Orientational Correlation Factor Research Articles

Orientation correlation and local field in liquid nitrobenzene.

Hyper-Rayleigh scattering (HRS) is sensitive to long-range molecular orientation correlation in isotropic liquids composed of dipolar molecules. Measurements of the polarization, angle, and spectral dependence for HRS from liquid nitrobenzene (NB) are analyzed to determine the NB molecular orientation correlations at long range. The longitudinal and transverse orientation correlation functions for r > 3 nm are BL(r) = (a/r)(3) and BT(r) = - BL(r)/2, where a = 0.20 ± 0.01 nm. Measurements of HRS induced by dissolved ions are also analyzed and combined with molecular dynamics simulation and dielectric response results, to determine the molecular dipole moment μ = 3.90 ± 0.04 D, Kirkwood orientation correlation factor gK = 0.68 ± 0.02, and local field factor f(0) = 0.85 ± 0.04 × Onsager local field factor in liquid nitrobenzene.

Intermolecular interactions and molecular dynamics in bovine serum albumin solutions studied by small angle X-ray scattering and dielectric relaxation spectroscopy

We used small angle X-ray scattering (SAXS) and dielectric relaxation spectroscopy (DRS) to clarify static structure and molecular dynamics of bovine serum albumin (BSA) in solution. SAXS allowed us to access spatial correlations of the protein molecules in concentrated solutions at different ionic strength. Using a well-established Fourier inversion technique, called SQ-IFT, we deduced the effective pair correlation functions, g(r)eff, from the effective (or experimental) structure factors, S(q)eff, without assuming any potential models for protein–protein interactions. In terms of S(q)eff and g(r)eff, the mean nearest-neighbor distance, d⁎, the osmotic compressibility, κosm, and the coordination number, NC, were evaluated.The complex dielectric spectra of aqueous BSA solutions measured in the frequency range from 1MHz to 10GHz were able to be decomposed into three relaxation processes having different physical origins. The highest frequency process, whose relaxation time was ca. 8ps, was assigned to cooperative rearrangement of H-bond network of bulk-water. We evaluated the effective hydration number of a BSA molecule, Zhyd, using the bulk-water relaxation amplitude. This approach yielded ca. 1200 hydrated water molecules per a BSA molecule, corresponding to ca. 0.3g hydrated water per 1g protein. The lowest frequency process having a relaxation time of ca. 50ns was assigned to rotational diffusion of the BSA molecule. We confirmed that an effective molar volume of BSA calculated with Stokes–Einstein–Debye equation was identical to that predicted from its molecular weight and specific density. According to the Kirkwood relationship, the dipole–dipole orientational correlation factor decreased with an increase of protein concentration, which indicated the operation of BSA–BSA interaction and favored antiparallel dipolar correlation between the protein molecules.

Hydrogen network fluctuations: Dielectric spectra of glycerol–ethanol mixtures

At temperatures between 10 and 50°C complex dielectric spectra of mixtures of glycerol and ethanol have been measured in the frequency range from 400kHz to 3GHz. Within the frequency range of measurement the dielectric spectra reveal one dispersion/dielectric loss region, indicating a rather uniform relaxation of both constituents. Exhibiting a continuous but asymmetric relaxation time distribution, the spectra are analyzed in terms of a Davidson–Cole relaxation function to yield the static permittivity, an effective dipole orientation correlation factor, the principal relaxation time, the enthalpy of activation and the Davidson–Cole parameter that measures the width of the relaxation time distribution. These parameters are discussed and compared to those for mixtures of glycerol with water. Effects from the chain-like hydrogen bond structure of the monohydric alcohol, on the one hand, and from the tetrahedral hydrogen network of water, on the other hand, are explored thereby.

