Cates model

The higher exponent for the hydrogen bonded compound was consistent with the Cates model for concentration-dependent association (Cates 1987). 

As said before, when entangled worm-like micelles are formed, viscoelastic behavior only follows Cates model at low and intermediate frequencies, indicating that other fast relaxation processes exist (see Figure 12.5). Moreover, at cosurfactant-surfactant ratios above the viscosity maximum, further addition of cosurfactant decreases viscosity and viscoelastic functions up to phase separation, where lamellar liquid crystal appears. As said above, this has been related to the fact that, after the maximum in viscosity, the decrease in spontaneous curvature produces branching of micelles before phase separation [9, 10). 

As has already been said and can be observed in Figures 12.5 and 12.7, results deviate from Maxwellian behavior at high frequencies. An upturn is observed in G", which has been ahributed in other systems to a transihon of the relaxation mode from reptation-scission (Cates model) to breathing or Rouse modes [28, 31]. In the systems presented in this chapter, if the relaxation mechanisms were just living reptation at long times -I- Rouse relaxations at short ones, results should be fitted by Equations 12.3 and 12.4, where a Rouse relaxation mode has been added to the Maxwell model, subscripts M and R referring to Maxwell and Rouse relaxations, respectively ... 

SpartanView and SpartanBuild are lo cated on Learning By Modeling Both programs are CD protected... 

Models for batch culture can be constructed by assuming mechanisms for each phase of the cycle. These mechanisms must be reasonably comph-cated to account for a lag phase and for a prolonged stationary phase. Unstructured models treat the cells as a chemical entity that reacts with its environment. Structured models include some representation of the internal cell chemistry. Metabolic models focus on the energy-producing mechanisms within the cells. 

Moreover, as a consequence of their transient character, a hierarchy of clusters in dynamic equilibrium that may differ in shape and size can be hypothesized [253], Mass, momentum, and charge transport within a cluster of reversed micelles is expected to be strongly enhanced as compared to that among isolated reversed micelles. It has been shown that the dynamics of a network of interacting reversed micelles is successfully described by a model developed by Cates [35,69,254],... 

Ten Cate, A., Bermingham, S. K., Derksen, J. J., and Kramer, H. M. J., Compartmental Modeling of a 1,100 L Crystallizer Based on Large Eddy Flow Simulation . Proceedings of the 10th European Conference on Mixing, Delft, Netherlands, 255-264 (2000). 

Klont B, Damen JJM and Ten Cate JM (1991) Degradation of bovine incisor root collagen in an in vitro caries model. Arch Oral Biol 36, 299-304. 

Fig. 2.4 Structure of goethite. a) Hexagonal close packed anion arrangement and distribution of cations in the octahedral interstices projection on (010) with the cation pairs indicated and the unit cell outlined, b) Projection on (001) with the unit cell and the octahedral arrangementindi-cated. c) Projection down [001]. Dashed circles represent Fe in the next lower layer, d) Arrangement of octahedral double chains. H atoms also shown, e) Ball-and-stick model with unit cell out-...

The complexes obtained can be considered as structural models of two states of catechol oxidase the native met state and the reduced deoocy state. In order to investigate whether the dicopper(II) complex also possesses the functionality of the natural enzyme, for example, if it can perform the catalytic oxidation of cate-... 

Granek, R. and Cates, M.E. (1992) Stress relaxation in living polymers results from a poisson renewal model. /. Chem. Phys., 96,4758-69. 

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