NMR approach to kinetics of polymer ordering in polyacrylonitrile solutions and acrylonitrile-sodium methallylsulfonate copolymer solutions: Solution-concentration and polymer-tacticity effect

Partial crystallinity of polyacrylonitrile and acrylonitrile-sodium methallylsulfonate copolymer is detected by X-ray diffraction in dimethyl formamide and glycerol-dimethyl formamide solutions in the range of polymer concentration (0.14, 0.325 mol/mol). Kinetics of isothermal ordering are followed by NMR for various temperatures, polymer concentration of the solutions and polymer tacticities. The rate of polymer ordering increases upon either a decrease of the temperature, an increase of the polymer concentration or an increase of the percentage of isotactic triads. Mandelkern's model of isothermal polymer crystallisation is applied to estimate the size of critical crystalline nuclei. Assuming that crystallites growth is negligible along polymer chain axis, one can deduce the maximal size of crystallites along this axis. The size of the crystallites perpendicularly to polymer chain axis is evaluated by X-ray diffraction. It is found to be of the order of 100 Å.     

Structure and ordering kinetics of micelles in triblock copolymer solutions in selective solvents

We have used small-angle x-ray scattering (SAXS), and small-angle neutron scattering (SANS) to study the micelle structure of a polystyrene-block-poly(ethene-co-butene)-block-polystyrene triblock copolymer in dilute - semidilute solutions in solvents selective for either the outer styrene block (dioxane) or for the middle block (heptane or tetradecane). Measurements of equilibrium structure factors showed that micelles were formed in both types of selective solvents. In the case of dioxane, the micelles are isolated whereas in the case of heptane or tetradecane, a bridged micellar structure may be formed at higher copolymer concentrations. In both cases we observed an ordered cubic structure of insoluble domains (micellar cores) at high concentrations (> 8 %). The micellar scattering function was fit to the Percus-Yevick interacting hard-sphere model. The temperature dependence of the core radius, the hard-sphere interaction radius and the volume fraction of hard spheres were obtained. We also used synchrotron-based time-resolved SAXS to examine the kinetics of ordering of the micelles on a cubic lattice for many different temperature jumps into the ordered cubic phase starting from the disordered micellar fluid phase in different solvents at different concentrations. The time evolution of the structure changes was determined by fitting the data with Gaussians to describe the structure factor of the ordered Bragg peaks and the Percus-Yevick structure factor was used to describe the micellar fluid. The time dependence of the peak intensities and widths as well as of the micellar parameters will be presented. The results showing the kinetics of the transformation from the fluid to the ordered phase were analyzed using the Mehl-Johnson-Avrami theory of nucleation.     

A reduced phase space approach to collision processes

An exact master equation for the occupation of different states during a collision is derived. For a wide dass of initial states including those typical of scattering experiments, the transition probability matrix is independent of the initial state. The stationary solution of the master equation is the “prior” distribution.     

A statistical model for non-ionic micellar solutions and their phase diagrams

The micellar phase separation (cloud-point transition) of non-ionic surfactants is studied on the basis of a statistical theory, of liquids. The low value of the critical concentration is explained by the presence of an extended repulsive intermicellar interaction due to a region of structured water. Excellent agreement with experiment is found for the polyoxyethylene surfactants C₁₂E₈ and C₆E₃. Our model can give a closed solubility loop with a very different value of the concentration of the upper and lower consolution points. We study, also the osmotic compressibility and second virial coefficient and the correlation length.     

Solid + liquid phase diagrams,NMR and colorimetric measurements of mixtures

Solid+liquid equilibrium, NMR and colorimetric measurements have been made for the mixtures of o-phenylenediamine+phenol, p-phenylenediamine+hydroquinone, m-phenylenediamine+phenol, m-phenylenediamine+hydroquinone, p-phenylenediamine+phenol, and p-phenylenediamine+hydroquinone. The types and melting temperatures of the complexes formed in these mixtures were ascertained from phase diagrams. The nature of the complexes was ascertained from colorimetric and NMR data.     

