Dynamic structure factor large

In contrast to -conditions a large number of NSE results have been published for polymers in dilute good solvents [16,110,115-120]. For this case the theoretical coherent dynamic structure factor of the Zimm model is not available. However, the experimental spectra are quite well described by that derived for -conditions. For example, see Fig. 42a and 42b, where the spectra S(Q, t)/S(Q,0) for the system PS/d-toluene at 373 K are shown as a function of time t and of the scaling variable (Oz(Q)t)2/3. As in Fig. 40a, the solid lines in Fig. 42a result from a common fit with a single adjustable parameter. No contribution of Rouse dynamics, leading to a dynamic structure factor of combined Rouse-Zimm relaxation (see Table 1), can be detected in the spectra. Obviously, the line shape of the spectra is not influenced by the quality of the solvent. As before, the characteristic frequencies 2(Q) follow the Q3-power law, which is... 

The electron diffraction study was complemented by an all-electron theoretical calculation of Lu, Wei, and Zunger (LWZ) (1992), using the local density approximation for the exchange and correlation terms in the Hamiltonian. They find agreement within x0.6% between the calculated and dynamic structure factor values for the lowest three reflections, (100), (110), and (111). But for (200), with sin 0/A = 0.3464 A-1, the discrepancy is as large as 1.7%. The discrepancy is attributed to insufficiently accurate knowledge of the temperature factors in this diatomic crystal, which affect the derivation of the X-ray structure factor from the electron diffraction measurement, as well as the calculation of the dynamic theoretical structure factors needed for the comparison with experiment. For the monoatomic Si crystal for which the B values are well known, the agreement is... 

Recently, the PDF method was extended to describe the local dynamics of disordered materials (Dmowski W, Vakhrushev SB, Jeong I-K, Hehlen M, Trouw F, Egami T (2006) Abstracts American conference on neutron scattering, St. Charles, IL, 18-22 June 2006, unpublished). The total PDF is obtained by the powder diffraction method so that S(Q) includes both elastic and inelastic intensities. To determine the dynamics we have to use an inelastic neutron scattering spectrometer and measure the dynamic structure factor, S(Q,a>), over a large Q and co space, and Fourier-transform along Q to obtain the dynamic PDF (DPDF). While the interpretation of the DPDF is a little... 

It has been discussed in the previous section that the long-time part in the memory function gives rise to the slow long-time tail in the dynamic structure factor. In the case of a hard-sphere system the short-time part is considered to be delta-correlated in time. In a Lennard-Jones system a Gaussian approximation is assumed for the short-time part. Near the glass transition the short-time part in a Lennard-Jones system can also be approximated by a delta correlation, since the time scale of decay of Tn(q, t) is very large compared to the Gaussian time scale. Thus the binary term can be written as... 

The long-time tail in the solvent dynamic structure factor is responsible for the large value of the viscosity in supercooled liquid. The solute dynamics for smaller solutes are faster than that of the solvent. Thus, the solute dynamics is decoupled from this long-time tail of the solvent dynamic structure factor. 

Therefore, for the large values of k that play a role in the calculation, the dynamic structure factor is given by... 

As mentioned above, careful numerical inspection of the k integral in Equation (21) shows that all of the contribution to the integral occurs for k sufficiently large that Equation (26) is the appropriate form for the dynamic structure factor for evaluating the integral. Equation (23) is never used in the calculations, but it was presented to motivate the form of Equation (26). 

The aqueous LiCl solution with the composition of LiC1.6.0H2O was prepared in the same way as described for the X-ray samples. In the aqueous solution the proton ( H) has a very large incoherent scattering cross section the observed differential scattering cross section can be approximated to the incoherent dynamic structure factor through... 

Since rodlike polymers have a large optical anisotropy, they have a significant depolarized light scattering, which is particularly suitable for studying rotational diffusion. In the small-angle regime k L 1, the dynamic structure factor is written as ... 

In the last decade however, the dynamics of the exchange and correlation hole became an important topic, in view of the more accurate measurements of the dynamical structure factor at large wave vector, and because sum rules and causality arguments revealed that a static treatment of G[q, w)... 

Reptation quantum Monte Carlo (RQMC) [15,16] allows pure sampling to be done directly, albeit in common with DMC, with a bias introduced by the time-step (large, but controllable in DMC e.g. [17]) and the fixed-node approach (small, but not controllable e.g. [18]). Property estimation in this manner is free from population-control bias that plagues calculation of properties in diffusion Monte Carlo (e.g. [19]). Inverse Laplace transforms of the imaginary time correlation functions allow simulation of dynamic structure factors and other properties of physical interest. 

When a large rigid sphere is suspended in a solvent, its dynamical properties, such as the velocity autocorrelation function, mean square displacement, dynamic structure factor, etc., are well known, and form the basis of suspension theory from Einstein onwards. 

In the limit of large wavevectors, the length scale probed is smaller than the blob size and the portion of chain of interest exhibits individual chain behavior. In particular, the initial decay rate of the dynamical structure factor has the same value as in a dilute solution... 

The discussion of the large- tail in S(q) in Section 7.4.1.1, which is characteristic for a short-ranged attraction, enables one to formulate a simplified theory of bond formation within MCT with the result that the long-time limit of the dynamic structure factor is controlled by a single interaction parameter, F = fP-(p/b. Bond formation occurs at T, = 3.02... [34]. For small values of F, the dynamic structure factor decays to zero for all wavevectors. Physically, this means that concentration fluctuations decay into equilibrium at long times, just as expected for a colloidal fluid. However, for F > F, the solutions yield a nonzero glass form factor, namely, the system arrests in a metastable state. This simple result requires the approximate expression for S(q) given above and needs to be replaced by a full numerical solution whenever this approximation fails. 

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