Noise-spike-induced escape in a bistable system driven by colored noise: Noise with long correlation times

An escape mechanism in a bistable system driven by colored noise of large but finite correlation time (tau) is analyzed. It is shown that the fluctuating potential theory [Phys. Rev. A 38, 3749 (1988)] becomes invalid in a region around the inflection points of the bistable potential, resulting in the underestimation of the mean first passage time at finite tau by this theory. It is shown that transitions at large but finite tau are caused by noise spikes, with edges rising and falling exponentially in a time of O(tau). Simulation of the dynamics of the bistable system driven by noise spikes of the above-mentioned nature clearly reveal the physical mechanism behind the transition.

Correlation times in stochastic equations with delayed feedback and multiplicative noise

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

133Cs relaxation times in rat tissues

133Cs relaxation-time studies of tissues from rats into which cesium has been incorporated by dietary loading have been carried out in vivo and in vitro. Whereas tissue T1 values are on the order of seconds, T2 values are as low as a few tens of milliseconds, 133Cs tissue relaxation times are analogous to those of 39K in the same tissues, but are more readily measured because of the greater sensitivity of 133Cs compared with 39K, T1 and T2 data of excised tissue at two resonance frequencies (65.60 and 39.37 MHz) and temperatures (302 and 278 K) have been analyzed in terms of a general description of spin- relaxation. The results are consistent with most of the cesium ions being in a free state, undergoing fast exchange with bound ions having long correlation times located in one or more intracellular compartments,

Studies of the effects of molecular encounters on N.M.R. spin-lattice relaxation times

This thesis is concerned with investigations of the effects of molecular encounters on nuclear magnetic resonance spin-lattice relaxation times, with particular reference to mesitylene in mixtures with cyclohexane and TMS. The purpose of the work was to establish the best theoretical description of T1 and assess whether a recently identified mechanism (buffeting), that influences n.m.r. chemical shifts, governs Tl also. A set of experimental conditions are presented that allow reliable measurements of Tl and the N. O. E. for 1H and 13C using both C. W. and F.T. n.m.r. spectroscopy. Literature data for benzene, cyclohexane and chlorobenzene diluted by CC14 and CS2 are used to show that the Hill theory affords the best estimation of their correlation times but appears to be mass dependent. Evaluation of the T1 of the mesitylene protons indicates that a combined Hill-Bloembergen-Purcell-Pound model gives an accurate estimation of T1; subsequently this was shown to be due to cancellation of errors in the calculated intra and intemolecular components. Three experimental methods for the separation of the intra and intermolecular relaxation times are described. The relaxation times of the 13C proton satellite of neat bezene, 1,4 dioxane and mesitylene were measured. Theoretical analyses of the data allow the calculation of Tl intra. Studies of intermolecular NOE's were found to afford a general method of separating observed T1's into their intra and intermolecular components. The aryl 1H and corresponding 13C T1 values and the NOE for the ring carbon of mesitylene in CC14 and C6H12-TMS have been used in combination to determine T1intra and T1inter. The Hill and B.P.P. models are shown to predict similarly inaccurate values for T1linter. A buffeting contribution to T1inter is proposed which when applied to the BPP model and to the Gutowsky-Woessner expression for T1inter gives an inaccuracy of 12% and 6% respectively with respect to theexperimentally based T1inter.

ESR measurements of the partitioning of some new spin probes in n-octanol-water

The stable free radical 1,1,3,3-tetramethylisoindolin-2-yloxyl (TMIO) has proved to be very suitable for use as a spin probe for a number of applications. Because it is soluble mainly in non-polar liquids, there is a need for new derivatives that can be used in a variety of environments. This has been done by introducing substituents in the 5-position of the aromatic ring, namely carboxyl (CTMIO), trimethylamino (TMTMIOI) and sodium sulphonate (NaTMIOS). An accurate ESR method was developed for the measurement of partition coefficients in n-octanol–water. For comparison purposes the method was also applied to some Tempo derivatives. The effect of temperature on the rotational correlation times and the nitrogen-14 hyperfine coupling constant of some of the spin probes was investigated. There is evidence for dimerization of CTMIO to form a biradical

Calorimetric, infrared and ESR studies of the plastically crystalline state of organic compounds