NMR relaxation investigation of water “ordering” in aqueous lysozyme solutions

Lysozyme in aqueous dilute solution has been chosen as a model system to investigate the state and the mobility of water molecules near macromolecular surfaces. The dependence of the water proton NMR T₁ on temperature and on denaturing processes is interpreted in terms of long-range interactions giving rise to“ordering” of water, as seen on the NMR time scale.     

From ergodicity to extended phase diagrams

Structure prediction of stable and metastable phases is put on equal footing for the first time, with a solid thermodynamical background. How to estimate the lifetime of metastable phases is demonstrated by recent groundbreaking work of Jansen, Pentin, and Sch?n. At the heart lies the exploration of the Gibbs free-energy landscapes and the extended phase diagrams for complex systems.     

Analytic calculation of phase diagrams for solutions containing colloids or globular proteins

Second-order Barker–Henderson perturbation theory gives phase diagrams for colloid and protein solutions that include stable and metastable fluid–fluid, solid–fluid, and solid–solid phases. The potential of mean force is described by a hard-sphere interacting with a Yukawa potential. Calculations for different ranges of attraction show that, as expected, fluid–fluid coexistence becomes metastable when the potential becomes short-ranged. For a very short-ranged Yukawa potential, the phase diagram shows isostructural solid–solid equilibria with a critical point. To test more simplified models, phase diagrams from second-order Barker–Henderson perturbation theory are compared with those from the random-phase approximation for the fluid phase and the van der Waals theory for the solid phase; this comparison shows significantly different phase diagrams. Moreover, with a potential of mean force with primary and secondary minima, calculations using second-order perturbation theory identify conditions where colloidal and protein solutions can present two fluid–fluid regions, each with a critical point; however, the higher-density fluid–fluid region is likely to be metastable. The analytic calculations described here may be useful for interpretation of experimental phase diagrams and for guiding design of separation processes.     

Calculated phase diagrams for cellulose/ammonia/ammonium thiocyanate solutions in comparison to experimental results

Flory's lattice theory for rigid rod molecules and Kuhn chains is used to calculate phase diagrams for cellulose/ammonia/ammonium thiocyanate solutions. Persistence length values measured by light scattering and reported previously are used as rod length values. Variations in the phase diagram based on varying rod length/solvent composition and cellulose molecular weight are explored. Spinodal curves are calculated in a region of the phase diagram predicting phase separation between two anisotropic solutions. Finally, calculated phase diagrams are compared to published data for the system. Discrepancies between theory and data may be accounted for by soft interactions between cellulose molecules and solvent which are not incorporated into the lattice theory.     

Correlation of the volumes and heat capacities of solutions with their solid-liquid phase diagrams

Liquid systems which have strong non-idealities, as seen from their thermodynamic properties, often show evidence of these interactions in the solid-liquid phase diagrams. This suggests that some of the structures present in the solid state can persist in the solution state, on a time average, up to temperatures much higher than the melting point. Volumes and heat capacities of typical systems were either taken from the literature or measured to illustrate this correlation with the phase diagrams. With mixtures of aprotic solvents which show nearly-ideal simple eutectic phase diagrams, the properties of the solutions are also nearly ideal. Examples of systems investigated which show strong non-idealities are ionic surfactant solutions, alcohol-water mixtures, chloroform-triethylamine mixtures and lithium salts in aprotic solvents.Paper written in the honor of Loren Hepler on the occasion of his retirement.     

NMR investigations of phase transition in aqueous polymer solutions and gels

The use of NMR spectroscopy in investigations of phase transitions in aqueous polymer solutions and gels is reviewed. Results on this subject as obtained mostly for thermoresponsive polymers (e.g., poly(N-isopropylacrylamide) and its copolymers, poly(N-isopropylmethacrylamide) and its copolymers, poly(vinyl methyl ether)) from temperature dependences of ¹H and ¹³C NMR spectra, spin–lattice and spin–spin relaxation times, diffusion coefficients and NMR images are discussed.     

