Viscosity and relaxation

Liquids lower the glass transition temperature, and according to the WLF theory, the viscosity and relaxation times are decreased. 

Williams,M.C. Concentrated polymer solutions. Part II. Dependence of viscosity and relaxation time on concentration and molecular weight. A.I.Ch.E. J. 13, 534-539 (1967). 

The formation of strong hydrogen bonds in glycerol leads to a very high viscosity and also a long relaxation time (see Table 1.2) however, a comparison with the data for alcohols with comparable volumes suggests that the relationship between viscosity and relaxation time is not the simple linear one implied by the Debye expression. 

Silverman developed Maxwell s relation between viscosity and relaxation time 6.VIIIE), and by combining Batschinsky s equation ( 5.VIII E) and McLeod s equation for surface tension, a ( 4.VIIIG), found ... 

In practice, the gel point is often difficult to determine with sufficient precision to test these scaling laws. Instead, viscosity and relaxation time can be correlated with weight-average molar mass (M e with 7 1.82) [Eq. (6.103)] ... 

The relationship between viscosity and relaxation modulus is given by equation (3-90) and (4-7). For the latter... 

Before discussing the Kerr measurements on the solutions, we briefly outline how the size of the polymers was obtained from viscosity and relaxation data. Two well-known expressions which are useful in interpreting these data are the Simha and Burgers equations. The Simha equation (20) relates the intrinsic viscosity of a solution of elongated ellipsoids... 

WilhamsM. C. Concentrated Polymer Solutions Part II. Dependence of Viscosity and Relaxation Time on Concentration and Molecular Weight /M. C. Williams, A. I. Ch. E. Journal. 1967, v. 13, Ra 3 534-539. 

MICROWAVE ABSORPTION AND MOLECULAR STRUCTURE OF POLAR MOLECULES IN SOLUTIONS. AVERAGED MUTUAL VISCOSITIES AND RELAXATION TIMES OF SOME SUBSTITUTED BENZENES. 

However Gleeson e.a. [60] note that molecular elasticity may play an indirect role, since below a threshold value of the Deborah number, bands do not form at all. For example, for a solution of PBG of molecular weight 186000 this critical shear rate was about 40 s , while for a solution of PBG of molecular weight of 86000 bands were formed at a shear rate of 0.25 s . For four solutions of widely varying viscosity and relaxation time, a critical value of De 0.01—0.04 was obtained. Thus molecular elastic effects during shear seem to be necessary to produce the texture that in turn drives band formation after shearing ceases. ... 

Glass Science andTechnology,Vol. 1 Glass-Forming Systems, 1983 ibid. Vol. 3 Viscosity and Relaxation, edited by D. R. Uhhnann and H. J. Kreidl (Academic Press, Inc., Corpus Christie, 1986). 

It can be noted that the first-order corrections for the reaction rate coefficients depend on the same functions and G ij which define the additional diagonal elements of the pressure tensor connected to the bulk viscosity and relaxation pressure. 

Kustova, E. (2009). On the role of bulk viscosity and relaxation pressure in non-equilibrium flows, in T. Abe (ed.). Rarefied Gas Dynamics 26th International Symposium, Vol. 1084 of AIP Conference Proceedings, pp. 807-812. 

We consider here a solution (or melt) with two types of polymer chains, A and B, and a slight incompatibility between A and B. We want to investigate the dynamics of the fluctuations of concentration <1> near the critical point in the one-phase region. Experimentally it will help if we add a fraction of solvent to the AB mixture, thereby decreasing the viscosities and relaxation times. However, for simplicity here we consider [Pg.238]

Figure 10.5 shows a simulation of the poly(ethylene terephthalate) pilot plant experiments of George that were discussed in Section 7.4.4. PET is a difficult material to work with, and it has very small G and normal stresses. No uniform uniaxial extensional data are available. As noted in Chapter 7, Gregory has published extensive data on the zero-shear viscosity and relaxation time of PET, where the relaxation time is defined as the reciprocal of the shear rate at which non-Newtonian... 

Gagon and Denn estimated the linear viscoelastic parameters for two modes from Gregory s viscosity and relaxation time data by choosing a wedge spectrum, in which Gi = rjo/NXi, where N is the number of relaxation modes. They arbitrarily chose X2/X1 = 5. The parameter f was taken to be zero to reflect the shear insensitivity of the viscosity of PET, while e was taken to be 0.015. The results were insensitive to in the range from 0 to 0.015, so the simulation was in effect carried out for a two-mode Maxwell model. The results depended on the choice of the coefficient for the air drag coefficient, but the variation was small in the range 0.37 to 0.6. 

Free surface flows with viscosity, Tyvand P. A, WIT Press/Computational Meehan., 1997, 84 Glass science and technology viscosity and relaxation, Uhlmann D.R,... 

Nonlinear Mechanical Models It is possible to represent nonlinear behavior by introducing nonlinear spring and damper elements into the derivation of differential stress-strain relations. For example, for the four-parameter fluid shown in Fig. 10.5, the spring moduli, damper viscosities and relaxation times are functions of stress, i.e.,... 

The mass exponent value x decreases as the temperature increases to reach a value of 3-45 at 55 C when cyclohexane can be considered as a good solvent for polystyrene. One has to note that the exponent x is larger than the predicted va e x = 3. Self-diffusion coefficient measurements lead to Dg -- Af. Assuming that is the time required for the polymer chain to diffuse on a distance of order of its radius of gyration R - (R = Tffig) we should have Present results for relaxation time therefore disagree with self-diffusion coefficient measurements. From viscosity and relaxation time measurements, we can deduce the shear elastic modulus at short times G We find that G is mass-independent and increases with concentration ... 

In the semidiluted entangled regime, the viscosity and relaxation time change to [94] ... 

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