NMR self-diffusion studies in heterogeneous systems

The principles and main limitations of the application of the NMR field gradient technique to self-diffusion measurements are discussed. Due to their higher sensitivity for small diffusion coefficients and due to several advantages with the analytical treatment of the experimental data, the pulsed gradient methods are of special importance for the investigation of heterogeneous systems. Examples of the application of these techniques to diffusion studies in multicomponent systems and bounded media are given.     

Time dependence of the NMR line shape for systems with chemical exchange in a zero saturation limit

An expression has been derived for the time dependence of the NMR line shape for systems with many-site chemical exchange in the absence of spin-spin coupling, in a zero saturation limit. The dynamics of variation of the NMR line shape with time is considered in detail for the case of two-site chemical exchange. Mathematica programs have been designed for numerical simulation of the NMR spectra of chemical exchange systems. The analytical expressions obtained are useful for NMR line shape simulations for systems with photoinduced chemical exchange.     

Glass transition of heterogeneous polymeric systems studied by calorimetry

This personal review focuses on two aspects. First, glass transition dynamics and hence also calorimetry is connected to dynamic heterogeneity. This results in an interplay of the corresponding dynamic length scales and length scales from structural heterogeneities in polymeric samples. Second, the complexity of the dynamic glass transition itself results in different effects of this interplay for different experimental observables. Hence the comparison of results from calorimetry with other relaxation methods gives important clues to an understanding of the complex glass transition phenomenon.     

Interphase interaction in heterogeneous polymeric systems containing liquid-crystalline component

Some problems of analysis of interphase interactions in heterogeneous polymeric systems containing liquid-crystalline component are considered. Special attention is given to the methods of optical interferometry and dynamic mechanical spectrometry. The formation of interphase layers due to either partial compatibility or chemical interaction causes considerable improvement in mechanical properties of composite materials.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1862–1878, November, 1994.The authors wish to thank O. V. Vasil'eva for the study of dynamic mechanical properties of melts of polysulfone-LC polyester Ultrax blends.     

Statistical mechanical theory for steady state systems. VII. Nonlinear theory

The second entropy theory for nonequilibrium thermodynamics is extended to the nonlinear regime and to systems of mixed parity (even and odd functions of molecular velocities). The steady state phase space probability density is given for systems of mixed parity. The nonlinear transport matrix is obtained and it is shown to yield the analog of the linear Onsager-Casimir reciprocal relations. Its asymmetric part contributes to the flux and to the production of second entropy. The nonlinear transport matrix is not simply expressible as a Green-Kubo fluctuation equilibrium time correlation function. However, here the first nonlinear correction to the transport coefficient is given explicitly as a type of the Green-Kubo equilibrium time correlation function. The theory is illustrated by application to chemical kinetics.     

Probing microscopic architecture of opaque heterogeneous systems using double-pulsed-field-gradient NMR

Microarchitectural features of opaque porous media and biological tissues are of great importance in many scientific disciplines ranging from chemistry, material sciences, and geology to biology and medicine. Noninvasive characterization of coherently organized pores is rather straightforward since conventional diffusion magnetic resonance methods can detect anisotropy on a macroscopic scale; however, it remains extremely challenging to directly infer on microarchitectural features on the microscopic scale in heterogeneous porous media and biological cells that are comprised of randomly oriented compartments, a scenario widely encountered in Nature. Here, we show that the angular bipolar double-pulsed-field-gradient (bp-d-PFG) methodology is capable of reporting on unique microarchitectural features of highly heterogeneous systems. This was demonstrated on a toluene-in-water emulsion system, quartz sand, and even biological specimens such as yeast cells and isolated gray matter. We find that in the emulsion and yeast cells systems, the angular bp-d-PFG methodology uniquely revealed nearly an image of the pore space, since it conveyed direct microarchitectural information such as compartment shape and size. In two different quartz sand specimens, the angular bp-d-PFG experiments demonstrated the presence of randomly oriented anisotropic compartments. We also obtained unequivocal evidence that diffusion in interconnected interstices is restricted and therefore non-Gaussian. In biological contexts, the angular bp-d-PFG experiments could uniquely differentiate between spherical cells and randomly oriented compartments in gray matter tissue, information that could not be obtained by conventional NMR methods. The angular bp-d-PFG methodology also performs very well even when severe background gradients are present, as is often encountered in realistic systems. We conclude that this method seems to be the method of choice for characterizing the microstructure of porous media and biological cells noninvasively.     