Effect of salt on the phase diagrams of two binary lyotropic liquid crystalline solutions

The effect of adding salts NH₄OH and CsOH to aqueous solutions of NH₄PFO and CsPFO, respectively, was studied for concentrations in the range 0 to 2 wt %. In both systems, the isotropic to nematic and nematic to lamellar phase transition temperatures were elevated. There was an insignificant effect on the width of the nematic range in the NH₄PFO system, while the nematic phase was widened by as much as ∼3°C in the case of CsPFO. High-resolution X-ray scattering measurements were performed to determine the micellar size and its dependence on temperature for 52 wt % NH₄PFO solution in water.     

Topology of subsolidus sections of phase diagrams of quaternary reciprocal systems without solid solutions

A problem of constructing subsolidus isobaric–isothermal sections of phase diagrams of quaternary reciprocal systems with constant-composition compounds and limited solid solutions was considered. Relations between the topological characteristics of such sections were derived. Their topological classification was proposed. An algorithm for constructing sections using the theory of finite graphs was developed. A problem of enumerating sections for diagrams with a given set of classification characteristics was solved.     

A one-dimensional energy diffusion approach to multidimensional dynamical processes in the condensed phase

We propose a generalized one-dimensional energy diffusion approach for describing the dynamics of multidimensional dynamical processes in the condensed phase. On the basis of a formalism originally due to Zwanzig, we obtain a one-dimensional kinetic equation for a properly selected relevant dynamical quantity and derive new analytical results for the dynamics of a multidimensional electron-transfer process, nonequilibrium solvation, and diffusive escape from a potential well. The calculated results for electron-transfer reactions in solvent-separated and contact ion pair systems are found to be in good agreement with the experimental results. We are able to explain the rate of the electron-transfer reaction using much smaller and reasonable values of the solvent reorganization energy in contrast to earlier works that had to use a much larger value. The proposed theory is not only conceptually simpler than the conventional approaches but is also free from many of their limitations. More importantly, it provides a single theoretical framework for describing a wide class of dynamical phenomena.     

Third law of thermodynamics as applied to phase diagrams

Consequences from the third law of thermodynamics are analyzed from the standpoint of low-temperature phase equilibria. The kinetics of attainment of low-temperature equilibria and some ordering and decomposition features of solid solutions are considered.     

Interpolymer complex between hydroxypropyl cellulose and maleic acid-styrene copolymer: phase behavior of semi-dilute solutions

The phase behavior of a water/hydroxypropyl cellulose/maleic acid-styrene copolymer (H2O/HPC/MAc-S) system was investigated in the semi-dilute range by turbidimetry, rheology, and optical microscopy. The two polymers under investigation form interpolymer complexes via hydrogen bonding. In the case of a total polymer concentration of cpol = 5 mg . mL(-1) a second phase segregates upon heating the homogeneous ternary system. By applying a constant shear rate (gamma = 50 s(-1)) the phase separation temperature of the system is 10-15 degrees C lower than for an unsheared one. For cpol = 10 mg . mL(-1) phase separation has already occurred at room temperature when the two binary polymer solutions are mixed. The distribution of the partners among the coexisting phases was examined by FT-IR spectroscopy. The stoichiometry of the interpolymeric complex (IPC) was estimated to be HPC/MAc-S = 40:60 (w/w) independent of cpol.     

A new approach to the structure of concentrated aqueous electrolyte solutions using pulsed NMR methods

It is shown that selective measurements of the magnetic dipole—dipole interactions between specific pairs of nuclear spins in glasses of concentrated aqueous electrolytes can provide detailed structural information of relevance to the liquid. The validity of the approach is demonstrated by selective measurements of the inter- and intra-molecular (H₂O) proton—proton interactions in LiCl and LiBr solutions at 100 K. For LiCl,4H₂O, these measurements are consistent with a short range (≈0.8 nm) distorted sodium chloride structure with Cl^? and Li(H₂O)⁺₄ as basic units: each Cl^? ion is octahedrally coordinated to six OH bonds. For LiCl,RH₂O solutions in the composition range 4 <R < 10, the excess H₂O is packed interstitially at the interfaces between clusters of LiCl,4H₂O. This structure is consistent with various properties of the solution at room temperature. LiBr solutions have similar structures.