Structure factor excess

We denote the excess structure factor per mass cocncentration of solution by S k) an simply call it the structure factor. Here by excess we mean the value for a solution minus that for its solvent. As before, k is the magnitude of the scattering vector. Textbooks of physical chemistry explain how S k) can be determined from measurements of the intensity of scattered light or X-ray or neutrons. For the polymer solution under consideration it can be shown that S k) is related to h r) by [15]... 

Stockholm convention 60 stoichiometric number 42 stokes 112 strain 12 bulk 12 linear 12 shear 12 volume 12 stress 12, 72 Strouhal number 65 structural formula 45 structure factor 36 sublimation 51 substance concentration 5 substitution structure distance 24 sum over states 39 surface amount 63 surface charge density 14, 59 surface chemistry 63 surface concentration 42 surface coverage 63 surface density 12 surface electric potential 59 surface excess 63 surface excess concentration 63 surface pressure 63 surface properties 64 surface tension 12, 48, 63 susceptance 15 svedberg 111 symbols 5... 

Peaks occur in a difference map in positions in the unit cell where the model did not include enough electron density valleys appear in places where the model contained too much electron density. This information may be used to obtain more precise atomic positions, atomic displacement parameters, or atomic numbers. For example, in the last category, the identities of atoms (carbon or nitrogen) in a tricyclic molecule were established by setting all atoms to one type (carbon in this case) in the structure factor calculation. A difference map was calculated with the calculated phases and examined for excess electron density at atomic positions (Table 9.2). It was found to be possible to distinguish between nitrogen (seven electrons) and carbon (six electrons), even though these atoms are adjacent in the Periodic Table. 

Thirteen structural parameters may seem excessive, but these parameters are general, they incorporate the very complex structural factors determining Tg, and they obviate the need for group contributions. Even with a vastly larger number of group contributions, the Tg of many new polymers cannot be estimated because of the lack of some of the group contributions. 

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 ... 

In region (1), the electron can be considered as quasifree. (An electron is regarded as completely free only in the vacuum.) The structure of the fluid is unperturbed by the presence of the excess electron. The wave function is extended. The basic electron/liquid interaction may be treated as single scattering of an electron on a molecule or atom modified by the structure factor of the liquid, S(q) (Lekner, 1967), or it is considered as multiple scattering off density fluctuations in the framework of the deformation potential theory (Basak and Cohen, 1979). 

In a static fight scattering experiment the effective structure factor, S(0) at zero scattering vector was obtained from the extrapolated forward scattering. In Fig. 4 is shown the variation of the excess Rayleigh ratio dR(0) extrapolated zero scattering vector with the volume fraction of droplets, (f> [3]. In the monodisperse case, S(0) is finked to the osmotic compressibility for which, in the case of hard spheres, an accurate expression exists due to Carnahan and Starling [17]. The experimental data were... 

Statistical mechanics also relate the shear viscosity of simple electrolytes to the structure factor S(q). Hess and Klein [30] derived the excess shear viscosity r for weak and strong interactions, the latter of which was obtained from a modemode coupling approach with the result... 

The SANS observations also show the interest of performing full contrast variation experiments. Indeed, the information given by the two partial structure factors of the polymer are not equivalent because of the very singular nature of the profile at close distances from the wall. The experimental data yield values of the surface excess F. They correspond roughly to one full monolayer of dense polymer. It must be stressed, however, that the chains are not adsorbed in a flat configuration on the solid surface, as demonstrated as well by the EWIF method. 

Fig. 17. Flory x parameter as a function of composition based on SC/PRISM calculations open symbols) and MD simulations closed symbols) for the = 96 iPP/PE blend atT = 453 K. The AH ix values are obtained from the excess energy of the blend. The xs front SC/PRISM is the sum of the athermal Xath> Eq. (44), and XAH Eq. (43), while XRPA i obtained by fitting the partial structure factor to the RPA formula...

Optical response in OPC Excess Rayleigh ratio Radius of gyration Siuface area Power spectrum Entropy function Structure factor Scattering amplitude function Absolute temperature Pulse amplitude Stokes parameter Velocity Volume... 

In general there are two factors capable of bringing about the reduction in chemical potential of the adsorbate, which is responsible for capillary condensation the proximity of the solid surface on the one hand (adsorption effect) and the curvature of the liquid meniscus on the other (Kelvin effect). From considerations advanced in Chapter 1 the adsorption effect should be limited to a distance of a few molecular diameters from the surface of the solid. Only at distances in excess of this would the film acquire the completely liquid-like properties which would enable its angle of contact with the bulk liquid to become zero thinner films would differ in structure from the bulk liquid and should therefore display a finite angle of contact with it. 

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