Statistical theory of turbulent mass transfer in electrochemical systems

The paper presents an overview of the statistical theory of turbulent mass transfer in electrochemical systems and some new results which generalize the previously obtained relations for the flows of complex geometry. The developed theory does not use traditional semi-empirical hypotheses and analogies, but directly addresses to the solving of the critical for turbulent transfer the closure problem. The mathematical procedure for solving of the closure problem makes use of new equations for the correlations between concentration and velocity fluctuations in different space points and at different time moments; the dumping of turbulent pulsations in the viscous sublayer allows to neglect high order moments and obtain a closed equation for the turbulent mass flux. In general, the relation between the turbulent mass flux and the mean concentration gradient is non-local. Using available experimental information, the non-local equation for the turbulent mass flux is reduced to the traditional local one and the functional form of the turbulent diffusion coefficient is obtained. It is demonstrated that Reynolds analogy cannot been used for the prediction of the turbulent diffusivity. Applications of the developed theory to chemical engineering and to electrochemical flow diagnostics (prediction of flow characteristics using limiting diffusion current measurements) are discussed.     

A reduced density-matrix theory of absorption line shape of molecular aggregate

A theory for the absorption line shape of molecular aggregates in condensed phase is formulated based on a reduced density-matrix approach. Intermolecular couplings in the aggregates are assumed to be weak (F?rster type of energy transfer mechanism). The spin-Boson model is employed to include the effect of electron-phonon coupling. Using the projection operator technique, we derive kinetic equations for the reduced electronic density matrix associated with the absorption spectrum. General expressions of time-dependent rate constants in the kinetic equations are derived by using the cumulant expansion technique. The resulting time-dependent kinetic equations are solved numerically. We illustrate the applicability of the present theory by calculating the line shape of a dimer (a pair of donor and acceptor of energy transfer). For a J-aggregate type of molecular pair (with excitonic redshift), a tail appears on the blue side of the absorption spectrum due to the existence of inhomogeneity in electronic state mixing which is originated from the electron-phonon coupling.     

Statistical mechanical theory for steady state systems. VI. Variational principles

Several variational principles that have been proposed for nonequilibrium systems are analyzed. These include the principle of minimum rate of entropy production due to Prigogine [Introduction to Thermodynamics of Irreversible Processes (Interscience, New York, 1967)], the principle of maximum rate of entropy production, which is common on the internet and in the natural sciences, two principles of minimum dissipation due to Onsager [Phys. Rev. 37, 405 (1931)] and to Onsager and Machlup [Phys. Rev. 91, 1505 (1953)], and the principle of maximum second entropy due to Attard [J. Chem.. Phys. 122, 154101 (2005); Phys. Chem. Chem. Phys. 8, 3585 (2006)]. The approaches of Onsager and Attard are argued to be the only viable theories. These two are related, although their physical interpretation and mathematical approximations differ. A numerical comparison with computer simulation results indicates that Attard's expression is the only accurate theory. The implications for the Langevin and other stochastic differential equations are discussed.     

Inhomogeneous NMR line shape as a probe of microscopic organization of bicontinuous cubic phases

NMR line shapes of the lipid and aqueous species in bicontinuous cubic phase (BCP) samples prepared by centrifugation are inhomogeneously broadened. The broadening of the lipid peaks is removed by magic-angle spinning (MAS). In this work, we studied the mechanism of this broadening using (1)H and (13)C NMR spectroscopy of a myverol/water BCP. It is demonstrated that the inhomogeneity possesses an intrinsic contribution that is independent of instrumental or setup factors and can be attributed to the microscopic organization of the BCP bilayer. A mechanism of the inhomogeneous broadening is proposed, which involves a spatially nonuniform diamagnetically induced magnetic field determined by the mesoscopic structure and the diamagnetic susceptibilities of the two BCP domains. The proposed mechanism does not require that molecular reorientation of the lipid be slow for the inhomogeneous broadening to survive. We discuss how this inhomogeneous broadening can be employed as a probe of compositional uniformity and microscopic organization of BCP samples.     

Statistical mechanical theory for steady state systems. V. Nonequilibrium probability density

The phase space probability density for steady heat flow is given. This generalizes the Boltzmann distribution to a nonequilibrium system. The expression includes the nonequilibrium partition function, which is a generating function for statistical averages and which can be related to a nonequilibrium free energy. The probability density is shown to give the Green-Kubo formula in the linear regime. A Monte Carlo algorithm is developed based upon a Metropolis sampling of the probability distribution using an umbrella weight. The nonequilibrium simulation scheme is shown to be much more efficient for the thermal conductivity of a Lennard-Jones fluid than the Green-Kubo equilibrium fluctuation method. The theory for heat flow is generalized to give the generic nonequilibrium probability densities for hydrodynamic transport, for time-dependent mechanical work, and for nonequilibrium quantum statistical mechanics.     

