Spectrum Of Correlation Times Research Articles

Nuclear magnetic relaxation, correlation time spectrum, and molecular dynamics in a linear polymer

The pulsed nuclear magnetic resonance (NMR) method at a proton frequency of 25 MHz at temperatures of 22–160°C is used to detect the transverse magnetization decay in polyisoprene rubbers with various molecular masses, to determine the NMR damping time T 2, and to measure spin-lattice relaxation time T 1 and time T 2eff of damping of solid-echo signals under the action of a sequence of MW-4 pulses modified by introducing 180° pulses. The dispersion dependences of T 2eff obtained for each temperature are combined into one using the temperature-frequency equivalence principle. On the basis of the combined dispersion dependence of T 2eff and the data on T 2 and T 1, the correlation time spectrum of molecular movements is constructed. Analysis of the shape of this spectrum shows that the dynamics of polymer molecules can be described in the first approximation by the Doi-Edwards tube-reptation model.

Zero-field microSR measurements in CuMn and AuMn spin glasses interpreted in the frame of a fractal cluster model.

We present a detailed analysis of zero-field muon-spin-relaxation (\ensuremath{\mu}SR) measurements in CuMn and AuMn spin glasses in the framework of a fractal cluster model. The latter is reformulated in terms of a probability distribution of spin-correlation times from which an expression for the spin autocorrelation function S(t) is inferred. The fractal cluster model predicts that the upper limit ${\ensuremath{\tau}}_{\ensuremath{\xi}}$ of the correlation time spectrum diverges at the freezing temperature ${T}_{f}$ and decreases below ${T}_{f}$. The \ensuremath{\mu}SR method measures the average amplitude ${a}_{s}$ of a static part and the effective correlation time ${\ensuremath{\tau}}_{\mathrm{eff}}$ of a rapidly fluctuating part of the local magnetic field at the muon site. The scaled quantities ${a}_{s}$/${a}_{0}$, where ${a}_{0}$ denotes the static field amplitude in the limit T\ensuremath{\rightarrow}0, and ${\ensuremath{\tau}}_{\mathrm{eff}{T}_{f}}$ turn out to be universal functions of the reduced temperature T/${T}_{f}$ for all investigated spin glasses. ${\ensuremath{\tau}}_{\mathrm{eff}}$ decreases below ${T}_{f}$ and qualitatively reflects the temperature dependence predicted by the fractal cluster model for the characteristic correlation time ${\ensuremath{\tau}}_{\ensuremath{\xi}}$. To relate the local-field time correlations and the spin autocorrelation function S(t) quantitatively, we discuss two different models for the local-field dynamics as probed by \ensuremath{\mu}SR. As a result the \ensuremath{\mu}SR data do not reflect a spatial arrangement of spin clusters reorienting with size-dependent relaxation times. Rather the local field appears to be similar at each muon site and seems to consist of many contributions from different spins fluctuating with different correlation times. We analyze neutron and ac susceptibility data for the spin autocorrelation S(t) within the fractal cluster model and show that they agree well with the \ensuremath{\mu}SR results.

Proton magnetic relaxation of slightly crosslinked polybutyl acrylate

Small-scale intramolecular mobility of polybutyl acrylate crosslinked with allyl methacrylate has been investigated by the proton magnetic relaxation method. The mobility of units located next to crosslinks is more inhibited and is characterised by a wider correlation time spectrum compared with that of remote units. About ∼0·2 mole% of the units form fluctuational type contacts with lifetimes of the same order (or longer) than the spin-spin relaxation time. The number of these contacts in the crosslinked polymer is proportional to the degree of crosslinking, while about one-half of the long-lived crosslinks are eliminated during swelling of the polymer. Only about 6 mole % of the crosslinking agent from effective interchain crosslinks.

Distribution of the correlation times and patterns of 13C nuclear magnetic relaxation and the overhauser effect

The dependences of the spin lattice relaxation time T1c and the Overhauser effect for different correlation time distributions used to describe the relaxational properties of polymers are examined. The dependence of Tc and the value of the nuclear Overhauser effect has been established (as a function of ωcτ where ωc is the resonance frequency and τ is the time characteristic of the given spectrum) on the form, width and asymptotic behaviour of the correlation time spectra for short and long times. These values are sensitive to the parameters of the relaxation spectra and may serve for their discrimination.

