Showing papers on "Relaxation (NMR) published in 1981"

Amorphous solids : low-temperature properties

Abstract: 1. Introduction.- 1.1 Historical Background.- 1.2 Tunneling States.- 1.2.1 Energy Levels.- 1.2.2 Transition Probabilities and Relaxation Times.- 1.3 Organization of the Book.- References.- 2. The Vibrational Density of States of Amorphous Semiconductors.- 2.1 The Vibrational Density of States.- 2.2 Experimental Techniques.- 2.3 The Theoretical Problem.- 2.4 Brute Force Theory.- 2.4.1 Turning the Handle.- 2.4.2 Some Results of Brute Force.- 2.5 More Refined Approaches.- 2.5.1 Analytical Ideas.- 2.5.2 The Bethe Lattice.- 2.5.3 Indirect Numerical Methods.- 2.6 The Incorporation of Matrix Elements.- 2.7 Can One Derive Structural Information from g(?)?.- 2.8 A Less Myopic View of the Field.- References.- 3. Low Temperature Specific Heat of Glasses.- 3.1 Review of the Experimental Situation.- 3.2 Comparison with Theoretical Models.- 3.2.1 The Tunneling Model.- 3.2.2 The Cellular Model.- 3.3 Summary and Outlook.- References.- 4. The Thermal Expansion of Glasses.- 4.1 Theoretical Background.- 4.2 The High Temperature Expansion of Vitreous Silica.- 4.3 The Low Temperature Expansion of Glasses.- 4.3.1 Experimental Results.- 4.3.2 Discussion.- References.- 5. Thermal Conductivity.- 5.1 Thermal Transport in Crystalline Materials.- 5.2 Thermal Transport in Amorphous Materials.- 5.2.1 The Phonon Mean Free Path.- 5.2.2 Phonon Scattering Mechanisms.- 5.2.3 Summary.- 5.3 Probing the Localized Excitations.- 5.4 Synopsis.- References.- 6. Acoustic and Dielectric Properties of Glasses at Low Temperatures.- 6.1 General Comments.- 6.2 Acoustic and Dielectric Properties Above 10 K.- 6.2.1 Absorption.- 6.2.2 Sound Velocity and Dielectric Constant.- 6.3 Acoustic and Dielectric Properties Below 10 K.- 6.3.1 Acoustic and Dielectric Absorption.- a) Relaxation Effects.- b) Resonant Interaction.- 6.3.2 Sound Velocity and Dielectric Constant.- 6.3.3 Acoustic Dielectric "Cross"-Experiments.- 6.4 Theoretical Description of the Acoustic and Dielectric Properties by Two-Level Systems.- 6.4.1 Dynamical Properties of Two-Level Systems.- 6.4.2 Absorption Due to a Distribution of Two-Level Systems.- 6.4.3 Variation of Sound Velocity and Dielectric Constant.- 6.5 Comparispn Between Theory and Experiment.- 6.6 Microscopic Description: Tunneling Model.- 6.7 Summary.- References.- 7. Relaxation Times of Tunneling Systems in Glasses.- 7.1 Background.- 7.2 Resonance Dynamics of Two-Level Systems.- 7.2.1 Tunneling Model.- 7.2.2 Longitudinal Relaxation Time T1.- a) One-Phonon Relaxation.- b) Conduction Electron Relaxation.- 7.2.3 Transverse Relaxation Time T'2.- 7.2.4 Spontaneous Echo Decay.- 7.2.5 Stimulated Echo Decay.- 7.3 Experiments Measuring Relaxation Times.- 7.3.1 Acoustic Saturation.- 7.3.2 Saturation Recovery.- 7.3.3 Linewidth.- 7.3.4 Two-Pulse Phonon Echo.- 7.3.5 Two-Pulse Electric Echo.- 7.3.6 Three-Pulse Phonon Echo.- 7.3.7 Three-Pulse Electric Echo.- 7.4 Critical Assessment of Data.- 7.4.1 T1 Results.- a) Three-Pulse Echoes.- b) Saturation Recovery.- c) Distribution of Decay Times.- 7.4.2 T'2 Results.- a) Two-Pulse Echoes.- b) Linewidth.- 7.5 Conclusions.- References.- 8. Low Frequency Raman Scattering in Glasses.- 8.1 Introductory Comments.- 8.2 Vibrational Raman Spectrum of First Order.- 8.2.1 Experimental Results.- 8.2.2 Theory of Low-Frequency Spectrum.- a) Continuum Theory.- b) Bond Polarizabil ity Model.- 8.3 Quasielastic Spectrum.- 8.3.1 Experimental Results.- 8.3.2 Theory.- a) Physical Origin of the Quasielastic Scattering.- b) Relation Between Raman Scattering and Ultrasonic Absorption.- c) Defect Model.- 8.4 Conclusion.- References.- Additional References with Titles.- Subject and Material Index.

