Dynamic structure factors dilute solutions

Hamau, L., Winkler, R. G., and Reineker, P., Influence of polydispersity on the dynamic structure factor of macromolecules in dilute solution, Macromolecules, 32, 5956, 1999. 

For non-interacting, incompressible polymer systems the dynamic structure factors of Eq. (3) may be significantly simplified. The sums, which in Eq. (3) have to be carried out over all atoms or in the small Q limit over all monomers and solvent molecules in the sample, may be restricted to only one average chain yielding so-called form factors. With the exception of semi-dilute solutions in the following, we will always use this restriction. Thus, S(Q, t) and Sinc(Q, t) will be understood as dynamic structure factors of single chains. Under these circumstances the normalized, so-called macroscopic coherent cross section (scattering per unit volume) follows as... 

Fig. 40a, b. NSE spectra of a dilute solution under 0-conditions (PDMS/ d-bromobenzene, T = = 357 K). a S(Q,t)/S(Q,0) vs time t b S(Q,t)/S(Q,0) as a function of the Zimm scaling variable ( t(Q)t)2/3. The solid lines result from fitting the dynamic structure factor of the Zimm model (s. Tablet) simultaneously to all experimental data using T/r s as adjustable parameter. 

The crossover from 0- to good solvent conditions in the internal relaxation of dilute solutions was investigated by NSE on PS/d-cyclohexane (0 = 311 K) [115] and on PDMS/d-bromobenzene(0 = 357K) [110]. In Fig. 45 the characteristic frequencies Qred(Q,x) (113) are shown as a function of t = (T — 0)/0. The QZ(Q, t) were determined by fitting the theoretical dynamic structure factor S(Q, t)/S(Q,0) of the Zimm model (see Table 1) to the experimental data. This procedure is justified since the line shape of the calculated coherent dynamic structure factor provides a good description of the measured NSE-spectra under 0- as well as under good solvent conditions. 

The dynamics of highly diluted star polymers on the scale of segmental diffusion was first calculated by Zimm and Kilb [143] who presented the spectrum of eigenmodes as it is known for linear homopolymers in dilute solutions [see Eq. (77)]. This spectrum was used to calculate macroscopic transport properties, e.g. the intrinsic viscosity [145], However, explicit theoretical calculations of the dynamic structure factor [S(Q, t)] are still missing at present. Instead of this the method of first cumulant was applied to analyze the dynamic properties of such diluted star systems on microscopic scales. 

Figure 61 presents the Q(Q)/Q2 relaxation rates, obtained from a fit with the dynamic structure factor of the Zimm model, as a function of Q. For both dilute solutions (c = 0.02 and c = 0.05) Q(Q) Q3 is found in the whole Q-range of the experiment. With increasing concentrations a transition from Q3 to... 

Relatively few theoretical studies have been devoted to the conformational characteristics of nonlinear block copolymers in different solvent environments. Burchard and coworkers [284] studied theoretically the behavior of the static and dynamic structure factors for regular star-block copolymers in dilute solutions. They considered different cases where the refractive index (n)s of the solvent takes certain values with respect to the corresponding refractive indices of the inner and outer blocks. A different dependence of the ratios... 

Dynamic Structure Factor and Mean Square Displacement Here we learn how gi(T) obtained in DLS gives an estimate of the diffusion coefficient. We are concerned with dilute solutions here. Hence, gi(T) = Si(k, t). 

M. Benmouna and A. Z. Akcasu. Temperature effects on the dynamic structure factor in dilute polymer solutions. Macromolecules, 11 (1978), 1187-1192. 

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... 

---