Monte carlo studies of phase transitions in polymer blends and block copolymer melts

Summary The unmixing transition of both symmetrical polymer blends AB (i.e. chain lengthsN _A=N _B=N) and asymmetrical ones (N _B/N _A=2,3) is studied by large-scale Monte Carlo simulations of the bond fluctuation model. Combination of semi-grand-canonical simulation techniques, ?histogram reweighting? and finitesize scaling allows an accurate location of the coexistence curve in the critical region. The variation of the critical temperature with chain length (N) is studied and compared to theoretical predictions. For the symmetrical case, use of chain lengths up toN=512 allows a rough estimation of crossover scaling functions for the crossover from Ising to mean-field exponents. The order-disorder transitions in melts of both symmetric (compositionf=N _A/(N _A+N _B)=1/2) and asymmetric (f=3/4) block copolymers is studied for very short chains (16≤N≤60). The interplay between structure and chain configuration is emphasized. Qualitative evidence for ?dumbell formation? of chains and vacancy enrichment in A-B-interfaces and near hard walls is presented. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Thermomechanics of the interface between a body and its environment

We formulate integral statements of force balance, energy balance, and entropy imbalance for an interface between a body and its environment. These statements account for interfacial energy, entropy, and stress but neglect the inertia of the interface. Our final results consist of boundary conditions describing thermomechanical interactions between the body and its environment. In their most general forms, these results are partial differential equations that account for dissipation and encompass as special cases Navier’s slip law, Newton’s law of cooling, and Kirchhoff’s law of radiation. When dissipation is neglected, our results reduce to the well-known zero-slip, free-surface, zero-shear, prescribed temperature, and flux-free conditions. Dedicated to James K. Knowles: teacher, colleague, friend     

Energy release,friction, and supplemental relations at phase interfaces

An Eulerian expression for the dissipation due to a moving surface of discontinuity in mass density, velocity, stress, energy, and heat flux is obtained. This leads to Eulerian measures forenergy release andfriction — measures that are work conjugate tomass flux andvelocity slip, respectively. Constitutive equations involving these quantities are proposed as a means to determine transition kinetics in materials that change phase.     

Computational chemistry and molecular simulations of phosphoric acid

Quantum mechanics (QM) calculations, molecular dynamics (MD) simulations using the condensed‐phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field, and the atom‐centered density matrix propagation (ADMP) approach have been used to investigate properties of phosphoric acid (PA). QM using B3LYP/6‐31++G(d,p) density functional theory were used to calculate gas‐phase proton affinities and interaction energies of PA and its derivatives. Detailed single coordinate driving, followed by quadratic synchronous transit optimization was used to determine energy barriers for different proton transfer (PT) pathways. Determined energy barrier heights in ascending order are (unit: kJ/mol): H₃O⁺→H₃PO₄ (0); H₄P₂O₇→H₃PO₄ (2.61); H₃PO₄→H₂PO (5.31); H₄PO→H₃PO₄ (～7.33); H₃PO₄→H₄P₂O₇/H₃PO₄→H₃PO₄ (15.99); H₄P₂O₇→H₂O (28.61); H₃PO₄→H₂O (47.14). The COMPASS force field was used to study condensed‐phase properties of PA. Good agreement between experimental data and MD results including density, radial distribution functions, and self‐diffusion coefficient at different temperatures provides validation of the COMPASS force field for PA. Finally, preliminary ADMP studies on a cluster of three PA molecules shows that the ADMP approach can reasonably describe the PT and self‐dissociation processes in PA. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Über Folgen Bairescher Funktionen

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Bose–Einstein condensation in atomic hydrogen

The addition of atomic hydrogen to the set of gases in which Bose–Einstein condensation can be observed expands the range of parameters over which this remarkable phenomenon can be studied. Hydrogen, with the lowest atomic mass, has the highest transition temperature, 50 μK in our experiments. The very weak interaction between the atoms results in a high ratio of the condensate to normal gas densities, even at modest condensate fractions. Using cryogenic rather than laser precooling generates large condensates. Finally, two-photon spectroscopy is introduced as a versatile probe of the phase transition: condensation in real space is manifested by the appearance of a high-density component in the gas, condensation in momentum space is readily apparent in the momentum distribution, and the phase transition line can be delineated by following the evolution of the density of the normal component.