Interpretation of magnetic resonance data from water nuclei in heterogeneous systems

Abstract: Nuclear magnetic resonance (NMR) data from water nuclei (1H, 2H, and 17O) can provide much information about the state of water in heterogeneous systems. In the present work, we present a theoretical framework for the interpretation of such data and discuss the implications of the theory. Due to the local anisotropy in heterogeneous systems, it is necessary to consider two components of water motion: a fast anisotropic reorientation superposed on a more extensive slow motion. On the basis of the experimentally verified assumption that these motions occur on different time scales, we develop a ’’two‐step’’ model of relaxation, showing that both motions may give important contributions to the relaxation. We derive a simple expression for the relevant correlation function, valid for isotropic systems. Anisotropic systems are also treated, making use of a new symmetry theorem for time correlation functions. The proof of this theorem is given in an Appendix. The magnitudes of the water 2H and 17O quadrupole coupling constants are estimated to 0.222 and 6.67 MHz, respectively. Results of ab initio quantum chemical calculations are presented, demonstrating the insensitivity of the water 17O field gradient to nearby ionic species. The possibilities and limitations of the NMR technique in answering the fundamental questions about water structure and dynamics in heterogeneous systems are discussed. We suggest a novel interpretation of the well‐known invariance of the ratio of 1H and 2H splittings. Furthermore, we argue that the available NMR data are consistent with a short‐ranged (≲2 molecular layers) perturbation of the water tumbling rate and anisotropy.

Investigation of the flexibility of DNA using transient electric birefringence.

Abstract: In the preceding article, a Monte Carlo analysis was presented which provides a quantitative numerical relationship between the rotational diffusion coefficients, as measured by the decay of optical anisotropy following an electric field pulse, and the flexibility (persistence length) of short, wormlike chains. In the present article, the results of the foregoing analysis are applied to the observed rates of decay of birefringence for a series of sequenced DNA fragments ranging in size from 104 to 910 base pairs. Under the conditions used in this study, the DNA fragments exist as native, duplex molecules. Furthermore, conditions are defined in which the observed relaxation times are not dependent on DNA concentration, field strength, or the duration of the pulse. It is pointed out that the ionic atmosphere associated with a wormlike polyion does not exert any significant (direct) influence on the rotational diffusion of the polyion and, therefore, that the rotational relaxation times are a true measure of the configurations of the DNA molecules in solution. Moreover, excluded-volume effects are shown not to be significant for the moderately short molecules employed in this study. The major conclusion of this study is that there is no strong ionic strength dependence of the persistence length for ionic strengths above 1 mM and that the persistence length, under conditions where electrostatic contributions are negligible, is approximately 500 A. For ionic strengths significantly lower than 1 mM, electrostatic contributions to the stiffness of DNA become significant.

Monte Carlo approach to the analysis of the rotational diffusion of wormlike chains

Abstract: Synopsis A Monte Carlo analysis is presented which establishes a relationship between the rotational diffusion coefficients and the flexibility (persistence length, P) of short, wormlike chains. The results of this analysis are presented in terms of experimentally observable quantities; namely, the rotational relaxation times for the field-free decay of optical anisotropy. The pertinent theoretical quantity is R, defined as the ratio of the longest rotational relaxation time of a wormlike chain to the transverse rotational relaxation time of a rigid cylinder having the same axial length (L) and segmental volume. R, so defined, is essentially independent of the axial ratio of the cylinder for any value of LIP within the range of validity of the present analysis (axial ratio > 20; 0.1 < L/P < 5). It is pointed out that P can be determined with reasonable accuracy even in the absence of a precise knowledge of the local hydrodynamic radius of the chain.

