Mobility in thin polymer films ranging from local segmental motion, Rouse modes to whole chain motion: A coupling model consideration

Large increases of mobility of local segmental relaxation observed in polymer films as the film thickness is decreased, as evidenced by decreases of the glass temperature, are not found for relaxation mechanisms that have longer length scales including the Rouse relaxation modes and the diffusion of entire polymer chains. We show that the coupling model predictions, when extended to consider polymer thin films, are consistent with a large increase of the mobility of the local segmental motions and the lack of such a change for the Rouse modes and the diffusion of entire polymer chains. There are two effects that can reduce the coupling parameter of the local segmental relaxation in thin films. One is the chain orientation that is induced parallel to the surface when the film thickness h becomes smaller than the end-to-end distance of the chains and the other is a finite-size effect when h is no longer large compared to the cooperative length scale. Extremely thin ( ≈ 1.5 nm) films obtained by intercalating a polymer into layered silicates have thickness significantly less than the cooperative length scale near the bulk polymer glass transition temperature. As a result, the coupling parameter of the local segmental relaxation in such thin films is reduced almost to zero. With this plausible assumption, we show the coupling model can explain quantitatively the large decrease of the local segmental relaxation time found experimentally. Received 1 August 2001 and Received in final form 1 December 2001     

Anisotropic relaxation and motion of half-integer quadrupole nuclei studied by central transition nuclear magnetic resonance spectroscopy

An efficient theoretical formalism and advanced experimental methods are presented for studying the effects of anisotropic molecular motion and relaxation on solid-state central transition NMR spectra of half-integer quadrupole nuclei. The theoretical formalism is based on density operator algebra and involves the stochastic Liouville–von Neumann equation. In this approach the nuclear spin interactions are represented by the Hamiltonian while the motion is described by a discrete stochastic operator. The nuclear spin interactions fluctuate randomly in the presence of molecular motion. These fluctuations may stimulate the relaxation of the system and are represented by a discrete relaxation operator. This is derived from second-order perturbation theory and involves the spectral densities of the system. Although the relaxation operator is valid only for small time intervals it may be used recursively to obtain the density operator at any time. The spectral densities are allowed to be explicitly time dependent making the approach valid for all motional regimes. The formalism has been applied to simulate partially relaxed central transition ¹⁷O NMR spectra of representative model systems. The results have revealed that partially relaxed central transition lineshapes are defined not only by the nuclear spin interactions but also by anisotropic motion and relaxation. This has formed the basis for the development of central transition spin-echo and inversion-recovery NMR experiments for investigating molecular motion in solids. As an example we have acquired central transition spin-echo and inversion-recovery ¹⁷O NMR spectra of polycrystalline cristobalite (SiO₂) at temperatures both below and above the α–β phase transition. It is found that the oxygen atoms exhibit slow motion in α-cristobalite. This motion has no significant effects on the fully relaxed lineshapes but may be monitored by studying the partially relaxed spectra. The α–β phase transition is characterized by structural and motional changes involving a slight increase in the Si–O–Si bond angle and a substantial increase in the mobility of the oxygen atoms. The increase in the Si–O–Si angle is supported by the results of ¹⁷O and ²⁹Si NMR spectroscopy. The oxygen motion is shown to be orders of magnitude faster in β-cristobalite resulting in much faster relaxation and characteristic lineshapes. The measured oscillation frequencies are consistent with the rigid unit mode model. This shows that solid-state NMR and lattice dynamics simulations agree and may be used in combination to provide more detailed models of solid materials.     

Spin relaxation studies on conducting poly(tetrathiafulvalene)

Magnetic parameters and the relaxation behavior of paramagnetic centers in an iodine-doped poly(tetrathiafulvalene) semiconductor with a d.c. conductivity of 10^?5 S·cm^?1 have been studied using mainly the 2 mm waveband EPR technique in the temperature range of 110–270 K. The EPR line shape analysis confirms the existence of immobile radicals pinne on short polymer chains and mobile polarons with different relaxation parameters in slightly doped poly(tetrathiafulvalene). The temperature dependences of electron spin-lattice and spin-spin relaxation times of paramagnetic centers of both types have been determined independently using the saturation method at the operation frequency ν _e = 140 GHz. An anisotropic slow libration of immobile polarons with an activation energy of 0.02 eV have been registered for the first time using the saturation transfer EPR method. The temperature dependences of intrachain diffusion and interchain hopping rates in poly(tetrathiafulvalene) are determined from theT ₁ andT ₂ EPR data. The interchain spin dynamics is shown to correlate with libration of polarons trapped on polymer chains and is in good agreement with a hopping charge transport mechanism.     

