Theory of Systems of RodIike Particles: II. Thermotropic systems with orientation-dependent interactions

Abstract

A system of rigid, inpenetrable, rodlike molecules subject to orientation-dependent mutual attractions is treated by extension of the theory presented in the preceding paper. This energy is formulated, for a system at constant volume, by considering interactions between pairs of segments in contact, rather than in terms of interactions between entire molecules. The orientation-dependent energy between a pair of segments is taken to be proportional to cos² Ψ_ij, where Ψ_ij is the angle between the principal axes of their polarizability tensors, assumed to be cylindrically symmetric with respect to the molecular axis. A characteristic temperature T? measures the intensity of these interactions. The orientational energy of the system as a whole is of the form derived by Maier and Saupe. The orientation distribution with respect to the domain axis and the partition function are formulated with T? and the axial ratio x as parameters, Steric effects of molecular shape asymmetry, embodied in x, are of foremost importance. The reduced temperature [Ttilde]_ni = T_ni/xT? at which the nematic-isotropic transition takes place in the neat liquid decreases with decrease in x below its athermal limit x_erit = 6.417 for [Ttilde]^–1 _ni = 0. Both the entropy difference between isotropic and nematic phases and the orientational heat capacity C^p, are monotonic through the transition; C_p, diverges at a temperature appreciably above T_nl, where the metastable anisotropic state becomes unstable. Comparison of theory with experiments on those nematogens whose molecules can be approximated by rigid rods lends encouragement to the prospect of relating characteristics of the nematic-isotropic transition to molecular structure.     

Mathematical Description of Strongly Nonlinear Pressure Dependence of Phase Transition Temperatures

In order to describe mathematically the pressure dependence of phase transition temperatures we have derived an equation using the following assumption: i. The transition enthalpy Δ_tH = const. ii. The transition volume Δ_tV depends on the pressure p according to: The modified Simon-Glatzel-equation T = T₀(1 + p/b)^a exp (cp) allows to calculate the transition temperatures T also in cases of strongly non-linear relations.     

Pressure Effects of Nematic Liquid Crystals

There exists a variety of important new phenomena and plenty of experimental data on the pressure effects of liquid crystals. Yet, no systematic phenomenological or microscopic theory is available. In this paper, the ordinary Landau-deGennes theory is generalized so that the free energy becomes G = G _o(P, T) + a/2 [T - T*(P)]S ² - B(P)/3 S ³ + C(P)/4 S ⁴, T*(P) = T _o + bP - eP ². All the known pressure experiments of nematic PAA (where B and C are independent of P) are explained in one stroke and all parameters are determined. New results including reentrant I phase (I represents isotropic phase), and the independence of T _c—T* and T*—T _c on P, etc., are predicted. Simple methods of experimental confirmation are proposed. Similar discussions on the cases of MBBA, EBBA, etc. are also given. Our theory differs from that of Lin-Keyes-Daniels but agrees better with experiments. Results related to G _O(P, T) will be reported in a separate paper.     

Bismuth germanate and bismuth silicate glasses in cryogenic detectors

We present and discuss the results of measurements of conductivity and secondary electron emission coefficient of Bi_xGe_1−xO_2−0.5x (where x=0.13, 0.23, 0.33, 0.47) and Bi_xSi_1−xO_2−0.5x (where x=0.47, 0.57, 0.67) glasses reduced in hydrogen. The surface conductivity of reduced glasses strongly depends on reduction temperature, reduction time and bismuth content. The temperature dependence of the surface conductivity in a high temperature regime is well described by σ∼exp[−(T₀/T)ⁿ] law where n=1/4. The secondary electron emission coefficient of reduced glasses is practically independent of the degree of reduction but increases when binary glasses are modified by alkali ions. The research results confirmed that bismuth silicate and bismuth germanate glasses modified by alkali ions may be good materials for detectors working in cryogenic temperature.     

Transport behavior of yttrium substituted polycrystalline La0.7Pb0.3MnO3

The transport properties in La_0.7?xY_xPb_0.3MnO₃ (0.0 ? x ? 0.2) is investigated. The substitution of La³⁺ ions by smaller nonmagnetic Y³⁺ leads to greater spin disorder and induces variations in the magnetotransport behavior. From resistivity versus temperature curves a metal–insulator transition phenomenon is observed at the transition temperature, T_P, decreases as the Y content increases. The resistivity is well fitted using the equation ρ(T) = ρ_nexp[(T¹/T)ⁿ] with n = 1/4 and n = 1/2 at high and intermediate temperatures, respectively. The characteristic temperature T¹ varies with Y content in a manner consistent with the localization model of variable range hopping. Below T_P, resistivity varies as a function of power law contributions, ρ = ρ₀ + ρ₂T² + ρ_5/2T^5/2, corresponding to the electron scattering processes in the ferromagnetic phase.     