Systematic study of the glass transition in polyhydric alcohols

We have investigated the glass transitions of trihydric alcohols using broadband dielectric spectroscopy, and compare the results with those previously reported for sugar alcohols. Although a systematic glass transition feature related to molecular size has been reported for sugar alcohols, the essential factor governing this feature is still unclear because the number of carbon atoms (N(C)) and the number of OH groups (N(OH)) per molecule are identical in sugar alcohols. By examining trihydric alcohols (N(C)≠N(OH)), we conclude that N(OH) is dominant for the characteristics of the slow dynamics, such as fragility and glass transition temperature. This result suggests that the topological structure of the hydrogen-bonding network (coordination number) plays an important role in the glass transition of polyhydric alcohols. Furthermore, the orientational correlation factor evaluated using the Kirkwood-Fröhlich theory reveals a similarity in hydrogen bond formation among a variety of polyhydric alcohols. Based on these two experimental results, we discuss a possible physical picture of the glass transition of polyhydric alcohols.

The effect of ions on the permittivity and dielectric relaxation of an uncrystallizableheptanol

Solvation of ions in a liquid tends to reduce the extent of intermolecular hydrogenbonding. This changes the effective dipolar orientation correlation factor,g, in most alcohols and in water, and hence the equilibrium permittivityεs, but not therelaxation time, τ. An increase in temperature has a similar effect onεs, butthe relaxation time also decreases. Here we study the dielectric relaxation spectra of two concentrationsof LiClO4 solutions in 5-methyl-2-hexanol, and compare the findings against those for thepure liquid. We also compare the effect of the ions against that observed ina similar study of 1-propanol (Power et al 2002 J. Chem. Phys. 116 4192).εs decreases by∼7% on adding1 mol% LiClO4 at 173 Kbut increases by ∼12% at 223 K, and there is similar change in the strength of the Debye relaxation process. This mayoccur partly as a result of the changing ion–ion pair equilibrium with temperature. Initial additionof LiClO4 (0.5 mol% solution) increases the dc conductivity,σdc, far more than further addition. The addition of electrolyte also causes the slowest relaxation todepart from the Debye process, but its characteristic relaxation rate does not change. Variation inσdc with τ does not follow the Debye–Stokes–Einstein relation for either the pure liquid or theLiClO4 solutions, which indicates that diffusion of ions does not follow the Brownian diffusion ofmolecules.

Dielectric studies of self assembling amphiphiles: Part-I: Kirkwood correlation factor of dielectric polarization of amphiphilic acids and alcohols in the solution state

Abstract The amphiphilic molecules of alcohols and acids form a two dimensional dipole array on air–water interface. There is a cooperative reorientation involving the average tilt and precisional angles and the surface potential is modified accordingly. The structure of amphiphiles and affinity of the polar groups towards the environmental dipoles determined the stability of the two dimensional array. We report here the orientational correlation factor of dielectric polarization obtained from a study of dielectric constant of amphiphiles in the solution state. The amphiphiles taken for study are tetra decanol, hexa decanol, stearyl alcohol, stearic acid and arachidic acid in 1–4 dioxane. It is shown that there exists a critical number density at which those amphiphiles exist as monomer and at other concentrations the head groups undergo a monomer, n-mer cluster and a non-specific interaction with the solvent.

Hydrogen network fluctuations of associating liquids: Dielectric relaxation of ethylene glycol oligomers and their mixtures with water

Complex dielectric spectra of ethylene glycol and of various derivatives as well as of mixtures of water with an ethylene glycol oligomer and with a poly(ethylene glycol) dimethyl ether oligomer have been measured. The spectra can be well represented by a Cole-Cole [Cole and Cole, J. Chem. Phys. 9, 341 (1941)] spectral function. The extrapolated low frequency (static) permittivity of this function has been evaluated to yield the effective dipole orientation correlation factor of the liquids. The relaxation time of the ethylene glycols displays a characteristic dependence upon the ratio of concentrations of hydrogen bond donating and accepting groups, indicating two opposing effects. With increasing availability of hydrogen bonding sites effects of association and also of dynamical destabilization increase. Both effects exist also in the mixture of water with the oligomers. They are discussed in terms of a wait-and-switch model of dipole reorientation in associating liquids. Another feature in the dependence of the dielectric relaxation time of poly(ethylene glycol)/water mixtures upon mixture composition has been tentatively assigned to precritical demixing behavior of the binary liquids in some temperature range.