Protein hydration from water oxygen-17 magnetic relaxation

Abstract: Water oxygen-17 magnetic relaxation is shown to be a powerful technique for studying protein hydration. Longitudinal and transverse 170 relaxation rates were measured at variable frequency (4-35 MHz), temperature, pH, and protein concentration in aqueous solutions of seven proteins. The data were analyzed in terms of a fast exchange two-state model with local anisotropy. A water 170 quadrupole coupling constant of 6.67 MHz and an order parameter of 0.06 (from I7O splittings in lyotropic liquid crystals) results in approximately two layers of hydration water having a reorientational rate less than 1 order of magnitude slower than that of bulk water. This rapid local motion has a small anisotropic component, which is averaged out by protein reorientation with a correlation time of the order of 10 ns. Due to electrostatic protein-protein interaction the protein reorientation is considerably slower than predicted by the Debye-Stokes-Einstein equation. Charged residues, particularly carboxylate, are more extensively hydrated than other residues, accounting for the variation in the extent of hydration between different proteins.

Nuclear spin relaxation by translational diffusion in liquids and solids: high- and low-frequency limits

Abstract: Nuclear spin relaxation rates due to magnetic dipole coupling between spins of a single species undergoing relative diffusion depend on two-spin correlation functions J(p)( omega ). The high- and low-frequency limits of J(p)( omega ) are discussed for liquids, cubic crystals and two- and one-dimensional systems. It is shown that the low-frequency form of J(p) ( omega ) is J(p)(0)-A3 omega 1/2 in liquids and crystals, A2ln omega -1 in two-dimensional systems and A1 omega -1/2 in one-dimensional systems and expressions for the coefficients A1, A2 and A3 are derived which are valid for any diffusive model whose long-range, long-time behaviour may be described by the diffusion equation. The high-frequency form of J(p)( omega ) is derived for a simple-hopping model of spins on one-, two- and three-dimensional lattices and in each case J(p)( omega ) is of the form B omega -2. Expressions are derived for the coefficient B, for each dimension, which correctly include the effect of correlations between the hops of the spins.

Matrix isolation spectroscopy

Abstract: 1 The history of matrix isolation spectroscopy- Section A - Techniques- 2 Infrared and Raman matrix isolation spectroscopy- 3 Electronic spectroscopy of matrix isolated solutes- 4 Magnetic circular dichroism - matrix isolation spectroscopy- 5 Electron spin resonance studies of radicals trapped in rare-gas matrices- 6 Moessbauer spectroscopy on matrix-isolated species- 7 Time and frequency resolved vibrational spectroscopy of matrix isolated molecules: Population and phase relaxation processes- 8 Stable molecules- 9 Generation and trapping of unstable solutes in low temperature matrices- 10 The characterisation of high temperature molecules using matrix isolation and vibrational spectroscopy- 11 High pressure studies- 12 Non-traditional matrix isolation: adducts- Section B - Matrix Effects- 13 Interpretation of infrared and Raman spectra of trapped molecular impurities from interaction potential calculations- 14 Matrix induced changes in the electronic spectra of isolated atoms and molecules- 15 Matrix effects studied by electron spin resonance spectroscopy- 16 Molecular motion in matrices- 17 Vibrational band intensities in matrices- Section C - Applications- 18 Matrix isolation spectroscopy of metal atoms and small clusters- 19 Vibrational spectra of matrix isolated gaseous ternary oxides- 20 Matrix isolation spectra (IR, Raman) of transition metal compounds- 21 Metal carbonyls - structure, photochemistry, and IR lasers- 22 Matrix isolation vibrational spectroscopy on organic molecules- 23 Conformational isomerism studied by matrix isolation vibrational spectroscopy- 24 Hydrogen bonding in matrices- Author Index

Padé approximants to correlation functions for restricted rotational diffusion

Abstract: Simple closed‐form approximate expressions are presented for time‐correlation functions of spherical harmonics, with l = 2, m = 0, ±1, and ±2, within the framework of the diffusion in the cone model. In this model, a unit vector, with orientation specified by the polar angles ϑ and φ, is restricted to diffuse in a cone of semiangle ϑ0. By comparing with exact numerical results, it is shown that our expressions are highly accurate when m = 0, ±2 for 0°⩽ϑ0⩽90° and when m = ±1 for 0°⩽ϑ0⩽75°. The utility of our results is demonstrated in the context of modeling the effect of hindered motion of probes in membranes on the fluorescence emission anisotropy and the effect of internal motions on the nuclear magnetic resonance relaxation times of protons in nucleic acids.

Electron spin echoes of a photoexcited triplet: Pentacene in p‐terphenyl crystals

Abstract: Electron spin echo observations of the photoexcited triplet state of 0.1 mol % pentacene‐h14 and ‐d14 in p‐terphenyl crystals at room temperature are presented. Theory is presented for calculation of the echo envelope modulations for an S = 1, I = 1/2 spin system including zero field splittings in the high field limit. Echo envelope modulations due to proton and deuteron hyperfine interactions in the pentacene molecule have been observed. The echo decay data are used to calculate triplet state decay parameters.

