Exact solution for the extended Debye theory of dielectric relaxation of nematic liquid crystals

The exact solution for the transverse (i.e. in the direction perpendicular to the director axis) component α_⊥(ω) of a nematic liquid crystal and the corresponding correlation time T_⊥ is presented for the uniaxial potential of Martin et al. [Symp. Faraday Soc. 5 (1971) 119]. The corresponding longitudinal (i.e. parallel to the director axis) quantities α_⊥(ω), T_⊥ may be determined by simply replacing magnetic quantities by the corresponding electric ones in our previous study of the magnetic relaxation of single domain ferromagnetic particles Coffey et al. [Phys. Rev. E 49 (1994) 1869]. The calculation of α_⊥(ω) is accomplished by expanding the spatial part of the distribution function of permanent dipole moment orientations on the unit sphere in the Fokker-Planck equation in normalised spherical harmonics. This leads to a three term recurrence relation for the Laplace transform of the transverse decay functions. The recurrence relation is solved exactly in terms of continued fractions. The zero frequency limit of the solution yields an analytic formula for the transverse correlation time T_⊥ which is easily tabulated for all nematic potential barrier heights σ. A simple analytic expression for T_∥ which consists of the well known Meier-Saupe formula [Mol. Cryst. 1 (1966) 515] with a substantial correction term which yields a close approximation to the exact solution for all σ, and the correct asymptotic behaviour, is also given. The effective eigenvalue method is shown to yield a simple formula for T_⊥ which is valid for all σ. It appears that the low frequency relaxation process for both orientations of the applied field is accurately described in each case by a single Debye type mechanism with corresponding relaxation times (T_∥, T_⊥).     

Investigation of impurity diffusion in dilute alloys by nuclear magnetic resonance

The diffusion of Al in a Cu: 3.8 at % Al alloy has been investigated by observing the rotating-frame nuclear magnetic relaxation time T_1π of ²⁷Al as a function of temperature. It is shown that relaxation measurements of the solute atoms in a dilute alloy provide the correlation time of the diffusive motion of these atoms, if quadrupolar interactions form the main contribution to the relaxation time. From the correlation times the Al-diffusion coefficient in the alloy has been determined.     

The Random Average Process and Random Walk in a Space-Time Random Environment in One Dimension

We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale n ^1/4, where n is the ratio of macroscopic and microscopic scales in the system. The limits of the fluctuations are described by a family of Gaussian processes. In cases of known product-form invariant distributions, this limit is a two-parameter process whose time marginals are fractional Brownian motions with Hurst parameter 1/4. Along the way we study the limits of quenched mean processes for a random walk in a space-time random environment. These limits also happen at scale n ^1/4 and are described by certain Gaussian processes that we identify. In particular, when we look at a backward quenched mean process, the limit process is the solution of a stochastic heat equation.     

Rotational diffusion of a tracer colloid particle: I. Short time orientational correlations

We extend the generalized Smoluchowski equation to descrbe the diffusional relaxation of position and orientation in a suspension of interacting spherical colloid particles. Considering a tracer particle which interacts with other particles through spherically symmetric pair potentials and with an external field we obtain a cluster expansion representation of the orientational time correlation functions for the tracer. The one and two body cluster contributions are studied explicitly at short times. Working to first order in volume fraction φ we show that the initial slope of the time correlation functions is described by a modified diffusion coefficient D^r = D^r₀(1 −C^rφ) where C^r is a number determined by hydrodynamic and potential interactions. We evaluate C^r numerically for spheres with slip-stick hydrodynamic boundary conditions and also for permeable spheres.     

Response of lysozyme internal dynamics to hydration probed by13C and1H solid-state NMR relaxation