Dielectric properties of glycerol/water mixtures at temperatures between 10 and 50°C

At six temperatures T between 10 and 50 degrees C and at mole fractions x(g) of glycerol (0<x(g)<or=0.9) the complex (electric) permittivity epsilon(nu) of glycerol/water mixtures has been measured as a function of frequency nu between 1 MHz and 40 GHz. The spectra of the glycerol/water mixtures can be well represented by a Davidson-Cole [J. Chem. Phys. 18, 1417 (1950)] relaxation function that reveals an unsymmetric relaxation time distribution. The effective dipole orientation correlation factor derived from the static permittivity displays an unspectacular behavior upon mixture composition. The dielectric relaxation time reveals a simple relation to the shear viscosity of the mixtures, but both quantities are not proportional to one another. The relaxation times at high temperatures nicely complement previously determined low temperature data, following a Vogel-Fulcher-Tammann-Hesse [Z. Phys. 22, 645 (1925); J. Am. Chem. Ceram. Soc. 8, 339 (1923); Z. Anorg. Allg. Chem. 156, 245 (1926)] (VFTH) temperature dependence. When the Eyring behavior is assumed a limiting high temperature form of the VFTH relation, enthalpy, and entropy of activation values are found which adopt significantly higher values in the glycerol rich mixtures than in the water rich liquids. The relaxation time distribution parameter at high water content indicates a dynamically heterogeneous structure of the liquids. Likely there exist glycerol rich and water rich microphases.

Zwitterion Headgroup Orientation Correlation and Mobility and the Domain Structure of Membranes

Complex electric permittivity spectra of aqueous vesicle solutions, prepared by extrusion of lecithin suspensions, have been measured as a function of temperature in order to study the dielectric relaxation of the dipolar phospholipid headgroups. Solutions of unilamellar liposomes from dimyristoylphosphatidylcholine and from a mixture of dimyristoyl- and dipalmitoylphosphatidylcholine (mole fraction x = 0.5) have been investigated. Based on a theoretical model that considers the internal electric fields of the dielectrically heterogeneous liquids, the vesicle radius, the zwitterion relaxation time, a relaxation time distribution parameter, and a quantity that is directly related to the dipole orientation correlation factor are calculated from the measured spectra. The radii indicate a noticeable swelling when T exceeds the gel/fluid phase transition temperatures Tm of the membranes. There clearly exists an effect of correlation of dipole orientations. Either the dipole orientation correlation factor or th...

Mechanism of the Major Orientation Polarization in Alcohols, and the Effects of Steric Hindrance-, and Dilution-Induced Decrease on H-Bonding

To gain insight into the effects of intermolecular H-bond association on the changes in permittivity and relaxation characteristics of supercooled alcohols, two techniques were used here: (i) introducing a C6H5 group in 2-propanol to obtain 1-phenyl-2-propanol, and thus increasing the steric hindrance to H-bonding, and (ii) dissolving the latter in 2-methylpentane and thus decreasing the extent of H-bonding by separating molecules in a nonpolar solvent. Broad-band dielectric spectroscopy studies of supercooled liquid 1-phenyl-2-propanol and its 1:1 (mol:mol) mixture in 2-methylpentane were performed over the 188−238 K range. These show that ∼94% of the total polarization decays according to the Davidson−Cole distribution of relaxation times and that the equilibrium permittivity decreases when phenyl group is substituted in 2-propanol. Analysis in terms of the statistical theories of dielectric behavior shows that the decrease is due to a decrease in the orientation correlation factor, and that this also occurs in the mixture with 2-methylpentane. The induced steric hindrance reduces the extent of intermolecular H-bonding in comparison with that of 2-propanol. The relaxation rate follows the non-Arrhenius temperature dependence. It has been examined qualitatively in terms of the Dyre theory which considers that the apparent Arrhenius energy itself is temperature-dependent, as in the classical interpretations, and quantitatively in terms of the cooperatively rearranging region's size, without implying that there is an underlying thermodynamic transition in its equilibrium liquid. The relaxation rate also fits the power law with the critical exponent of 14.52 for 1-phenyl-2-propanol and 12.9 for the mixture, instead of 2 to 4, usually required by the mode-coupling theory. This indicates the ambiguity of the power-law equations. The excess dielectric loss observed at high frequencies may indicate Nagle's “wing”, or else a merged Johari−Goldstein relaxation.

