Scattering length solvents

Let us take two polymers (one deuterated and one hydrogenated) and dissolve them in a solvent (or another polymer) having a scattering length b. The coherent scattered intensity can be derived from (B 1.9.117), which gives... 

Considering only scattering at small momentum transfers, we may neglect the detailed atomic arrangements within e.g. a monomer or a solvent molecule and take into account only the scattering length densities pM or ps of such scattering units... 

A variant of the zero average contrast method has been applied on a solution of a symmetric diblock copolymer of dPS and hPS in benzene [331]. The dynamic scattering of multicomponent solutions in the framework of the RPA approximation [324] yields the sum of two decay modes, which are represented by exponentials valid in the short time limit. For a symmetric diblock the results for the observable scattering intensity yields conditions for the cancellation of either of these modes. In particular the zero average contrast condition, i.e. a solvent scattering length density that equals the average of both... 

The solvent is usually treated as an incompressible continuum. However, it must be kept in mind that SAXS- or SANS-studies in solution only probe the difference between the scattering length density of the dissolved object and the solvent. Hence, the scattering intensity is determined by the contrast between solute and solvent. This contrast may fluctuate too because of the density fluctuations of the solvent and there is a small but non-zero contribution to I (q), even at vanishing contrast. 

Fig. 6. Mass (top and right-hand y axis) and neutron scattering length (bottom and left-hand y axis) density increments for AMDH as functions of the respective solvent densities. From Zaccai et al. (1989), with permission.

Dibromomethane is a solvent with an x-ray scattering length density (18.95 x 1010 cm-2) very similar to that for graphite (19.18 x 1010 cm-2). In addition, the size of the molecule of dibromomethane, calculated from the liquid density, is around 0.61 nm. Thus, this solvent will be able to access only the micropores with size larger than that value. These two characteristics make this solvent suitable for this type of experiment. 

Consider a polymer solution consisting of protonated and deuterated polymers (concentrations CH and CD respectively) that have the same degree of polymerization N. The scattered intensity is proportional to the structure factors for the polymer-polymer correlations SHH(Q), SDD(Q), SHIj(Q), polymer-solvent correlations SpS(Q), and solvent-solvent correlations Sss(Q). The protonated, deuterated and solvent molecule scattering lengths are called aH, aD and as and ap is the average polymer scattering length. The scattered intensity can be expressed in terms of an absolute cross section as ... 

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