We have studied the hydration dependence of the internal protein dynamics of hen egg white lysozyme by naturally abundant¹³C and¹H nuclear magnetic resonance (NMR) relaxation. NMR relaxation timesT ₁, off-resonanceT _1p and proton-decoupled on-resonanceT _1p (only for carbon expriments) were measured in the temperature range from 0 to 50°C. The spectral resolution in carbon cross-polarization magic angle spinning spectrum allows to treat methine, methylene and methyl carbons separately, while proton experiments provide only one integral signal from all protons at a time. The relaxation times were quantitatively analyzed by the well-established correlation function formalism and model-free approach. The whole set of the data could be adequately described by a model assuming three types of motion having correlation times around 10^?4, 10^?9 and 10^?12 s. The slowest process originated from correlated conformational transitions between different energy minima, the intermediate process could be identified as librations within one energy minimum, and the fastest one is a fast rotation of methyl protons the symmetry axis of methyl groups. A comparison of the dynamic behavior of lysozyme and polylysine obtained from a previous study (A. Krushelnitsky, D. Faizullin, D. Reichert, Biopolymers 73, 1–15, 2004) reveals that in the dry state both biopolymers are rigid on both fast and slow time scales. Upon hydration, lysozyme and polylysine reveal a considerable enhancement of the internal mobility, however, in different ways. The side chains of polylysine are more mobile than those of lysozyme, whereas for the backbone a reversed picture is observed. This difference correlates with structural features of lysozyme and polylysine discussed in detail. Due to the presence of a fast spin diffusion, the analysis of proton relaxation data is a more difficult task. However, our data demonstrate that the correlation functions of motion obtained from carbon and proton experiments are substantially different. We explained this by the fact that these two types of NMR relaxation experiments probe the motion of different internuclear vectors. The comparison of the proton data with our previous results on proton relaxation timesT ₁ measured over a wide temperature range indicates that at low temperatures lysozyme undergoes structural rearrangements affecting the amplitudes and/or activation energies of motions.     

Dynamics of the biopolymers in articular cartilage studied by magic angle spinning NMR

To understand the viscoelastic properties of cartilage tissue and for the development of tissue-engineered cartilage, we have studied the physicochemical properties of bovine nasal and pig articular cartilage by¹³C nuclear magnetic resonance (NMR) methods. The major macromolecular components of cartilage can be investigated individually by applying¹³C high-resolution (HR) NMR with scalar decoupling (for the polysaccharide component) and solid-state NMR with dipolar decoupling (for the collagen component). Partially resolved NMR spectra of the cartilage polysaccharides can be obtained by HR¹³C NMR indicating that these polysaccharides are highly mobile. Resonance lines have been assigned to chondroitin sulfate, the most mobile component of cartilage. To characterize time scales of molecular motions, we have measuredT ₁ andT ₂ relaxation times as a function of temperature and analyzed these data by means of a broad distribution of molecular correlation times. Typical correlation times for the large amplitude motions of chondroitin sulfate are of the order of 0.1–10 ns. For the detection and dynamical characterization of the cartilage collagen cross-polarization magic angle spinning (CP MAS) and high-power decoupling are indispensable.¹³C CP MAS spectra of cartilage are dominated by resonances from rigid collagen, while only low-intensity signals from the polysaccharides are observed. The good sensitivity at a magnetic field strength of 17.6 T allows the site-specific investigation of cartilage collagen dynamics by two-dimensional NMR methods. The cartilage collagen is essentially rigid with low-amplitude segmental motions on the fast time scale. Considering the high water content of cartilage and the almost isotropic mobility of the chondroitin sulfate molecules it is remarkable how little this affects the collagen dynamics. The dynamics of cartilage macromolecules is broadly distributed from almost completely rigid to highly mobile, which lends cartilage its mechanical strength and shock-absorbing properties.     

Velocity correlation functions for finite one-dimensional systems

Certain systems consisting of a one-dimensional gas of a finite number of point particles interacting with a “hard-core” potential are considered.We use the technique developed by Jepsen to calculate exactly the velocity correlation functions for these systems. We discover that after a slow decay for times of the order of the relaxation time, there is a “fast” decay to the equilibrium value on a macroscopic time scale characterized by L/v_TH (L is the length of the container and v_TH the thermal velocity).The dependence of the velocity correlation functions on the initial position of the specified particle is also considered. In particular, the behaviour approaching the boundary of the container is analyzed. These considerations are generalized to systems of higher spatial dimension.     

Analysis of the magnetic field dependence of the nuclear magnetic relaxation times in solid He

We have analyzed the field dependence of the magnetic relaxation time T₁ in solid He³ and find that the experimental data are in good agreement with the theory of Blume and Hubbard for the time dependence of the spin correlation function.     

Stochastische Theorie der magnetischen Relaxation

Let a single magnetic dipole be in a constant magnetic field ?₀ and a fluctuating field ?′(t). For this problem the equation of motion is solved exactly. Averaging the magnetic moment over a convenient ensemble relations of relaxation of a macroscopic system of many spins are obtained. In this way a relaxation tensorΦ for magnetisation is derived from the stochastic properties of the fluctuating field which is a generalization ofKubo's oscillator model. For small timesΦ approaches a Gaußian for large times an exponential function. There are two relaxation times which may be expressed by two correlation times of the fluctuating field. The results give a classification of the absorption line shape in Gaußian and Lorentzian type.     

