High pressure studies of the static permittivity tensor components in the nematic phase of 6CB

The dielectric permittivity tensor components, ε_II and ε_⊥, in the nematic phase of 6CB (4‐n‐hexyl‐4′‐cyanobiphenyl) were measured in the pressure range 0.1–130 MPa and the temperature range 12–58°C. The dielectric anisotropy, Δε(p, V, T) = ε_II ‐ ε_⊥, was analysed in isothermal, isobaric and isochoric conditions taking into account the pVT data and the well known Maier and Meier equation. On that basis the nematic order parameter S(p, V, T) was determined. This was used to calculate the parameter Γ relating the interaction potential with the volume (density). Its value Γ = 4.1 agrees very well with other estimates.     

Chain orientation and anisotropies in optical and dielectric properties in thin films of stiff polyimides

Thin films of poly(p-phenylene biphenyltetracarboximide) (BPDA-PDA), prepared by thermal imidization of the precursor poly(amic acid) on substrates, have been investigated by optical waveguide, ultraviolet-visible (UV-VIS), infrared (IR), and dielectric spectroscopies. The polyimide films exhibit an extraordinarily large anisotropy in the refractive indices with the in-plane index n_∥ = 1.806 and the out-of-plane index n_⊥ = 1.589 at 1064 nm wavelength. No discernible effect of the film thickness on this optical anisotropy is found between films of ca. 2.1 and ca. 7.8 μm thickness. This large birefringence is attributed to the preferential orientation of the biphenyltetracarboximide moieties with their planes parallel to the film surface, coupled with the strong preference of BPDA-PDA chains to align along the film plane. The frequency dispersion of the in-plane refractive index n_∥ is consistent with the results calculated by the Lorentz–Lorenz equation from the UV-visible spectrum exhibiting several absorption bands in the 170–500 nm region. The contribution from the IR absorption in the range 7000–400 cm,^?1 computed by the Spitzer-Kleinmann dispersion relations from the measured spectra, adds ca. 0.046 to the in-plane refractive index n_∥. Tilt-angle–dependent polarized IR results indicate nearly the same increase for the out-of-plane index n_⊥. Application of the Maxwell relation then leads to the out-of-plane dielectric constant ε^⊥ ? 2.7 at 1.2 × 10¹³ Hz, as compared with the measured value of ca. 3.0 at 10⁶ Hz. Assuming this small difference to remain the same for the in-plane dielectric constants ε_∥, we obtain a very large anisotropy in the dielectric properties of these polyimide films with the estimated in-plane dielectric constant ε_∥ ? 3.4 at 1.2 × 10¹³ Hz, and ε_∥ ? 3.7 at 10⁶ Hz. © 1992 John Wiley & Sons, Inc.     

Dielectric studies of liquid crystals under high pressure II. Low frequency relaxation process in 4-n-pentyl-4′-cyanobiphenyl in relation to theories of the nematic state

Abstract

The results of high pressure dielectric studies of 4-n-pentyl-4′-cyanobiphenyl (5CB) are analysed in terms of theories of the nematic state. The retardation factor g∥ = τ∥/τ₀ and the effective, single-particle potential of mean torque were calculated at the nematic–isotropic transition temperature T _NI and along the isothermal, isobaric and isochoric paths within the nematic phase of 5CB. The potential of mean torque is compared with the order parameter known for the same conditions. The values of parameter γ relating the potential to the volume is discussed.     

Ionic impurities in nematic liquid crystal displays

This paper shows that the dielectric anisotropy of conductivity in cells composed of nematic liquid crystal E7 (NLC-E7) is related to the fact that the diffusion constant (D) is greater in a cell with homeotropic alignment than in one with homogeneous alignment (D _∥ > D _⊥). This behaviour can be understood by the study of the dielectric properties of the NLC based on the ionic hopping behaviour and on the analysis of the electrical conductivity in relation to the voltage applied.     

