Alan A. Jones

Improved computational methods for the calculation of Kohlrausch-Williams/Watts (KWW) decay functions☆

Abstract Convergence-accelerating methods have been applied to series expansions for the stable-law density Q α (Z)= 1 π ∫ 0 ∞ e −u α cos (zu) d u which is, in turn, simply related to the spectral density of the Kohlrausch-Williams/Watts (KWW) decay function λ(t)=e−(t/τ)α]. N.m.r. relaxation parameters such as NOEF, T1 and T1π are computed for polycarbonate and polydimethylsiloxane using the new series and the results compared to experiment and to earlier computations which employed a decomposition of the KWW function into a sum of exponential terms.

A lattice model for dynamics in a mixed polymer-diluent glass

Abstract A lattice model is developed to interpret NMR lineshape and relaxation data on polymer-diluent systems. The lattice is used to count nearest-neighbor contacts which are assumed to influence local dynamics. When applied to the polymer chain, the presence of one diluent-polymer repeat unit contact is considered to suppress sub-glass transition motion through improved packing. Polymer repeat units in contact with more than one diluent molecule on the lattice are presumed to have enhanced mobility. Polymer repeat units surrounded by other polymer repeat units are thought to have no change in their sub-glass transition dynamics. When applied to the diluent, isotropic rotational motion of diluent surrounded by polymer is considered to commence at the apparent thermal glass transition. For those diluent molecules in contact with other diluent molecules on the lattice, sub-glass transition rotational motion occurs at a temperature determined by the intrinsic mobility of the diluent. The motions of the chain and the diluent are reflected in the modulus and are traditionally discussed in terms of plasticization and antiplasticization.

The application of a simultaneous model for multisite exchange to solid-state NMR lineshapes

Abstract A multisite exchange treatment is developed to simulate NMR powder lineshapes in cases where motional processes of more than one type occur simultaneously. An example is presented where one type involves rotational diffusion, libration, or oscillation over a limited range whereas the other includes jumps of larger amplitudes between potential minima, the axis of motion being the same for both types. Restricted rotation of lower angular amplitude is conceived in terms of jumps between sites within one well with the amplitude of this restricted rotation being the key parameter which can be the same or different for each potential minimum. The second motional process of larger amplitude involves a series of jumps between sites in one well to sites in the other well. In the cases treated, the first process is always considered too fast to exhibit rate-dependent effects. One rate parameter is used for all jumps. This rate is always kept sufficiently large to keep the first process in the rapid exchange limit. At very large rates, both motions exhibit rate-independent effects. At slower rates, the rate dependence of the second process leads to conspicuous changes in the lineshape. The model sets an equal probability for all jumps and represents an alternative to the conventional treatment where one deals with the processes sequentially. The method is illustrated for the case of bisphenol-A polycarbonate (BPAPC), where results show an improvement over the previously published treatment based on a sequential approach.

Measurement of Diffusion Coefficients in Polystyrene Using Xenon-129 NMR

A sample of polystyrene beads, 18 μm in diameter, has been sealed in an NMR tube under 10 atm of xenon gas. Two dimensional,129Xe NMR spectra show cross peaks between the resonances corresponding to xenon in the free gas and the sorbed state, indicating that appreciable exchange occurs during the mixing time of the NMR experiment. Selective saturation of the free gas resonance attenuates the integrated intensity of the sorbed xenon resonance as a function of saturation time, thus allowing the accurate measurement of the exchange rates between the gas and the sorbed states. A model has been developed using a slightly modified form of Crank’s treatment of diffusion in a sphere which allows for the accurate determination of the diffusion coefficient for xenon in the sorbed state. The diffusion coefficient for xenon in polystyrene at 25°C is determined to be 2.9·10−9 cm2/s.