Applying structural transition theory to describe enzyme kinetics in heterogeneous systems

Enzyme action was investigated by assuming the occurrence of different states of enzyme-substrate affinities. These states were considered to involve enzyme species with distinct abilities to form reaction product. The results obtained showed strong agreement with the experimental data for the action of peroxidase. This approach provides a powerful tool for predicting the kinetic behavior of other enzymatic processes in conditions not described before. An additional feature of this approach is the ability to characterize processes at any enzyme-substrate concentration ratio, including high enzyme-substrate ratios and enzyme inhibition by substrate or product. This proposal can also be used in systems with heterogeneity concerning the investigated enzyme.     

Dynamics of polymeric systems

Using dielectric and mechanical relaxation data of polymeric systems, an alternative formula is examined. The formula describes the experimental data with a high degree of accuracy, not received by the other model functions (Arrhenius and non-Arrhenius type) under investigation. The proposed formula gives the answer on questions concerning a supermolecular structure and the nature of the structural relaxation. New definition of the glass-transition temperature is proposed. It is shown how we should combine the results of different experimental methods to conduct an unambiguous analysis of polymeric systems.     

Statistical mechanical theory for steady-state systems. III. Heat flow in a Lennard-Jones fluid

A statistical mechanical theory for heat flow is developed based upon the second entropy for dynamical transitions between energy moment macrostates. The thermal conductivity, as obtained from a Green-Kubo integral of a time correlation function, is derived as an approximation from these more fundamental theories, and its short-time dependence is explored. A new expression for the thermal conductivity is derived and shown to converge to its asymptotic value faster than the traditional Green-Kubo expression. An ansatz for the steady-state probability distribution for heat flow down an imposed thermal gradient is tested with simulations of a Lennard-Jones fluid. It is found to be accurate in the high-density regime at not too short times, but not more generally. The probability distribution is implemented in Monte Carlo simulations, and a method for extracting the thermal conductivity is given.     

Interpretation of flow data for multicomponent polymeric systems

A model based on the altered free volume state concept has been proposed here to predict the melt flow index values of multicomponent systems as a function of the amount of the dispersed phase. The predictions of the model have been compared with experimental results reported in the literature on a diverse range of multicomponent polymeric systems. The agreement between the model predictions and the experimentally determined values is good.     

Statistical theory of spectra

The rapidly developing field of statistical theory of spectra of many-electron systems is briefly reviewed. In particular, new formal developments, their implementations in studying general properties of the model spaces, and links to the reduction problem are addressed. Applications in molecular and atomic spectroscopy are also discussed. © 1994 John Wiley & Sons, Inc.     

Extended kinetic theory of polymeric fluids

The setting of classical configuration space kinetic theory of polymeric fluids is extended by adopting the field of internal momentum into the set of independent state variables. The internal momentum predicated by the extended theory compares well with the internal momentum seen in molecular simulations. The extended theory is also shown to provide an intrinscially consistent formulation of the time evolution of macromolecules with internal friction.     

A particle growth theory for heterogeneous Ziegler polymerization

Samples of “as produced” polypropylene particles at progressively higher yield levels (grams polymer/gram catalyst) were sliced and examined by electron microscopy. In the polymerization of propylene with the TiCl₃–(C₂H₅)₂AlCl catalyst system the catalyst breaks up immediately into basic 100–1000 Å particles. As the yield increases, the catalyst particles gradually disappear and finally become completely dispersed in the polymer particle. These results are compatible with a theory which views the catalyst as a porous crystal containing a single species of active sites uniformly distributed. As polymerization progresses, all sites should eventually initiate a polymer chain whose length should be inversely proportional to the depth of the site below the surface of the particle. Two apparently equivalent statistical models were developed on the basis of this concept. Both models predict a slow increase in the X?_w/X?_n ration (Q) with increasing molecular weight, after an initial rapid increase. The most useful of these models states that Q is equal to the sum of X?_w terms of the simple harmonic series, and that a complete spectrum of x-mers should be present in the product. This agrees satisfactorily with analytically determined values.     

NMR Studies of polymeric materials - an overview

NMR has been used extensively in studies of synthetic polymers. The approaches employed may require solution NMR, solid state NMR, or NMR imaging. In each case, different techniques and analytical methodologies have been devised to facilitate experimentation or to maximize information output. These techniques are not mutually exclusive and often provide complementary information. A selective review is made herewith of polymer/NMR studies, with emphasis on the contributions made at NMR symposia held in Detroit in October, 1993 as part of the 20th FACSS meeting.