Theory of X-ray diffraction by a crystal with surface relief

It is well known that surface diffraction gratings are commonly used in X-ray optics [1], opto- and nanoelectronics [2]. Surface diffraction gratings are an optical component with a periodic structure formed on crystal surface. Thin 0.2 μm surface gratings with period of 10-20 μm were for the first time studied by Aristov et al. [3,4] on a triple-axis diffractometer. Results of X-ray diffraction on InP and GaAs crystals with significantly shorter surface relief period were reported in papers [5–7]. The purpose of the current paper is to provide further development of the coplanar X-ray diffraction theory on surface diffraction gratings. The problem is formulated in general within the framework of two wave dynamic X-ray diffraction. Stroke profile can be specified in any shape. Since the period and the thickness of the surface relief do not exceed 1 μm, we can study it using the kinematic approximation. New stroke profile models for specific surface reliefs are proposed. These models were used to solve the X-ray diffraction problem analytically in the kinematic approximation. Boundaries of applicability for every solution were indicated. Those solutions may be used to reconstruct profile models from experimental data of high-resolution X-ray diffraction. Results of the current work are applicable to the X-ray and neutron optic studies

"Protein-like" copolymers: Effect of polymer architecture on the performance in bioseparation process

Recently, a new class of copolymers, so-called protein-like copolymers has been predicted theoretically by computer simulation. In these copolymers. the conformation of the copolymer determines the exposure of certain comonomer units to the outer solution. Depending on the conformation, copolymer molecules with essentially the same comonomer composition could have pronouncedly different properties. The authors demonstrated experimentally such behavior in case of poly[(N- vinylcaprolactam)-co-(N-vinylimidazole)] (Dokl. Chem. 2001,375, 637). One more group of copolymers with protein-like behavior is copolymers of N-isopropylacryl-amide with N-vinylimidazole. Poly[(N-isopropylacryl-amide)-co-(N-vinylimidazole)] was synthesized by radical polymerization and separated into two fractions using immobilized metal affinity chromatography on Cu2+-loaded iminodiacetic acid Sepbarose CL 6B (Cu2+-IDA-sepharose). The unbound fraction which passed through the column and bound fraction eluted with ethylenediaminetetraacetic acid, disodium salt (EDTA) solution differed significantly in molecular weight, 1.4 x 10(6) and 1.35 x 10(5), respectively but were very close in comonomer composition, 7.8 and 9.1 mol-% of imidazole, respectively. The composition of bound fraction was confirmed by titration of imidazole groups. Despite close chemical composition, the bound and unbound fraction behaved differently with respect to temperature-induced phase separation at different pH values, the dependence of hydrodynamic diameter on pH and concentration of Cu2+- ions, and the coprecipitation of soybean trypsin inhibitor with the copolymer in the presence of Cu2+-ions. The differences in the behavior of copolymer fractions are rationalized assuming that the bound fraction presents a protein-like copolymer. The dependence of hydrodynamic diameter of bound (closed symbols) and unbound (open symbols) poly(NI-PAAM-VI) at different Cu2+/vinylimidazole ratios (n(Ca)/n(VI)), The polymer concentration was 4.5 mg (.) ml(-1) and pH 7.5 was obtained in all systems by using 0.010 m HEPES as a buffer. Mean values from five correlation functions are given