Acrylonitrile-sodium methallylsulfonate copolymer solutions. NMR approach to phase diagrams and ordering processes

The physical behavior of solutions of an acrylonitrile-sodium methallylsulfonate copolymer in dimethyl sulfoxide is described from NMR and calorimetric observations by varying concentration, temperature and thermal history of the systems. Both the solvent and the polymer can crystallize in the studied range of temperature. A method is proposed to determine the composition of the phases present in solution. At high polymer concentration, we observe that the physical state of a given solution depends on its thermodynamic history and that three distinct phases can coexist over a large temperature interval.     

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.     

NMR Approach to the kinetics of polymer crystallization. II. Polydimethylsiloxane solutions

The dilution effect on the crystallization kinetics of PDMS/toluene solutions, ranging from a polymer volume fraction of ? = 1.00 (pure PDMS) to ? = 0.32, was studied using ¹H high-power NMR. Spin-spin magnetic response was analyzed into relaxation components, arising from the different phases of the semicrystalline sample, through a spin-echo technique. The intensity and shape of the amorphous component provide relevant information concerning (1) the global crystallization process and (2) the state of hindrance of the amorphous chains induced by the growing crystalline domains. It was shown that, in solutions, the main effect on the crystallization kinetics of changing concentration is to depress the equilibrium melting temperature of the system. However, a radically distinct crystallization rate between the pure and the more concentrated system must be explained in terms of the activation energy for interphase chain transport. Thermodynamic parameters of PDMS crystallites were also deduced from a model. Comparison between the isothermal development of the overall crystallinity and the variation of a characteristic relaxation time of the amorphous PDMS proton response gives an insight into the relative predominance of nucleation or growth rates in the crystallization mechanisms.     

NMR approach to the kinetics of polymer crystallization. 1. Cis-1,4-polybutadiene

The isothermal crystallization kinetics of cis-1,4-polybutadiene (PB) in bulk, was studied over the temperature range 193 to 235 K, using ¹H pulsed high-resolution FT-NMR. Analysis of the spectral line area and width, corresponding to the resonance of protons bonded to noncrystalline chain segments, yields two major results:

• (i) The line area variations are associated with the overall progression of crystallization in the sample, which is shown to obey on Avrami law. The time exponent n and rate constant k were determined for each isotherm; their temperature dependence reflects the nucleation and crystal growth mechanisms and provides an estimate of relevant thermodynamic parameters.
• (ii) The line-width is assumed to be closely related to a statistical network with the average mesh size determined by a random distribution of crystallites. Finally, concomitant spin-lattice relaxation time (T₁) measurements show an increase of this parameter which parallels the development of the crystalline fraction.

     

Mechanism and kinetics of ordering in diblock copolymer thin films on chemically nanopatterned substrates

Lamellae forming diblock copolymer domains can be directed to assemble without defects and in registration with chemically nanopatterned substrates. Initially, thin films of the lamellar poly(styrene-b-methyl methacrylate) block copolymer form hexagonally close-packed styrene domains when annealed on chemical nanopatterned striped surfaces. These styrene domains then coalesce to form linear styrene domains that are not fully registered with the underlying chemical surface pattern. Defects coarsen, until defect-free directed assembly is obtained, by breaking linear styrene domains and reforming new structures until registered lamellae have been formed. At all stages in the process, two factors play an important role in the observed degree of registration of the block copolymer domains as a function of annealing time: the interfacial energy between the blocks of the copolymer and the chemically nanopatterned substrate and the commensurability of the bulk repeat period of the block copolymer and the substrate pattern period. Insight into the time-dependent three-dimensional behavior of the block copolymer structures is gained from single chain in mean field simulations. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3444–3459, 2005     

Interconversion kinetics and ordering of 1,4- and 1,1-dimethylcyclohexane in liquid-crystalline solutions by 1D and 2D deuterium NMR

Deuterium NMR spectra of perdeuteriated 1,4-dimethylcyclohexane-d₁₆ and 1,1-dimethylcyclohexane-d₁₆ dissolved in the nematic solvent ZLI 2452 are reported for the temperature range -40 to +80°C. Between -30 and +60°C the spectra exhibit characteristic exchange broadening and coalescence due to the ring inversion process. In the extreme slow exchange regime, peak assignment and determination of relative signs of the deuterium quadrupole interactions were made using 2D exchange spectroscopy and structural parameters derived from molecular mechanics calculations. In the intermediate temperature range the lineshapes were interpreted quantitatively in terms of the ring interconversion kinetics yielding the kinetic equations, k = 1.38 × 10¹³ exp (-45.2/RT)s^-1 for 1,4-dimethylcyclohexane, and k = 4.05 × 10¹³ exp (-49.0/RT)s^-1 for 1,1-dimethylcyclohexane, where R is in kJ mol^-1. The complete ordering matrix of both compounds was determined over the whole temperature range of the measurements.     

