Viscosity macroscopic

Since [n] is a physically measurable quantity and is more directly relatable than the usual SEC calculated Mn and Mw values to the macroscopic viscosity parameters of the polymer solution, a routine SEC-[n] method brings SEC a step closer to practical evaluation of the strength and processibility of different polymer samples. 

In summary, the chain dynamics for short times, where entanglement effects do not yet play a role, are excellently described by the picture of Langevin dynamics with entropic restoring forces. The Rouse model quantitatively describes (1) the Q-dependence of the characteristic relaxation rate, (2) the spectral form of both the self- and the pair correlation, and (3) it establishes the correct relation to the macroscopic viscosity. 

On the other hand, it was found that the microscopic parameter pH(c) exhibits close similarities to the macroscopic viscosity r (c)/r s of a low molecular mass (M 7.400 g/mol) PDMS/d-chlorobenzene system at 373 K. For that low molar mass the terminal Zimm time tz [see Eq. (80)] is comparable to the time scale of the NSE experiment. Thus, the macroscopic viscosity can relax towards... 

Fig. 66. Concentration dependence of r H(c)/r s result of seperate fits o results of viscosity measurements on PDMS solutions (Mw = 7400). The result of the simultaneous fit considering the linear term in r H(c) = r 0(l + [r ]c + kH[r ]2c2) is given by the solid line the inclusion of a quadratic term leads to the dashed line. The point-dashed line indicates the macroscopic viscosity for M = 60000 g/mol. (Reprinted with permission from [40]. Copyright 1984 American Chemical Society, Washington)...

The term microviscosity is often used, but again no absolute values can be given, and the best we can do is to speak of an equivalent viscosity, i.e. the viscosity of a homogeneous medium in which the response of the probe is the same. But a difficulty arises as to the choice of the reference solvent because the rotational relaxation rate of a probe in various solvents of the same macroscopic viscosity depends on the nature of the solvent (chemical structure and possible internal order). 

Fig. 4.3 Scaling representation of the spin-echo data at the first static structure factor peak Qmax- Different symbols correspond to different temperatures. Solid line is a KWW description (Eq. 4.8) of the master curve for 1,4-polybutadiene at Qmax=l-48 A L The scale r(T) is taken from a macroscopic viscosity measurement [130]. Inset Temperature dependence of the non-ergodicity parameter/(Q) near the lines through the points correspond to the MCT predictions (Eq. 4.37) (Reprinted with permission from [124]. Copyright 1988 The American Physical Society)...

When the temperature is increased above the 0-temperature the enhanced local viscosity at higher concentration drops. The variation is the same as observed for the macroscopic viscosity [329]. In [328] polyisoprene (PI) and PS in different solvents have also been investigated and the authors observe that the slopes of the concentration dependence of the scaled local viscosities for PS and PI have a ratio of 1.7, which matches the value of the concentration ratio either on the Kuhn length (1.6) or the persistence length (1.7) for the two polymers. 

Bylaite, E., Meyer, A.S., and Adler-Nissen, J. Changes in macroscopic viscosity do not affect the release of aroma aldehydes from a pectinaceous food model system of low sucrose content, J. Agric. Food Chem., 51(27) 8020-8026, 2003. 

It may be seen that the mobilities of the abnormally conducting ions in BuSO and D2S04 are quite comparable with those of the corresponding ions in HgO and B20 despite the fact that the viscosity of sulphuric acid is 27 5 times that of water at 25°. The macroscopic viscosity evidently has little effect on the rate of the proton-transfer conduction process. It is interesting to note that in both water and sulphuric acid, the mobilities of the abnormal ions are decreased by substituting deuteri urn for hydrogen, and that in each case the mobilities of the anions are less than those of the corresponding cations. 

It was also assumed that internal times such as xe are proportional to the macroscopic viscosity xe = t]/ri0 (xe)0 (xe)0 or x0 is the mean entanglement time at equilibrium. The viscosity was then calculated from the expression tj = v/y2,... 

Any change in the medium, i.e. the solvent, the concentration, the pH value, and in the temperature will affect the mobility of the molecules and hence also the spin-lattice relaxation. However, few systematic studies have so far been performed on the concentration dependence or on the precise influence of the macroscopic viscosity, the main reason, in the case of 13C, lying in the need for highly protracted measurements in concentration studies. Moreover, little is known about the pH dependence of 13C relaxation [188], Nevertheless, the concentration dependence of 13C relaxation is apparent in the case of saccharose (Table 3.20) [166], and intramolecular hydrogen bonds can be detected by measuring the concentration dependence of Tx [189]. 

As opposed to the liquid-crystal transformation, the liquid-glass transformation is not a phase transition and therefore it can not be characterized by a certain transition temperature. Nevertheless, the term "the vitrification temperature , Tv, is widely used. It has the following physical meaning. As opposed to crystallization, vitrification occurs when the temperature changes continuously, i.e. over some temperature interval, rather than jump-wise. Inside this interval, the sample behaves as a liquid relative to some of the processes occurring in it, and as a solid relative to other processes occurring in it. The character of this behaviour is determined by the ratio between the characteristic time of the process, t, and the characteristic relaxation time of the matrix, x = t//G, where tj is the macroscopic viscosity and G is the matrix elasticity module. If t x, then the matrix should be considered as a solid relative to the process, and if t > x it should be considered as a liquid. The relation tjx = 1 can be considered as the condition of the matrix transition from the liquid to the solid (vitreous) state, and the temperature Tv at which this condition is realized as the temperature of vitrification. Evidently, Tv determined by such means will be somewhat different for the processes with different characteristic times t. However, due to the rapid (exponential) dependence of the viscosity rj on T, the dependence of Tw on t (i.e. on the kind of process) will be comparatively weak (logarith-... 

On the basis of these considerations it can be expected that the Einstein Stokes model will be applicable for vitrified solutions consisting of the particles with comparable sizes. In other words, for the order of magnitude estimations of the microscopic translational mobility of molecules in such solutions, the value of the diffusion coefficient, which is obtained by using the macroscopic viscosity t] in eqn. (1), can be used. 

This indicates that kinetic parameters of orientational process are defined mostly by the macroscopic viscosity of a polymer. The substantial difference in mesophase... 

Moreover, the macroscopic viscosity is related according to Einstein58 and Simha78 to the volume fraction () of the particle in the total volume of the system,... 

Therein, D-1 is the positive definite, isotropic, fourth order viscous compliance, where r/ s and (s are the macroscopic viscosity parameters, D, , is the inelastic solid deformation rate and = F, 1 rfEQ F 71 is the corresponding non-equilibrium stress tensor. Furthermore, the superscript ( ) indicates the belonging to the intermediate configuration. 

The rate of diffusion in ELs appears to vary inversely with macroscopic viscosity, as expected, but there do appear to be significant effects arising from the chemical structure of solute and solvent species. 

Figure 19 Parent bleach kinetics (open circles) of Re2(CO)io in (a) hexanes, (b) CC14, (c) CHCI3, and (d) CH2CI2. Fits to a diffusion model to account for geminate recombination are shown as solid lines. Except for the macroscopic viscosity, identical molecular parameters (see Fig. 20) are used for all the solvents studied.

An additional information relates to the microviscosity of the PP solutions. Their macroscopic viscosity is very high. However, the Ps reaction rate constant measured above Rc0 is only slightly lower than what it is in water on a microscopic scale, the diffusive properties of Ps inside the net created in the PP solution by the polymeric chains are similar to those in neat water... 

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