On phase transitions for subshifts of finite type

It has recently been shown that a strongly irreducible subshift of finite type in two or more dimensions may have more than one measure of maximal entropy. In this paper we obtain some results on when (i.e. for what kinds of subshifts of finite type) this happens, and when it does not. In particular, we show that the parameter of a certain subshift of finite type introduced by Burton and Steif has a critical value, below which we have a unique measure of maximal entropy, and above which we have non-uniqueness.     

The Influence of a Nonconstant Magnetic-Field Gradient on PFG NMR Diffusion Experiments. A Brownian-Dynamics Computer Simulation Study

The influence of a nonconstant magnetic-field gradient on the performance of pulsed-field-gradient NMR diffusion experiments was investigated by performing Brownian-dynamics simulations for two different coil designs using two different active sample volumes for each coil. The active sample volumes were chosen in order to represent different degrees of deviation from a perfectly constant magnetic-field gradient. The results show that one can actually tolerate a rather large deviation from a perfectly constant magnetic-field gradient and still obtain accurate values of the self-diffusion coefficients. The dependence of Δ (the observation time) and the dependence ofD(the self-diffusion coefficient) while keepingDand Δ constant, respectively, were also investigated for three of the active sample volumes. The simulations show that the effects due to a nonconstant field gradient depend only slightly on the values of Δ andD. In conclusion, the Brownian-dynamics computer simulations procedure is a quantitative way of investigating the performance characteristics of a gradient coil of a certain design before it is built.     

Ribbon phases in surfactant systems Comparisons between experimental results and predictions of a theoretical model

Ribbon phases consist of long cylindrical aggregates that have non-circular normal sections. We have recently pointed out that scattering data for a large number of different intermediate ribbon phases of lower than hexagonal symmetry found in ionic surfactant systems indicate that these phases have a structure possessing a centred rectangular symmetry. In this communication, we have investigated the aggregate dimensions for the phases with cylindrical aggregates, i.e., the hexagonal phases and the centred rectangular ribbon phases. Previously published phase diagrams, small angle X-ray and neutron scattering data and ²HNMR data for these phases in different systems have been used for this purpose. The results are that the axial ratios of the aggregates increase when the temperature decreases, when the surfactant concentration increases, and when the average surfactant charge decreases. Models that semi-quantitatively describe the thermodynamics of the micellar, hexagonal and lamellar phases, which are based on the Poisson-Boltzmann cell model approach, have previously been presented in the literature. We have extended these models to treat also the ribbon phases. The results from the calculations show the same trends with respect to changes in the dimensions of the non-circular aggregates upon changes in temperature, surfactant concentration and average surfactant charge, as those obtained experimentally. Theoretically calculated phase diagrams with ribbon phases are also presented. Based on the predictions of the model and some previously published experimental data for hexagonal phases, it is proposed that the formation of non-circular, cylindrical aggregates is a general property of single-chain, ionic surfactant/water systems, and that these aggregates in general pack on hexagonal lattices. The normal sections of these aggregates are circular on average, on account of the fact that the degree of deformation and the orientation of deformation changes along the axis of the aggregates and with time. Only for some systems, temperatures and surfactant concentrations do the asymmetric aggregates line up and ribbon phases with centred rectangular symmetry are obtained. The driving mechanisms for the transition from the hexagonal phase with asymmetric (fluctuating) cylinders and further to the centred rectangular phase with asymmetric (stiff) cylinders is also discussed. It is argued that this phase transition is of the first order.     

Can the structure of proteins be calculated?

In contrast to soluble proteins, membrane proteins offer the possibility, to predict their secondary structure with some reliability. Based on such predictions a set of initial conformation can be constructed on which molecular dynamics simulations are performed in order to find the most stable state. The important point is that all those degrees of freedom which change slowly in time must be varied artificially in the set of initial conformations. This procedure is demonstrated for the membrane protein bacteriorhodopsin.Dedicated to Professor W. Brenig on the occasion of his 60th birthday     

Order parameters in hydrocarbon chains

Order in lipid bilayers is often described by order parameters S_CD, S_HH and S_chain which are rather directly obtained from deuterium NMR, proton NMR and ESR spectroscopy respectively. A relation is derived that makes one of these parameters redundant from purely geometrical reasons. Further, the effect of conformational disorder upon these order parameters is investigated theoretically using a trans—gauche model. Corrections from the finite of the trans—gauche wells and from non-fixed valence angles are shown to be negligible.     