Nonexponential proton relaxation from cross-correlation in dissolved poly(2,6-dimethyl-1,4-phenylene oxide)

Abstract The methyl proton spin-lattice relaxation of poly(2,6-dimethyl-1,4-phenylene oxide) dissolved in CDCl 3 is strongly nonexponential at long times, but this behavior can be quantitatively accounted for by the cross-correlation descriptions of Hubbard and Werbelow and Marshall in combination with a dynamic model for local motions in randomly coiled polymer chains. The pronounced nonexponential decay stems from rapid anisotropic methyl group rotation, which is much faster than the other motions modulating the dipole-dipole interaction. An estimate of the correlation time for methyl group rotation is obtained by simulating the nonexponential character of the return to equilibrium, yielding values of 2 to 15 psec. The uncertainty in these values is rather high, a factor of 5, since three different exponential time constants describe the return to equilibrium; the difficulties associated with such a fitting procedure are well known. The initial spin-lattice relaxation is almost free of cross-correlation effects and independent of the value of the correlation time for methyl group rotation as long as it is short. This permits an analysis of the other motions contributing to relaxation.

NMR characterization of penetrants in high permeability polymers

Spectra of xenon-129 sorbed into two high permeability polymers are reported. The polymers are the copolymer of tetrafluoroethylene and 2,2-bis(trifluoromethyl)-4,5-difluoro-1,3-dioxole as well as poly(1-trimethylsilyl-1-propyne). At room temperature, the xenon-129 shifts are smaller than in conventional glassy polymers. The smaller xenon-129 shift indicates the presence of larger sorption sites in high permeability polymers relative to conventional polymers. The temperature dependence of solubility in these polymers is drastically different from the behavior in conventional polymers. There is a rapid exponential increase in solubility in high permeability polymers as temperature decreases corresponding to a large negative enthalpy change on sorption and it is this increase in solubility which leads to a large increase in shift with decreasing temperature. Pulse field gradient (PFG) determinations of the self-diffusion constant are made for xenon, propane, pentane and a decafluoropentane in the copolymer. Rapid diffusion is observed as well as a dependence of the apparent diffusion constant on the time scale of the PFG experiment. The translational mobility of smaller simpler moieties depends less on the time scale or equivalently, the length scale of observation in the PFG NMR experiment. For larger, more complex species, the interconnectedness of high free volume domains plays a role in reducing the apparent diffusion constant as the time of measurement increases.

Concentration and temperature dependence of diluent dynamics studied by line shape experiments on a phosphate ester in polycarbonate

31P Hahn spin echo line shape and proton line shape experiments are reported on bisphenol A polycarbonate (BPAPC)-tris(2-ethylehexyl)phosphate (TOP) systems to study the concentration and temperature dependence of the local dynamics. In an earlier 31P line shape study a lattice model was presented as a framework to interpret the plasticization and antiplasticization behavior of the diluent based on a fractional population given by the type of nearest neighbor contacts in the mixed polymer-diluent glass. In this study, 31P spin echo line shapes of BPAPC, with 5%, 10% and 15% TOP, which monitor the diluent dynamics, at different temperatures and echo delay times are simulated in terms of fast- and slow-moving components, and the resulting fractional populations are compared with that predicted by the lattice model. Comparisons with the lattice model calculations are also made in the simulation of the 1H line shapes on BPAPC with 5% and 10% TOP, which probes both the polymer and diluent dynamics, and on BPAPC with 5% and 10% perdeuterated trioctylphosphate (DTOP), which detects only the polymer motion. Fairly good line shape simulations and agreement between the lattice model and the fitting results at low diluent concentrations are obtained in all cases. Restricted cone motion best describes the slow-moving component in the 31P line shape fittings. For the fast component, rotational Brownian diffusion with a distribution of correlation times corresponding to a stretched exponential function is used. An activation energy Ea of 56 kJ/mol and an exponent alpha of 0.7 for the fractional exponential correlation function are obtained and used to calculate the mechanical loss peak which was compared with the experimental loss data. The plateau character of the fractional population as a function of temperature can also be interpreted and understood in terms of the lattice model.

