A variational approach to the relaxation of single domain magnetic particles based on Brown's model

Brown's model for the relaxation of the magnetization of a single domain ferromagnetic particle is considered. This model results in the Fokker-Planck equation of the process. The solution of this equation in the cases of most interest is non- trivial. The probability density of orientations of the magnetization in the Fokker-Planck equation can be expanded in terms of an infinite set of eigenfunctions and their corresponding eigenvalues where these obey a Sturm-Liouville type equation. A variational principle is applied to the solution of this equation in the case of an axially symmetric potential. The first (non-zero) eigenvalue, corresponding to the largest time constant, is considered. From this we obtain two new results. Firstly, an approximate minimising trial function is obtained which allows calculation of a rigorous upper bound. Secondly, a new upper bound formula is derived based on the Euler-Lagrange condition. This leads to very accurate calculation of the eigenvalue but also, interestingly, from this, use of the simplest trial function yields an equivalent result to the correlation time of Coffey et at. and the integral relaxation time of Garanin. (C) 2004 Elsevier B.V. All rights reserved.

The role of Mittag-Leffler functions in anomalous relaxation

The inertia-corrected Debye model of rotational Brownian motion of polar molecules was generalized by Coffey et al. [Phys. Rev. E, 65, 32 102 (2002)] to describe fractional dynamics and anomalous rotational diffusion. The linear- response theory of the normalized complex susceptibility was given in terms of a Laplace transform and as a function of frequency. The angular-velocity correlation function was parametrized via fractal Mittag-Leffler functions. Here we apply the latter method and complex-contour integral- representation methods to determine the original time-dependent amplitude as an inverse Laplace transform using both analytical and numerical approaches, as appropriate. (C) 2004 Elsevier B.V. All rights reserved.

Microscopic models for dielectric relaxation in disordered systems

It is shown how the Debye rotational diffusion model of dielectric relaxation of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to yield the empirical Havriliak-Negami (HN) equation of anomalous dielectric relaxation from a microscopic model based on a kinetic equation just as in the Debye model. This kinetic equation is obtained by means of a generalization of the noninertial Fokker-Planck equation of conventional Brownian motion (generally known as the Smoluchowski equation) to fractional kinetics governed by the HN relaxation mechanism. For the simple case of noninteracting dipoles it may be solved by Fourier transform techniques to yield the Green function and the complex dielectric susceptibility corresponding to the HN anomalous relaxation mechanism.

Polarization Relaxation in an Ionic Liquid Confined between Electrified Walls

The response of a room temperature molten salt to an external electric field when it is confined to a nanoslit is studied by molecular dynamics simulations. The fluid is confined between two parallel and oppositely charged walls, emulating two electrified solid-liquid interfaces. Attention is focused on structural, electrostatic, and dynamical properties, which are compared with those of the nonpolarized fluid. It is found that the relaxation of the electrostatic potential, after switching the electric field off, occurs in two stages. A first, subpicosecond process accounts for 80% of the decay and is followed by a second subdiffusive process with a time constant of 8 ps. Diffusion is not involved in the relaxation, which is mostly driven by small anion translations. The relaxation of the polarization in the confined system is discussed in terms of the spectrum of charge density fluctuations in the bulk.

Relaxation processes in room temperature ionic liquids: The case of 1-butyl-3-methyl imidazolium hexafluorophosphate

A detailed investigation on the nature of the relaxation processes occurring in a typical room temperature ionic liquid (RTIL), namely, 1-butyl-3-methyl imidazolium hexafluorophosphate ([bmim][PF6]), is reported. The study was conducted using both elastic and inelastic neutron scattering over a wide temperature range from 10 to 400 K, accessing the dynamic features of both the liquid and glassy amorphous states. In this study, the inelastic fixed energy scan technique has been applied for the first time to this class of materials. Using this technique, the existence of two relaxation processes below the glass transition and a further diffusive process occurring above the glass-liquid transition are observed. The low temperature processes are associated with methyl group rotation and butyl chain relaxation in the glassy state and have been modeled in terms of two Debye-like, Arrhenius activated processes. The high temperature process has been modeled in terms of a Kohlraush-Williams-Watts relaxation, with a distinct Vogel-Fulcher-Tamman temperature dependence. These results provide novel information that will be useful in rationalizing the observed structural and dynamical behavior of RTILs in the amorphous state.

