Free energy of semiflexible polymers and structure of interfaces

The free energy of semiflexible polymers is calculated as a functional of the compositional scalar order parameter and the orientational order parameter of second-rank tensor S_ij on the basis of a microscopic model of wormlike chains with variable segment lengths. We use a density functional theory and a gradient expansion to evaluate the entropic part of the free energy, which is given in a power series of .The interaction term of the free energy is derived with a random phase approximation. For the rigid rod limit, the nematic-isotropic transition point is given by , N and w being the degree of polymerization and the anisotropic interaction parameter, respectively, and the degree of ordering at the transition point is 0.33448. We also find that the contour length of polymer chains becomes larger in a nematic phase than in an isotropic phase. Interface profiles are obtained numerically for some typical cases. In the neighborhood of isotropic-isotropic interfaces, polymer chains tend to align parallel to the interface on the polymer-rich side and perpendicular on the poor side. When an isotropic region and a nematic region coexist, orientational order parallel to the interface is preferred in the nematic region. Received: 28 May 1998 / Revised: 12 August 1998 / Accepted: 8 September 1998     

Fluctuations of orientational order in a uniaxial nematic liquid crystal with biaxial molecules and its response to an external field

Homogeneous thermal fluctuations of the orientational order parameters S and G of biaxial molecules in a uniaxial nematic liquid crystal are investigated in the framework of the molecular-statistical theory. It is demonstrated that the molecular biaxiality significantly affects the order parameters S and G, their temperature dependences in the nematic phase, the amplitude and the temperature dependence of the order parameter fluctuations in the nematic and isotropic phases, and the character of the transition from the nematic phase to the isotropic liquid phase. It is established that the fluctuations of the parameters S and G in the nematic phase are related to the temperature dependences of S and G and the susceptibilities χ_S and χ_G of the nematic liquid crystal to external fields, which leads to a change in the parameters S and G at a fixed director orientation. Explanations are offered for the known experimental data on the orientational ordering of biaxial molecules under the action of external fields in the isotropic phase of nematic liquid crystals.     

Structure, phase transitions and molecular dynamics in 4-methylpyridinium tetrachloroantimonate(III), [4-CH3C5H4NH][SbCl4]

Crystal structure of the 4-methylpyridinium tetrachloroantimonate(III), [4-CH₃C₅H₄NH][SbCl₄], has been determined at 240 K by X-ray diffraction as monoclinic, space group, P2₁/n, Z=8. Differential scanning calorimetry and dilatometric studies indicate the presence of two reversible phase transitions of first order type, at 335/339 and 233/289 K (cooling/heating) with ΔS=0.68 and 2.2 J mol⁻¹ K⁻¹, respectively. Crystal dynamics is discussed on the basis of the temperature dependence of the ¹H NMR spin-lattice relaxation time T₁ and infrared spectroscopic studies. The low temperature phase transition at 233 K of an order-disorder type is interpreted in terms of a change in the motional state of the 4-methylpyridinium cations. The phase transition at 335 K, probably of a displacive type, is characterised by a complex mechanism involving the dynamics of both the cationic and anionic sublattice. The ¹H NMR studies show that the low temperature phase III is characterised only by the dynamics of the CH₃ groups.     

Correlation of the molecular structure of discotic nematic liquid crystals with their orientational order and specific features of the nematic-isotropic phase transition

The orientational order parameter S of molecules in high-temperature discotic nematic liquid-crystal phases of triphenylene derivatives is investigated as a function of the length of side flexible molecular chains at different temperatures. It is established that the orientational order parameters S in the range of the transition from the nematic phase to the isotropic liquid phase (the N _D -I transition) are smaller than those predicted from the molecular-statistical theory and computer simulation. It is shown that the N _D -I transition is close to both the isolated Landau point and the tricritical point (regardless of the chemical structure of the molecules and the anisotropy of dispersion intermolecular interactions). Consistent explanations are offered for a number of experimental findings, such as the anomalously small changes in the enthalpy and entropy upon the N _D -I transition (as compared to those revealed upon the N-I transition in calamitic nematic liquid crystals), the anomalously strong response of the isotropic phase of discotic nematic liquid crystals to external fields (thermodynamically conjugate to the order parameter S) and the long relaxation times of this response, and the formation of cybotactic discotic molecular clusters in the isotropic phase in the vicinity of the N _D -I transition.     

