Calculation of the Relaxation Time and the Activation Energy Close to the Lower Phase Transition in Imidazolium Perchlorate

The temperature dependence of the relaxation time of imidazolium perchlorate (Im-ClO4) was calculated from the pseudospin-phonon coupled (PS) and the energy fluctuation (EF) models close to the first-order phase transition temperature of 247 K. This calculation was performed in terms of the proton second moment M2 that was associated with the order parameter which was predicted from the mean-field theory. Our results were in good agreement with the observed data. In addition, values of the activation energy were deduced in terms of the Arrhenius plot using our calculated values of the relaxation time from both PS and EF models

Temperature Dependence of the Tilt Angle for the Smectic A-Smectic C* Transition in a Mixture of C7-70PDOB Ferroelectric Liquid Crystals near the Tricritical Point

The temperature dependence of the tilt angle theta is studied in the smectic C* phase near the smectic A-smectic C* tricritical point for a mixture of 70PD0B in the ferroelectric liquid crystal C7 (X = 16.92). The mean-field models with the biquadratic P-2 theta(2) (P is the spontaneous polarization) and P-2 theta(2) + P theta (bilinear) coupling terms in the free energy expansion are used to analyze the experimental data for the tilt angle in this binary mixture. From our analysis, the coefficients given in the free energy expansion of the mean-field models are determined. Our results show that the mean-field theory explains adequately the observed behaviour of the C7-70PD0B mixture near the AC* tricritical point

Calculation of the infrared frequency and the damping constant (full width at half maximum) for metal organic frameworks

The rho(NH2) infrared (IR) frequencies and the corresponding full width at half maximum (FWHM) values for (CH3)(2)(NH2FeMII)-M-III(HCOO)(6) (DMFeM, M = Ni, Zn, Cu, Fe, and Mg) are analyzed at various temperatures by using the experimental data from the literature. For the analysis of the IR frequencies of the rho(NH2) mode which is associated with the structural phase transitions in those metal structures, the temperature dependence of the mode frequency is assumed as an order parameter and the IR frequencies are calculated by using the molecular field theory. Also, the temperature dependence of the IR frequencies and of the damping constant as calculated from the models of pseudospin (dynamic disorder of dimethylammonium (DMA(+)) cations)-phonon coupling (PS) and of the energy fluctuation (EF), is fitted to the observed data for the wavenumber and FWHM of the rho(NH2) IR mode of the niccolites studied here. We find that the observed behavior of the IR frequencies and the FWHM of this mode can be described adequately by the models studied for the crystalline structures of interest. This method of calculating the frequencies (IR and Raman) and FWHM of modes which are responsible for the phase transitions can also be applied to some other metal organic frameworks

Calculation of the Dielectric Constant of a Ferroelectric Liquid Crystal From a Mean Field Model

The static dielectric constant epsilon(perpendicular to) of the ferroelectric liquid crystal 4-(3-methyl-2-chlorobutanoyloxy)-4'--heptyloxybiphenyl (A7) with high spontaneous polarization is calculated as a function of temperature using a mean field model. This calculation is performed close to the smectic A-isotropic liquid (SmA-I) transition for pure optically active compound (T-c = 81.6 degrees C). For this calculation of epsilon(perpendicular to), the free energy of the SmA phase is expanded in terms of the orientational order parameter. and spontaneous polarization P with P-2 psi(2)

Temperature dependence of the Raman frequencies and bandwidths close to phase transitions in ammonium halides

In this study, we give the temperature dependence of our observed frequencies and bandwidths for the Raman optical modes in the ammonium halides close to the phase transitions of the first order (NH4 Br), tricritical (NH4Cl) and second order (NH4Cl). Using the predictions of an [sing pseudospin-phonon coupled model, which considers interactions between two spin and two phonons, our observed Raman data have been interpreted qualitatively. Our results show that an Ising model considered here can explain the observed behaviour of the Raman phonons near the phase transitions of the first order, tricritical and second order in the ammonium halides. (C) 2001 Elsevier Science B.V. All rights reserve

Raman Frequencies calculated as a function of pressure for the rotatory lattice mode in ammonia solid II near the melting point

This study gives our calculations for the Raman frequencies of the rotatory lattice mode in ammonia solid II near the melting point. The Raman frequencies of this mode are calculated as a function of the pressure using the volume data for the fixed temperatures of 230.4 K, 263.4 K, and 297.5 K by means of our Gruneisen relation. Our calculated frequencies can be examined experimentally when the Raman measurements are performed at various pressures for the constant temperatures considered

Calculation of the Raman frequencies of the translational mode in ammonia solid II

We report here our calculated Raman frequencies of the translational mode as a function of temperature for the. fixed pressures of 3.65, 5.02 and 6.57 kbars in the ammonia solid II. They were calculated by means of our Gruneisen relation using the volume data from the literature for all the pressures indicated within the temperature regions close to the melting point in this system. Our calculated frequencies are in very-good agreement with those observed experimentally for this translational mode of the ammonia solid II. This shows that the observed behaviour of ammonia solid II can be described adequately by means of the calculation employed here

Pippard relation modified for the rotatory lattice mode in ammonia solid II

In this study we obtain a linear variation of the specific heat Cp with the Raman frequency shifts 1/v (partial derivative v/partial derivative T)p for the rotatory lattice (librational) mode in the ammonia solid II near the melting point. From this linearity, we deduce values of the slope dP(m)/dT for the pressures of 3.65, 5.02 and 6.57 kbars in the ammonia solid II. Our calculated value of dP(m)/dT for the pressure of 3.65 kbar, is in good agreement with the experimentally measured value in the P-T phase diagram of this crystalline system. This indicates that the first Pippard relation modified for the rotatory lattice mode in the ammonia solid II, is satisfactory near the melting point

Bandwidths studied as a function of temperature in ammonium halides near T-lambda

This study gives our analysis of the Raman bandwidths using the soft mode-hard mode coupling model applied to ammonium halides. The temperature dependence of our observed bandwidths for the nu(5)(174 cm(-1)) Raman mode of NH4Cl and nu(5)(177 cm(-1)) Raman mode of NH4Br, is analyzed close to phase transitions. From our analysis, we obtain beta = 0.13 as the values of the critical exponent for the order parameter in the first order phase region for the ammonium halides

WEAKLY FIRST-ORDER OR NEARLY 2ND-ORDER PHASE-TRANSITIONS

In this study we have developed a model which is mainly for a spin system (Ising model) superimposed on a system of lattice vibrations (Einstein and/or Debye model). Under this model we have derived the thermodynamic functions and predicted their critical behaviour near T-c