Asymmetric systems scattering

In very asymmetric systems where the radius ratio o is either very large or very small, the mutual virial coefficient Gab (o equivalently the mutual interpenetration function Was) is very difficult to measure because it gives only a small contribution to the osmotic pressure or scattering intensity. In the symmetric case where the masses of the two different polymers are equal, Waa Was are of the same order of magnitude and their difference has been measured recently by lightscattering using the so-called optical 0-solvent method which gives direct access to the monomer virial coefficient difference... 

Correction for Reflection Effects in the Cylindrical Cell. Since HEC is an asymmetric molecule, corrections for reflections in the cylindrical cell are needed. In the literature, different corrections are proposed, adapted to the geometrical system of the apparatus and cells. Kratohvil (21) proposed a new formula for the reflections in cylindrical cells, taking into account four contributions to the scattering at a certain angle. He did not take into account the correction for the reverse reflected incident intensity due to reflection effects at the inner cell wall. On Figure 1 of his article (21) counts, e.g. 3 in solution equals 3 multiplied by ti We propose the following correction formula ... 

In contrast to osmotic pressure, light-scattering measurements become easier as the particle size increases. For spherical particles the upper limit of applicability of the Debye equation is a particle diameter of c. A/20 (i.e. 20-25 nm for A0 600 nm or Awater 450 nm or a relative molecular mass of the order of 10 ). For asymmetric particles this upper limit is lower. However, by modification of the theory, much larger particles can also be studied by light scattering methods. For polydispersed systems a mass-average relative molecular mass is given. 

Fraunhofer, W., G. Winter and C. Coester (2004). Asymmetrical flow field-flow fractionation and multiangle light scattering for analysis of gelatin nanoparticle drug carrier systems. Anal Chem 76(7) 1909-20. 

Addressing this problem Implies discussing the notion of liquid structure and the influence exerted on It by a nearby, different, phase. The notion of structure of a system In which the molecules are continually changing their positions can only be made rigorously concrete by statistical means, and it is embodied in the notions of radial and angle-dependent distribution functions, g(r) and g[r,B], respectively. Distribution functions have been introduced in secs. I.3.9d and e, the structure of solvents, emphasizing water, in sec. 1.5.3d. Distribution functions are in principle measurable by scattering techniques, see I.App.ll. For liquids near phase boundaries these distribution functions become asymmetrical. However, it is not always possible, and. for that matter, not always necessary to consider the structure in such detail. 

Experimental evidence for the vibrational structure of XHX transition states has been provided by photoelectron spectroscopy of XHX- anions with X = Cl, Br, and I (134,160-163). This technique, by inducing photodetachment of an electron from the XHX" anions, probes the Franck-Condon region, which is believed for these systems to include geometries in the vicinity of the transition state region for the neutral systems. Spectral bands have been interpreted as evidence for trapped-state resonances associated with asymmetric stretch-excited levels of the transition state (160-163), and they are in general agreement with synthetic photoelectron spectra calculated from the scattering computations of Schatz (17-19). In recent experimental spectra (158,162), more closely spaced oscillations have been observed these are apparently related to rotational thresholds as described by Schatz. 

Anharmonicitv-tvpicallv refers to vibrations that lead to a shift in the center of mass of the vibrating system. However, for X-ray scattering experiments we often refer to anharmonic pair correlation functions (PCF) as well as anharmonic vibrations. Such an anharmonic PCF is asymmetric with mean and median having different values. Anharmonicity requires that a PCF must be described by an increased number of moments of the distribution, and if these can not all be extracted from an experiment (e g., EXAFS) then the true distribution is not obtained. There is a general impression that anharmonic effects in EXAFS can usually be evaluated (i.e., corrected ) by suitable analysis, though this is untrue. However modeling may suggest permissible options when corrections are impossible. 

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