Solution structure factor

In order to extract information on the single chain structure from SLS data, it is necessary to fulfill the condition of a single mode scattering, similarly to the extraction of molecular weight and second virial coefficient from SLS data (see Sec. VII). A further condition is that the scattering from polyions should not be influenced by intermolecular interference due to intermolecular interactions, i.e., the solution structure factor S(0) = 1. In this case the total... 

FIG. 19 Schematic representation of the radial pair distribution function g(r) and corresponding solution structure factor S(q) for two cases discussed in the text liquidlike structure (left) and correlation hole effect (right). See text for more details. 

In the thermodynamic limit (< ->0), measurement of the solution structure factor is a good method for obtaining the osmotic second virial coefficient. Measmements of the excess Rayleigh ratio as a function of concentration yield the molecular weight of the solute within this limit. The usual procedure is to plot the quantity Kc/AR c) against concentration ... 

For the Flory-Huggins theory, tire solution structure factor is given by... 

By changing from the simplest to larger aliphatic and cyclic ketones, structural factors may be introduced which favor alternative unimolecular primary photoprocesses or provide pathways to products not available to the simple model compound. In addition, both the increase in molecular size and irradiation in solution facilitate rapid vibrational relaxation of the electronically excited reactant as well as the primary products to thermally equilibrated species. In this way the course of primary and secondary reactions will also become increasingly structure-selective. In a,a -unsym-metrically substituted ketones, the more substituted bond undergoes a-cleavage preferentially. 

Usually, the cychc isomers 272 are preferred in the sohd state. X-Ray structural evidence was obtained for compound 272 [R = COPh, R = Me, R = R" = H, R = CF3 X = O (92KK1184)]. In solution, the cyclic and ring-opened isomers are found in equihbria in ratios depending on polarity of the solvent and structural factors (see 88KGS3 95ZOB705 96AHC(66)1 for reviews). 

Crump MP, Gong JH, Loetscher P et al (1997) Solution structure and basis for functional activity of stromal cell-derived factor-1 dissociation of CXCR4 activation from binding and inhibition of HIV-1. EMBO J 16 6996-7007... 

The recollless fraction, that Is, the relative number of events In which no exchange of momentum occurs between the nucleus and Its environment. Is determined primarily by the quantum mechanical and physical structure of the surrounding media. It Is thus not possible to observe a Mossbauer effect of an active nucleus In a liquid, such as an Ion or a molecule In solution. This represents a serious limitation to the study of certain phenomena It allows, however, the Investigation of films or adsorbed molecules on solid surfaces without Interference from other species In solution. This factor In conjunction with the low attenuation of Y-rays by thin layers of liquids, metals or other materials makes Mossbauer spectroscopy particularly attractive for situ studies of a variety of electrochemical systems. These advantages, however, have not apparently been fully realized, as evidenced by the relatively small number of reports In the literature (17). 

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. 

The dynamical properties of polymer molecules in solution have been investigated using MPC dynamics [75-77]. Polymer transport properties are strongly influenced by hydrodynamic interactions. These effects manifest themselves in both the center-of-mass diffusion coefficients and the dynamic structure factors of polymer molecules in solution. For example, if hydrodynamic interactions are neglected, the diffusion coefficient scales with the number of monomers as D Dq /Nb, where Do is the diffusion coefficient of a polymer bead and N), is the number of beads in the polymer. If hydrodynamic interactions are included, the diffusion coefficient adopts a Stokes-Einstein formD kltT/cnr NlJ2, where c is a factor that depends on the polymer chain model. This scaling has been confirmed in MPC simulations of the polymer dynamics [75]. 

Under general hypotheses, the optimisation of the Bayesian score under the constraints of MaxEnt will require numerical integration of (29), in that no analytical solution exists for the integral. A Taylor expansion of Ao(R) around the maximum of the P(R) function could be used to compute an analytical expression for A and its first and second order derivatives, provided the spread of the A distribution is significantly larger than the one of the P(R) function, as measured by a 2. Unfortunately, for accurate charge density studies this requirement is not always fulfilled for many reflexions the structure factor variance Z2 appearing in Ao is comparable to or even smaller than the experimental error variance o2, because the deformation effects and the associated uncertainty are at the level of the noise. 

Fox, A.G., and Fisher, R.M. (1986) Accurate structure factor determination and electron charge distributions of binary cubic solid solutions, Phil. Mag. A, 53, 815-832. 

Since the phase angles cannot be measured in X-ray experiments, structure solution usually involves an iterative process, in which starting from a rough estimate of the phases, the structure suggested by the electron density map obtained from Eq. (13-3) and the phase computed by Eq. (13-1) are gradually refined, until the computed structure factor amplitudes from Eq. (13-1) converge to the ones observed experimentally. 

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. 

T divided by the viscosity of the solvent r s. For n-octane this number is 837 K/cP at T = 323 K. The results of the fitting process are all below this theoretical value. This is not surprising, since even in the case of dilute solutions of unattached linear chains, the theoretical values are never reached (see Sect. 5.1.2). In addition the experimental T/r s values differ considerably for the different labelling conditions and the different partial structure factors. Nevertheless, it is interesting to note that T/r s for the fully labelled stars is within experimental error the arithmetic mean of the corresponding core and shell values. 

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... 

When aqueous solutions of the polymerisation initiators 2,2/-azobis(2-amidinio-propane) chloride and sodium peroxodisulfate are mixed, the title compound separates as a water insoluble shock-sensitive salt. The shock-sensitivity increases as the moisture level decreases, and is comparable with that of lead azide. Stringent measures should be used to prevent contact of the solutions outside the polymerisation environment. (The instability derives from the high nitrogen (21.4%) and oxygen (31.6%) contents, and substantial oxygen balance, as well as the structural factors present in the salt.)... 

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