Orientational order and polarizability of molecules in a nematic liquid crystal

The influence of the orientational order of molecules in a nematic liquid crystal on the mean value $\bar \gamma$ and anisotropy Δγ of the molecular polarizability has been studied in the framework of the molecular statistical approach with allowance for the perturbation of the electronic structure of molecules due to the change in the conformation of their aromatic core and intermolecular interactions. Experimental dependences of $\bar \gamma$ and Δγ on the molecular orientational order parameter S have been derived, and their specific features for the known objects have been explained. The possibility of separating the contributions of opposite signs to the dependence Δγ(S) due to the change in the conformation of molecules and intermolecular interactions has been shown using nematic MBBA as an example.     

Influence of nematic and smectic orders on polarizability of molecules of ethyl-p-(4-ethoxybenzylideneamino-)α-methyl cinnamate liquid crystals

Experimental values of the polarizability tensor γ components of molecules of ethyl-p-(4-ethoxybenzylideneamino-)α-methyl cinnamate liquid crystals in the nematic and smectic A phases have been obtained. Quadratic dependences of the longitudinal, γ _l , and transverse, γ _t , components, the mean value $\bar \gamma $ , and anisotropy Δγ in both phases have been established as functions of the orientational order parameter S of molecules in a maximally wide range of S. The nematic-smectic A phase transition with a continuous variation of S manifests itself as kinks in the linear dependences of $\bar \gamma $ , Δγ, and γ _l on S ² and does not influence the dependence γ _t (S ²). The observed dependences have been derived in the framework of the theory of the nematic-smectic A phase transition. The factors responsible for different influences of the orientational and positional orderings of molecules on the polarizability parameters have been determined.     

Structure and elastic properties of a nematic liquid crystal: A theoretical treatment and molecular dynamics simulation

The Frank elasticity constants which describe splay (K ₁), twist (K ₂), and bend (K ₃) distortion modes are investigated for 4-n-pentyl-4'-cyanobiphenyl (5CB) in the nematic liquid crystal. The calculations rest on statistical-mechanical approaches where the absolute values of K _i (i=1,2,3) are dependent on the direct correlation function (DCF) of the corresponding nematic state. The DCF was determined using the pair correlation function by solving the Ornstein-Zernike equation. The pair correlation function, in turn, was obtained from molecular dynamics (MD) trajectory. Three different approaches for calculations of the elasticity constants were employed based on different level of approximation about the orientational order and molecular correlations. The best agreement with experimental values of elasticity constants was obtained in a model where the full orientational distribution function was used. In addition we have investigated the approximation about spherical distribution of the intermolecular vectors in the nematic phase, often used in derivation of various mean-field theories and employed here for the construction of the DCF. We found that this assumption is not strictly valid, in particular a strong deviation from the isotropic distribution is observed for short intermolecular distances. Received 22 March 2000 and Received in final form 9 June 2000     

Molecular dynamics and phase transitions in paramagnetic [Mn(H2O)6][SiF6] investigated by H NMR

The temperature dependences of ²H NMR spectra and spin-lattice relaxation time T₁ have been measured for paramagnetic [Mn(H₂O)₆][SiF₆]. The obtained ²H NMR spectra were simulated by considering the quadrupole interaction and paramagnetic shift. The variation of the spectra measured in phase III was explained by the 180° flip of water molecules. The activation energy E_a and the jumping rate at infinite temperature k₀ for the 180° flip of H₂O were obtained as 35 kJ mol⁻¹ and 4×10¹⁴ s⁻¹, respectively. The spectral change in phases I and II was ascribed to the reorientation of [Mn(H₂O)₆]²⁺ around the C₃ axis where the E_a and k₀ values were estimated as 45 kJ mol⁻¹ and 1×10¹³ s⁻¹, respectively. From the almost temperature independent and short T₁ value, the correlation time for electron-spin flip-flops, τ_e, and the exchange coupling constant J were obtained as 3.0×10⁻¹⁰ s and 2.9×10⁻³ cm⁻¹, respectively. The II-III phase transition can be caused by the onset of the jumping motion of [Mn(H₂O)₆]²⁺ around the C₃ axis.     