Hole spin relaxation in Ge quantum dots

Hole spin relaxation in an isolated Ge quantum dot due to interaction with phonons is investigated. Spin relaxation in this case occurs through the mechanism of the modulation of the spin-orbit interaction by lattice vibrations. According to the calculations performed, the spin relaxation time due to direct single-phonon processes for the hole ground state equals 1.4 ms in the magnetic field H = 1 T at the temperature T = 4 K. The dependence of the relaxation time on the magnetic field is described by the power function H^?5. At higher temperatures, a substantial contribution to spin relaxation is made by two-phonon (Raman) processes. Because of this, the spin relaxation time decreases to nanoseconds as the temperature is raised to T = 20 K. Analysis of transition probabilities shows that the third and twelfth excited hole states, which are intermediate in two-step relaxation processes, play the main part in Raman processes.     

The T 1 and T 2 Relaxation Times Distribution for the 35Cl and 14N NQR in Micro-composites and in Porous Materials

The paper describes the results of an experimental study of the ³⁵Cl and ¹⁴N nuclear quadrupole resonance in composite and porous materials, the influence of the environment and the crystallite size of powder on the nuclear quadrupole resonance line widths, as well as on the spin–spin and spin–lattice relaxation times. It is established that the spin–lattice relaxation time has a unimodal distribution, and the spin–spin relaxation time—bimodal distributions for all the investigated samples. The idealized distribution function of the relaxation times is obtained on the assumption that the concentration of inhomogeneities and relaxativity decreases with an increasing distance from the surface into the interior of the crystallite exponentially. It is shown that the model with the spin diffusion explains the shortening of the decay signal with decreasing grain size, but this is not confirmed by the experimental distribution of relaxation times obtained by means of the inverse Laplace transformation.     

Spin charge carrier dynamics in poly(bis-alkylthioacetylene)

Initial and laser-irradiated poly(bis-alkylthioacetylene) (PATAC) samples were investigated by electron paramagnetic resonance (EPR) at X-band (9.6 GHz), Q-band (37 GHz), and D-band (140 GHz) in a wide temperature range. Two types of paramagnetic centers were proved to exist in laser-modified polymer, namely, localized and mobile polarons with the concentration ratio and susceptibility depending on the irradiation dose and temperature. Superslow torsion motion of the polymer chains was studied by the saturation transfer method at D-band EPR. Additional information on the polymer chain segment dynamics was obtained by the spin probe method at X-band EPR. Spin-spin and spin-lattice relaxation times were measured separately by the steady-state saturation method at D-band EPR. Intrachain and interchain spin diffusion coefficients and conductivity arising from the polaron dynamics were calculated. It was shown that the polaron dynamics in laser-modified polymer is affected by the spin-spin interaction. The interchain charge transfer is stimulated by torsion motion of the polymer chains, whereas the total conductivity of irradiated PATAC is determined mainly by the dynamic of diamagnetic charge carriers. Magnetic, relaxation and dynamics parameters of PATAC were also shown to change during polymer storage.     

Dipolar Relaxation of Multiple Quantum NMR Coherences as a Model of Decoherence of Many-Qubit Coherent Clusters

Dipolar relaxation of multiple quantum (MQ) nuclear magnetic resonance (NMR) coherence is investigated on the evolution period of the MQ NMR experiment in chains of ¹⁹F nuclei in a single crystal of calcium fluorapatite. The dependence of the relaxation time of the MQ coherence of the second order on the size of the coherent spin cluster formed on the preparation period is obtained. The dipolar relaxation of MQ NMR coherences is considered as a model for the investigation of decoherence of quantum states of many-qubit spin clusters.     