Elasticity and Orientational Order in Some trans-p-n-Alkoxy-α-methyl Cyanophenyl Cinnamates

The splay (k ₁₁), twist (k ₂₂) and bend (k ₃₃) elastic constants determined by the Freedericksz method and the orientational order parameters (s) derived from optical measurements in the nematic phase of six homologues of trans-p-n-alkoxy-α-methyl cyanophenyl cinnamates (n OMCPC) are reported. The data close to the nematic-isotropic transition point (T _NI) are compared with T _NI and the heats of transition (ΔH). The temperature-variation of elastic constants is discussed in terms of existing theories. The pretransitional increase in the twist and bend constants near the nematic-smectic A transition point (T _NA ) of 10 OMCPC has also been analysed.     

Magnetic and electric properties of the ternary alloys AB

The results of experimental studies of the electrophysical and magnetic properties of solid solutions based on the AB compounds with anion (Zn₃(P_xAs_1−x)₂ and cation (Zn_xCd_1−x)₃ P₂ substitution are reported. The Zn₃(As_xP_1−x)₂ solid solutions are characterized by p-type conductivity (∼ 10¹⁵  10¹⁷ cm⁻³), low Hall mobility and conductivity of ∼ 10⁻² — 10⁻³ ohm⁻¹ cm⁻¹. In the (Zn_xCd_1−x)₃P₂ solid solutions the samples rich in zinc are p-type, those rich in cadmium — n-type, the carrier concentration is ∼ 10¹⁶ — 10¹⁸ cm⁻³. From the measurements of the magnetic properties of the above mentioned alloys it is shown that in the investigated solid solutions a transition from the structure with direct optical transition to those with indirect optical transition occurs.     

High-temperature in situB NMR study of network dynamics in boron-containing glass-forming liquids

In situ high-temperature nuclear magnetic resonance (NMR) spectroscopy can be very useful for probing changes in structure and dynamics in glass-forming liquids, and is a unique method for observing chemical exchange among structural species (e.g. BO₃–BO₄, Qⁿ–Qⁿ⁺¹, and NBO–BO) at the seconds to microseconds time scales. High-temperature ¹¹B MAS NMR line shape measurements were made at about 100 K above the glass transitions on (Na₂O)_0.3(B₂O₃)_0.7 and (Na₂O)_0.2(B₂O₃)_0.21(Al₂O₃)_0.08(SiO₂)_0.51 glass-forming liquids. BO₃ and BO₄ groups are well resolved in ¹¹B MAS NMR spectra at 14.1 T with sample spinning at 5000 Hz. At higher temperatures, partial peak coalescence occurred due to exchange of BO₃ and BO₄. Temperature effects on borate speciation were also determined by varying the fictive temperature (T_f) of glasses, where T_f estimated from differential scanning calorimetry measurements. We combined these complementary data sets to model structural exchange in the liquid state. The time scale of BO₃–BO₄ exchange from NMR data, τ_NMR, appears to be “decoupled” from that of the macroscopic shear relaxation process τ_s derived from the viscosity, however, at higher temperatures, τ_s approaches τ_NMR. The “decoupling” at lower temperature may be related to intermediate-range compositional heterogeneities, and/or fast modifier cation diffusivities which trigger “unsuccessful” network exchange events.     

Fragility in mixed alkali tellurites

Linear viscoelastic stress relaxation and calorimetric measurements were performed on a series of mixed alkali tellurite glasses of composition 0.3([xNa₂O+(1−x)Li₂O])+0.7TeO₂ at temperatures near and above the glass transition temperature, T_g. The stress relaxation data were well described by the stretched exponential function, G(t)=G₀exp[−(t/τ)^β], where τ is the relaxation time, β is the distribution of relaxation times and G₀ is the high frequency modulus. The fragility, determined from the temperature dependence of τ, exhibited a minimum in the middle of the mixed alkali composition. A possible connection between the kinetic and the thermodynamic dimensions of this system was established, wherein the heat capacity change at the T_g, ΔC_p(T_g), and the fragility are correlated.     

The Investigation of Relation Between the Transition Temperature and the Unit Cell Volume in (K1-xCsx)2ZnCl4 Mixed Crystals

The relation between the phase transition temperature and unit cell volume in the (K_1-xCs_x)₂ZnCl₄ mixed crystals was studied. The phase transition temperature of A₂BX₄ family is dependent on the size of cation and anion (FABRY and PEREZ-MATO). That is, the transition temperature of crystal decreases with increasing unit cell volume. In this study we investigated this property of mixed crystals with the increasing mixture ratio. From the current study, we obtained the result that in the mixed crystals (K_1-xCs_x)₂ZnCl₄, the increase of x induces the increase of unit cell volume, so that T_I decreases with increasing unit cell volume. In order to determine the distribution of the substituted Cs⁺, using the near IR and UV spectrophotometer, we investigated both the band gap energy and the type of transition.     