GLP-1 and related peptides cause concentration-dependent relaxation of rat aorta through a pathway involving KATP and cAMP

increasing evidence from both clinical and experimental studies indicates that the insulin-releasing hormone, glucagon-like peptide-1 (GLP-1) may exert additional protective/reparative effects on the cardiovascular system. The aim of this study was to examine vasorelaxant effects of GLP-1(7-36)amide, three structurally-related peptides and a non-peptide GLP-1 agonist in rat aorta. Interestingly, all GLP-1 compounds, including the established GLP-1 receptor antagonist, exendin (9-39) caused concentration-dependent relaxation. Mechanistic studies employing hyperpolarising concentrations of potassium or glybenclamide revealed that these relaxant effects are mediated via specific activation of ATP-sensitive potassium channels. Further experiments using a specific membrane-permeable cyclic AMP (cAMP) antagonist, and demonstration of increased cAMP production in response to GLP-1 illustrated the critical importance of this pathway. These data significantly extend previous observations suggesting that GLP-1 may modulate vascular function, and indicate that this effect may be mediated by the GLP-1 receptor. However, further studies are required in order to establish whether GLP-1 related agents may confer additional cardiovascular benefits to diabetic patients. (c) 2008 Elsevier Inc. All rights reserved.

A density functional theory study of the surface relaxation and reactivity of Cu2O(100)

Density functional theory has been used to investigate the surface relaxation of Cu2O(100) and the adsorption of NO. The calculations indicate the formation of surface copper dimers on relaxation coupled with a large contraction of the spacing between the first and second layers. Local density of states for atoms in the top three layers shows that the third layer copper atoms have the greatest change in bonding character. Adsorption energies have been calculated for the N-down and O-down adsorption of NO on the Cu2O(100) surface. These indicate that N-down adsorption is favoured and that in this case NO-lattice oxygen interactions dominate the adsorbate structure. (C) 2000 Elsevier Science B.V. All rights reserved.

Listening to lanthanide complexes: Determination of the intrinsic luminescence quantum yield by nonradiative relaxation

The photophysical properties of lanthanide complexes have been studied extensively; however, fundamental parameters such as the intrinsic quantum yield as well as radiative and nonradiative decay rates are difficult or even impossible to measure experimentally. Herein, a photoacoustic (PA) method is proposed to determine the intrinsic quantum yield of lanthanide complexes with lifetimes in the order of milliseconds. This method is used to determine the intrinsic quantum yields for europium (III)-containing metallomesogens as well as terbium(III) complexes. The results show that the PA signal is sensitive to both the lifetime and the ratio of the fast-to-slow heat component of the samples. It is found that there is an efficient ligand sensitization and a moderate intrinsic quantum yield for the complexes. The intrinsic quantum yield of Eu3+ in the metallomesogens exhibits an obvious increase upon the isotropic liquid to smectic A transition. The proposed PA method is quite simple, and con contribute to a clearer understanding of the photophysical processes in luminescent lanthanide complexes.

Temperature Dependence of the Primary Relaxation in 1-Hexyl-3-methylimidazolium bis{(trifluoromethyl)sulfonyl}imide

We present results from complementary characterizations of the primary relaxation rate of a room temperature ionic liquid (RTIL), 1-hexyl-3-methylimidazolium bis{(trifluoromethyl)sulfonyl} imide, [C(6)mim][Tf2N], over a wide temperature range. This extensive data set is successfully merged with existing literature data for conductivity, viscosity, and NMR diffusion coefficients thus providing, for the case of RTILs, a unique description of the primary process relaxation map over more than 12 decades in relaxation rate and between 185 and 430 K. This unique data set allows a detailed characterization of the VTF parameters for the primary process, that are: B = 890 K, T-0 = 155.2 K, leading to a fragility index m = 71, corresponding to an intermediate fragility. For the first time neutron spin echo data from a fully deuteriated sample of RTIL at the two main interference peaks, Q = 0.76 and 1.4 angstrom(-1) are presented. At high temperature (T > 250 K), the collective structural relaxation rate follows the viscosity behavior; however at lower temperatures it deviates from the viscosity behavior, indicating the existence of a faster process.