Viscosities of dilute polymer solutions in nematic liquids

A nematic fluid is characterized by five friction coefficients. When dilute polymer coils are added to the fluid, all these coefficients are modified. Three Miesowicz viscosities (measured under an aligning magnetic field) and two coupling coefficients between orientation and flow are discussed. In our calculation, elastic dumbbells are used to model the flexible polymer chains. The results are written in terms of two size parameters R_∥ and R_⊥ and two chain friction coefficients λ_∥ and λ_⊥ (the label ∥ refers to a direction parallel to the nematic axis). This could be compared to other experiments (such as translational diffusion) which measure λ_∥ and _⊥ directly. They may give useful estimates of coil conformation in nematic solvents.     

Low-frequency dielectric behavior of poly(vinylidene fluoride)

An explicit mechanism is described for the anomalous increase in dielectric constant and dielectric loss at low frequencies and high temperatures for poly(vinylidene fluoride) containing ionic impurities. Relations are proposed for the ionic contributions, ε_i″ and ε_i″, to the dielectric constant and dielectric loss: where v₀ and D₀ are the concentration and the diffusion coefficient of the mobile ions at infinite temperature, q is the charge of an ion (in cgs electrostatic units), l is the distance between electrodes, k is the Boltzmann constant, T is the absolute temperature, E_d is the apparent activation energy for diffusion of the ions, and W is the dissociation energy of the ionic impurities. From the slopes of curves of log εT′ versus 1/T and log ε″T versus 1/T for poly(vinylidene fluoride), energies E_d = 34 kcal/mole and W = 342 kcal/mole were obtained.     

Dielectric studies of liquid crystals under high pressure III. Low frequency relaxation process in 4-(trans-4′-n-hexylcyclohexyl)isothiocyanato benzene

Abstract

Dielectric studies of 4-(trans-4′-n-hexylcyclohexyl) isothiocyanatobenzene (6CHBT) were performed in the pressure range 0·1–150 MPa, the frequency range 1 kHz–13 MHz and the temperature range 295–325 K. The temperature and pressure dependencies of the static permittivity ?_0∥ and of the relaxation time τ_∥ are analysed and compared with the analogous data obtained recently for 4-n-pentyl-4′-cyanobiphenyl (5CB) (Parts I and II of this series). Marked differences in the dielectric properties of the nematic phases of the two substances are observed. They are interpreted as a result of varying degrees of molecular association in particular compounds. It is concluded that in the nematic phase of 6CHBT dipole–dipole correlations do not exist or are very weak, whereas for 5CB they are easily broken by a relatively low pressure.     

Transitions between the B2 phase and more usual smectic phases in binary systems of banana-shaped with calamitic mesogens

Deuterium NMR spectroscopy is used to study a ring-deuteriated chiral liquid crystal 4-(2-methylbutyl)oxycarbonylphenyl 4-(10-undecenyloxy)benzoate. The quadrupolar and proton-deuteron dipolar splittings, and deuteron quadrupolar and Zeeman spin-lattice relaxation times were measured as a function of temperature in the smectic A phase at two different Larmor frequencies. The derived spectral densities of motion at different temperatures were analysed simultaneously using a rotational diffusion model which also includes internal ring rotations. Motional parameters (D _⊥, D _∥, D _R) and order parameter tensors (S_zz , S_xx -S_yy ) were obtained. Although the present data seem insufficient to draw a definitive conclusion, we believe that it is possible for this particular chiral molecule to have D_⊥ >D_∥ , which is different from non-chiral rod-like liquid crystals.     

Photon correlation spectroscopy of polystyrene as a function of temperature and pressure

Photon correlation spectroscopy is employed to study the slowly relaxing density and anisotropy fluctuations in bulk atactic polystyrene as a function of temperature from 100 to 160°C and pressure from 1 to 1330 bar. The light-scattering relaxation function is well described by the empirical function ?(t) = exp[?(t/τ)^β], where for polystyrene β = 0.34. The average relaxation time is determined at each temperature and pressure according to 〈τ〉 = (τ/β)Γ(1/β) where Γ(x) is the gamma function. The data can be described by the empirical relation 〈τ〉 = 〈τ〉₀ exp[(A + BP)/R(T ? T₀)] where R is the gas constant and T₀ is the ideal glass transition temperature. The empirical constant A/R is in good agreement with that determined from the viscosity or the dielectric relaxation data (1934 K). The empirical constant B can be interpreted as the activation volume for the fundamental unit involved in the relaxation and is found to be comparable to one styrene subunit (100 mL/mol). The quantity B appears to be a weak function of temperature. The use of pressure as a tool in the study of light scattering near the glass transition now has been established.     

