Influence of intrachain hydrogen bonding on the cyclization of a polystyrene chain

Cyclization of a polystyrene chain (M_n = 10,600; M_w/M_n = 1.09) both ends labeled with 4-(1-pyrenyl)butanoamide groups was studied in cyclohexane between 25 and 95°C. The amide groups (peptide bonds) at both ends can form an intrachain hydrogen bond between the amide hydrogen at one chain end and the carbonyl oxygen at the other. The presence of two sets of conformers, random coils, and chains cyclized through hydrogen bonding, complicates the data analysis. The pyrene excimer kinetics of this polymer is well described by a model composed of two monomers (hydrogen bonded and nonbonded chains) and one excimer, in equilibrium. The cyclization rate constant for hydrogen-bonded chains is larger than the one for nonhydrogen-bonded chains. The pyrene excimer binding energy (ca. 1.6 kcal/mol) is lower than the published value for nonhydrogen-bonded chains (～ 9 kcal/mol), suggesting that intrachain hydrogen bonding hinders the stabilization of the excimer. © 1994 John Wiley & Sons, Inc.     

NONLOCAL INITIAL PROBLEM FOR NONLINEAR NONAUTONOMOUS DIFFERENTIAL EQUATIONS IN A BANACH SPACE

The nonlocal initial problem for nonlinear nonautonomous evolution equati-ons in a Banach space is considered. It is assumed that the nonlinearities havethe local Lipschitz properties. The existence and uniqueness of mild solutionsare proved. Applications to integro-differential equations are discussed.The main tool in the paper is the normalizing mapping (the generalizednorm).     

Dynamic response of doubly curved honeycomb sandwich panels to random acoustic excitation. Part 2: Theoretical study

In this paper a single-degree-of-freedom model is developed to predict the dynamic response of an acoustially excited doubly curved sandwich panel. Three variants of the model are investigated, based on differing assumptions regarding the spatial distribution of the applied loading. When the loading is assumed to be uniform then the model reduces to the Miles approach, and when the loading is assumed to conform to the structural mode shape then the method is very similar to the Blevins approach. The third variant involves a more detailed consideration of the travelling wave characteristics of the applied loading, and this is found to give much improved agreement with experimental results obtained in a progressive wave tube facility. In addition, an approach using the finite element method is presented in which the response to grazing incidence excitation is computed, and this is also found to yield good agreement with the experimental results.     

CRYSTAL STRUCTURE AND MORPHOLOGY OF NASCENT SAMPLES OF SYMMETRIC AROMATIC POLYESTERS——Ⅱ. POLY(p-PHENYLENE 2,6-NAPHTHALATE)

Confined thin film melt polymerization (CTFMP) of naphthalene chloride/hydroquinone (NCMQ, 1/1, molar)mixtures at polymerization temperatures (T_p) below ca. 300℃ resulted in relatively thick, elongated crystals. Polymerizationof NC/HQ above 300℃ between glass yielded well-formed lamellar crystals ca. 100 A thick. Phase Ⅰ and Ⅱ [001] EDpatterns were obtained for all T_p, the relative amount of phase Ⅰ increasing with T_p. Polymerization of naphthalenedicarboxylic acid/hydroquinione diacetate 1/1 mixtures at high T_p also yielded lamellar crystals that "curled up" off of thesubstrate. When the high temperature CTFMP polymerization was conducted between mica, aggregates of lamellae on-edgedeveloped but epitaxial growth did not occur. Epitaxial growth of lamellae between mica could be obtained, however, byconfined thin film solution polymerization, with both of the latter samples yielding apparently related ED patterns from adifferent unit cell than phase Ⅰ or Ⅱ. Fiber patterns, obtained from sheared samples, indicated considerably greater crystaldisorder than in the nascent crystals. Refinement of the phase Ⅰ unit cell parameters, based on the [001] and [01 1] EDpatterns, with modeling based on Cerius~2, suggests a monoclinic phase Ⅰ unit cell with a = 7.76, b = 5.71, c = 14.99 A, α = γ= 90°, β= 99.7°, ρ = 1.47 g/cm~3, space group P12_1/al.     

Exact solutions and geometric phase factor of time-dependent three-generator quantum systems

There exist a number of typical and interesting systems and/or models, which possess three-generator Lie-algebraic structure, in atomic physics, quantum optics, nuclear physics and laser physics. The well-known fact that all simple 3-generator algebras are either isomorphic to the algebra sl (2, C) or to one of its real forms enables us to treat these time-dependent quantum systems in a unified way. By making use of both the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation, the present paper obtains exact solutions of the time-dependent Schr?dinger equations governing various three-generator Lie-algebraic quantum systems. For some quantum systems whose time-dependent Hamiltonians have no quasialgebraic structures, it is shown that the exact solutions can also be obtained by working in a sub-Hilbert-space corresponding to a particular eigenvalue of the conserved generator (i.e., the time-independent invariant that commutes with the time-dependent Hamiltonian). The topological property of geometric phase factors and its adiabatic limit in time-dependent systems is briefly discussed. Received 6 July 2002 / Received in final form 21 October 2002 Published online 11 February 2003     

Orders of Zeros of Polynomials on Trajectories of Solutions of a System of Linear Differential Equations with Regular Singular Points

Mathematical Notes -     

Mother-to-child transmission of HIV: a simulation-based approach for the evaluation of intervention strategies

Mother-to-child transmission (MTCT) of HIV is the most significant source of HIV infection in children below the age of 15 years. In 2000 alone, about 600 000 new infections occurred, the vast majority from mothers living in developing countries who were not aware of their HIV-positive status. To date, at least 4.3 million children have died from AIDS. In this paper, we discuss the development of an operational model that can be used to evaluate intervention options for the prevention of MTCT of HIV. The problem was approached by defining suitable pregnancy risk groups, prevention options and the required model outputs to evaluate different intervention strategies. The method chosen to approach the problem was a discrete-event, three-phase simulation, built in Visual Basic, with a stochastic semi-Markov structure. The developed model takes individual pregnant women through each stage of their pregnancy, labour and birth. Different intervention strategies may be modelled at any time, including short-course antiretroviral drugs and cessation of breastfeeding. The model is demonstrated with data from Botswana, which has one of the highest HIV-infection rates in the world.     

Domain size equilibration in sphere‐forming block copolymers

The kinetics of domain size equilibration were studied for asymmetric poly(ethylene‐alt‐propylene)‐b‐poly(dimethyl siloxane) (EPDMS) and polyisoprene‐b‐poly(dimethyl siloxane) (IDMS) block copolymers in the body‐centered cubic ordered phase. Small‐angle X‐ray scattering measurements of the principal peak position (q*) were made as a function of time after temperature jumps within the ordered state. The equilibration times were remarkably long, especially on cooling and for temperatures below 100 °C. For example, after a quench to 40 °C, q* for EPDMS had not fully equilibrated even after several weeks of annealing; IDMS required several days to equilibrate at the same temperature. In contrast, a lamella‐forming EPDMS sample was able to adjust q* within the timescale of the measurements (i.e., minutes) with both heating and cooling over the same temperature range. Measurements of tracer diffusion indicated that chain mobility was not the rate‐limiting step, although differences in mobility did account for the differences between EPDMS and IDMS. Rather, the limiting step was the required reduction in the number density of spheres on cooling; the disappearance of spheres, either by evaporation or by fusion, provided a large kinetic barrier. Lamellae, however, could adjust domain dimensions simply by local displacements of individual chains. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 715–724, 2003