Estimation from viscoelastic

The ability to correctly reproduce the viscosity dependence of the dephasing is a major accomplishment for the viscoelastic theory. Its significance can be judged by comparison to the viscosity predictions of other theories. As already pointed out (Section II.C 22), existing theories invoking repulsive interactions severely misrepresent the viscosity dependence at high viscosity. In Schweizer-Chandler theory, there is an implicit viscosity dependence that is not unreasonable on first impression. The frequency correlation time is determined by the diffusion constant D, which can be estimated from the viscosity and molecular diameter a by the Stokes-Einstein relation ... 

In summary, the QCM-D technique has successfully demonstrated the adsorption of pectin on the BSA surface as well as determined the viscoelastic properties of the pectin layer. As pectin concentrations increase, the adsorbed mass of pectin estimated from the Voigt model show higher values than those estimated from the Sau-erbrey equation because the former takes into account the hydrated layer. But the similar increase of thickness of pectin suggests that the pectin chains form a multilayer structure. In agreement with our previous rheology results, the main elastic character of the pectin layer in terms of Q-tool software tells us the network structure of the pectin layer on the BSA surface. In summary, QCM-D cannot only help to better understand the polysaccharide/protein interactions at the interface, but also to gain information of the nanoscale structure of polysaccharide multilayers on protein surface. 

Williams, Landel, and Ferry described an empirical equation to represent the shift of time and temperature of the viscoelastic parameters, so that a very wide frequency range can be estimated from a narrow range of measurements, limited by the resonance of the apparatus at the high end and by one s patience and sample degradation change at the low-frequency end [26]. 

The use of fractal analysis makes it possible to relate molecular parameters to characteristics of supermolecular structure of polymers. Figure 11.12 illustrates the linear correlation between D and df [dj was estimated from Equation (11.27)] for epoxy polymers. When the molecular mobility is suppressed (D = 1), the structure of the polymer has the fractal dimension df = 2.5, which corresponds to p. = 0.25. The given value of the Poisson coefficient corresponds to the boundary of ideally brittle structure at p< 0.25, the polymer is collapsed without viscoelastic or plastic dissipation of energy [3]. This is fnlly consistent with the Kansch conclnsion [117] stating that any increase in the molecular mobility enhances dissipation of the mechanical energy supplied from the outside and, as a conseqnence, increases plasticity of the polymer. When D = 2 the df value is equal to 3, which corresponds to p = 0.5, typical of the rubbery state. 

A viscoelastic shift factor, as, can be found from the ratio of the experimentally measured zero shear rate viscosity (at test conditions of P, T, and SCF cOTicentratiOTi), to the experimentally measured zero shear rate viscosity (at some reference conditions of Fref> Iref, and reference SCF concentration). Once as is determined experimentally, a master curve can be constmcted by plotting ij/as vs. as 7 where tj is the measured viscosity and y is the measured shear rate. If the fractional free volume, /, is estimated from an equation of state as/ = 1 — pjp, where p is the mixture density and p is the mixture close-packed density, then the shift factor due to the presence of the SCF can be calculated from Eq. (18.3), provided the constant B is known. Experimentally, B for SCF-swoUen polymers has been found to be near unity [130,131], in agreement the universal constants of the WLF equation [132] for the temperature dependence of pure polymers. 

From a single isochrone, neither the temperature dependence of or nor any of the basic viscoelastic functions can be determined. However, if ar(T ) is known from another source e.g., dielectric measurements under circumstances where a judicious identification can be made) or if a reasonable assumption of its form can be made, the isochrone can be transformed to an effective isotherm simply by plotting against war. and the other viscoelastic functions can be obtained by the methods of Chapter 4. In particular, in the transition zone, ar(T ) can be estimated from the WLF equation in one or another of its forms provided Tg is known. 

Abstract We have studied the dynamics of poly(vinyl alcohol) (PVA) in aqueous borax solution by dynamic light scattering (DLS) and dynamic viscoelastic (DVE) measurements. DLS measurement showed the presence of two dominant modes with decaying rates of Ff and Tj (Cf > rj. Different dynamical behaviors were observed above and below a critical concentration, C. The slow mode was manifested to be the diffusive mode for PVA concentration C < Cp, and the relaxation mode for C > Cn. Dynamical correlation length, fg, estimated from Ff exhibited a jump at Cm with increasing C. Detailed analysis revealed the apphcability of the dynamic scaling theory to F for... 

Persistence length and bead friction due to Ferry (Ref. 14). Note that the viscoelastic bead friction is obtained from entangled polymers. Thus for the Rouse diffusion equation used for comparison, we use the long-chain bead friction (Section 4.4). The data are for T = 274 K. For T = 373 K, would change to 1.0 X 10" s because of the reduced bead friction. This reduction however is partially compensated for by the increase in M. M data estimated from Ref. 126. 

In order to estimate the cloud point from viscoelastic oscillatory measurements, we propose to extrapolate the critical temperature to -> 0,... 

Lipatov et al. [116,124-127] who simulated the polymeric composite behavior with a view to estimate the effect of the interphase characteristics on composite properties preferred to break the problem up into two parts. First they considered a polymer-polymer composition. The viscoelastic properties of different polymers are different. One of the polymers was represented by a cube with side a, the second polymer (the binder) coated the cube as a homogeneous film of thickness d. The concentration of d-thick layers is proportional to the specific surface area of cubes with side a, that is, the thickness d remains constant while the length of the side may vary. The calculation is based on the Takayanagi model [128]. From geometric considerations the parameters of the Takayanagi model are related with the cube side and film thickness by the formulas ... 

Bubbles are formed instantaneously. This conclusion made in [33] is based on estimates taken from earlier works [37]. As seen from the above cited works by S. E. Sosin et al., this is not always true viscoelastic liquids under triaxial stretching stress are not destroyed instantly. The existence of an induction period may produce a considerable effect on foam growth kinetics upon free foaming, when pressure is lowered instantaneously from P > Pcr to P < Pcr in a melt with dissolved gas. However, it would appear that microfaults in polymer melts, which are caused by factors... 

Different viscoelastic materials may have considerably different creep behavior at the same temperature. A given viscoelastic material may have considerably different creep behavior at different temperatures. Viscoelastic creep data are necessary and extremely important in designing products that must bear long-term loads. It is inappropriate to use an instantaneous (short load) modulus of elasticity to design such structures because they do not reflect the effects of creep. Viscoelastic creep modulus, on the other hand, allows one to estimate the total material strain that will result from a given applied stress acting for a given time at the anticipated use temperature of the structure. 

Distributions of relaxation or retardation times are useful and important both theoretically and practicably, because // can be calculated from /.. (and vice versa) and because from such distributions other types of viscoelastic properties can be calculated. For example, dynamic modulus data can be calculated from experimentally measured stress relaxation data via the resulting // spectrum, or H can be inverted to L, from which creep can be calculated. Alternatively, rather than going from one measured property function to the spectrum to a desired property function [e.g., Eft) — // In Schwarzl has presented a series of easy-to-use approximate equations, including estimated error limits, for converting from one property function to another (11). 

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