Viscoelasticity and Diffusion

We can rewrite Eq. (8.20) as given by the Doi-Edwards theory for the diffusion constant Dq as 

Shortly after the Doi-Edwards theory was published, Graessley proposed using the viscosity value at Me to calculate the K value on the basis of the Rouse theory 

As shown by the above analyses of the viscoelasticity and diffusion data in terms of the ERT, the paradox between the scaling relations r]o oc M and Dg oc predicted by the pure reptational model, that occurs in their comparison with the experimental results, is resolved. Furthermore, the relation between viscoelasticity and diffusion as given by the ERT is quantitatively supported by the data of polystyrene. The analysis of the viscosity data at Me in relation to the Kd value obtained from the diffusion measurements also supports the ERT. Considering the different nature of the experiments of viscoelasticity and diffusion, the quantitative agreement between these two kinds of data as analyzed in terms of the ERT is remarkable and thus indeed significant. 

The existence of entanglement in between Mg and Mg will be further supported by the study in Chapter 11 — the direct observation of the onset of entanglement at Mg by monitoring the initial deviation of the viscoelastic 

Valnes in a bracket are calculated from the shown valnes at the other temperature using the ratio of the two average K values. 

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For example, at MW = 4 X 10, c = 12 g/liter, and at MW = 5 X 10, c " = 62 g/liter. A polymer solution with concentration c > c is called a semidilute solution because mass concentration is low yet repulsive interactions between solutes are strong. Thermodynamics, viscoelasticity, and diffusion properties of semidilute polymer solutions have been studied extensively since the 1960s. 

W Graessley. Viscoelasticity and diffusion in entangled polymer melt. In M Nagasawa, ed. Molecular Conformation and Dynamics of Macromolecules in Condensed Systems pp (163-184). Amsterdam Elsevier, 1988. 

Gell B. Carol, Krishnamoorti Ramanan, Kim Eugene, Graessley W. William, and Fetters J. Lewis. Viscoelasticity and diffusion in miscible blends of saturated hydrocarbon polymers. Rheol. Acta. 36 (1997) 217-228. 

Diffusion of moisture or solvent into the adhesive can significantly change the state of the stress field and hence the reliability of the bonded joint. Various researchers modeled the effects of viscoelasticity and diffusion in the analysis of bonded joints.( 9-42) in all these works, either the effects of moisture or the coupling between the viscoelastic stress field and the moisture/solvent concentration were not considered. In general, the diffusion coefficient is a function of the dilatational strain, temperature field, and solvent concentration. Recently,... 

S. Roy and J. N. Reddy, Finite-element models of viscoelasticity and diffusion in adhesively bonded joints, Int. J. Numer. Methods Eng. 26, 2531-2546 (1988). 

Lin Y-H (1985) Comparison of the pure reptational times calculated from linear viscoelasticity and diffusion motion data of nearly monodisperse polymers, Macromolecvles 18 2779-2781. 

A theory has been developed for the viscoelasticity and diffusion of miscible fluid blends of entangled linear polymers with dissimilar chemical structure. The architecture and molecular dynamics of the... 

Besides kinetic applications, which are still to be fully realized, hydro-dynamic modulation is useful for Schmidt number and diffusion coefficient measurements not only in Newtonian fluids but also in viscoelastic polymer solutions (Ostwald fluids) [291]. 

Abstract The discussion of relaxation and diffusion of macromolecules in very concentrated solutions and melts of polymers showed that the basic equations of macromolecular dynamics reflect the linear behaviour of a macromolecule among the other macromolecules, so that one can proceed further. Considering the non-linear effects of viscoelasticity, one have to take into account the local anisotropy of mobility of every particle of the chains, introduced in the basic dynamic equations of a macromolecule in Chapter 3, and induced anisotropy of the surrounding, which will be introduced in this chapter. In the spirit of mesoscopic theory we assume that the anisotropy is connected with the averaged orientation of segments of macromolecules, so that the equation of dynamics of the macromolecule retains its form. Eventually, the non-linear relaxation equations for two sets of internal variables are formulated. The first set of variables describes the form of the macromolecular coil - the conformational variables, the second one describes the internal stresses connected mainly with the orientation of segments. 

The FID results in toluene show the need for a theory of vibrational dephasing that works throughout the range from low-viscosity liquid to solid glass. It is also important that such a theory address the different roles of inertial and diffusive solvent dynamics explicitly. We developed the viscoelastic (VE) theory of vibrational dephasing to address these issues (8). 

Acoustic wave (AW) devices are ideally suited to thin film characterization due to their extreme sensitivity to thin film properties [10]. The sensitivity of AW devices to a variety of film properties (see Chapter 3), such as mass density, viscoelasticity and conductivity, makes them versatile characterization tools. The ability to rapidly monitor changes in device responses resulting from changes in thin film properties permits their use for monitoring dynamic processes such as film deposition, chemical modification (e.g., photo-polymerization, corrosion), and diffusion of species into and out of films. 

The use of thickeners such as H EC and xanthan gum this will increase the low shear rate viscosity of the medium and hence slow down the diffusion of the small particles, preventing their entry into the oil droplets. These thickeners can produce gels in the continuous phase that is viscoelastic, and this can prevent particle diffusion. 

Water, sodium ion, and hydroxide ion concentrations have been measured within the membrane phase as a function of bulk caustic solution concentration and temperature. These internal membrane concentrations are important because of their influence on the membrane polymer morphology, structural memory, plasticity and the resultant effects on its internal resistance, viscoelasticity and material transport. In addition, the self-diffusion coefficient of the sodium ions in various Nafion membranes has been measured as a function of temperature and external caustic concentration... 

Reptation theory has been developed further by Doi and Edwards (1986) and is being applied to both viscoelastic and solution behavior. It has been shown that for a chain moving in the melt, over time-scales that greatly exceed the lifetime of the tube X, a reptation self-diffusion coefficient D p, can be measured, which is inversely proportional to rP-, i.e., the diffusion law is... 

Martiel I, Sagalowicz L, Mezzenga R. Viscoelasticity and interface bending properties of lecithin reverse wormlike micelles studied hy diffusive wave spectroscopy in hydrophobic environment. Langmuir. 2014 30(35) 10751-10759. 

Until now, open channel viscoelastic eddy diffusivity measurements have not been available. Only few measurements were reported with water by Jobson, et al. C21) and Ueda, et al, C22) who measured the eddy diffusivity of momentum in wide open channels as shown in Fig, 3. 

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