Molecular dynamics during linear chain polymerization from real-time dielectric spectrometry and calorimetry

To obtain physical insight into the slowing of the molecular dynamics when a macromolecule grows as a result of polymerization, (i) the dielectric relaxation spectra, and (ii) the heat evolved during the growth of a linear chain structure by means of the reaction of diepoxide with a monoamine have been measured simultaneously and continuously over time, at a fixed temperature of 314.2 K, during fixed-rate heating to 341.5 K and thereafter cooling from this temperature. An instrument was designed for the purpose. The studies yield information, almost simultaneously, on the changes in the dc conductivity, on the static and dynamic behaviours of the dipolar relaxation, and on the number of covalent bonds, n, in the states of the structures formed by irreversible polymerization. The dc conductivity decreases with increase in n, but this decrease cannot be attributed entirely to the increase in viscosity. The decrease in the ion population has a significant effect on the change in dc conductivity. Both the equilibrium permittivity and the limiting high-frequency permittivity decrease on polymerization. This decrease is attributed mainly to a decrease in the dipolar orientational correlation factor in the former case, and to a predominant increase in the phonon frequencies in the latter case. It is found that the slowing of the molecular dynamics that occurs here on increase in n is more than compensated by the acceleration of the dynamics on increase in the thermal energy. This effect is interpreted in terms of the changes in the configurational entropy, , which leads to relations expressing the dependence of on n, as well as on the temperature. A faster molecular dynamics of the Johari - Goldstein relaxation evolves as n increases. This dynamics does not depend on the decrease in with decrease in n, but depends only on the change in with temperature. The dielectric behaviour of the completely polymerized state obtained after repeated thermal cycling of the initially molecular liquid has been studied, and the results are related to the molecular dynamics observed during the growth of the macromolecules.

The frequency and wavelength dependent dielectric permittivity of water

The static and dynamic dielectric behaviour of a model of liquid water is studied in the supercooled region, as a function of wavelength. The data used for this analysis were obtained in a previous molecular dynamics simulation of a sample of 343 water molecules, modelled by the TIP4P potential, at 245 K. A substantial wavelength dependence of the static dielectric permittivity is observed, while the value found for ϵ(0) seems to indicate that the TIP4P model is able to account qualitatively for the increase of dielectric constant upon temperature decrease, as found in real water. The time correlation function of the longitudinal and transverse components of the dipole density as well as that of the individual and total dipole moment is also calculated, to relate collective dielectric properties to the single molecule relaxation. The collective and single molecule dielectric relaxation times are obtained and their ratio seems to be close to a static property, namely the short-range orientational correlation factor, g s (k). The frequency dependence of the dielectric constant is compared with previous simulation and experimental values. Furthermore, the longitudinal and transverse components of the hydrogen current are discussed. The molecular symmetry relates the latter properties to the corresponding component of the dipole density in the frequency range 80–200 THz, typical of the librational motions of water. From these results, a simple and unifying picture of the dynamics underlying the three dielectric bands of water in the frequency range 1–200 THz emerges.