19F nuclear spin relaxation and spin diffusion effects in the single-ion magnet LiYF4:Ho3+

Temperature and magnetic field dependences of the ¹⁹F nuclear spin-lattice relaxation in a single crystal of LiYF₄ doped with holmium are described by an approach based on a detailed consideration of the magnetic dipole-dipole interactions between nuclei and impurity paramagnetic ions and nuclear spin diffusion processes. The observed non-exponential long time recovery of the nuclear magnetization after saturation at intermediate temperatures is in agreement with predictions of the spin-diffusion theory in a case of the diffusion limited relaxation. At avoided level crossings in the spectrum of electron-nuclear states of Ho^{3 +} ions, rates of nuclear spin-lattice relaxation increase due to quasi-resonant energy exchange between nuclei and paramagnetic ions in contrast to the predominant role played by electronic cross-relaxation processes in the low-frequency ac-susceptibility.     

Dynamics of conformations,hydrogen bonds and translational diffusion of poly(methacrylic acid) in aqueous solution and the concentration transition in MD simulations

The dynamic behaviour of chain conformations, hydrogen bonds and translational diffusion of aqueous poly(methacrylic acid) (PMA) solution as a function of polymer volume fraction Φ_p across dilute to concentrated regimes inclusive of the pure polymer amorphous state was studied by molecular dynamics simulations. The behaviour of the relaxation time (τ) of the backbone dihedral angle auto-correlation function (ACF) reveals slower relaxation at higher level of polymer concentration and the existence of a concentration-driven relaxation transition for the aqueous polymer solution which occurs in the polymer volume fraction range, specifically 54% < Φ_p < 82% for this system. The relaxation constant τ for backbone dihedral angle exhibits a linear variation with Φ_p, indicating a first-order kinetic transition. The intermittent ACF for decay of the H-bond correlation shows that H-bonds among water molecules relax faster than those of the PMA–PMA and PMA–water type. The relaxation rate of PMA–water H-bonds shows a decrease up to Φ_p = 72% and becomes faster at Φ_p = 82% due to the confining influence of neighbouring PMA chains. PMA–water and water–water H-bond dynamics show transitions around Φ_p = 72% PMA. With increase in Φ_p PMA diffusion coefficient decreases exponentially and water diffusion coefficient decreases linearly, in agreement with experimental observations using fluorescence and nuclear magnetic resonance (NMR) spectroscopic studies.     

Spin–lattice relaxation dispersion in polymers: Dipolar-interaction components and short- and long-time limits

The Mori–Zwanzig projection operator technique was employed to derive the effective Hamiltonian for spin-segment coupling. The fluctuations of this operator are responsible for spin–lattice relaxation in polymer chains. In detail, dipolar interaction of spins is rigorously analyzed by components representing fluctuations of the Kuhn segment end-to-end vectors and local fluctuations on a length scale shorter than the root mean square Kuhn segment length. The former correspond to the usual coarse-grain picture of polymer chain mode theories. It is shown that these non-local chain modes dominate proton spin–lattice relaxation dispersion of flexible polymers at frequencies up to about 10⁸ Hz. A corresponding evaluation of experimental data for polybutadiene melts is presented.     

NMR study of holographic Mn-doped yttrium orthoaluminates

The quadrupole coupling constants, asymmetry parameters and spin-lattice relaxation time of²⁷A1 nuclei have been studied in Mn-doped YAlO₃ crystals. The dependence of the relaxation time on temperature and concentration of Mn ions implies a mechanism of relaxation via Mn²⁺ paramagnetic ions taking into account the nuclear spin diffusion partly restricted by the diffusion barrier. A substantial increase of the relaxation times was observed in the photoexposed samples. We ascribe this effect to the appearance of fast-relaxing Mn⁵⁺ ions produced by photoionization of Mn⁴⁺ centers.     

