Molecular scattering data

Buck U 1974 Inversion of molecular scattering data Rev. Mod. Phys. 46 369 Buck U 1975 Elastic scattering Adv. Chem. Phys. 30 313... 

A graphical method, proposed by Zimm (thus tenned the Zinnn plot), can be used to perfomi this double extrapolation to detemiine the molecular weight, the radius of gyration and the second virial coefficient. An example of a Zinnn plot is shown in figure Bl.9.6 where the light scattering data from a solution of poly... 

There are many different data analysis schemes to estimate the structure and molecular parameters of polymers from the neutron scattering data. Herein, we will present several connnon methods for characterizing the scattering profiles, depending only on the applicable q range. These methods, which were derived based on different assumptions, have... 

In Example 10.5 we extracted both the molecular weight and the radius of gyration from Ught-scattering data. There may be circumstances, however, when nothing more than the dimensions of the molecule are sought. In this case a simple alternative to the analysis discussed above can be followed. This technique is called the dissymmetry method and involves measuring the ratio of intensities scattered at 45° and 135°. The ratio of these intensities is called the dissymmetry ratio z ... 

More recently, simulation studies focused on surface melting [198] and on the molecular-scale growth kinetics and its anisotropy at ice-water interfaces [199-204]. Essmann and Geiger [202] compared the simulated structure of vapor-deposited amorphous ice with neutron scattering data and found that the simulated structure is between the structures of high and low density amorphous ice. Nada and Furukawa [204] observed different growth mechanisms for different surfaces, namely layer-by-layer growth kinetics for the basal face and what the authors call a collected-molecule process for the prismatic system. 

PIB s prepared with r-BuBr/Et2AlCl/MeCl show similar characteristics. Figure 2 and Table 2 show the molecular weight data obtained in the range from —30° to -60 °C. M and Mw of the total polymer show some scatter, though Mw and MWD tend to increase with decreasing temperatures. The data obtained at -45 °C, Le., the exceptionally high M and Mw, are difficult to explain. 

Figure 3 and Table 3 give the data for PIB prepared with f-BuCl/Et2AlBr/MeBr in the range from -30° to -65 °C. All GPC traces are monomodal, even for samples prepared below -50 °C (an exception was the sample prepared at -65 °C, which showed a small shoulder). While the molecular weight data are scattered and a trend... 

The PCP (Aldrich, catalogue no. 18,168-4, lot no. 03) had no listed molecular weight data. A broad MMD polystyrene (PS) standard (National Bureau of Standards) had a light scattering fl = 257,800 (SRM 706, R7R =2.1). Six of the narrow MMD PS standards (Pressure ChemTcaT Co.) had nominal molecular weights... 

Except for biopolymers, most polymer materials are polydisperse and heterogeneous. This is already the case for the length distribution of the chain molecules (molecular mass distribution). It is continued in the polydispersity of crystalline domains (crystal size distribution), and in the heterogeneity of structural entities made from such domains (lamellar stacks, microfibrils). Although this fact is known for long time, its implications on the interpretation and analysis of scattering data are, in general, not adequately considered. 

However, certain contradictions can be seen from the data of Tables 1 and 2. Indeed, the molecular weights determined for aqueous solutions of these p- and s-fraclions in the SEC experiments (Table 1) coincided well with the results of light scattering for DMSO solutions (Table 2) but why did the molecular weights differ so considerably from the light scattering data (Table 2) for the solutions of given copolymers in pure water, where, in... 

Equation 3.27 forms the basis for determination of Molecular weight from light scattering data. Like Osmotic pressure measurements, it is essential to consider the non-ideality of solutions and the concentration dependence. Following Debye, eq. 3.27 gets modified to... 

Diagrammatic representation of scattering data on large particles, obtained at different angles but at the same concentration, constructed by plotting sin (.6y2)AR(6) versus sin(0/2), or q AR 9) versus q, and used for the determination of molecular shape. For definitions of symbols, see Definition 3.3.12. 

Figure 17 shows the temperature dependence of the lateral forces measured at the scanning rate of 10 nms for a high-density PMMA brush (a = 0.8 chains nm ) and an equivalent spin-coated film. The a-relaxation process was clearly observed accompanying a small peak, which was assigned to a surface /1-process. They commented that the surface molecular motion of the brush layer possibly differs from that of the spin-coated film but that it was rather difficult to conclude this because of shghtly scattered data. 

There are a number of estimates of the actinic flux at various wavelengths and solar zenith angles in the literature (e.g., see references in Madronich, 1987, 1993). Clearly, these all involve certain assumptions about the amounts and distribution of 03 and the concentration and nature (e.g., size distribution and composition) of particles which determine their light scattering and absorption properties. Historically, one of the most widely used data sets for actinic fluxes at the earth s surface is that of Peterson (1976), who recalculated these solar fluxes from 290 to 700 nm using a radiative transfer model developed by Dave (1972). Demerjian et al. (1980) then applied them to the photolysis of some important atmospheric species. In this model, molecular scattering, absorption due to 03, H20, 02, and C02, and scattering and absorption by particles are taken into account. 

Gold s method has been used by a number of workers, including Siska (1973), who applied it to molecular-beam scattering data, MacNeil and Dixon (1977), who applied it to photoelectron spectra, and Jones et al. (1967), who restored infrared spectra of condensed-phase samples. The author is unaware of any experimental results with this method, however, that illustrate the full potential achievable by constrained methods to be described later in this chapter. In the work of Jones et al., the resulting resolution is probably limited by the inherent breadth of spectral lines observed with condensed-phase samples. 

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