Electrical conductivity and dielectric constant measurements of liquid crystal–gold nanoparticle composites

The behaviour of the anisotropic electrical conductivity of liquid crystal–gold nanoparticle (LC‐GNP) composites consisting of a commercially available room temperature nematic compound doped with alkylthiol‐capped GNPs has been investigated. The nematic–isotropic transition of the composite decreases nearly linearly with increasing X, the concentration of GNP (in weight %) at a rate of about 1°C /weight %. The inclusion of GNPs increases the electrical conductivity of the system with the value increasing by more than two orders of magnitude for X = 5%. However, the anisotropy in conductivity, defined as the ratio of the conductivity along (σ_∥) and orthogonal (σ_⊥) to the director shows a much smaller but definite decrease as X increases.     

Dielectric relaxation of poly(phenylene sulfide) containing a fraction of rigid amorphous phase

The dielectric relaxation behavior of poly(phenylene sulfide), PPS, has been investigated from room temperature to 180°C. This study was undertaken to examine the mobility of the amorphous phase through the glass transition region, to determine the contribution that rigid amorphous phase material makes to the relaxation process. Semicrystalline samples contain a fraction of the rigid amorphous phase, which was determined from the heat capacity increment at the glass transition, using degree of crystallinity determined from x-ray scattering. In the dielectric experiment, we measured the temperature and frequency dependence of the real and imaginary parts of the dielectric function. ε″ vs. ε′ was used to determine the dielectric relaxation intensity, δε = ε_s–ε∞, at temperatures above the glass transition. For amorphous PPS, δε decreases as temperature increases, while for all semicrystalline PPS, δε increases with temperature. The ratio of semicrystalline intensity to amorphous intensity determines the total fraction of dipoles which are already relaxed at a given temperature. Results indicate that more and more rigid amorphous phase material relaxes as the temperature is increased. This provides the first evidence that rigid amorphous phase material in PPS contains chains that possess different levels of molecular mobility. Finally, to the temperature of the loss peak maximum, at a given frequency, we assign the value of the dielectric T_g. For both melt and cold crystallization, the dielectric T_g systematically decreases as the crystallization temperature increases, and as the fraction of rigid amorphous phase decreases.     

Dielectric properties of some semiconducting polyazophenylenes

The dielectric properties of a series of semiconducting polyazophenylenes were studied as a function of temperature and molecular weight in the temperature range 293–600°K and for molecular weights between 5,100 and 62,800 at a constant frequency of 1 kHz. The compounds studied included poly-2,4-diaminotoluene, poly-2,4-diaminoanisole, and poly-2,5-diaminotoluene. The dielectric properties are presented in the usual way in terms of a complex dielectric constant ε^* = ε′—jε″. Activation energies of relaxation processes were evaluated from the areas and widths of the dielectric loss factor, ε″, against reciprocal temperature at constant frequency. The dielectric activation energies were found to be roughly equal to the activation energies from the DC conductivity. This indicates that the conduction mechanism is based on rotational movements of molecules or parts of molecules.     

Thermal conductivity of oriented crystalline polymers

Thermal conductivities of six oriented semicrystalline polymers which range from 0.37 to 0.63 in crystallinity and 1 to 5 in draw ratio λ (up to about 15 for two polymers) have been measured between 100 and 340 K. It was found that for increasing λ the conductivity K_∥ (along the draw direction n?) increases rapidly while K_⊥ (normal to n?) decreases slightly; K_∥ also increases with temperature, but K_⊥ shows no simple pattern in temperature dependence. These general features can be reproduced reasonably well at low draw ratio (λ < 5) by the modified Maxwell model, and the discrepancy in details may be attributed to the fact that the model does not take into account the possible anisotropy of the amorphous phase of the oriented polymers. At high draw ratio the intercrystalline bridge effect becomes important, and one must resort to the Takayanagi model, but the lack of corroborating x-ray data has rendered a detailed comparison impossible.     