Enthalpy changes of the crystal-plastic and plastic-liquid transitions are related to the temperature range of stability of the plastic phase. Thermodynamics of the plastic state of binary mixtures have been examined. Infrared correlation times, τc, and activation energies have been measured for a few molecules in the plastic state. Molecular tumbling times, τt, have also been measured employing ESR spectra of a spin-probe. Plots of log τc(τt) 1/T are continuous through the plastic-liquid transition. Activation energies for molecular motion seem to vary in the same direction as the ΔH of the plastic-crystal transition. Infrared correlation times of solute molecules in binary solutions in the plastic and the liquid states show interesting variations with solute concentration.

Molecular Dynamics in [(CH8)aN]z Cd14 A Proton Magnetic Relaxation Study

second moment measurements are carried out on [(CH,),N], CdI, in the temperature range 77 to 400 K. The results are interpreted based on a molecular dynamical model of randomly reorienting methyl groups and isotropically tumbling tetramethyl ammonium group. The relaxation data show contributions from spin-rotation interaction at high temperatures and presence of inequivalent methyl groups. The correlation times and associated activation energies, connected with this model, are calculated from the data. The structure in the absorption line and in the free-induction decay signal at 77 K indicates the possibility of tunnelling motion of the methyl groups. Im Temperaturbereich 77 bis 400 K werden an [(CH,),N],CdI, Protonen-Spin-Gitter-Relaxationsexperimente (bei Larmorfrequenzen von 10,20 und 30 MHz) und Messungen des zweiten Moments durchgefiihrt. Die Ergebnisse werden an Hand eines molekularen dynamischen Modells sich statistisch umorientierender Methylgruppen und isotrop taumelnder Tetramethyl-Ammoniumgruppen interpretiert. Die Relaxationswerte zeigen Beitriige von Spin-Rotations-Wechselwirkung bei hohen Temperaturen und die Anwesenheit von inaquivalenten Methylgruppen. Die Korrelationszeiten und verknupften Aktivierungsenergien, die mit diesem Model1 verbunden sind, werden am den Werten berechnet. Die Struktur in der Absorptionslinie und im Abklingsignal der freien Induktion bei 77 K zeigt die Moglichkeit einer Tunnelbewegung der Methylgruppen.

Structure and dynamics of benzene in one-dimensional channels

Molecular dynamics investigation of benzene in one-dimensional channel systems A1PO(4)-5, VPI-5, and carbon nanotube is reported. The results suggest that, in all the three host systems, the plane of benzene is almost perpendicular to the channel axis when the molecule is near the center of the channel and the plane of benzene is parallel to the channel axis when the molecule is near the wall of the channel. The density distribution of benzene as a function of channel length, z and the radial distance, r, from the channel axis is also different in the three host structures. Anisotropy in translational diffusion coefficient, calculated in body-fixed frame of benzene, suggests that benzene prefers to move with its plane parallel to the direction of motion in A1PO(4)-5 and VPI-5 whereas in carbon nanotube the motion occurs predominantly with the plane of the benzene perpendicular to the direction of motion.;Anisotropy associated with the rotational motion is seen to alter significantly in confinement as compared to liquid benzene. In A1PO(4)-5, the rotational anisotropy is reversed as compared to liquid benzene thereby suggesting that anisotropy arising out of molecular geometry can be reduced. Reorientational correlation times for C-6 and C-2 axes Of benzene are reported. Apart from the inertial decay of reorientational correlation function due to free, rotation, two other distinct regimes of decay are observed in narrower channels (AIPO(4)-5 and carbon nanotube): (i) an initial fast decay (0.5-2 ps) and (ii) a slower decay (>2 ps) of reorientational correlation function where C-6 decays slower than C-2 Similar to what is observed in liquid benzene. In the initial fast decay, it is seen that the decay for C-6 is faster than C-2 which is in contrast to what is observed in liquid benzene or for benzene confined in VPI-5.