Determination of the energy relaxation time in GaSb from microwave harmonic mixing and transport phenomena

The energy relaxation time τ_? of GaSb has been determined independently from microwave harmonic mixing experiments in the range of 160–200 K and from the current-voltage characteristics at 300 and 77 K. From measurements of the i.r. Faraday effect at 300 K valley populations as a function of the electric field strength are obtained which are in agreement with values calculated with help of the energy relaxation time obtained by methods mentioned before. For the evaluation of the data a two-band model has been used. The results obtained from the microwave experiments are extrapolated to 300 and 77 K assuming polar optical mode scattering. Good agreement of these values and the results obtained from the current-voltage characteristics and the Faraday measurements was found. The values for 300 and 77 K are 4 × 10⁻¹² sec and approximately 1·6 × 10⁻¹¹ sec, respectively.     

Heating and Cooling Transients in the DyPO<Subscript>4</Subscript> Nanocrystals under Femtosecond Laser Irradiation in the NIR Spectral Range

We compared the heating and cooling theoretical and experimental transient times of DyPO₄ nanoparticles as a result of their heating by themultiphonon relaxation after femtosecond laser excitation in the near IR spectral range into different absorption spectral lines of the Dy³⁺ ion. We have shown that the relaxation of the heat flux to a stationary value occurs according to an exponential law. Depending on the value of the Biot number, two different relaxation mechanisms can be realized, in one of which the relaxation time depends on the thermal conductance of the interface, and in the other on the thermal diffusivity. It is shown that, after averaging over the ensemble of nanoparticles, the kinetics of the relaxation of the heat flux in these limiting cases has a substantially different character. The results might be helpful for assessing the prospects of the dielectric crystalline nanoparticles doped with rare-earth ions in the local hyperthermia treatment of cancer cells.     

Relaxation mechanism in γ-ray-irradiated L-alanine studied by transfer saturation EPR and pulse EPR

Stable paramagnetic centers in γ-ray-irradiated L-alanine dosimeters exhibit a maximum in relaxation rate in the vicinity of 190 K. The mechanism of this relaxation rate has been investigated on the first stable alanine radical center, SARI, by employing continuous-wave transfer saturation electron paramagnetic resonance and pulse electron paramagnetic resonance techniques. The detected in-phase and out-of-phase spectra as well as phase memory times,T _M, indicate that besides the well-known τ_p of the CH₃ group of SAR1 an additional correlation time, τ_l (ΔElk=2689±50 K and 0 τ₁₀ = 0.15 ± 0.03 ps), is involved in the transverse relaxation process and effects the SAR1 center. For the SAR1 center this mechanism originates from the hindered motion of undamaged CH₃ and NH ₃ ⁺ groups in the lattice. The motion of these groups additionally effects the spectrum of the SAR1 center through averaging out of the anisotropic splitting.     

The optical conductivity of free carriers in GaAs

The optical conductivity of free electrons in polar semiconducting compounds has recently been calculated by use of a generalized Boltzmann equation derived from the equation of motion of the quantum density matrix. This reduces to the quasi-classical Boltzmann transport equation in the low frequency limit: the optical conductivity thus obtained spans a spectral range from around 30cm^?1 to 1.2 × 10⁴cm^?1 in GaAs. In this paper, the optical conductivity is calculated for GaAs as a function of carrier concentration in terms of a frequency dependent relaxation time which reduces to the usual relaxation time in the limit of low frequencies and an elastic scattering mechanism. The low frequency limit of the relaxation time is used to estimate the mobility as a function of carrier concentration. The frequency dependent relaxation time is given for GaAs at 298 K over the spectral region from 45 cm^?1 to 2.3 × 10³cm^?1 for carrier concentrations from 3.4 × 10¹⁵cm^?3 to 8.7 × 10¹⁸cm^?3.     