Determining the transition-state structure for different SN2 reactions using experimental nucleophile carbon and secondary alpha-deuterium kinetic isotope effects and theory

Nucleophile (11)C/ (14)C [ k (11)/ k (14)] and secondary alpha-deuterium [( k H/ k D) alpha] kinetic isotope effects (KIEs) were measured for the S N2 reactions between tetrabutylammonium cyanide and ethyl iodide, bromide, chloride, and tosylate in anhydrous DMSO at 20 degrees C to determine whether these isotope effects can be used to determine the structure of S N2 transition states. Interpreting the experimental KIEs in the usual fashion (i.e., that a smaller nucleophile KIE indicates the Nu-C alpha transition state bond is shorter and a smaller ( k H/ k D) alpha is found when the Nu-LG distance in the transition state is shorter) suggests that the transition state is tighter with a slightly shorter NC-C alpha bond and a much shorter C alpha-LG bond when the substrate has a poorer halogen leaving group. Theoretical calculations at the B3LYP/aug-cc-pVDZ level of theory support this conclusion. The results show that the experimental nucleophile (11)C/ (14)C KIEs can be used to determine transition-state structure in different reactions and that the usual method of interpreting these KIEs is correct. The magnitude of the experimental secondary alpha-deuterium KIE is related to the nucleophile-leaving group distance in the S N2 transition state ( R TS) for reactions with a halogen leaving group. Unfortunately, the calculated and experimental ( k H/ k D) alpha's change oppositely with leaving group ability. However, the calculated ( k H/ k D) alpha's duplicate both the trend in the KIE with leaving group ability and the magnitude of the ( k H/ k D) alpha's for the ethyl halide reactions when different scale factors are used for the high and the low energy vibrations. This suggests it is critical that different scaling factors for the low and high energy vibrations be used if one wishes to duplicate experimental ( k H/ k D) alpha's. Finally, neither the experimental nor the theoretical secondary alpha-deuterium KIEs for the ethyl tosylate reaction fit the trend found for the reactions with a halogen leaving group. This presumably is found because of the bulky (sterically hindered) leaving group in the tosylate reaction. From every prospective, the tosylate reaction is too different from the halogen reactions to be compared.     

Diffusion NMR for determining the homogeneous length-scale in lamellar phases

The size of the anisotropic domains in a lyotropic liquid crystal is estimated using a new protocol for diffusion NMR. Echo attenuation decays are recorded for different durations of the displacement-encoding gradient pulses, while keeping the effective diffusion time and the range of the wave vectors constant. Deviations between the sets of data appear if there are non-Gaussian diffusion processes occurring on the time-scale defined by the gradient pulse duration and the length-scale defined by the wave vector. The homogeneous length-scale is defined as the minimum length-scale for which the diffusion appears to be Gaussian. Simulations are performed to show that spatial variation of the director orientation in an otherwise homogeneous system is sufficient to induce non-Gaussian diffusion. The method is demonstrated by numerical solutions of the Bloch-Torrey equation and experiments on a range of lamellar liquid crystals with different domain sizes.     

A new insight into using chlorine leaving group and nucleophile carbon kinetic isotope effects to determine substituent effects on the structure of SN2 transition states

Chlorine leaving group k(35)/k(37), nucleophile carbon k(11)/k(14), and secondary alpha-deuterium [(kH/kD)alpha] kinetic isotope effects (KIEs) have been measured for the SN2 reactions between para-substituted benzyl chlorides and tetrabutylammonium cyanide in tetrahydrofuran at 20 degrees C to determine whether these isotope effects can be used to determine the substituent effect on the structure of the transition state. The secondary alpha-deuterium KIEs indicate that the transition states for these reactions are unsymmetric. The theoretical calculations at the B3LYP/aug-cc-pVDZ level of theory support this conclusion; i.e., they suggest that the transition states for these reactions are unsymmetric with a long NC-C(alpha) and reasonably short C(alpha)-Cl bonds. The chlorine isotope effects suggest that these KIEs can be used to determine the substituent effects on transition state structure with the KIE decreasing when a more electron-withdrawing para-substituent is present. This conclusion is supported by theoretical calculations. The nucleophile carbon k(11)/k(14) KIEs for these reactions, however, do not change significantly with substituent and, therefore, do not appear to be useful for determining how the NC-C(alpha) transition-state bond changes with substituent. The theoretical calculations indicate that the NC-C(alpha) bond also shortens as a more electron-withdrawing substituent is placed on the benzene ring of the substrate but that the changes in the NC-C(alpha) transition-state bond with substituent are very small and may not be measurable. The results also show that using leaving group and nucleophile carbon KIEs to determine the substituent effect on transition-state structure is more complicated than previously thought. The implication of using both chlorine leaving group and nucleophile carbon KIEs to determine the substituent effect on transition-state structure is discussed.     

Homogeneous length scale of shear-induced multilamellar vesicles studied by diffusion NMR

A recently developed protocol for pulsed gradient spin echo (PGSE) NMR is applied for the size determination of multilamellar vesicles (MLVs). By monitoring the self-diffusion behavior of water, the technique yields an estimate of the homogeneous length scale λ(hom), i.e. the maximum length scale at which there is local structural heterogeneity in a globally homogeneous material. A cross-over between local non-Gaussian to global Gaussian diffusion is observed by varying the experimentally defined length- and time-scales. Occasional observation of a weak Bragg peak in the PGSE signal attenuation curves permits the direct estimation of the MLV radius in favorable cases, thus yielding the constant of proportionality between λ(hom) and radius. The microstructural origin of the Bragg peak is verified through Brownian dynamics simulations and a theoretical analysis based on the center-of-mass diffusion propagator. λ(hom) is decreasing with increasing shear rate in agreement with theoretical expectations and results from (2)H NMR lineshape analysis.