Quantitative magnetization transfer by trains of radio frequency pulses in human brain: extension of a free evolution model to continuous-wave-like conditions

A theoretical model of free evolution between repeated magnetic transfer (MT) pulses was extended to continuous-wave (CW)-like conditions showing that only the repetitive "direct" saturation of bulk water changes the transient and stationary behavior. The influence of the pulse repetition period (PR) on progressive saturation was studied in cortical gray matter (GM) and central white matter (WM) under conditions of short periods of free evolution and strong macromolecular saturation. Interpulse delays of 3 ms were achieved in vivo on a 1.5-T MR system with bell-shaped MT pulses of 12-ms duration and nominal flip angles of up to 1440 degrees and single-shot readout by a stimulated echo acquisition mode localization sequence. The frequency offset was chosen between 1 and 3 kHz to avoid excessive direct saturation. The stationary MT ratio (MTR) followed an inverse linear PR dependence, showing a consistent partial saturation of about 90% at zero PR for both WM and GM. Comparison to a relaxation-matched liquid indicated the presence of MT, but not necessarily of direct saturation. The transient behavior indicated considerable direct saturation, but this could also be explained by MT. These inconsistencies showed that the intervals of time evolution in our experiments were too long to be modeled by CW-like conditions. Free evolution takes place during the whole PR rather than during the interpulse delay only. Quantification using the rates of free evolution theory yielded the saturations and rate constants necessary to explain the observed behavior. The theory of rapid CW-like pulsing provides an upper limit for the rate of progressive saturation. This limit is approached at PR below an estimated value of 5 ms. The phenomenological PR dependence of the steady-state MTR may indicate that MT exceeded the direct saturation. Unlike to an idealized CW experiment, the extrapolated value at zero PR is subject to direct effects and not a physically meaningful constant.     

Absorption spectra related to heterogeneous electron transfer reactions: the perylene TiO2 system

Linear absorption spectra of dye-semiconductor systems (perylene attached to nanostructured TiO2) are studied theoretically and experimentally. The systems show ultrafast photoinduced heterogeneous electron transfer (HET). By applying a time-dependent formulation of the absorbance, the theoretical analysis of the measured data is carried out. The respective electron-vibrational wave packet propagation fully accounts for the electronic coupling to the conduction band continuum of TiO2 and is based on a single-reaction-coordinate model (corresponding to a perylene in-plane C-C stretching vibration with a quantum energy of 1370 cm(-1)). By the insertion of different bridge-anchor groups, the electronic coupling responsible for HET is varied. The dye absorbance in a solvent and the trends in the line broadening of the vibrational progression due to the coupling to the conduction band continuum are reproduced for all investigated types of bridge-anchor groups. HET rates deduced from the calculations on the absorbance displaying line broadenings follow the qualitative trend obtained from transient absorption spectra.     

Bounds on the oscillation of spin system

A birth and death process is used to compare the dynamics of two finite Markov spin systems with different initial configurations. This procedure results in bounds on the oscillation of functionals of the finite spin system as a function of the initial configuration. Such bounds are used, in the one- and two-dimensional cases, to prove the existence of infinite Feller spin systems which do not satisfy T. Liggett's “bounded variation” condition on the interaction functions.     

Electronic structure of clusters modeling silica

Self-consistent-field-Xα-scattered wave calculations on clusters Si₂O₇^6? and H₆Si₂O₇ modeling silica have been performed. Incorporation of Si 3d orbitals produces significant changes in the overall valence structure. In addition to σ Si — O bonds, there exists a bonding π character due to the participation of O 2p and Si 3d. Hydrogen terminators do not seem to correct edge effects for these π states.     

Temperature dependence of the conformation of isotactic polystyrene in toluene

In order to obtain information about a possible helix–coil transition of isotactic polystyrene (i-PS) at 80°C in toluene, as has been reported in other solvents, solution properties were examined at temperatures between 10 and 110°C. Use was made of viscometry, high-resolution nuclear magnetic resonance, infrared spectroscopy, calorimetry, and light scattering. No distinct transition was found at 80°C but rather a second-order transition between 62 and 65°C. A similar transition occurred in toluene solutions of atactic polystyrene. The transition may be attributed to a sudden change in the mobility of the phenyl side-group of the polymer. From this study it is concluded that i-PS has a helical conformation in toluene, the mean helix length decreasing smoothly with increasing temperature.     

Conformational Entropy as a Means to Control the Behavior of Poly(diketoenamine) Vitrimers In and Out of Equilibrium

Control of equilibrium and non‐equilibrium thermomechanical behavior of poly(diketoenamine) vitrimers is shown by incorporating linear polymer segments varying in molecular weight (MW) and conformational degrees of freedom into the dynamic covalent network. While increasing MW of linear segments yields a lower storage modulus at the rubbery plateau after softening above the glass transition (T_g), both T_g and the characteristic time of stress relaxation are independently governed by the conformational entropy of the embodied linear segments. Activation energies for bond exchange in the solid state are lower for networks incorporating flexible chains; the network topology freezing temperature decreases with increasing MW of flexible linear segments but increases with increasing MW of stiff segments. Vitrimer reconfigurability is therefore influenced not only by the energetics of bond exchange for a given network density, but also the entropy of polymer chains within the network.     

Effect of silicon surface cleaning procedures on oxidation kinetics and surface chemistry

The effect of surface cleaning procedures on the kinetics of thermal oxide growth on silicon is presented. The goal is to relate the properties of the cleaned surface (composition, chemistry, impurity content) to the changes in oxide growth mechanisms. Experimentally, silicon (100) wafers were given different variations of an RCA clean, and then oxidized in dry O₂ at 900°C producing oxides with thicknesses between 170 and 3900 Å. The results, in general agreement with earlier studies, show that the percentage difference in thickness is strongly dependent on oxide thickness. The data, which are explained in terms of the predictions of a linear-parabolic and a parallel oxidation model, suggest that the surface cleans do not alter the diffusion of molecular oxygen in the oxide. Auger analysis of the surfaces shows that there is a substantial carbon contamination on the HF stripped wafer which is considerably reduced after a 5 min N₂ anneal.     

Fitting differential equation models to observed economic data—I. quasilinearization

This paper discusses the fitting of differential equation models to economic data. In particular, it treats the problem of describing the growth of capital in terms of a differential equation containing several parameters. The parameters are to be estimated on the basis of data. This estimation problem is formulated as a nonlinear boundary value problem. The rapidly convergent successive approximation method of quasilinearization is described and applied. Representative results of numerical experiments are presented, showing the effectiveness of the approach. Suggestions for additional studies are made.