A theoretical approach to the kinetics of polymer degradation in solution

After main-chain scission in a polymer, the frequency of encounter between segments in the different fragments is related to the separating process between the fragments. The relationship obtained shows that the separating time is proportional to M ^½, where M is the molecular weight, when the excluded volume disappears. When good solvent is used, the half-time for the separation is obtained as τ_½ = const. M ^0.16–0.22, which is approximated to the experimental data obtained previously (τ_½ = const. M ^0.34 and τ_½ = const. M ^0.22) for the degradations of polyisobutene and poly(phenyl vinyl ketone), respectively. The increase of the half-time with increasing coil density can be explained by the excluded volume. The inverse proportionality of the diffusion of segments to solvent viscosity explains the proportionality of the half-time to microviscosity. The above separating process reverses the reaction between polymer radicals. From their dependence on the chain length, τ_½/k_D = const. M ^½ (where k_D is the specific rate for the reaction), is estimated. Such an approximation holds, regardless of the type of solvent.     

Solvent self-diffusion,polymer NMR relaxation,and free volume in polymer solutions

The self-diffusion coefficient of chloroform in poly(isopropyl acrylate)—chloroform solutions has been studied as a function of concentration and temperature by using the pulsed-field-gradient spin-echo NMR method. It is found that the self-diffusion coefficient of the solvent can be adequately fitted by using a simple free-volume approach with either a concentration or temperature superposition. It was noted that the free-volume parameters derived from the self-diffusion data are the same as those derived from deuterium NMR transverse relaxation-time measurements of the polymer in the same system. The equality of these two sets of experiments suggests a fundamental relationship between the two different processes. The simplest explanation is that the free volume necessary for the local segmental motion of the polymer and the translation of the solvent are similar.     

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.     

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.     

NMR studies of polymer solutions. II. Polyethylene

The intramolecular structure of polyethylene in solution was studied by a high-resolution nuclear magnetic resonance technique. Highly purified n-alkanes (99.5%) from C₅H₁₂ to C₃₆H₇₄ were used as its oligomers. The NMR spectra of the polyethylenes (oligomers) are very sensitive to the solvents used. The internal methylene protons of all polyethylenes of various chain length resonance at an identical frequency in carbon tetrachloride. A sharp transition in the NMR spectrum of polyethylene in α-chloronaphthalene at 35°C. was observed at n-C₁₇H₃₆, above which there exist two distinguishable NMR peaks for internal methylene protons, and below which (fewer carbons) only a single peak was seen. The NMR spectra of the internal methylene protons of the polyethylenes (oligomers) taken in benzene are very similar to those taken in pyridine. They are not as easily resolved as those NMR spectra taken in α-chloronaphthalene solutions. The effect of the size of the aromatic solvent molecule on the NMR spectra of the internal methylene protons of the polyethylenes (oligomers) in solutions was demonstrated by using aromatic solvents of various sizes, such as chlorobenzene, α-chloronaphthalene, and 9-chloronathracene. The results indicate that the formation of polymeric structure of the internal methylene groups in the polyethylene chain is very sensitive to the size of the solvent used. The interaction of the solvent with the methylene groups of the polyethylenes varies as a function of chain length; it is stronger for those low member n-alkanes and decreases gradually to an asymptotic value.     

Structure of inhomogeneous polymer solutions: a density functional approach

The structure of polymer solutions confined between surfaces is studied using a density functional theory where the polymer molecules have been modeled as a pearl necklace of freely jointed hard spheres and the solvent as hard spheres. The present theory uses the concept of universality of the free energy density functional to obtain the first-order direct correlation function of the nonuniform system from that of the corresponding uniform system, calculated through the Verlet-modified type bridge function. The uniform bulk fluid direct correlation function required as input has been calculated from the reference interaction site model integral equation theory using the Percus-Yevick closure relation. The calculated results on the density profiles of the polymer as well as the solvent are shown to compare well with computer simulation results.     

Carbon-13 NMR studies of local dynamics in polymer solutions and melts

Carbon-13 spin-lattice relaxation time measurements have been performed at two experimental frequencies on a series of amorphous polymers in the bulk state at temperatures well above the glass-transition temperatures and in solution. The high experimental values of the T₁ minimum as a function of temperature cannot be accounted for only by the specific orientation autocorrelation functions developed for polymers. They indicate the existence of an additional fast anisotropic motion, which we have assigned to librations of limited but significant extent of the internuclear CH vectors about their rest position. Moreover, in most cases, the temperature dependence of the segmental motions proves that they are involved in the glass-rubber transition phenomena.     