The dielectric and dynamic mechanical behaviour of molecularly disordered phases

Abstract Two aspects of dielectric behaviour of disordered condensed phases are presented here. In the first, it is shown that the theory of orientation polarization can provide a useful description of the static dielectric behaviour of the polymorphs of ice. This is done by calculating from their crystallographic data the orientational correlation factor of water molecules and the increase in their dipole moments resulting from their mutual electrostatic fields. The correlation factor is greater than 2.4 and the dipole moment in the ices is 30–45% greater than in the vapours phase. The smallest values are for ice VI and the largest for cubic ice. The contribution to static permittivity due to orientation polarization calculated from these values agrees reasonably well with the measured values for the ices. In the second, the thermally activated translational-rotational motions of groups of atoms or molecules that occur in localized regions of the rigid matrix of glasses, glassy liquid crystals and glassy crystals are described. Known as secondary relaxations, these are observed by dielectric and mechanical relaxation spectroscopy at temperatures near and below Tg and show features which are remarkably similar amongst the various types of disordered solids. The relevance of the kinetic and thermodynamic aspects of such relaxations to the properties of the liquids, their temperature, density and time dependence and their link with the low-temperature tunneling states in a glass are considered. All of these seem to suggest that the concept of a disordered solid as an elastic continuum is unsatisfactory and that its description should also include the energy associated with the configurational states involved in secondary relaxations. Finally, a brief account of a molecular theory for for the relaxations in glass is given.

Molecular dynamics calculation of the dielectric constant

In the previous papers of this series it was shown, by molecular dynamics simulations, that 2D fluid systems of pure Stockmayer molecules have a higher dielectric constant than predicted by the Onsager model or, equivalently, that their Kirkwood orientational correlation factor g k is greater than unity. In this paper this observation is further considered; it is shown that it is due to the fact that the longitudinal positive correlations are enhanced, while the negative correlations in the transverse direction are diminished, compared with those induced in a continuum by a polar molecule. Modified Stockmayer model molecules are then studied. The adopted modifications are of two kinds: (i) the molecular point dipole is excentred and (ii) a central quadrupole is added to the central dipole. In both cases g k is found to be closer to unity than for the pure Stockmayer systems. However, this is not due to a better local validity of the Onsager picture: rather, the map of the local polarization around a refer...

Local orientational order in ice

A cluster expansion approach for the Kirkwood orientational correlation factor gk in ice has been examined. The expansion parameter measures the extent to which neighboring molecules obey bonding requirements of the ``ice rules.'' For cubic ice, leading terms have been evaluated in the series for the separate contributions to gk from the first three shells of neighbors. These series tend to confirm the validity of a recent Monte Carlo estimate of gk, but they also suggest that orientational order in cubic and hexagonal ices has long range and is analogous to local order of critical point pair correlations in Ising models. As a result, the cluster expansion for gk itself likely converges very slowly, if at all.

Dielectric Properties of Ices II, III, V, and VI

The dielectric properties of Ices II, III, V, and VI have been measured up to 300 kc/sec over a range of temperatures and pressures. All except Ice II exhibited well-defined dielectric dispersion and so are orientationally disordered under the experimental conditions. The dispersion loci were slightly broader than Debye curves, which may reflect the presence of nonequivalent crystal sites. As for Ice I, the static dielectric constants correspond to values of about 3 for the Kirkwood orientational correlation factor. This suggests that these forms of ice are four coordinated, in agreement with infrared and (for Ice III) x-ray evidence at low temperatures. The relaxation rates are considerably faster than for Ice I, and the activation energies and entropies somewhat lower. The volumes of activation are all about 4.6 cm3 mole−1. The relaxation mechanism appears to be similar to that in Ice I, i.e., relaxation occurs by diffusion of orientational defects. X-ray and infrared studies have indicated that Ice II is rotationally ordered near liquid-nitrogen temperature. The absence of orientational polarization in Ice II at temperatures as high as −30° shows it to be ordered throughout its region of stability.