Crystal → nematic phase transition in the liquid crystalline system 1‐isothiocyanato‐4‐(trans‐4‐propylcyclohexyl) benzene (3CHBT) probed by temperature‐dependent micro‐Raman study and DFT calculations

Raman spectra of 3CHBT in unoriented form were recorded at 14 different temperature measurements in the range 25–55 °C, which covers the crystal → nematic (N) phase transition, and the Raman signatures of the phase transition were identified. The wavenumber shifts and linewidth changes of Raman marker bands with varying temperature were determined. The assignments of important vibrational modes of 3CHBT were also made using the experimentally observed Raman and infrared spectra, calculated wavenumbers, and potential energy distribution. The DFT calculations using the B3LYP method employing 6‐31G functional were performed for geometry optimization and vibrational spectra of monomer and dimer of 3CHBT. The analysis of the vibrational bands, especially the variation of their peak position as a function of temperature in two different spectral regions, 1150–1275 cm⁻¹ and 1950–2300 cm⁻¹, is discussed in detail. Both the linewidth and peak position of the ( C H ) in‐plane bending and ν(NCS) modes, which give Raman signatures of the crystal → N phase transition, are discussed in detail. The molecular dynamics of this transition has also been discussed. We propose the co‐existence of two types of dimers, one in parallel and the other in antiparallel arrangement, while going to the nematic phase. The structure of the nematic phase in bulk has also been proposed in terms of these dimers. The red shift of the ν(NCS) band and blue shift of almost all other ring modes show increased intermolecular interaction between the aromatic rings and decreased intermolecular interaction between two  NCS groups in the nematic phase. Copyright © 2009 John Wiley & Sons, Ltd.     

Theoretical study of metal-insulator transition in rhombohedral vanadium sesquioxide

The electronic structure and the metal-insulator transition (MIT) of V₂O₃ are investigated in the framework of density functional theory and GGA+U. It is found that, both the insulating and metallic phases can be realized in rhombohedral structure by varying the on-site Coulomb interaction, and the MIT in V₂O₃ can take place without any structure phase transition. Our calculated energy gap (0.63 eV) agrees with experimental result very well. The metallic phase exhibits high spin (S=1) character, but it becomes S=1/2 in insulating phase. According to our analysis, the Mott-Hubbard and the charge-transfer induce the MIT together, and it supports the mechanism postulated by Tanaka (2002) [11].     

Change in the polarizability of MBBA molecules upon the nematic-isotropic liquid transition and physical consequences

The Lorentz tensor components L _j and the polarizability tensor components γ _j of 4-methoxyben-zylidene-4′-butylaniline (MBBA) liquid crystal molecules in nematic and isotropic phases have been determined experimentally. The quadratic dependences of the mean value $\bar \gamma $ (S) and anisotropy Δγ(S) of the polarizability in the nematic phase on the orientational order parameter S of molecules have been established. Within the phenomenological approach, the dependences $\bar \gamma $ (S) and Δγ(S) have been derived, and their features for MBBA and other known objects have been interpreted. The relation of the dependences $\bar \gamma $ (S) and Δγ(S) to the features of the nematic-isotropic liquid phase transition has been found.     

Time-dependent density functional theory study on electronic excited states of the hydrogen-bonded solute-solvent phenol-(H2O)n (n=3-5) clusters

The solute-solvent interactions of hydrogen-bonded phenol-(H₂O)_n (n=3-5) clusters in electronic excited states were investigated by means of the time-dependent density functional theory (TDDFT) method. The geometric structures and IR spectra in ground state, S₁ state, and T₁ state of the clusters, were calculated using the density functional theory (DFT) and TDDFT methods. Only the ring form isomer, the most stable one of the cluster, was considered in this study. Four, five and six intermolecular hydrogen bonds were formed in phenol-(H₂O)₃, phenol-(H₂O)₄, and phenol-(H₂O)₅ clusters, respectively. Based on the analysis of IR spectra, it is revealed that the “window region” between unshifted and shifted absorption bands in both S₁ and T₁ state becomes broader compared with that in ground state for the corresponding clusters. Furthermore, two interesting phenomenon were observed: (1) with the anticlockwise order of the ring formed by the intermolecular hydrogen bonds in the H-bonded phenol-(H₂O)_n (n=3-5) clusters, the strengths of the intermolecular hydrogen bonds decrease in all the S₀, S₁ and T₁ states; (2) upon electronic excitation, the smaller the distance between phenol and water is, the larger the change of intermolecular hydrogen bonds strength is. Moreover, the intermolecular hydrogen bond (phenolic OH is the H donor) is strengthened in excited state compared with that in ground state. But the intermolecular hydrogen bond (phenolic OH is the H acceptor) is weakened in excited state.     

