harder to account for (but see Sect. 3.2.4.). However, there are still some outstanding issues and questions ... 

The challenge within our programme is to follow up the consequences of the tube model for the non-linear rheology of branched polymers - would such a theoretical framework lead to any understanding of the special behaviour of, for example, LDPE in complex flows We build up our tools as before in the context of linear polymers. 

Vermonden T, van Steenbergen MJ, Besseling NAM, Marcehs ATM, Hennink WE, Sudholter EJR, Stuart MAC. Linear rheology of water-soluble reversible neodymium(III) coordination polymers. J Am Chem Soc 2004 126 15802-15808. 

Palierne JF (1990) Linear rheology of viscoelastic emulsions with interfacial-tension. Rheol Acta 29 204-214... 

The material behaviors considered will include linear elasticity plus linear or nonlinear creep behavior. The nonlinear case will be restricted to power-law rheologies. In some cases the elasticity will be idealized as rigid. In ceramics, it is commonly the case that creep occurs by mass transport on the grain boundaries.1 This usually leads to a linear rheology. In the models considered,... 

MSI) that uses the same time-dependent Ginzburg Landau kinetic equation as CDS, but starts from (arbitrary) bead models for polymer chains. The methods have been summarized elsewhere. Examples of recent applications include LB simulations of viscoelastic effects in complex fluids under oscillatory shear,DPD simulations of microphase separation in block copoly-mers ° and mesophase formation in amphiphiles, and cell dynamics simulations applied to block copolymers under shear. - DPD is able to reproduce many features of analytical mean field theory but in addition it is possible to study effects such as hydrodynamic interactions. The use of cell dynamics simulations to model non-linear rheology (especially the effect of large amplitude oscillatory shear) in block copolymer miscrostructures is currently being investigated. ... 

The reassuring agreement of ITT results on 5 with the data from simulations and experiments shows that in the ITT approach the correct expansion parameter Pe has been identified. This can be taken as support for the ITT-strategy to connect the non-linear rheology of dense dispersions with the structural relaxation studied at the glass transition. 

Doraiswamy et al. (1991) developed a non-linear rheological model combining elastic, viscous and yielding phenomena for filled polymers. The model predicts a modified Cox Merz relationship for filled melts ... 

Small strain-amplitude frequency sweep is usually used to collect linear rheological data, which are reproduced for repeated measurements within a certain experimental error. Generally, rheology is used to assess the state of dispersion of fillers in the melt. 

It should be noted that dynamic rheology in the linearity regime is sensitive to filler dispersion in polymers. However, a straightforward description of how linear rheology varies with volume fraction is still missing so far [14-20. ... 

Dreiss CA (2007) Wormlike micelles where do we stand Recent developments, linear rheology and scattering techniques. Soft Matter 3 956-970... 

Figure 4.7 A linear rheological illustration for the stress response. Source [61] Reproduced with permission from Elsevier...

---