Phonon-assisted spin diffusion in solids

The spin flip-flop transition rate is calculated for the case of spectral spin diffusion within a system of dipolarly coupled spins in a solid where the lattice vibrations are present. Long-wavelength acoustic phonons time-modulate the interspin distance r_ij and enhance the transition rate via the change of the 1/r³_ij term in the coupling dipolar Hamiltonian. The phonon-assisted spin diffusion rate is calculated by the golden rule in the Debye approximation of the phonon density of states. The coupling of the spins to the phonons introduces temperature dependence into the transition rate, in contrast to the spin diffusion in a rigid lattice, where the rate is temperature-independent. The direct (one-phonon absorption or emission) processes introduce a linear temperature dependence into the rate at temperatures not too close to T = 0. Two-phonon processes introduce a more complicated temperature dependence that again becomes simple analytical for temperatures higher than the Debye temperature, where the rate is proportional to T², and in the limit T → 0, where the rate varies as T⁷. Raman processes (one-phonon absorption and another phonon emission) dominate by far the phonon-assisted spin flip-flop transitions.     

13C NMR investigation of carbon nanotubes and derivatives

We report on nuclear magnetic resonance on single wall carbon nanotubes. Depending on the chemical preparation the electronic and dynamical properties of carbon nanotubes are presented and discussed. From a room temperature study of the spin lattice relaxation of carbon nanotubes prepared with various catalysts we clearly identified two components. In agreement with previous NMR studies and theoretical predictions, one-third of the intensity of the signal is found with a short relaxation time (about 5 s) attributed to metallic nanobutes while the rest of the signal presents a relaxation time of about 90 s corresponding to semiconducting nanotubes. In the case of oxidized or cut nanotubes only one relaxation time is observed with characteristics similar to the slow component. The disappearance of the fast relaxing component is associated with the absence of metallic nanotubes damaged by the chemical or mechanical treatments. In this case, the T dependence of the spin lattice relaxation reveals the effect of thermally activated small amplitude motions (twistons) of the nanotube in ropes. If diffusion of twistons might induce movement of ¹³C sites and local magnetic field fluctuations, orientational order could appear below the transition temperature of 170 K. In the last part, we present the theoretical predictions of chemical shift tensor in carbon nanotubes.     

Measurement of the nuclear spin diffusion coefficient in organic glasses doped with paramagnetic centers: Orthoterphenyl and polymeric glasses

We have recently developed a method of studying spin diffusion coefficients by doping the materials with paramagnetic centers and measuring the nuclear relaxation in a tilted rotating frame. Using this method, we measure here the spin diffusion coefficient of orthoterphenyl, a molecular organic glass, and of three polymer glasses: poly(4-vinylpyridine), poly(vinylacetate) and poly(methyl methacrylate). We explore a possible dependence of the measured orthoterphenyl spin diffusion coefficient on the electronic relaxation time and concentration of the paramagnetic centers. We conclude that the experiments can be performed at higher concentrations than previously thought. We also show that our method applies to polymers in the glassy state if one works at sufficiently small tilt angle, in spite of a short value ofT _1ρ. We had anticipated that the distribution of proton pairs in these materials precludes the standard dependence of the spin diffusion coefficient on the proton density and free induction decay characteristic decay time. Our results fully confirm such expectation.     

EPR Study of Sc<Subscript>2</Subscript>SiO<Subscript>5</Subscript>:Nd<Superscript>143</Superscript> Isotopically Pure Impurity Crystals

The Sc₂SiO₅ single crystals doped with 0.001 at.% of the ¹⁴³Nd³⁺ ion were studied by continuous-wave and pulse electron paramagnetic resonance methods. The g-tensors and hyperfine structure tensors for two magnetically non-equivalent Nd ions were obtained. The spin–spin and spin–lattice relaxation times were measured at 9.82 GHz in the temperature range from 4 to 10 K. It was established that three relaxation processes contribute to the spin–lattice relaxation processes. There are one-phonon spin–phonon interaction, two-phonon Raman interaction and two-phonon Orbach–Aminov relaxation processes. It was established that spin–spin relaxation time is of the same magnitude for neodymium ion doped in Sc₂SiO₅ and in Y₂SiO₅.     