A study of molecular motion and Raman processes in K3H(SO4)2 and KHSO4 single crystals by observation of H and K spin-lattice relaxation

The spin-lattice relaxation rates for ¹H and ³⁹K nuclei in K₃H(SO₄)₂ and KHSO₄ single crystals, which are potential candidate materials for use in fuel cells, were determined as a function of temperature. The spin-lattice relaxation recovery of ¹H can be represented for both crystals with a single exponential function, but cannot be represented by the Bloembergen-Purcell-Pound (BPP) function, so is not related to HSO₄ motion. The recovery traces of ³⁹K, which predominantly undergoes quadrupole relaxation, can be represented by a linear combination of two exponential functions. The temperature dependences of the relaxation rates for ³⁹K can be described with a simple power law T₁⁻¹=αT². The spin-lattice relaxation rates for the ³⁹K nucleus in K₃H(SO₄)₂ and KHSO₄ crystals are in accordance with a Raman process dominated by a phonon mechanism.     

Spin Relaxation in the quantized Hall regime in the presence of disorder

We study the spin relaxation (SR) of a two-dimensional electron gas in the quantized Hall regime and discuss the role of spatial inhomogeneity effects on the relaxation. The results are obtained for small filling factors ν?1) or when the filling factor is close to an integer. In either case, SR times are essentially determined by a smooth random potential. For small n, we predict a “magneto-confinement” resonance manifested in the enhancement of the SR rate when the Zeeman energy is close to the spacing of confinement sublevels in the low-energy wing of the disorder-broadened Landau level. In the resonant region, the B-dependence of the SR time has a peculiar nonmonotonic shape. If ν?2n+1, the SR is going nonexponentially. Under typical conditions, the calculated SR times range from 10^?8 to 10^?6 s.     

NMR relaxation study of molecular motions in liquid chlorobenzotrifluorides

The temperature dependences of the ¹H and ¹⁹F nuclear spin-lattice relaxation times T₁ in liquid o-, m-, and p-chlorobenzotrifluorides have been measured. The analysis of the temperature dependences of the ¹H spin-lattice relaxation times leads to the conclusion that the overall molecular reorientational motion in o-, m-, and p-benzotrifluorides is nearly the same. Data for ¹H and ¹⁹F spin-lattice relaxation times of o-chlorobenzotrifluoride jointly lead to the determination of the individual contributions to relaxation rate in the entire temperature range studied. A knowledge of these contributions for o-chlorobenzotrifluoride, together with the assumption of equal correlation times for overall molecular reorientation in o- and p-chlorobenzotrifluorides, leads to the determination of the spin-internal-rotation interaction contribution to relaxation for p-chlorobenzotrifluoride in the same range of temperature.     

Longitudinal dynamic susceptibility of superparamagnetic particles with cubic anisotropy

We study the linear response of a system of single-domain ferromagnetic particles with cubic magnetic anisotropy to a weak external a.c. magnetic field. By averaging the Gilbert equation with a fluctuating field for the magnetization of an individual particle we derive a system of recurrence equations for the spectra of equilibrium correlation functions describing the longitudinal relaxation of the system. We find the solution of this system by using matrix continued fractions. We also evaluate the longitudinal relaxation time and the spectrum of the complex-valued magnetic susceptibility. Finally, we show that the nature of susceptibility dispersion is determined by the anisotropy and dissipation parameters. Zh. éksp. Teor. Fiz. 115, 101–114 (January 1999)     

Electron-phonon relaxation time in mercury

Electron scattering times determined by Azbel'-Kaner cyclotron resonance in mercury are discussed in terms of the electron-phonon interaction. Anisotropy in the electron-phonon relaxation time is explained in terms of an orbital α _k ² (ω)F _k (ω) function which describes the electron-phonon interaction and the phonon spectrum. AT ⁵ temperature dependence of the electron-phonon relaxation frequency is also considered.     

Nuclear relaxation and anisotropic molecular reorientation of o-dichlorobenzene

Proton recovery curves are reported for nonselective 180°-τ-90°-FT spin-lattice relaxation of a dilute solution of o-dichlorobenzene in carbon disulfide. An exact density matrix analysis, combined with measured¹³C relaxation rates, is used to obtain the principal reorientational correlation times. Differences between these values and those found previously for 1,2,3-trichlorobenzene in the same solvent can be rationalized in terms of molecular shape. Exact density matrix calculations of proton relaxation are compared with an approximate treatment in which dipolar cross correlation and nonlinear mixing effects of strong pulses are ignored. It is shown that simple formulae arising from the approximate treatment successfully account for the average relaxation rate of a given multiplet, but fail to account for differential relaxation of lines within a multiplet.