We consider entanglement measures in 2-2 scattering in quantum field theories, focusing on relative entropy which distinguishes two different density matrices. Relative entropy is investigated in several cases which include \phi^4ϕ4 theory, chiral perturbation theory (\chi PTχPT) describing pion scattering and dilaton scattering in type II superstring theory. We derive a high energy bound on the relative entropy using known bounds on the elastic differential cross-sections in massive QFTs. In \chi PTχPT, relative entropy close to threshold has simple expressions in terms of ratios of scattering lengths. Definite sign properties are found for the relative entropy which are over and above the usual positivity of relative entropy in certain cases. We then turn to the recent numerical investigations of the S-matrix bootstrap in the context of pion scattering. By imposing these sign constraints and the \rhoρ resonance, we find restrictions on the allowed S-matrices. By performing hypothesis testing using relative entropy, we isolate two sets of S-matrices living on the boundary which give scattering lengths comparable to experiments but one of which is far from the 1-loop \chi PTχPT Adler zeros. We perform a preliminary analysis to constrain the allowed space further, using ideas involving positivity inside the extended Mandelstam region, and other quantum information theoretic measures based on entanglement in isospin.

Blends and copolymers of PS and PMMA were analysed by LC coupled to 1H NMR at the critical point of adsorption. The separation of the polymers was achieved at chromatographic conditions that correspond to the critical point of PS and the size‐exclusion mode of PMMA. Copolymers and blends were analysed by on‐line coupled 1H NMR. For the homopolymer blends, separation into the components was achieved, while the copolymers were separated with regard to the block lengths of the PMMA blocks. The tacticity of the PMMA blocks could be determined as a function of molar mass by HPLC‐NMR. This technique can deliver the true molar mass and the true chemical composition of the copolymers.

The online coupling of liquid chromatography at critical conditions (LCCC) and NMR was used for the analysis of block copolymers. Polyisoprene-b-poly(methyl methacrylate) (PI-b-PMMA) copolymers synthesized by living anionic polymerization were separated regarding chemical composition by LCCC using single solvents as mobile phases. The analysis of the chemically different LCCC fractions was conducted by on-flow 1 H NMR. To separate the copolymers from the respective homopolymers, critical conditions of polyisoprene (PI) and poly(methyl methacrylate) (PMMA) were used. Critical conditions were obtained by varying the column temperature. The comprehensive chemical composition and microstructure analysis by 1 H NMR revealed that quantitative information on the PI/PMMA content as well as the microstructure of PMMA (isotactic, atactic, and syndiotactic triads) and PI (1,2-PI, 1,4-PI, 3,4-PI) was obtained. For the first time the determination of the true molar masses and true chemical compositions of the block copolymers was achieved by determining the microstructure distribution.

EXPERIMENTAL SECTIONSamples. Two series of polyisoprenes of different molar masses were used (Table 1). One series consists of samples containing predominantly 1,4-isoprene units with a small content of 3,4-isoprene units (samples 1-5), and the other series is samples containing predominantly 3,4-isoprene units and additionally 1,2-and 1,4-isoprene units (samples 6-10). The corresponding structures are drawn in Scheme 1. LCCC.The LCCC experiments were performed with an Agilent 1100 HPLC system (Agilent Technologies GmbH, B€ oblingen, Germany)

PS‐b‐PMMA copolymers and blends of PS and PMMA were analyzed by the online coupling of LC at the critical point of adsorption and 1H NMR. The separation of the polymers was carried out at chromatographic conditions which correspond to the critical point of PMMA and the size exclusion mode of PS. It was shown that blends of PS and PMMA homopolymers could be well separated at critical conditions of PMMA. The analysis of both the copolymers and the blends were carried out by online coupled 1H NMR. The block copolymers were analyzed with respect to the chemical composition. LCCC‐NMR coupling was allowed to determine the individual blocks of the copolymers regarding molar mass. The data were compared with the separation at critical conditions of PS.