Nonequilibrium response of a disordered Ising chain

The relaxation behaviour of a model disordered system is studied. The model considered is a nearest neighbour Ising chain in which the bond strengths are distributed at random between the discrete values +J and -J with equal probability. The system is prepared in a given state and is allowed to relax to a new state of equilibrium. This approach to equilibrium is probed by means of an applied, weak, time-dependent magnetic field. The relevant physical quantity is a nonequilibrium susceptibility which is calculated exactly. A comparison between this, and the corresponding quantity for the pure chain, reveals certain distinctive features of the time-dependent properties of disordered systems.Deceased     

Gorsky relaxation in the presence of traps

It has been shown recently that a linear response theoretic formalism leads to a straightforward derivation of the theory of the Gorsky effect at low interstitial concentrations, for arbitrary specimen geometry and applied stress inhomogeneity. We now extend this formalism to the practically important situation in which traps (e.g., N interstitials) inhibit the diffusion of the H interstitials, in order to motivate the experimental application of the Gorsky relaxation technique to the determination of the trap parameters. An explicit calculation is done for a typical specimen geometry, using Schroeder's phenomenological model for diffusion in the presence of traps. Exact expressions are obtained for the anelastic creep function, the relaxation strength and the internal friction. The structure and physical implications of these expressions are discussed using numerical values for the parameters deduced by other methods (in particular, neutron scattering). Noteworthy features of the predicted dynamic response include shifts in the position and height of the Gorsky peak owing to the occurrence of an effective diffusion constant and the difference in the values of the trace of the elastic dipole tensor in the free and trapped states; and an additional Snoek-like contribution due to local free trapped transitions of the diffusing particles.     

Kinetics and Mechanism of the Reactions of Picolinic Acid with Dichloro-{1-alkyl-2-(arylazo)imidazole}palladium(II) Complexes

The reaction between Pd(N,N′)Cl₂ [N,N′ ≡ 1-alkyl-2-(arylazo)imidazole (N,N′) and picolinic acid (picH) have been studied spectrophotometrically at λ = 463 nm in MeCN at 298 K. The product is [Pd(pic)₂] which has been verified by the synthesis of the pure compound from Na₂[PdCl₄] and picH. The kinetics of the nucleophilic substitution reaction have been studied under pseudo-first-order conditions. The reaction proceeds in a two-step-consecutive manner (A → B → C); each step follows first order kinetics with respect to each complex and picH where the rate equations are: Rate 1 = {k′₀ + k′₂[picH]₀} × [Pd(N,N′)Cl₂] and Rate 2 = {k′′₀ + k′′₂[picH]₀}[Pd(N,O)(monodentate N,N′)Cl₂] such that the first step second order rate constant (k′₂) is greater than the second step second order rate constant (k′′₂). External addition of Cl⁻ (as LiCl) suppresses the rate. Increase in π-acidity of the N,N′ ligand, increases the rate. The reaction has been studied at different temperatures and the activation parameters (Δ^‡H° and Δ^‡S°) were calculated from the Eyring plot.     

Kinetic and mechanistic studies of the interaction of 2-mercapto pyridine with dichloro[1-alkyl-2-(arylazo)imidazole]palladium(II) complexes

Nucleophilic substitution of Pd(RaaiR′)Cl₂ [(RaaiR′ = 1-alkyl-2-(arylazo)imidazole, p-R-C₆H₄-N=N-C₃H₂NN-1-R′; where R = H(a)/ Me(b)/ Cl(c) and R′ = Et(1)/Bz(2)] with 2-Mercaptopyridine (2-SH-Py) in acetonitrile (MeCN) at 298 K, to form [Pd₂(2-S-Py)₄], has been studied spectrophotometrically under pseudo-first-order conditions and the analyses support the nucleophilic association path. The reaction follows the rate law, Rate = {k ₀ + k [2-SH-Py] ₀ ² }[Pd(RaaiR′)Cl₂]: first order in Pd(RaaiR′)Cl₂ and second order in 2-SH-Py. The rate of the reaction follows the order: Pd(RaaiEt)Cl₂ (1) < Pd(RaaiBz)Cl₂ (2) and Pd(MeaaiR′)Cl₂ (b) < Pd(HaaiR′)Cl₂ (a) < Pd(ClaaiR′)Cl₂ (c). External addition of Cl⁻ (LiCl) and HCl suppresses the rate (Rate ∝ 1/[Cl⁻]₀ & ∝1/[HCl]₀). The reactions have been studied at different temperatures (293–308 K) and activation parameters (Δ^‡ H° and Δ ^‡ S°) of the reactions were calculated from the Eyring plot and support the proposed mechanism.     