Influence of pressure on the electric-field-induced phase transitions in liquid crystals

Within the framework of Landau-de-Gennes formulation, we analyse the effect of pressure on electric-field-induced phase transitions in a liquid crystal which shows spontaneously an isotropic-smectic A transition. Inferring from the experimental pressure dependences on the layer spacing in smectic A phase, as well as the nematic-smectic A metastable temperature T^*_AN, we incorporated the pressure dependence in the free energy through (the surface energy term) and the coupling between the quadrupolar nematic ordering Q_ij and the smectic order parameter ψ. From the S-T phase diagram, we found that the stability of field-induced nematic phase increases with pressure, whereas the discontinuity of the transition decreases. Also, the region where paranematic phase transits directly to smectic A phase increases with pressure.     

Diffusion of hydrogen isotopes in the monohydride phase of Ti1−zVzHxDy studied by H and H NMR spin-lattice relaxation times

The ¹H and ²H spin-lattice relaxation times in the monohydride phase of the V-H-D and Ti_0.1V_0.9-H-D systems have been re-analyzed by Bloembergen-Purcell-Pound (BPP) equations with a log-normal distribution of correlation times, and the obtained parameters have been compared with those of the Ti_0.33V_0.67-H-D system. The mean activation energy and the magnitude of the distribution of H and D diffusions are discussed in relation to the metal compositions, the hydrogen site, the crystal structure and the [H]/[D] ratios.     

Interpretation of thermoelectric power behaviour of Zinc nanowire composites: Phonon-scattering mechanism

We develop a theoretical model for quantitative analysis of temperature-dependent thermoelectric power (S) of Zn nanowires. In doing so, we first use the Mott expression to compute the electron diffusive thermoelectric power (S_c^diff.) using Fermi energy as electron-free parameter, S_c^diff. shows linear temperature dependence. Further, the S_c^diff. contribution is subtracted from the experimental data and the difference (S_experimental-S_c^dif) is characterized as phonon drag thermoelectric power (S_ph^drag) which is obtained within the relaxation time approximation where the thermoelectric power is limited by the scattering of phonons with impurities, grain boundaries, charge careers and phonons in the nanowires. The S_ph^drag shows anomalous temperature-dependent behaviour, which is an artifact of various operating scattering mechanisms. The observed anomalies are well accounted in terms of interaction among the phonons-impurity, phonon-grain boundaries, phonon-electron and the umklapp scattering. It is also shown that for phonons the scattering and transport cross-sections are proportional to ω⁴ in the Rayleigh regime where ω is the frequency of the phonons. Numerical analysis of thermoelectric power from the present model shows similar results as those revealed from experiments.     

Structural, vibrational and dielectric properties of new potassium hydrogen sulfate arsenate: K4(SO4)(HSO4)2(H3AsO4)

A new compound, K₄(SO₄)(HSO₄)₂(H₃AsO₄) was synthesized from water solution of KHSO₄/K₃H(SO₄)₂/H₃AsO₄. This compound crystallizes in the triclinic system with space group P1¯ and cell parameters: a=8.9076(2) Å, b=10.1258(2) Å, c=10.6785(3) Å; α=72.5250(14)°, β=66.3990(13)°, γ=65.5159(13)°, V=792.74(3) Å³, Z=2 and ρ_cal=2.466 g cm⁻³. The refinement of 3760 observed reflections (I>2σ(I)) leads to R₁=0.0394 and wR₂=0.0755. The structure is characterized by SO₄²⁻, HSO₄⁻ and H₃AsO₄ tetrahedra connected by hydrogen bridge to form two types of dimer (H(16)S(3)O₄⁻?S(1)O₄²⁻ and H(12)S(2)O₄⁻?H₃AsO₄). These dimers are interconnected along the [1¯ 1 0] direction by the hydrogen bonds O(3)-H(3)?O(6). They are also linked by the hydrogen bridge assured by the hydrogen atoms H(2), H(3) and H(4) of the H₃AsO₄ group to build the chain S(1)O₄?H₃AsO₄ which are parallel to the “a” direction. The potassium cations are coordinated by eight oxygen atoms with K-O distance ranging from 2.678(2) to 3.354(2) Å.Crystals of K₄(SO₄)(HSO₄)₂(H₃AsO₄) undergo one endothermic peak at 436 K. This transition detected by differential scanning calorimetry (DSC) is also analyzed by dielectric and conductivity measurements using the impedance spectroscopy techniques. The obtained results show that this transition is protonic by nature.     