New modification of model-free approach to analysis of nuclear magnetic relaxation data in proteins.

A formal approach to the analysis of 13C magnetic relaxation data in proteins has been developed. It is based on the concepts of one of the authors on the internal motions in solid polymers (Fedotov, V.D., Pulse NMR in bulk polymers, Doctoral dissertation, Kazan, USSR, 1981). According to this approach the intermolecular motions in proteins are considered as anisotropic ones and described in terms of a spectrum of correlation times. To characterize the motions a set of formal microdynamic parameters has been introduced. They are: the anisotropy parameter (a measure of spatial restriction of motion), the most probable correlation time, the parameter of the correlation time distribution width. The analysis of protonated carbon relaxation in globular proteins (bovine pancreatic trypsin inhibitor and ribonuclease S) and polymers has been carried out by the model-free approach. Microdynamic parameters of CH3-, CH2-, aromatic CH-groups have been considered within the framework of the diffusional rotation-oscillation models. To explain the backbone CH-group relaxation the model of the defect diffusion has been applied. The distinctive feature of the results obtained is the broad correlation time distribution for all groups of any type. The causes of nonexponential correlation function of local motion have been discussed. To elucidate the nature of the correlation time the carbon magnetization decays in the wide range of microdynamic parameter values imitating various experimental conditions have been calculated.

The effect of deformation of plasticized polyvinyl chloride on molecular mobility

It was shown that uniaxial deformation of polyvinyl chloride, plasticized with dibutyl phthalate retards the molecular mobility of the plasticizer, displacing the correlation time spectrum towards higher values and distorting its shape. Appreciable anisotropy of the motion of dibutyl phthalate molecules is not observed. The behaviour of the parameters of nuclear relaxation of the polymer under strain is explained by the assumption of the existence of a 3-dimensional network in plasticized PVC.

Rayleigh Scattering of Mössbauer Radiation (RSMR) Data, Hydration Effects and Glass-like Dynamical Model of Biopolymers

Specific features of the Rayleigh Scattering of Mössbauer Radiation (RSMR) technique in the study of biological systems are described. Experimental data show that the temperature and hydration degree are the principal parameters which influence intramolecular mobility in biopolymers. Data on temperature dependencies of elastic fraction, f, and spectrum line-shape do not fit neither Debye or Einstein models of solids nor the free diffusion in liquids and demand for their explanation a multimode approximation (i.e. a wide spectrum of correlation times, at T = 293 K from 10-6 s to 10-12-10-13 s). On the basis of RSMR, low temperature specific heat and X-ray dynamic analysis data and from the general conditions that information macromolecule must be in a non-equilibrium state (an independent confirmation of this fact comes from the kinetic model of protein folding) a glass-like dynamical model of biopolymers is formulated. A possible interpretation of RSMR data shows that fluctuatively prepared tunneling between quasiequilibrium positions (QEP) can prevail activated transitions up to a room temperature.

Unresolved correlation time spectra and interpretation of NMR relaxation time data for superionic conductors

Problems in relating the results of NMR relaxation time measurements to the results of bulk conductivity/diffusion studies for superionics have been discussed in a number of ways, such as their being a result of lack of knowledge of the appropriate motional correlation function. It is argued that, in the case of hydrated proton conductors at least, the problem is more fundamental. When previously unrecognized temperature-dependent correlation time spectra are present, these cannot be resolved in reduction of relaxation time data and information on any single contributory motion is not simply available.

Correction of the expression for the form of the nuclear-induction signal in linear magnetic systems

A method of modifying the expression for the drop in transverse nuclear magnetization is considered; the method is based on taking account of the linearity of the system of nuclear moments in a weak magnetic field. It is shown that, in the presence of a broad spectrum of correlation times, a multicomponent structure of the drop may arise.