High‐Potential Perfluorinated Phthalocyanine–Fullerene Dyads for Generation of High‐Energy Charge‐Separated States: Formation and Photoinduced Electron‐Transfer Studies

High oxidation potential perfluorinated zinc phthalocyanines (ZnF_nPcs) are synthesised and their spectroscopic, redox, and light‐induced electron‐transfer properties investigated systematically by forming donor–acceptor dyads through metal–ligand axial coordination of fullerene (C₆₀) derivatives. Absorption and fluorescence spectral studies reveal efficient binding of the pyridine‐ (Py) and phenylimidazole‐functionalised fullerene (C₆₀Im) derivatives to the zinc centre of the F_nPcs. The determined binding constants, K, in o‐dichlorobenzene for the 1:1 complexes are in the order of 10⁴ to 10⁵ M ^?1; nearly an order of magnitude higher than that observed for the dyad formed from zinc phthalocyanine (ZnPc) lacking fluorine substituents. The geometry and electronic structure of the dyads are determined by using the B3LYP/6‐31G* method. The HOMO and LUMO levels are located on the Pc and C₆₀ entities, respectively; this suggests the formation of ZnF_nPc^.+–C₆₀Im^.? and ZnF_nPc^.+–C₆₀Py^.? (n=0, 8 or 16) intra‐supramolecular charge‐separated states during electron transfer. Electrochemical studies on the ZnPc–C₆₀ dyads enable accurate determination of their oxidation and reduction potentials and the energy of the charge‐separated states. The energy of the charge‐separated state for dyads composed of ZnF_nPc is higher than that of normal ZnPc–C₆₀ dyads and reveals their significance in harvesting higher amounts of light energy. Evidence for charge separation in the dyads is secured from femtosecond transient absorption studies in nonpolar toluene. Kinetic evaluation of the cation and anion radical ion peaks reveals ultrafast charge separation and charge recombination in dyads composed of perfluorinated phthalocyanine and fullerene; this implies their significance in solar‐energy harvesting and optoelectronic device building applications.     

GeneralizedM-diffusion model of molecular rotations

The widely usedM-model of rotational diffusion of molecules in fluid phases is generalized. The ordinaryM-model assumes that intermolecular collisions causeinstantaneous changes in the orientation of an otherwise free rotor. The present scheme takes cognizance of the ubiquitous intermolecular torques which should make the molecular orientation a continuously variable random function of time. It is assumed here that the component of the angular velocity, which is conjugate to the angle specifying the orientation of the molecule, is a stationary Gaussian-Markov process. The ordinaryM-model emerges then as a special case of the more general treatment presented here. The results derived for the dipole correlation function of a linear rotor on the basis of the generalized scheme are applied to a series of infrared data. The observed agreement is highly satisfactory. The present analysis affords a justification for the Gordon scheme which generalizes theM-model by assigning to the mean rate of collision anad-hoc dependence on the angular speed of the rotor. It is argued also that the model treated here incorporates certain memory effects which are ignored in the ordinaryM-model, and may yield, in some cases, results which are similar to those based on certain memory function formalisms.     

Crystal and molecular structure of hexahydropyridine (piperidine) hydrochloride

The structure of hexahydro pyridine (piperidine), a compound of psychobiological importance, has been determined in the form of its hydrochloride by the heavy-atom technique, using three-dimensional X-ray data. Hexahydro pyridine hydrochloride, (C₅H₅N)H₆.HC1, crystallizes in the orthorhombic space groupPbcm with four molecules per unit cell of dimensionsa = 9.68(2),b = 7.30(3),c = 9.67(2) Å. The positions of the hydrogen atoms were located from a difference-Fourier synthesis. The structure was refined by the full-matrix least-squares method, using anisotropic temperature factors, leading to the finalR-value of 0.094. The hexahydro pyridine ring has a chair conformation. The crystallographic mirror plane atz = 1/4 coincides with the molecular mirror plane passing through the C1, N and C(3) atoms of the molecule in such a way that C(1)′ and C(2)′ are the mirror images of C(1) and C(2). The dihedral angles which plane I, containing C(1), C(2), C(2)′ and C(1)′, makes with plane II, containing C(2), C(3) and C(2)′, and planeIII, containing C(1), N and C(1)′, are 120.47 and 116∶42 °, respectively. The molecules are held together by a network of hydrogen bonds of type N⁺ —H ... C1^? in thexy-plane, and by van der Waals forces in thez-direction. Both the hydrogen atoms in the NH ₂ ⁺ group of the molecule take part in the formation of hydrogen bonds.