Nucleotide Conformational Analysis by 31P Nuclear Magnetic Resonance Spectroscopy

Abstract: With the widespread utilization of Fourier transform (F1) and high field nuclear magnetic resonance (NMR) spectrometers, 31 P NMR spectroscopy of biological phosphates has now become quite common. This is not surprising, since the 31p nucleus has convenient NMR properties: spin 1/2, 100% natural abundance, moderate relaxation times, wide range of chemical shifts, and a key role in many biomolecu­ lar structures. Fourier transform NMR has substantially reduced the one serious limitation to the use of 31p NMR in biological systems, which is the low sensitivity of the phosphorus nucleus (6.6% at constant field compared to IH NMR). Routinely, millimolar (or lower) con­ centrations of phosphorus nuclei are conveniently monitored. NMR spectroscopic information includes the resonant line positions (chemical shifts, 8), the spin-spin coupling constants (J), and spin-lattice (TI) and spin-spin (1;) relaxation times. In addition, signal areas are often directly related to nuclei concentration. With these parameters NMR spectroscopy provides a unique, nonperturbing probe in solution of the structure and time-dependent properties of molecules. Much of this review is concerned with 31p chemical shifts. Effective use of 31p NMR as a probe of nucleotide conformation requires an understanding of the structural and environmental factors that influence these shifts. I will therefore first discuss some of the factors that alter

Magnetic resonance properties of hydrogen: imaging the posterior fossa

Abstract: Posterior fossa scans were performed on five healthy volunteers using a nuclear magnetic resonance (NMR) machine constructed by Thorn-EMI Ltd. Three different NMR scanning sequences were used. In the first, a type of saturation-recovery technique was used to produce images strongly dependent on the density of hydrogen nuclei, but with some dependence on the spin-lattice relaxation time (T1). In the second, an inversion-recovery technique was used to produce images with a stronger dependence on the spin-lattice relaxation time. In the third, a spin-echo technique was used to obtain images with a dependence on the spin-spin relaxation time (T2). All three types of NMR image were unaffected by bone artifact. Visualization of brain adjacent to the skull base was obtained without loss of detail due to partial-volume effect from bone. The saturation-recovery images highlighted arteries and veins that were clearly visible without the use of contrast agents. The inversion-recovery images showed remarkable gray-wh...

Determination of transient regime of hot carriers in semiconductors, using the relaxation time approximations

Abstract: It is shown that in a semiconductor, where impurity and polar optical phonon scatterings are not involved, the transient velocity is the solution of a relaxation time equation. Relaxation times can be defined as functions of the stationary energy, thus leading to relaxation time equations which are good approximations for describing the transient average energy and drift velocity. Comparisons between the relaxation time description, and the transient response obtained by iterative or Monte Carlo methods, are performed on p‐Ge and n‐Si, and show an agreement better than 10% in a wide range of electric fields and lattice temperatures.

NMR relaxation parameters in molecules with internal motion: exact Langevin trajectory results compared with simplified relaxation models

Abstract: The interpretation of NMR relaxation experiments on flexible molecules is explored by use of stochastic dynamics trajectories. The effect of internal motion on the relaxation parameters (TI, T,, and NOE) of simple alkanes and of aliphatic side chains of proteins is determined. The correlation functions and spectral densities required for the evaluation of \"C NMR relaxation times are evaluated from trajectories lasting up to 100 ns and the results are compared with the predictions of simplified analytical models for the motion. It is shown that for small molecules tumbling in the motional narrowing limit it is possible to approximately separate the NMR relaxation into contributions from tumbling and internal motions. For butane and heptane in aqueous solution, the spin-lattice relaxation times (TI) are predicted and the gradient in relaxation times along the heptane chain is found to be close to that observed in the pure liquid. Detailed trajectory results are presented for \"C relaxation of an alkane side chain on macromolecules. Wigner functions are used to express the side chain relaxation with respect to the coordinate frame embedded in the macromolecule. Uncoupling the motions about the individual side chain internal rotation axes or introduction of the independent lattice jump model for the motion is shown to describe incorrectly the short-time and long-time relaxation behavior. Nevertheless, for short side chains with barriers to rotation on the order of 3 kcal/mol, both models provide a good approximation for the \"C NMR relaxation. This suggests that the models can be used for the interpretation of NMR experiments on lipids and aliphatic amino acid side chains protruding into solution, although errors are expected when the motion of the chain under consideration is constrained by the rest of the system.