Evidence of dynamic heterogeneity as obtained from dielectric and brillouin light-scattering studies of poly(n-hexylmethacrylate)

We report dielectric relaxation and Rayleigh-Brillouin spectroscopic measurements on the side chain polymer poly(n-hexylmethacrylate), PHMA (T_g = 268 K), exhibiting a broad glass transition region. The dielectric loss curves can be represented by single Havriliak-Negami functions in the temperature range of 260–450 K. The width of the distribution relaxation function is a decreasing function of temperature up to T = 333 K ≊ 1.24 × T_g and remains virtually constant above that temperature. This is interpreted as marking the merging of the α-process with a slow β-relaxation in agreement with the value of the cooperativity length associated with the α-mode. Hence above that temperature, the relaxation times confirm well to an Arrhenius temperature dependence. The hypersonic dispersion deduced from the Brillouin spectra (210–550 K) surprisingly peaks at temperatures near T_g which bears no relation to the main α-relaxation. This structural relaxation is rather associated with the side hexyl group motion showing striking resemblance with the hypersonic dispersion in molecular liquids. It is conceivable that the observed damping in PHMA is dynamically related to the internal plasticization effect of the hexyl group. © 1996 John Wiley & Sons, Inc.     

Study of the Dielectric Properties of the Perovskite LaMn0.5Co0.5O3–δ

Polycrystalline samples of the charge ordered mixed oxide LaMn_0.5Co_0.5O_3?δ (T_CO = 400 K) have been prepared by the nitrate decomposition method. These samples are biphasic, according to XRPD, and except one, oxygen defficient (δ ≈ 0.04‐0.05). The study of the dielectric properties of these samples reveal that LaMn_0.5Co_0.5O_3?δ displays a high dielectric constant, specially at room temperature and low frequencies. This ε′_r is seen to be strongly dependent on the particle size and not so much on the oxygen defficiency and the best properties are found in the sample with biggest particle size (? = 7 μm) for which ε′_r (300 K) ≈ 10⁵ up to 2x10⁴ Hz. Analysis of the role of the grain size and the electrode contacts on the obtained data reveal that this mixed oxide has an intrinsic dielectric constant that is rather high for this type of compounds (ε′_r,∞ ≈ 30) and that is further enhanced by extrinsic Maxwell‐Wagner effects. We relate such enhanced intrinsic dielectric constant to the electronic process of charge ordering present in this material below 400 K.     

DTA,X-ray and dielectric relaxation studies of 14CB at atmospheric and elevated pressures

The pressure-temperature phase diagram of 4′-tetradecyl-4-cyanobiphenyl (14CB) up to 220 MPa (2.2 kbar) and between 320–400 K was established using DTA. The temperature range of the smectic A (SmA) phase slightly increases with pressure. The layer spacing d at 1 atm was determined as a function of temperature using X-ray diffraction. It was related to the molecular length l by the ratio d/l ? 1.4. The dielectric relaxation measurements in the isotropic and smectic A_d phases of 14CB at 1 atm were performed in the frequency range 10 kHz-3 GHz. Contributions from both principal rotational motions, i.e. around the short and long molecular axes, were separated. The relaxation measurements under high pressure in the SmA phase covered the low frequency process. The longitudinal relaxation time τ₁, characterizing the molecular reorientations around the short axis, was analysed with respect to the pressure and temperature dependences, giving activation volumes, Δ^# V = RT (? ln τ₁ / ?p)_T, and activation enthalpies, Δ^# H = RT(? ln τ₁ / ?T ^-1)_p, respectively. Surprisingly, all the activation quantities characterizing the rotational motions of 14CB molecules under different conditions are nearly the same as those determined recently for the much shorter homologue, 8CB. This indicates that the 14CB molecule is in fact relatively short due to conformational motions of the alkyl tail.     