Magic-angle-spinning-induced local ordering in polymer electrolytes and its effects on solid-state diffusion and relaxation NMR measurements

Magic-angle-spinning (MAS) enhances sensitivity and resolution in solid-state nuclear magnetic resonance (NMR) measurements. MAS is obtained by aerodynamic levitation and drive of a rotor, which results in large centrifugal forces that may affect the physical state of soft materials, such as polymers, and subsequent solid-state NMR measurements. Here, we investigate the effects of MAS on the solid-state NMR measurements of a polymer electrolyte for lithium-ion battery applications, poly(ethylene oxide) (PEO) doped with the lithium salt LiTFSI. We show that MAS induces local chain ordering, which manifests itself as characteristic lineshapes with doublet-like splittings in subsequent solid-state ¹ H, ⁷ Li, and ¹⁹ F static NMR spectra characterizing the PEO chains and solvated ions. MAS results in distributions of stresses and hence local chain orientations within the rotor, yielding distributions in the local magnetic susceptibility tensor that give rise to the observed NMR anisotropy and lineshapes. The effects of MAS were investigated on solid-state ⁷ Li and ¹⁹ F pulsed-field-gradient (PFG) diffusion and ⁷Li longitudinal relaxation NMR measurements. Activation energies for ion diffusion were affected modestly by MAS. ⁷Li longitudinal relaxation rates, which are sensitive to lithium-ion dynamics in the nanosecond regime, were essentially unchanged by MAS. We recommend that NMR researchers studying soft polymeric materials use only the spin rates necessary to achieve the desired enhancements in sensitivity and resolution, as well as acquire static NMR spectra after MAS experiments to reveal any signs of stress-induced local ordering.     

The measurement of diffusion and flow in polymer solutions using dynamic NMR microscopy

The new method of dynamic NMR microscopy has been used to obtain velocity and diffusion maps for polymer solutions in capillary flow. In particular we observe power law shear-thinning behaviour in poly(ethylene oxide) (PEO) solutions in the semi-dilute regime but without slip at the walls. Some evidence is apparent for enhanced solvent diffusion along the shear axis in region of high shear.     

A distribution kinetics approach for crystallization of polymer blends

The cluster distribution approach is extended to investigate the crystallization kinetics of miscible polymer blends. Mixture effects of polymer-polymer interactions are incorporated into the diffusion coefficient. The melting temperature, activation energy of diffusion, and phase transition enthalpy also depend on the blending fraction and lead to characteristic kinetic behavior of crystallization. The influence of different blending fractions is presented through the time dependence of polymer concentration, number and size of crystals, and crystallinity (in Avrami plots). Computational results indicate how overall crystallization kinetics can be expressed approximately by the Avrami equation. The nucleation rate decreases as the blending fraction of the second polymer component increases. The investigation suggests that blending influences crystal growth rate mainly through the deposition-rate driving force and growth-rate coefficient. The model is further validated by simulating the experimental data for the crystallization of a blend of poly(vinylidenefluoride)[PVDF] and poly(vinyl acetate)[PVAc] at various blending fractions.     

The effect of shear on ordered block copolymer solutions

Block copolymers are extensively used in solution, especially aqueous solution, because of their amphiphilic character. This leads to the formation of lyotropic mesophases under given conditions of concentration and temperature. In many applications, block copolymer solutions are subjected to shear during processing (for example in drug delivery or when washing in detergent solutions) and thus it is of considerable interest to understand how shear affects the mesophase structure. Recent research has focussed on probing shear-induced structural transformations in lamellar, hexagonal and cubic-packed micellar phases using small-angle X-ray and neutron scattering.     

Quasichemical approach to crosslinked polymer solutions and the swelling equation for polycondensation networks

The change of free enthalpy and the chemical potential of solvent for mixing of solvent with crosslinked structures formed by stepwise reactions of the polycondensation type has been derived by an adaptation of the quasichemical equilibrium method. Each monomer unit is supposed to bear a different number of crosslinkable contact points, the coupling of which gives rise to chemical bonds, and of uncrosslinkable contact points, involved in interactions with the solvent, which may be of different type. The results are used to analyze the effect of network topology on the parameters of the swelling equation, particularly on a parameter characterizing the network composition. This parameter may be obtained from analytical data or by using the crosslinking statistics; and model calculations show how it varies with monomer conversion.