Dynamics of Random One-Dimensional ±J Systems

Finite chains of a two-state random Potts spin model with periodic boundary conditions are studied within Glauber dynamics. The spin exchange is assumed random with frustration between ferro and antiferromagnetic values (±J). Time-dependent fluctuations are induced by periodic temperature oscillations. Master type differential equations for spin correlation functions are solved within linear response theory. The spectrum of relaxation times are calculated at different temperatures. The ±J Potts glass chains undergo a zero temperature phase transition. The barriers against inversion of the spin chain take only two values; 0 and 2|J|. The temperature behaviour of specific heat is characterized by rounded peaks. The frequency dependence displays two plateaus for the real part of specific heat and two corresponding peaks for the imaginary part. The dynamic specific heat is not affected by the longest relaxing mode like susceptibility. The time separation of the modes is demonstrated by the Cole-Cole plots.     

Dynamics of water in binary and ternary solutions of DNA and porphyrins

The dynamics of heavy water (at 20°C) in solutions with polyanionic DNA chains and ternary systems containing DNA and negatively charged tetraphenylporphyrins has been investigated using neutron resonance spin echo in the time range t = 1?1000 ps. The diffusion dynamics has been observed in the momentum transfer range q = 1.3?1.8 Å^?1, and the relaxation rates in single-component, binary, and ternary systems are close to each other. Apart from the relaxation, the vibrational mode in the solutions has been revealed at the momentum transfer q = 1.9 Å^?1. The introduction of porphyrins into the solution (one molecule per ten DNA base pairs) has resulted in a retardation of diffusion and a considerable increase (by 5–10%) in the frequency of translational vibrations of water molecules due to the interaction with porphyrin molecules.     

Spin lattice relaxation in TmNi5 above its curie temperature

The hexagonal compound TmNi₅ was investigated by means of ¹⁶⁹Tm Mössbauer spectroscopy in the temperature range 4–350 K. Above T_c=4.5 K the magnetic hyperfine interactions were found to be governed by paramagnetic relaxation. This behaviour was interpreted in terms of a stochastic spin-down model. The spin lattice relaxation time was found to follow an exponential temperature dependence.     

Exchange and dipolar spin-spin interaction and rotational diffusion in saturation transfer EPR spectroscopy

Saturation transfer EPR spectroscopy (STEPR) provides a means for investigating weak spin-spin interaction between spin-labelled molecules because the spectral intensity is proportional to the effective spin-lattice relaxation time,T ₁ ^eff. Rate equations for the spin population defferences yield equivalent results for the dependence ofT ₁ ^eff on the physical (or chemical) and Heisenberg spin exchange rates and show thatT ₁ ^eff depends on the extent of redistribution of saturation throughout the anisotropic spin label powder lineshape. This approach yields a particularly simple formulation for the dependence of the STEPR lineshape on slow rotational diffusion. The effects of spin exchange are readily distinguished from those of slow rotational diffusion because of the insensitivity of the STEPR lineshape in the former case. The characteristic dependence of the STEPR spectral intensity on spin concentration allows determination of the exchange rate and can be used for studying slow translational diffusion, e.g. of spin-labelled proteins. Dipolar relaxation induced by paramagnetic ions gives a linear dependence of the reciprocal spin label STEPR intensity on metal ion concentration. STEPR measurements with spin-labelled lipid molecules in gel phase membranes in the presence of Ni²⁺ ions yield reliable distance information and provide calibrations for use with other systems.     

Nuclear spin relaxation of 8Li adsorbed on surfaces

Nuclear spin relaxation experiments with ⁸Li adsorbed on various surfaces provide new information in surface science which is not obtainable othervise. Both dipolar (Korringa) and quadrupolar relaxation due to diffusion are observed. However, in addition, a fast and presently not understood spin relaxation mechanism is present while dosing during the first 0.5 s the surface with polarized ⁸Li. Most strange in this respect is the fact that those ⁸Li atoms which survive depolarization through this mechanism depolarize afterwards with modest spin lattice relaxation rates. The origin of the fast spin lattice relaxation mechanism is presently unknown. This revised version was published online in July 2006 with corrections to the Cover Date.