Correlation length dynamic

Q2 behavior takes place at decreasing Q. The position of the crossover point Q (c) is a direct measure of the dynamic correlation length (c) = 1/Q (c). The plateau value at low Q determines the collective diffusion coefficient Dc. A simultaneous fit of all low Q spectra where a simple exponential decay was found led to the concentration dependence and the numerical values of Dc... 

The result is shown in Fig. 62 where the different Dc values, obtained from separate fits at each concentration, are also presented. The dynamic correlation length (c)/A = (3.4 + 0.7) c 067 005 is of the same order of magnitude as the value obtained from a static experiment on the PS/d-cyclohexane system [104]. The exponents for the concentration dependence of Dc and (c) are in agreement... 

The Stokes-Einstein equation relates the cooperative diffusion coefficient (Dc) to the bare dynamic correlation length ( d ) defined in terms of the temperature-dependentviscosity ofthe solvent (ri )in Eq. 12 ... 

Despite numerous efforts, the dynamic properties of semidilute polymer solutions in organic solvents at T < 0 are poorly understood. To our knowledge, only one DLS experiment has been performed so far in the poor solvent domain of supercritical polymer solutions [4]. The most important issue which is yet to be resolved is whether the viscosity of the solvent or that of the solution should be used to calculate the dynamic correlation length from the Stokes-Einstein Eq.l2 [31]. 

Figure 9. The bare dynamic correlation length Figure 10., d, and 5 for solution PS (Eq.l2) vs. X. The symbols are spelled ontin the (M 5700)inCH-d. The sohd and dashed arrows insets. show the static and dynamic crossovers.

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... 

Fig. 2 Plot of the dynamical correlation length h estimated from Z>c using the Einstein-Stokes relationship against PVA concentration C...

The fast mode was the diffusive mode for all solutions since Ft/q was independent of q. The cooperative diffusion coefficient >c could be estimated as an average of Ff/q and the dynamical correlation length iJh was estimated using the Einstein-Stokes relationship,... 

The extrapolated value Z)(0) to the PS concentration of zero is plotted against O (see Fig. 17) [16]. For PS with any molecular weight, there are no visible differences between die PS in the PDMS gel and the solution. Thus, the chemical crosslinks have almost no influence on the diflhision of the probe polymer. The fluid dynamic radius obtained from the diffusion coefficient of PS in flie THF dilute solution was either smaller or the same as the dynamic correlation length calculated firom the concentration of PDMS. In the region where is greater, a difference between the gel and solution is expected to be observed. Unfortunately, preparation of such samples is difficult and no experimental results have yet been reported. The extrapolated value of PS of = 4140 and 7620 at = 0 equals approximately that of ttie diffusion coefficient of PS in THF. However, for PS wifli A/ = 14,100, the extrapolated value to = 0 is half that in THF. For the PS witii M, = 14,100,7 , > at > 1, it is inappropriate to extrapolate the value of 7 , I when approaching = 0. 

Table Vlll lists the norms of internal, semi-internal, and external excitation amplitudes obtained in the CASSCF(6e, 5o, NO)/L-CTSD calculations with the 6-3IG basis set. The percentage of retained amplitudes for internal and semi-internal excitations are also shown in the table. The norm of the external amplitudes, which primarily contribute to dynamic correlation, does not fluctuate much across the potential curve. The maximums of the internal and semi-internal amplitudes are found at the intermediate bond region. More internal and semi-internal excitation operators are retained as the bond length ron is increased.

The attachment-detachment model (see Fig. lb) can be described by using the probability function Eq. (23) but now assuming that the correlation length, L. Physically this means that infinite range conserved-order-parameter dynamics is the same as non-conserved order parameter dynamics. In that case the normalized... 

As regards the dynamics of the fluid composition, the experimental results are very difficult to understand [66,67]. We expect that, if the pore size b is very large, the diffusion constant should first behave as in bulk near-critical fluids, but it will cross over to a value of order kBTZb/Gntis 2, being the correlation length (see Eq. (6.67) below). It would also be interesting to find whether the time correlation function of c would be influenced by structural relaxation of network (see Sect 6.2). 

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