Electrical conductivity and thermoelectric power of lithium-cadmium ferrites

The electrical conductivity (σ) and thermoelectric power (Q) of polycrystalline lithiumcadmium ferrites having the chemical formula Li_0.5–x/2Cd_xFe_2.5–x/2O₄ where (x = 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0) have been investigated as a function of temperature. Lithium-cadmium ferrite with x = 0.4 is found to possess minimum electrical conductivity and lowest Seebeck coefficient. Plots of log (σT) versus 10³T are almost linear and have shown a transition near the Curie temperature except in the case of cadmium ferrite. The Seebeck coefficient is negative for all the compositions showing that these ferrites behave as n-type semiconductors. The values of charge carrier concentration and mobility have also been computed. The properties of cadmium-substituted lithium ferrites have been correlated with those of zinc-substituted lithium ferrites, cadmium and zinc being two non-magnetic divalent ions occupying essentially tetrahedral A sites when substituted in ferrites.     

Crystal structure of Li2MgSiO4

The crystal structure of Li₂MgSiO₄ was established by single-crystal X-ray diffraction analysis. The crystals are monoclinic, a = 4.9924(7) Å, b = 10.681(2) Å, c = 6.2889(5) Å, β = 90.46(1)°, Z = 4, sp. gr. P2₁/n, V = 335.54 ų, R = 0.062. In a Li₂MgSiO₄ crystal, four types of independent T(1–4) tetrahedra share vertices to form a three-dimensional framework. Three of these tetrahedra are occupied simultaneously by Li and Mg cations, which corresponds to the crystallochemical formula (Li_0.98Mg_0.02)(Li_0.80Mg_0.20) · (Li_0.22Mg_0.78)SiO₄. In slightly distorted SiO₄ tetrahedra denoted as T(1), the average Si-O distance is 1.635(2) Å. The distortions of other tetrahedra and the average (Li _x Mg_{1 ? x} )-O distances increase with an increase in lithium content. These distances in the T(2), T(3), and T(4) tetrahedra are 1.955(2), 1.971(4), and 2.019(6) Å, respectively. The structure of the new compound is compared with the crystal structures of other Li₂ M ²⁺SiO₄ compounds and the luminescence spectra of Cr⁴⁺: Li₂MgSiO₄.     

Structure and magnetic properties of heterometallic coordination carboxylate polymers with cobalt and lithium atoms

Reactions between lithium pivalate and cobalt coordination polymers [Co₅(OH₂)(OH)(Piv)₉)L ¹)₄] _n (I) and [Co₂(OH₂)(Piv)₄(L ²)₂] _n (II), where Piv—is the pivalate anion, L ¹ is pyrazine, and L ² is pyrimidine, result in new heterometallic polymers {[Li₂Co₂(Piv)₆(L ¹)₂]₂ MeCN} _n (III), {[Li₂Co₂(Piv)₆(L ²)]_0.5 MeCN} _n (IV), and [Li₂Co₂(Piv)₆(L ²)₂] _n (V). The resulting compounds contain tetra-nuclear {Li₂Co₂(Piv)₆} fragments connected by neutral bridging ligands (pyrazine or pyrimidine) into layer structures. Crystal structures III–V are determined, and the magnetic properties of III and IV are studied.     

Magneto‐transport properties of polycrystalline YBa2(Cu1‐xMx)3O7‐δ (M = B and Mn)

The magnetic and transport properties of polycrystalline YBa₂ (Cu_1‐xM_x)₃ O_7‐δ (M = B and Mn) superconductor was investigated. Samples of YBa₂(Cu_1‐xB_x)₃O_7‐δ doped with several concentrations of boron B(x = 0.05 and 0.1) were investigated using magnetization measurements. A YBa₂(Cu_1‐xMn_x)₃O_7‐δ sample doped with Mn with concentration of x = 0.02 was investigated using current‐voltage (I‐V) measurements. Our results on the YBa₂(Cu_1‐xB_x)₃O_7‐δ samples reveal a considerable increase in the hysterisis width of the magnetization, M versus the applied magnetic field H with increasing boron concentration. The lower critical field was also found to be enhanced by boron doping. The critical current density, J_c was found to be significantly enhanced in the Mn‐doped sample. The enhancement of J_c was found to be more significant at the lower temperatures for all applied magnetic fields used (0 Oe, 300 Oe, and 500 Oe). Thus, chemical doping is suggested to enhance the vortex pinning forces in the YBCO samples. From the resistivity (R‐T) measurements, chemical doping of the samples was found to have no significant effect on the critical temperature, T_c. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Absorption spectrum of octahedral CoCl4(H2O)2 units in [(CH3)3NH]CoCl3·2H2O single crystal