Contribution of the correlations of the director fluctuations to the neutron diffraction in the nematic phase

The intermolecular part of the nematic phase coherent neutron structure factor,S_inter(Q), including the correlations of the preferred molecular orientations, is calculated.     

The roles of “ammonium” and “hydrogen-bond” protons in single crystals of the superionic conductor NH4HSeO4 by H NMR relaxation

The variations with temperature of the line-shape, spin-lattice relaxation time, T₁, and spin-spin relaxation time, T₂, of the ¹H nuclei in NH₄HSeO₄ single crystals were investigated, and with these ¹H NMR results we were able to distinguish the crystals’ “ammonium” and “hydrogen-bond” protons. The line width of the signal due to the ammonium protons abruptly narrows near the temperature of the superionic phase transition, T_SI, which indicates that they play an important role in this phase transition. The ¹H T₁ for NH₄⁺ and HSeO₄⁻ in NH₄HSeO₄ do not change significantly near the ferroelectric phase transition of T_C1 (=250 K) and the incommensurate phase transition of T_i (=261 K), whereas they change near the temperature of the superionic phase transition T_SI (=400 K). Our results indicate that the main contribution to the low-temperature phase transition below T_SI is that of the molecular motion of ammonium and hydrogen-bond protons, and the main contribution to the conductivity at high temperatures above T_SI is the breaking of the O-H?O bonds and the formation of new H- bonds in HSeO₄⁻. In addition, we compare these results with those for the NH₄HSO₄ and (NH₄)₃H(SO₄)₂ single crystals, which have similar hydrogen-bonded structure.     

H nuclear magnetic resonance study of the ferroelastic and superionic phase transitions of (NH4)4LiH3(SO4)4 single crystals

We investigated the temperature dependences of the line shape, spin-lattice relaxation time, T₁, and spin-spin relaxation time, T₂, of the ¹H nuclei in (NH₄)₄LiH₃(SO₄)₄ single crystals. On the basis of the data obtained, we were able to distinguish the “ammonium” and “hydrogen-bond” protons in the crystals. For both the ammonium and hydrogen-bond protons in (NH₄)₄LiH₃(SO₄)₄, the curves of T₁ and T₂ versus temperature changed significantly near the ferroelastic and superionic phase transitions at T_C (=232 K) and T_S (=405 K), respectively. In particular, near T_S, the ¹H signal due to the hydrogen-bond protons abruptly narrowed and the T₂ value for these protons abruptly increased, indicating that these protons play an important role in this superionic phase transition. The marked increase in the T₂ of the hydrogen-bond protons above T_S indicates that the breaking of O-H?O bonds and the formation of new H-bonds with HSO₄^- contribute significantly to the high-temperature conductivity of (NH₄)₄LiH₃(SO₄)₄ crystals.     

Frequency dependence of ionic conductivity and dielectric relaxation studies in Na3H(SO4)2 single crystal

Electrical impedance measurements of Na₃H(SO₄)₂ were performed as a function of both temperature and frequency. The electrical conductivity and dielectric relaxation have been evaluated. The temperature dependence of electrical conductivity reveals that the sample crystals transformed to the fast ionic state in the high temperature phase. The dynamical disordering of hydrogen and sodium atoms and the orientation of SO₄ tetrahedra results in fast ionic conductivity. In addition to the proton conduction, the possibility of a Na⁺ contribution to the conductivity in the high temperature phase is proposed. The frequency dependence of AC conductivity is proportional to ω^s. The value of the exponent, s, lies between 0.85 and 0.46 in the room temperature phase, whereas it remains almost constant, 0.6, in the high-temperature phase. The dielectric dispersion is examined using the modulus formalism. An Arrhenius-type behavior is observed when the crystal undergoes the structural phase transition.