Nuclear magnetic relaxation and segmental motion of nitrocellulose in solution

The transverse and longitudinal magnetic relaxation of solutions of cellulose nitrate (CN) with nitrogen contents of 13·5 and 11·9% have been studied in deuterated acetone in the temperature range from −100 to +70°C al two concentrations (34 and 50 wt. %). The two-component nature of the decay of the transverse magnetization points to the structural non-uniformity of CN in solution. The observed minima on the temperature dependence of the spin-lattice relaxation time in the laboratory system of coordinates, T 1, and in a rotating system of coordinates are caused by segmental movement in open-packed regions of the solution. The contribution of slow movements to the spectrum of correlation times at the temperatures of the minimum T 1 has been assessed. The values obtained for the activation energy for segmental motion in the unordered regions show that a vibrational-rotational mechanism predominates in the segmental motion of CN.

Analysis of mechanisms of rotational motion of polybutadiene macromolecules

Times of spin-lattice, spin-spin and effective relaxations in the MW-4 sequence averaging dipole interaction have been measured in the temperature range 170–320°K for eight polybutadiene specimens with MW in the range 10 3–10 6. An analysis of temperature and MW dependences of the measured relaxation parameters shows that motion of the polybutadiene main chain may be described with the aid of three correlation time spectra corresponding to two anisotropic mechanisms of rotational motion and one isotropic mechanism.

Nuclear magnetic relaxation and the type of distribution of correlation times of segmental motion in rubber

An analysis was carried out of the NMR pulse experiment, which involved the study of the form of reduction of longitudinal and transverse intensity of magnetization and temperature dependence of spin-spin ( T 2) and spin-lattice ( T 1 and T 1 p) relaxation times in rubber (using polyisobutylene (PIB)), in order to explain the form and type of formation of correlation time spectra of segmental motion. It was shown that the correlation time spectrum of molecular motion in polyisobutylene is above T g, which may be satisfactorily described by the superposition of two Fuoss-Kirkwood distribution functions of varying intensity, of which the centres are at a distance of several orders of magnitude. The high-frequency part of the overall spectrum describes small-scale, segmental motion, while the low-frequency part describes large-scale motion related to network fluctuations of linkages. It was established that the existence of this spectrum is determined by special structural features of the macromolecular chain, while the heterogeneity of the sample expressed in structural features of the spin-system, reflects a second order effect-distribution of correlation time spectra.

Nuclear relaxation and the molecular movement in linear polyethylene

The temperature dependences of the nuclear spin-lattice ( T 1 and T 1 ϱ ) and spin-spin ( T 2) relaxations have been investigated in linear polyethylene (PE) over a wide range of temperatures. These dependences have been found to contain information about the four relaxation transitions, of which 2 (the γ c and α transitions) are connected with the local movements in the crystalline zones, while the other 2 ( γ a and β transitions) are linked with the local and segmental movements in the amorphous zones. The analysis of the experiment based on the nuclear relaxation theory considers the type of movements and existence of the correlation time spectra; it made it possible to establish that the γ c transition is described well by the CH 2 group gyrations as a model, while the model for the γ a is the anisotropic rotation of the CH 2 groups around a fixed axis, and the model for α is linked with the rotation of defects on the crystal surface, while that for β is the isotropic rotation of the chain segments.

Proton relaxation in linear poly(oxypropylene glycols)

Abstract The effect of molecular weight and polydispersity on the relaxational behaviour of linear poly(oxypropylene glycols) (POPGS) has been studied by pulse NMR spectroscopy. The length of the kinetic segment of the oligomer was determined. It is suggested that the nuclear magnetic relaxation characteristics of binary POPG mixtures obey the additivity principle. The spectrum of correlation times of molecular motion broadens as the polydispersity of the oligomer increases.

Application of Fourier analysis techniques for the interpretation of perturbed angular correlations

Fourier analysis is applied to the study of perturbed angular correlation time spectra. The effects of a finite measuring interval, discrete measuring points, statistical fluctuations, and nuclear relaxation on the Fourier spectra are shown using simulated time spectra. The effects of finite time resolution on the time spectra are reviewed and a method for partially removing them using Fourier techniques is presented.