Faraday rotation measurements of time dependent magnetic phenomena in insulating spin glasses (invited)

Abstract: We report here on a detailed study of the relaxation of the magnetization in an external field and of the remanent magnetization for the insulating spin glass: Eu0.4Sr0.6S. The Faraday rotation has allowed us to extend previous experiments near and just above the spin glass temperature Tfo = 1.55 K on a large time scale (10−6

Nuclear magnetic resonance relaxation in nucleic acid fragments: models for internal motion

Abstract: A variety of models incorporating internal motion, which can be used to extract information from nuclear magnetic resonance relaxation studies of deoxyribonucleic acid fragments, are formulated. Illustrative analyses of some recent multinuclear relaxation data are presented. Special emphasis is placed on determining whether the information extracted is unique. It is shown that the data are consistent with several physical pictures of the internal motion. However, all the models we have considered imply the existence of large-amplitude internal motions on the nanosecond time scale.

Spin-density wave ground state in the one-dimensional conductor (TMTSF) 2PF6: microscopic evidence from 77Se and 1H NMR experiments

Abstract: The vanishing of the 77Se nuclear resonance signal and the broadening by internal magnetic fields of the proton resonance line establish the existence of spin-density waves in the low temperature semiconducting state of (TMTSF) 2PF6. The thermally activated collective mode of the commensurate spin-density wave contributes significantly to the proton spin-lattice relaxation. It is also suggested that the very small amplitude of the spin-density wave is due to the coexistence of two diverging channels in the conducting state : the SDW and Superconductivity channels.

Homodyne light beating spectroscopy of o-terphenyl in the supercooled liquid state

Abstract: The laser light scattering intensity fluctuations of supercooled liquid o‐terphenyl at temperatures between 12 and −15 °C have been studied using the photon‐correlation technique. The time correlation functions obtained using the VV and VH scattering configurations at 90° scattering angle show a wide distribution of relaxation times. Angular‐dependent measurements at 45°, 90° and 135° scattering angles show that the time correlation functions for VH and for VV are independent of scattering angles. The VV and VH correlation functions cannot be fit to a bimodal distribution function; neither can they be fit to a cumulant expansion expression with less than four cumulants, but they can be satisfactorily fit to the William–Watts distribution function. The mean relaxation times derived for both isotropic and anisotropic scattering processes from the VV and VH correlation functions are nearly equal. The temperature dependence of the relaxation times cannot be described by an Arrhenius equation with a constant activation energy. The average orientational relaxation times change by more than ten orders of magnitude in the temperature range between 147 and −16 °C but the temperature dependence of the orientational relaxation times over this wide dynamic range can be excellently correlated with the modified Debye–Stokes–Einstein equation. The closeness of the mean orientational relaxation time to the mean structural relaxation time is interpreted as due to strong rotation–translation coupling in the viscoelastic state. It is found that within the dynamic range of the autocorrelator, the collective shear wave plays no role in the time dependence of the VV and VH correlation functions. Quentrec’s theory of viscoelasticity based on the coupling of the shear wave to local translational order and orientational order is found to disagree with the experimental result. Comparison with the dielectric relation time data shows that in o‐terphenyl the dielectric relaxation and the present light beating techniques probe different types of motions.

Phonon fluctuation model for flicker noise in elemental semiconductors

Abstract: Acoustic mode lattice scattering plays an important role in determining the carrier mobility in elemental semiconductors over a wide range of temperature. For germanium and silicon, over the temperature range of interest, these longitudinal acoustic phonons are primarily scattered by isotopes and chemical impurities. The relaxation time is directly proportional to the fourth power of the phonon wavelength. Hence, for a relatively small phonon wavelength spread of three decades, the phonon relaxation time spans full 12 decades. The number of phonons for a given acoustic mode fluctuates at random. Hence, the phonon population for each mode exhibits a g‐r noise spectrum characterized by its relaxation time. Through electron‐phonon interaction (assuming elastic scattering), this g‐r noise spectrum is transferred to electron mean free path (same holds for hole), where after superposition, it leads to 1/f spectrum. The theoretical results support the experimental findings of several authors.

