Kirkwood-Frohlich Theory Research Articles

Dielectric relaxation of dihydric alcohol–1,4-dioxane mixtures using time domain technique

Complex dielectric permittivity measurements of 1,2-propanediol–1,4-dioxane mixtures has been carried out at different concentration and in the frequency range of 10 MHz to 20 GHz using time domain reflectometry (TDR). The least squares fit method has been used to obtain the static dielectric constant, relaxation time, and Bruggeman factor for binary mixtures. The Kirkwood–Frohlich theory is applied to compute the dielectric constant for the mixtures. It adequately reproduces the experimental values of static dielectric constants for the 1,2-propanediol–dioxane mixtures. The excess parameters confirm that the heteromolecular hydrogen bonding interactions between 1,2-propanediol and dioxane molecules vary significantly in the mixture. The Bruggeman model for the nonlinear case has been fitted to the experimental dielectric data for mixtures. Keywords: dielectric relaxation, time domain reflectometry, alcohols

Hydrogen bond thermodynamic properties of water from dielectric constant data

We apply statistical mechanical principles to derive simple expressions relating the hydrogen bond thermodynamic properties to the static dielectric constant of water. The approach followed by us was to develop an expression for the Kirkwood’s structure factor (g) of water, taking into account the dipolar correlations between a central molecule and H-bonded neighbors present in infinite number of shells surrounding the central molecule. The number of H-bonded neighbors in a specific shell was related to the probability P for the various donor/acceptor sites of any given water molecule to be associated. Neglecting cooperativity effects, we evaluated P by focusing only on the correct counting of H-bonds formed between various association sites rather than on the oligomer distribution. The theory yielded an extremely simple expression for the structure factor (g) of the fluid at any given temperature in terms of the enthalpy (H) and entropy (S) changes associated with bond formation. The proposed theory was then combined with the Kirkwood–Frohlich theory for evaluating the dielectric constant (ε0). We have demonstrated that the theory correctly predicts the dielectric constant of ice-I without the use of any adjustable parameters. We have then deduced estimates for H-bond thermodynamic properties (H=−5.58 kcal/mole of H-bonds; S=−8.89 cal/deg⋅mole of H-bonds) by fitting the theoretical results for ε0 of liquid water to available experimental data over temperatures ranging from 0 °C to the critical point of water. The error in the theoretical values was found to be within 1% of the corresponding experimental values over the entire range of temperatures studied. To further test the theory, we have demonstrated that the temperature variation of the average number of H-bonds per water molecule, calculated using the proposed theory with the above mentioned values for H and S, compares quite well with those estimated from various available spectroscopic and molecular simulation studies.

Association of pure polar liquids: dielectric properties of docosanoic acid

The dielectric properties of liquid docosanoic acid as a function of temperature have been studied in order to establish a possible link between these properties and the association of monocarboxylic fatty acids. Measurements of the static dielectric permittivity are reported at different temperatures from ca. 10 K above the mp to 388 K. The molecular correlation factor has been evaluated according to the Kirkwood–Frohlich theory and has also been corrected on the basis of the Abbott–Bolton model, to take into account the non-spherical molecular shape. The static permittivity is almost constant over the considered temperature range, but the correlation factor tends towards unity because of thermal agitation as the temperature increases.

Associating behaviour of pure polar liquids: dielectric properties of lauric acid

The associating behaviour of liquid caprylic acid has been studied by the determination of its dielectric properties. Experimental results of measurements of dielectric permittivity are reported. The molecular correlation factor was obtained with reference to the Kirkwood-Frohlich theory and compared with the Abbott-Bolton model for non spherical molecules from above the MP to 392 K. On going from low to high temperature, the correlation factor increases from 0.2 to 0.5 and this, together with the increase of the static permittivity, suggests that the number of dimers in the liquid phase decreases with increasing temperature. A discussion of the associating behaviour of caprylic acid is reported, in view of a recent model for treating molecular systems in which dimerization occurs. According to this model a further correlation factor is introduced, besides that prescribed by the Kirkwood-Frohlich theory, to account for correlation among dipole moments carried by monomers. This correlation factor for monomers calculated at room temperature, indicates the existence of a prevailing antiparallel order among monomers

Associating behaviour of pure polar liquids : dielectric properties of caprylic acid

The associating behaviour of liquid caprylic acid has been studied by the determination of its dielectric properties. Experimental results of measurements of dielectric permittivity are reported. The molecular correlation factor was obtained with reference to the Kirkwood-Frohlich theory and compared with the Abbott-Bolton model for non spherical molecules from above the MP to 392 K. On going from low to high temperature, the correlation factor increases from 0.2 to 0.5 and this, together with the increase of the static permittivity, suggests that the number of dimers in the liquid phase decreases with increasing temperature. A discussion of the associating behaviour of caprylic acid is reported, in view of a recent model for treating molecular systems in which dimerization occurs. According to this model a further correlation factor is introduced, besides that prescribed by the Kirkwood-Frohlich theory, to account for correlation among dipole moments carried by monomers. This correlation factor for monomers calculated at room temperature, indicates the existence of a prevailing antiparallel order among monomers

Associating behaviour of pure polar liquids: Dielectric properties of undecylic acid

The associating behaviour of undecylic acid has been studied by the determination of its dielectric properties. The correlation factor between molecular pairs was obtained with reference to the Kirkwood-Frohlich theory and compared with the Abbott-Bolton model for non spherical molecules. The results indicate a high degree of association with number of dimers decreasing with increasing temperature.

Dipole correlation functions and Kirkwood g(1) factor in liquid chlorobenzene

The Kirkwood g(1) factor for room temperature liquid chlorobenzene has been measured from (a) the integrated intensity of the far IR rotation-translation band, and (b) the long time slopes of the single-particle and total-particle dipole correlation functions, using the Keyes–Kivelson rotational diffusion model. The values are 1.13±0.11 and 1.18±0.10, respectively, and do not agree with the Kirkwood–Frohlich theory, which predicts 0.83. The vibrational and far IR band shapes are presented, along with their second moments and the dipole correlation functions. The vibrational band second moment is within experimental error of the theoretical value; the far IR band second moment is in excess by 153%.

Ferroelectric Phase Transition and Anisotropy of Dielectric Constant in Ice Ih

The static dielectric constant of ice Ih is calculated, considering the energy differences between the configurations of hydrogen atoms obeying the Bernal-Fowler rule, by Takagi's method of KDP crystals in the framework of Kirkwood-Frohlich theory. This is the study of the phase transiton with thirteen order parameters. A model of water molecule, called the tetrapod model, is proposed, which is a four-point-charge model plus an additional quadrupole moment. Considering the multipole interaction, the Curie-Weiss law is derived. With the change of the quadrupole moment, ferroelectric or antiferroelectric phase transition occurs. With suitable quadrupole moment, the experimental Curie-Weiss constant 46 K parallel to the c -axis and the observed anisotropy of the dielectric constants can both be derived, where the transition temperature to ferroelectric phase is 69 K.