Rotational viscosity γ1 of nematic liquid crystals as a function of temperature,pressure and density

Abstract

Measurements of the rotational viscosity γ₁ and the density are presented for a mixture of 4′-methoxybenzylidenebutylaniline (MBBA) and its ethoxy homologue EBBA and a mixture of cyclohexylphenylnitriles (ZLI 2413 from Merck AG) as a function of temperature and pressure. A new set-up for the measurement of densities under pressures of up to 3kbar is described. It is shown that the pressure dependence of the kinematic rotational viscosity γ₁/ρ and the temperature dependence of γ₁ under isobaric and isochoric conditions have common features with that of the shear viscosity of isotropic liquids. Furthermore, it is found that the curves γ₁ = f(1/T) for constant p and γ₁ = g(ρ) for constant T can be shifted one onto another by an appropriate shift of the scale of the independent variable.     

Thermophysical properties of azomethine ether main-chain liquid crystalline polymers at pressures to 200 MPa

This article reports on an experimental investigation of the equation of state and the transition behavior of main-chain thermotropic liquid crystalline polymers over a wide temperature range, and at pressures to 200 MPa. The materials studied were a series of azomethine ether polymers. A varying number n (= 4, 7, 8, 9, 10 and 11) of methylene spacer units in the backbone provided systematic variation of the structure. Experimental techniques used included high-pressure dilatometry (PVT measurements) to 200 MPa, high-pressure differential thermal analysis, also to 200 MPa, and conventional (atmospheric-pressure) differential scanning calorimetry (DSC). The equation of state of the materials can be well represented by the Tait equation in distinct regions, separated by a glass transition, T_g(P), a first-order transition to a nematic state, T_k-n(P), and a first-order transition to an isotropic melt state T_c(P). The atmospheric pressure values of T_k-n and T_c decreased with increasing number of spacer units and showed a clear odd-even effect. T_g and T_k-n both increased with pressure. The pressure dependence of T_c could not be observed due to the onset of degradation in the same temperature region. On isobaric cooling at 3°C/min, the crystallization from the nematic state occurred a few tens of degrees below T_k-n. This supercooling was independent of pressure for some materials, while for others it increased with increasing pressure. The values of the enthalpy and entropy associated with the first-order transition into the nematic state were lower than those of typical isotropic polymers at their melting transitions. The transition enthalpy did not have any systematic variation with increasing number of spacer units. Values of the transition enthalpy calculated from the Ciapeyron equation did not always agree with the values measured by DSC. This may be due to the two-phase nature of the low-temperature state. At the transition to the isotropic state, the transition enthalpy at P = 0 decreased with n and showed an odd-even effect. © 1994 John Wiley & Sons, Inc.     

Equations of state for polyamide‐6 and its nanocomposites. 1. Fundamentals and the matrix

The pressure‐volume‐temperature (PVT) surface of polyamide‐6 (PA‐6) was determined in the range of temperature T = 300–600 K and pressure P = 0.1–190 MPa. The data were analyzed separately for the molten and the noncrystalline phase using the Simha‐Somcynsky (S‐S) equation of state (eos) based on the cell‐hole theory. At T_g(P) ≤ T ≤ T_m(P), the “solid” state comprises liquid phase with crystals dispersed in it. The PVT behavior of the latter phase was described using Midha‐Nanda‐Simha‐Jain (MNSJ) eos based on the cell theory. The data fitting to these two theories yielded two sets of the Lennard‐Jones interaction parameters: ε*(S‐S) = 34.0 ± 0.3 and ε*(MNSJ) = 22.8 ± 0.3 kJ/mol, whereas v*(S‐S) = 32.00 ± 0.1 and v*(MNSJ) = 27.9 ± 0.2 mL/mol. The raw PVT data were numerically differentiated to obtain the thermal expansion and compressibility coefficients, α and κ, respectively. At constant P, κ followed the same dependence on both sides of the melting zone near T_m. By contrast, α = α(T) dependencies were dramatically different for the solid and molten phase; at T < T_m, α linearly increased with increasing T, then within the melting zone, its value step‐wise decreased, to slowly increase at higher temperatures. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 299–313, 2009