A 129Xe NMR study on an ionomeric polymer blend system

The morphology of an ionomeric polymer blend consisting of an amino-silicone copolymer and zinc neutralized sulfonated polystyrene (ZnSPS) has been studied using proton spin diffusion and small angle X-ray scattering (SAXS). The extent of reaction between the two components in the blend was monitored by 13C CP MAS spectroscopy. All three types of experiment point to domain sizes in the nanometer range. 129Xe NMR was used to study exchange by translational diffusion between domains. A single xenon resonance was detected in temperatures ranging from 25 degrees C to -90 degrees C, and the chemical shift followed a weighted average of the isolated polymer shifts consistent with the small domain sizes. Pulse field gradient 129Xe NMR was used to determine the effective diffusion constants in the amino silicone starting material and the blend. The diffusion constant of xenon in poly(styrene) is known, allowing for comparison of the predictions of effective diffusion constants in the blend based on the values in the constituents of the blend. Simple two-site exchange equations incorrectly predict that diffusion in the blend would be dominated by the constituent with slow diffusion. The blend diffusion constant is close to the value of the amino silicone or the constituent with fast diffusion which is correctly predicted for a rapid exchange solution of the diffusion equation.

Proton and carbon‐13 relaxation and molecular motion in glassy bisphenol‐A polycarbonate

An interpretation of proton and carbon‐13 spin–lattice relaxation in glassy polycarbonate is developed which is consistent with the geometry, time scale, and amplitude determined from chemical shift anisotropy line shape collapse. The line shape data indicate π flips and libration about the same axis as the predominant motions. A correlation function incorporating these motions is developed to quantitatively interpret the proton spin–lattice relaxation data and the line shape collapse. The π flip process is described as an inhomogeneous distribution of correlation times using the Williams–Watts fractional exponential. An apparent activation energy of 46 kJ/mol is determined with the fractional exponent remaining constant at 0.15. The librational motion is described by the Gronski formalism where the amplitude increases with the square root of temperature; and the rotational diffusion constant, linearly with temperature. Rotational diffusion constants fall in the range of 108 to 109 s−1 which is comparable...

Multifield, temperature and concentration dependence of spin relaxation and local motion in 2,2-propane diyl-bis(4-hydroxyphenyl) polyformal

Abstract 13 C and proton spin-lattice relaxation data were determined as a function of field, temperature and concentration for 2,2-propane diyl-bis(4-hydroxyphenyl) polyformal in C 2 D 2 Cl 4 . The concentration of polymer was varied from a few per cent by weight up to the bulk rubber and temperature was varied from −20°C to +120°C. The relaxation data is interpreted in terms of several local motions including segmental motion, phenylene group rotation, methyl group rotation and formal group rotation. Segmental motion is described by a correlation function developed by Hall and Helfand which allows for cooperative and single bond transitions. The phenylene group rotation is described by the Woessner anisotropic stochastic diffusion model except at high concentration (⩾50 wt%) where the phenylene data is simulated by restricted rotation. Methyl group rotation is described by the Woessner three fold jump model, and the formal group rotation is described by double trans-gauche rotations about the C-O axes. At a concentration of 5 wt%, the time scale of segmental motion is slightly slower than in bisphenol-A-polycarbonate. However, the time scales of phenylene group and methyl group rotations are nearly identical for both polymers. A comparison is also made with chloral polyformal, another similar polyformal. The effect of concentration on local motion was monitored by 13 C spin-lattice relaxation measurements at three Larmor frequencies over the range of 5 to 100 wt% polymer at a temperature 40°C above the glass transition of this polyformal. The rate of local chain motion decreases as the concentration of polymer increases with the exception of methyl group rotation which remains constant. The correlation times for several local backbone motions are fit to free volume theory which yields a fractional free volume of 0.38 for the solvent (C 2 D 2 Cl 4 ) and 0.28 for the polymer.