Homonuclear NOE in spatially periodic spin systems

The nuclear Overhauser effect equations are solved analytically for a homonuclear group of spins whose sites are periodically arranged, including the special cases where the spins lie at the vertices of a regular polygon and on a one-dimensional lattice. t is shown that, for long correlation times, the equations governing magnetization transfer resemble a diffusion equation. Furthermore the deviation from exact diffusion is quantitatively related to the molecular tumbling correlation time. Equations are derived for the range of magnetization travel subsequent to the perturbation of a single spin in a lattice for both the case of strictly dipolar relaxation and the more general situation where additional T1 mechanisms may be active. The theory given places no restrictions on the delay (or mixing) times, and it includes all the spins in the system. Simulations are presented to confirm the theory.

Study of translational and rotational mobility and orientational preference of ethane in one-dimensional channels

Structural and dynamical properties of ethane in one-dimensional channels of AlPO4-5 and carbon nanotube have been investigated at dilute concentration with the help of molecular dynamics simulation. Density distributions and orientational structure of ethane have been analyzed. Repulsive interactions seem to play an important role when ethane is located in the narrow part of the AlPO4-5 channel. In AlPO4-5, parallel orientation is predominant over perpendicular orientation except when ethane is located in the broader part of the channel. Unlike in the case of single-file diffusion, our results in carbon nanotube show that at dilute concentrations the mean squared displacement, mu(2)(t) approximate to t(alpha), alpha = 1.8. The autocorrelation function for the z-component of angular velocity of ethane in space-fixed frame of reference shows a pronounced negative correlation. This is attributed to the restriction in the movement of ethane along the x- and y- directions. It is seen that the ratio of reorientational correlation times does not follow the Debye model for confined ethane but it is closer to the predictions of the Debye model for bulk ethane.

Local chain motions in a dilute solution of phenolphthalein poly(ether sulfone)

C-13 and H-1 relaxation times were measured as a function of temperature in two magnetic fields for dilute solutions of phenolphthalein poly(ether sulfone) (PES-C) in deuterated chloroform. The spin-lattice relaxation times were interpreted in terms of segmental motion characterized by the sharp cutoff model of Jones and Stockmayer (J. S. model). The phenyl group rotation is treated as a stochastic diffusion by the J. S. model. The restricted butterfly motion of the phenyl group attached to the cardo ring in PES-C is mentioned but is not discussed in detail in this work. Correlation times for the segmental motion are in the picosecond range which indicates the high flexibility of PES-C chains. The correlation time for the phenyl group internal rotation is similar to that of the segmental motion. The temperature dependence of these motions is weak. The apparent activation energy of the motions considered is less than 10 kJ/mol. The simulating results for PES are also reasonable considering the differences in structure compared with PES-C. The correlation times and the apparent activation energy obtained using the J. S. model for the main chain motion of PES-C are the same as those obtained using the damped orientational diffusion model and the conformational jump model.

NMR Spectra of polyimides: Interpretation and local chain motion study

Three kinds of high-performance polyimides 1 (poly(ketone-imide) PKI), 2 (poly(ether-imide) PEI) and 3 (poly(oxy-imide) POI) were studied using nuclear magnetic resonance (NMR). The NMR spectra of the polyimides were assigned according to the comprehensive consideration of the substitution effect of different substituting groups, viz. distortionless enhancement by polarization transfer (DEPT), no nuclear Overhauser effect (NNE), analysis of relaxation time, and two-dimensional correlated spectroscopy (COSY) techniques. The structural units of these three polyimides were determined. Carbon-13 and proton relaxation times for PEI and PKI were interpreted in terms of segmental motion characterized by the sharp cutoff model of Jones and Stockmayer (JS model) and anisotropic group rotation such as phenyl group rotation and methyl group rotation. Correlation times for the main-chain motion are in the tens of picosecond range which indicates the high flexibility of polyimide chains. Correlation times for phenyl group and methyl group rotations are more than 1 order of magnitude lower and approximately 1 order of magnitude higher than that of the main chain, respectively.