A model for rotational relaxation and resonance

Abstract: Depolarized Rayleigh and Raman scattering and far infrared absorption has revealed the rotational motion of polar molecules in liquids. The presence of both a Debye relaxation spectrum and a broad resonance indicates that the molecules oscillate and in addition are subject to some sort of relaxation mechanism. A model is proposed in which the molecule oscillates in a potential well until thermal fluctuations cause it to surpass the potential barrier and jump to a neighbouring well. For two-dimensional rotation approximate analytic expressions are obtained for the spectrum, which agree qualitatively with the measurements. The conclusion is that both resonance and relaxation can be obtained from a single mechanism, so that it is not necessary to introduce one mechanism for each of them.

Structural features in ethanol–water mixtures revealed by picosecond fluorescence anisotropy

Abstract: When an ensemble of molecules is excited with polarized light an anisotropic orientational distribution with respect to the transition dipole moment is produced. This anisotropy can decay in time due to the rotational motion of the molecules and consequently leads to depolarization of the fluorescence1–6. The rate of this rotational motion has been successfully predicted from hydrodynamic theory. How much the rotational relaxation depends on molecular geometry and how much on specific solvent–solute interactions has been studied by picosecond spectroscopy1–6 and other techniques7–9. In all cases so far reported, the rotational behaviour seems to be accounted for by the Debye–Stokes–Einstein (DSE) equation τR = f/kT. This relates the rotational relaxation time τR (inversely related to the rotational diffusion coefficient) to the frictional coefficient, f, which is proportional to the product of the shear viscosity, the molecular volume and a constant dependent on the ‘stick’ or ‘slip’ boundary conditions3,10,11. We report here, however, that large deviations from DSE behaviour have been observed in the rotational diffusion of the dye cresyl violet in ethanol–water mixtures. Different rotational relaxation times are observed in solutions of the same viscosity but differing composition. This behaviour can be rationalized using previously proposed models for water–ethanol mixtures.

Effects of fatigue on isometric force‐ and relaxation‐time characteristics in human muscle

Abstract: Effects of intermittent one leg isometric fatigue on maximal isometric force, force production, relaxation and blood lactate were studied using 29 male students as subjects. The relative changes of variables during fatigue and recovery were intercorrelated together with muscle structure variables, which were determined using needle biopsy technique. Maximal force decreased, force production and relaxation became slower and muscle lactate increased during fatigue. Change of maximal force, force production and lactate during fatigue as well as recovery of maximal force and lactate after fatigue were correlated significantly to muscle fiber distribution. Fatiguability of the force-time characteristics was therefore influenced by the differences in the metabolic profiles of the individual muscle fibers. However, ability to relax the muscle quickly was not observed to be dependent on muscle structure. This suggest that different fatigue mechanisms might be present in relaxation than in force production.

Ionic strength effects on macroion diffusion and excess light-scattering intensities of short DNA rods.

Abstract: Quasielastic and static light-scattering measurements were made on DNA isolated from chicken erythrocyte mononucleosomes as a function of ionic strength between 6 × 10−4 and 1.0M. A transition from single-exponential autocorrelation functions to markedly non-single-exponential decays was observed around 10−2M ionic strength and was accompanied by a large decrease in the excess light-scattering intensity. Autocorrelation functions recorded below 10−2M salt were well fit by the sum of two exponential relaxation which differed by as much as 100-fold in time constants. Apparent diffusion coefficients for the fast and slow processes plateaued around 10−3M with numerical values approximately 10-fold and 1/10, respectively, of the translational diffusion coefficient for mononucleosome DNA at high ionic strength. This behavior is similar to that observed with poly(L-lysine), for which the slow decay has been associated with a transition to an extraordinary phase. The strong and complex salt dependence observed here illustrates potential difficulties in deriving structural information from scattering by polyions at low ionic strength.

Dielectric relaxations in a copolymer of vinylidene fluoride and trifluoroethylene

Abstract: Dynamic dielectric measurements were carried out for a copolymer of vinylidene fluoride (55 mol %) and trifluoroethylene (45 mol %) over the frequency range of 50 Hz–50 MHz at temperatures between −15 and 130 °C. Observed relaxations associated with a crystalline phase transition at 70 °C were found to fit the Cole‐Cole arc with a distribution of relaxation times. The equilibrium dielectric constant e(0) shows a dielectric anomaly in that it rapidly increases to 70 just below 70 °C and then decreases. The logarithm of the observed relaxation time t vs 1/T (K−1) shows a shoulder near 70 °C which is interpreted as being the result of a critical slowing down phenomenon. The derived relaxation time t0 in the absence of cooperative effects exhibits an Arrhenius type temperature dependence from 40 to 130 °C with a potential barrier for dipole rotation of 13 kcal/mol.