The optical absorption spectrum of the octahedral moiety CoCl₄(H₂O)₂ in single crystal [(CH₃)₃NH]CoCl₃·2H₂O has been studied at room and liquidair temperatures. The observed ambient bands at 6800, 16,300, and 19,000 cm^–1 have been assigned, respectively, to the transitions⁴ T ₁(F) ⁴ T ₂(F),⁴ A ₂(F), and⁴ T ₁ (P). The crystal field parameters evaluated areD _q =B=850 cm^–1, andC=4.63B. At liquid-air temperatures the⁴ T ₁(P) band is seen to split into the expected four components ₇, ₈, ₈, and ₆, due to spin-orbit coupling, and the coupling coefficient was computed to be 525 cm^–1.     

Structure and properties of Ni60(Nb100−xTax)34Sn6 bulk metallic glass alloys

Refractory bulk metallic glasses and bulk metallic glass composites are formed in quaternary Ni-Nb-Ta-Sn alloy system. Alloys of composition Ni₆₀(Nb_100−xTa_x)₃₄Sn₆ (x = 20, 40, 60, 80) alloys were prepared by injection-casting the molten alloys into copper molds. Glassy alloys are formed in the thickness of half mm strips. With thicker strips (e.g., 1 mm), Nb₂O₅ and Ni₃Sn phases and the amorphous phase form an in situ composite. Glass transition temperatures, crystallization temperatures, and ΔT_x, defined as T_x1 − T_g (T_x1: first crystallization temperature, T_g: glass transition temperature) of the alloys increase dramatically with increasing Ta contents. These refractory bulk amorphous alloys exhibit high Young’s modulus (155-170 GPa), shear modulus (56-63 GPa), and estimated yield strength (3-3.6 GPa).     

The Order Parameters of Some Nematic Liquid Crystals Measured by the Resonance Raman Effect and Its Relevance to the Nematic-Isotropic Phase Transition

The second and fourth order parameters of nematic MBBA and 5CB have been determined near the nematic-isotropic transition temperatures by means of resonance Raman measurements on β-carotene dissolved as an orientational probe. The limiting behaviour of the second order parameter of MBBA near the transition point has been investigated on the basis of its fluctuation, which is deduced from the 2nd and 4th order parameter values.     

Spectroscopy of Molecualr Crystals: A Bibliography for 1975

Abstract

Our previous thermodynamical approach was reexamined to study phase transition of anion radical salts, [(C₆H₅)₃PCH₃]⁺ _{1 ? x}[(C₆H₅)₃AsCH₃]⁺ _x(TCNQ)^? ₂,(0≤x≤1). The mechanism of the phase transition of the solid solution at 1 atm pressure was confirmed to be αy [(C₆H₅)₃PCH₃]⁺ _{1 ? x}[(C₆H₅)₃AsCH₃]⁺ _x(TCNQ)^? ₂,(0≤x≤1) βy, and the volume change assoiated with the phase transition was estimated to be ΔV =-1.3 (1-x) cm³/mol.     

The annealing of alkaline-earth metal polymetaphosphate powders (I). Crystallisation and sintering processes

Amorphous barium, strontium, calcium and magnesium polymetaphosphate powders (MP₂O₆)_n, n = 20 were prepared by dehydration of the corresponding polymetaphosphate hydrate precipitates. These powders were annealed by different continuous and isothermal heat treatments over the temperature range 450° to 700 °C, the glass transition temperatures T_g to above (T_g + 120) °C. The morphologies at different degrees of crystallisation were studied by scanning electron microscopy. For the main crystallisation process (ten to sixty-seventy percent crystallisation), the powder particles retained their original pea-pod form; then after seventy percent crystallisation, these crystallised particles sintered laterally to lozenge-shaped twin-hexagonal crystals of lengths 0.5 to 3 μm. Differential thermal analysis confirmed that a markedly exothermic crystallisation process (overall enthalpy changes from about 30 to 45 kJ mol⁻¹) was occurring within the powder particles. Crystallisation rates varied from < 0.005 min⁻¹ at temperatures near T_g to > 0.5 min⁻¹ at higher temperatures; the activation energies for this process varied from 360 to 560 kJ mol⁻¹. The completely annealed crystals were studied by scanning electron microscopy, X-ray diffraction and further differential thermal analysis to 1000 °C. The X-ray diffraction d value patterns, the fusion temperatures and the enthalpies of fusion were all in close agreement with the literature values for the corresponding beta alkaline-earth metal polymetaphosphates prepared by melt crystallisation.