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Scattering length distribution

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. [Pg.20]

We notice that the ID projections are perfect candidates for structure modeling by ID models arrange sticks in a row For this purpose define stick-length distributions and the law of their arrangement. Fit such models to the measured scattering data (Sect. 8.7). [Pg.153]

Anti-protonic atoms. Recently neutron density distributions in a series of nuclei were deduced from anti-protonic atoms [30], The basic method determines the ratio of neutron and proton distributions at large differences by means of a measurement of the annihilation products which indicates whether the antiproton was captured on a neutron or a proton. In the analysis two assumptions are made. First a best fit value for the ratio I / of the imaginary parts of the free space pp and pn scattering lengths equal to unity is adopted. Secondly in order to reduce the density ratio at the annihilation side to a a ratio of rms radii a two-parameter Fermi distribution is assumed. The model dependence introduced by these assumptions is difficult to judge. Since a large number of nuclei have been measured one may argue that the value of Rj is fixed empirically. [Pg.107]

SEC-MALLS and SEC-LALLS Coupled chromatography and light-scattering photometry that allows the determination of a number of important values along with chain length distribution, sedimentation equilibrium experiment Ultracentrifugation technique that allows chain length information to be determined. [Pg.80]

Fig. 18. Reciprocal particle-scattering factors of star-molecules with polydisperse rays, where f denotes the number of rays per molecule. The same functions are obtained also for the ABC-type polycondensates, where nb denotes the number of branching points per molecule. The case f = 1 or nb = 0 is identical to linear chains obeying the most probable lengths distribution. It also represents the scattering behaviour of randomly branched f-functional polycondensates 1... Fig. 18. Reciprocal particle-scattering factors of star-molecules with polydisperse rays, where f denotes the number of rays per molecule. The same functions are obtained also for the ABC-type polycondensates, where nb denotes the number of branching points per molecule. The case f = 1 or nb = 0 is identical to linear chains obeying the most probable lengths distribution. It also represents the scattering behaviour of randomly branched f-functional polycondensates 1...
In PB networks, the variation of the line shape as a function of the applied stress was interpreted in terms of a chain length distribution. Shorter chains may be more oriented than longer ones, at a given elongation [18], which may lead to a non-affine behaviour at the chain scale. The question of the spatial scale to which the deformation is affinely transmitted, has been investigated intensively by small angle neutron scattering [64]. However, it may happen as well that the chain portions close to junction points are more oriented (have a more restricted mobility) than those in the middle of the chains [19]. [Pg.577]

A simplification which describes scattering at low q can be made for the case of a two-phase system composed of particles having a homogeneous scattering length density distributed in a second phase. If we assume that the particles are monosized, then the intensity can be expressed as [83]... [Pg.145]

The parameter Z represents a field-independent scattering length of the carriers. The factor 1/6 is included to account for the statistical distribution of motion directions. The net carrier flux in field direction is... [Pg.224]

But it was not to be. Try as we might, the difference in scattering lengths between the 6Li and 7Li isotopes was too small to permit us to measure the lithium ion distribution in the swollen state. We had to content ourselves with the results for the crystalline phase, where the behavior of the lithium ions is different from that of the larger alkali metal cations [27], Potassium and cesium ions bind directly to vermiculite clay surfaces rather than hydrating fully. Because only lithium-substituted vermiculites of the alkali metal series will swell macroscopically when soaked in water, it seems that interlayer cations must form fully hydrated ion-water complexes if the particles are to expand colloidally. This conclusion has since been supported... [Pg.163]


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See also in sourсe #XX -- [ Pg.23 , Pg.92 , Pg.158 ]




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Length distribution

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