LOCAL MAIN-CHAIN DYNAMICS OF PHENOLPHTHALEIN POLYETHERSULFONE

Local main chain dynamics of dissolved phenolphthalein polyethersulfone (PES-C) in solution with chloroform-d(1) were examined through C-13 NMR relaxation measurements. Spin-lattice relaxation times and NOE (nuclear Overhauser effects) factors were measured as a function of temperature. The relaxation data were interpreted in terms of main chain segmental motion by using the damped orientational diffusion model (DAMP) and the conformation jump model (VJGM) derived by Valeur, Jarry, Geny, and Monnerie. The simulation method used is N-SIMPLEX, which gives, in this study, a result of the object function less than 10(-4). Correlation times were obtained for the main chain motion of PES-C with these models and the results indicate that the main chain of PES-C are flexible. The comparison between PES-C and 1,2-polybutadiene is proposed. The distribution of the correlation time for the main chain motion by using VJGM model is discussed. The temperature dependence of correlation times for PES-C indicating the dynamical rigidity of its chains is obtained.

Development and application of NMR techniques to study water-in-CO2 microemulsions

Self-assembly is a phenomenon that occurs frequently throughout the universe. In this work, two self-assembling systems were studied: the formation of reverse micelles in isooctane and in supercritical CO2 (scCO2), and the formation of gels in organic solvents. The goal was the physicochemical study of these systems and the development of an NMR methodology to study them. In this work, AOT was used as a model molecule both to comprehensively study a widely researched system water/AOT/isooctane at different water concentrations and to assess its aggregation in supercritical carbon dioxide at different pressures. In order to do so an NMR methodology was devised, in which it was possible to accurately determine hydrodynamic radius of the micelle (in agreement with DLS measurements) using diffusion ordered spectroscopy (DOSY), the micellar stability and its dynamics. This was mostly assessed by 1H NMR relaxation studies, which allowed to determine correlation times and size of correlating water molecules, which are in agreement with the size of the shell that interacts with the micellar layer. The encapsulation of differently-sized carbohydrates was also studied and allowed to understand the dynamics and stability of the aggregates in such conditions. A W/CO2 microemulsion was prepared using AOT and water in scCO2, with ethanol as cosurfactant. The behaviour of the components of the system at different pressures was assessed and it is likely that above 130 bar reverse microemulsions were achieved. The homogeneity of the system was also determined by NMR. The formation of the gel network by two small molecular organogelators in toluene-d8 was studied by DOSY. A methodology using One-shot DOSY to perform the spectra was designed and applied with success. This yielded an understanding about the role of the solvent and gelator in the aggregation process, as an estimation of the time of gelation.

Self-assembling of phenothiazine compounds investigated by small-angle X-ray scattering and electron paramagnetic resonance spectroscopy

Small-angle X-ray scattering (SAXS) and electron paramagnetic resonance (EPR) have been carried out to investigate the structure of the self-aggregates of two phenothiazine drugs, chlorpromazine (CPZ) and trifluoperazine (TFP), in aqueous solution. In the SAXS studies, drug solutions of 20 and 60 mM, at pH 4.0 and 7.0, were investigated and the best data fittings were achieved assuming several different particle form factors with a homogeneous electron density distribution in respect to the water environment. Because of the limitation of scattering intensity in the q range above 0.15 angstrom(-1), precise determination of the aggregate shape was not possible and all of the tested models for ellipsoids, cylinders, or parallelepipeds fitted the experimental data equally well. The SAXS data allows inferring, however, that CPZ molecules might self-assemble in a basis set of an orthorhombic cell, remaining as nanocrystallites in solution. Such nanocrystals are composed of a small number of unit cells (up to 10, in c-direction), with CPZ aggregation numbers of 60-80. EPR spectra of 5- and 16-doxyl stearic acids bound to the aggregates were analyzed through simulation, and the dynamic and magnetic parameters were obtained. The phenothiazine concentration in EPR experiments was in the range of 5-60 mM. Critical aggregation concentration of TFP is lower than that for CPZ, consistent with a higher hydrophobicity of TFP. At acidic pH 4.0 a significant residual motion of the nitroxide relative to the aggregate is observed, and the EPR spectra and corresponding parameters are similar to those reported for aqueous surfactant micelles. However, at pH 6.5 a significant motional restriction is observed, and the nitroxide rotational correlation times correlate very well with those estimated for the whole aggregated particle from SAXS data. This implies that the aggregate is densely packed at this pH and that the nitroxide is tightly bound to it producing a strongly immobilized EPR spectrum. Besides that, at pH 6.5 the differences in motional restriction observed between 5- and 16-DSA are small, which is different from that observed for aqueous surfactant micelles.