Effects of near-neighbor correlations on the diffuse scattering from a one-dimensional paracrystal

The one-dimensional paracrystal model is generalized by folding the lattice sites with objects whose scattering lengths or sizes and separation display a spatial correlation from cell to cell. A general theory to calculate the diffuse scattering and the scattering-length autocorrelation function is developed. The investigated models of coupling along the paracrystalline chain are the correlations between (i) the sizes of the scatterers, (ii) the sizes of scatterers and their separations, and (iii) the sizes of scatterers and the fluctuation of their separation distances. In the first case (i), the size of a scatterer is, on average, linked to that of its neighbors. As a result, a continuous transition from the total lack of size correlation (known as decoupling approximation or DA) to the scattering from monodisperse domains (local monodisperse approximation or LMA) is obtained. In the second case of correlation (ii), the mean interobject distance is assumed to depend on the respective sizes of nearest neighbors. Depending on the introduced correlation parameter, aggregation or hard-core-type effects can be accounted for. Surprisingly, in some cases, it is possible to find a peak in the scattering curve without any structure in the total interference function. The size-separation correlations may also dramatically reduce the scattering intensity close to the origin compared to the completely uncorrelated case. The last model (iii) foresees a coupling between the sizes of neighboring objects and the variance of the separation between neighbors. Within this model, on average along the chain, the fluctuations of distances between scatterers become dependent on the respective sizes of neighbors, while the mean distance between objects remains constant.