Nuclear Magnetic Resonance Study of the Interaction of SBR with Carbon Black

Abstract The nuclear magnetic resonance relaxation characteristics of an amorphous styrene—butadiene copolymer (SBR-1500) containing HAF and ISAF carbon black and an HAF carbon black containing SBR-1500 adsorbed on it from solution have been investigated at 30 Mc/sec over a temperature range of −100° to 100° C. The spin-lattice relaxation time (T1) passes through a single, broad minimum at about 30° C. The precise location of this minimum which is ascribed to the onset of segmental motion in the copolymer is not strongly dependent on the presence of carbon black. The nuclear magnetic resonance results reported suggest that the spectrum of correlation times of the elastomer strongly associated with the carbon black particles, i.e., the “bound rubber” is not significantly different from that of the bulk elastomer containing no carbon black—at least for the frequencies sampled by the NMR technique used. The results thus fail to confirm recent proposals in the literature suggesting that filler particles in elastomers are covered with a layer of polymer in which segmental motion is severely restricted and which constitutes a significant, if not the major portion of the rubber.

Studies of Polybutenes. III. On the Molecular Motion Studied by Nuclear Magnetic Resonance

Abstract The molecular motion of polybutenes of low molecular weights has been studied by observing the NMR line widths and spin-lattice relaxation times at temperatures in the range from −180 to 200°C. The temperature dependence of these values is similar to that of polyisobutylene of a higher molecular weight. The correlation time spectra calculated from the spin-lattice relaxation time and the spin-spin relaxation time shift in the shorter-time direction with the decrease in the molecular weight. The dependence of the correlation frequency upon the temperature is also discussed in terms of the W. L. F. equation.

Theory of nuclear magnetic relaxation in liquid-phase polymers

MEASUREMENT of the nuclear magnetic resonance relaxation times permits information to be obtained on molecular motion in a substance. In low-moleelflar-weight liquids, this motion is characterized by the time of correlation of the energy of the magnetic dipole-dipole interaction of the nuclei. However. it has been shown in a number of experimental investigations [1-3] that polymeric liquids, as was to be expected, are characterized by a broad correlation time spectrum. In this case, the problem of the theoretical calculation of the form of the spectrtun of the correlation time in liquid-phase polymers (solutiol~ and melts) arises. I f the task is set of determining tbe spectrum of the correla*ion time to a rough approximation and calculating the relaxation time to an order of magnitude, it is possible to restrict oneself to the calculation of the interaction of the magnetic nuclei in a single group, since this interaction makes the main contribution to relaxation. This offers a possibility of considering melt sand solutions of polymers simultaneously. At the same time, the molecular motion can be described by a very simple model. In order to calculate the relaxation time it is necessary to know the correlat, ion function of the dipole-dipoJe interaction. We shall limit ourselves, for simplicity, to polymers in which the distances between the magnetic nuclei in the groups are constant and similar. Under these conditions it is nob difficult to convince oneself, using the usual definition of the correlation function (see, for example, [4]) and the isotropic nature of the liquid, that the correlation function .f(t) has the form of a sum of N correlation functions of the individual groups: 1 ~¢ .f(t) = ~q~=ifq(t ), (l)

高分子の粘弾性と誘電性・核磁気共鳴との関係

A few subjects on the relation of viscoelastic behavior of polymers to their dielectric and NMR behavior are discussed. The validity of temperature-time reduction rule is doubtful except for α-dispersion region of the amorphous polymers. The complicated relaxation mechanisms in polymers require the distributions of relaxation times, connected with the correlation function ‹F(t)F(0)av› of respective quantities F, which vary according as viscoelasticity, dielectricity or NMR is concerned, and respective spectra are so different in shape but are reflecting parts of the same molecular motion. The box shape of correlation time spectrum for PIB is the only spectrum known at pressent in NMR. The activation energies obtained from NMR data are often much smaller than those obtained from viscoelastic and dielectric data. As NMR data are corresponding to the temperature dependence data under constant frequency in viscoelastic and dielectric measurements, the neglect of correlation time distribution in NMR causes the underestimation of activation energy. We can show the apparent activation energies of viscoelasticity and dielectricity recalculated from the temperature dependence data only, assuming a single relaxation time, are much nearer to those of NMR, which are illustrated for PMMA, PIB and PTFMCE. If the temperature reduction rule is invalid, not only the shape of the correlation time spectrum but also its temperature variation play a role, so far as the temperature-dependent behavior is concerned.