Kirkwood Theory Research Articles

On the crystallization of macroionic solutions

The Kirkwood theory of solutions of spherical ions is applied to aqueous solutions of macroions plus counter ions and to macroions in strong salt solutions. It is shown that the theory exhibits a mean field phase transition which is interpreted as a transition to the crystalline phase. The theory provides a qualitative explanation of the solidification recently observed in polystyrene sphere and spherical virus solutions. For fixed macroion charge the results are shown to be only weakly dependent upon salt concentration.

Configurational Statistics

AbstractTheories of the dielectric constant in ice differ in three fundamentally different ways that are often confused with each other. First, there is the choice of interactions to include in the model, notably whether to try to include long-range dipolar interactions as in the Kirkwood theory or to include only the short-range ice-rule interactions. Second, there is the choice of the kind of statistical quantity calculated, e.g. the Kirkwood correlation factor g or the polarization factor G, which Stillinger and Cotter showed to be different. Finally, there is the choice of the kind of computational tool used, and in original papers this choice often obscures the first two differences. With these distinctions in mind a review is given of current theoretical calculations of the dielectric constant and the residual entropy and how the different theories relate to each other and to experiments.

Configurational Statistics

Abstract Theories of the dielectric constant in ice differ in three fundamentally different ways that are often confused with each other. First, there is the choice of interactions to include in the model, notably whether to try to include long-range dipolar interactions as in the Kirkwood theory or to include only the short-range ice-rule interactions. Second, there is the choice of the kind of statistical quantity calculated, e.g. the Kirkwood correlation factor g or the polarization factor G, which Stillinger and Cotter showed to be different. Finally, there is the choice of the kind of computational tool used, and in original papers this choice often obscures the first two differences. With these distinctions in mind a review is given of current theoretical calculations of the dielectric constant and the residual entropy and how the different theories relate to each other and to experiments.

Intrinsic critical length associated with oscillatory reactive processes in complex solutions: Hydrodynamic estimates

In a previous work [Nazarea, A. D. (1974)], a general expression was derived which yields an estimate of the intrinsic critical length when an oscillatory reactive mode couples to diffusional transport in reaction systems confined spatially such that translational diffusion can effectively be defined in terms of a principal axial co-ordinate. In this paper, it is shown how, under the assumption that the translational diffusion matrix is diagonal, this estimate can be applied to reactive processes in solutions in which an arbitrary number of inert components are present in addition to the buffered and unbuffered reactants. Hydrodynamic estimates of the intrinsic critical length, in terms of the period of the oscillatory reactive mode, of time-averaged viscosities and of equivalent Stokes radii, are obtained, making use of Kirkwood's theory of irreversible transport processes in solutions of large molecules. These estimates should be applicable to complex reaction systems of biological interest.

Urea-induced structural changes in chromatin obtained by sedimentation

Sedimentation coefficients have been determined for fractionated preparations of whole and stripped (depleted of very lysine-rich histones and non-histone proteins) chicken erythrocyte chromatin fragments in 0-10 M urea. Significant differences in urea effects are observed between these preparations; differences which can be interpreted structurally by use of Kirkwood's dynamical theory of the translational frictional coefficient. This type of analysis implies that urea-induced chain-swelling in stripped chromatin is due largely to the urea effect upon the constituent nu-bodies, whereas the much larger swelling observed in whole chromatin appears to involve also the effect of urea upon the region between adjacent nu-bodies.

Hydrogen bonding in polar liquid solutions. 1. Development of Kirkwood's dielectric theory in terms of a chemical model

Hydrogen bonding in polar liquid solutions. 1. Development of Kirkwood's dielectric theory in terms of a chemical model

Quasielastic light scattering by biopolymers. Conformation of chromatin multimers

Chicken erythrocyte chromatin was partially digested with micrococcal nuclease and separated into multimeric subunit fractions by gel permeation chromatography. The fractions were characterized by their Svedberg constant, diffusion coefficient, circular dichroism, and electrophoresis pattern of the extracted DNA. The molecular weight dependence of the sedimentation coefficient was found to be S 20,w = .011 × M .554. The molecular weight dependence of rmf f o is best represented in the Kirkwood theory by either a helical superstructure or a flexible coil with attractive interactions between nucleosome units. The dimer calculations of f f o suggest that the core particles are separated by spacer regions which contribute up to ∼20% of the frictional properties of the molecule.

Shape studies on macromolecules in aqueous and detergent solvents by transient electric birefringence

Transient electric birefringence of macromolecules is described by two exponential decay times, which are functions of two distinct rotary diffusion coefficients for their equivalent ellipsoids. The dimensions of the ellipsoid are calculated from these decay times. This method has been applied to hydrophilic and hydrophobic proteins in distilled water and in anionic and nonionic detergents. BSA and human transferrin in H 2O yield dimensions in agreement with published values. Helix pomatia hemocyanin (Hph) in H 2O, yields dimensions that are used to calculate values for s and [η], which agree with published values. Hph has been shown to be a circular cylinder of spherical subunits. The s value for this model, calculated according to Kirkwood's theory, agrees with the measured value. This agreement in s values supports the dimensions obtained by transient birefringence. The dimensions for seven proteins (11 700–72 000 mol wt) in SDS, obtained by this method, are in agreement with values reported by Reynolds and Tanford for mol wt < 26 000. Larger proteins show flexibility by this method, evidenced by shorter lengths than those reported by Reynolds and Tanford. However, in the two ranges of molecular weight, this method yields values of protein molecular weight, in agreement with the model of Reynolds and Tanford for proteins in SDS. The membrane protein, rhodopsin, dissolved in Ammonyx LO and digitonin, yields dimensions whose axial ratio is 6.8 in both detergents. This structure supports the model for rhodopsin proposed by Wald. Finally, this method is shown to be applicable to the study of detergent micelle structure, when the micelles resemble ellipsoids are shown for Triton X-100.

An analogy between Fuoss and Kirkwood's theory of dielectric relaxation and RC network synthesis

An analogy is given between the Fuoss-Kirkwood theory of dielectrics concerning distribution of relaxation time constants and the impedance of RC networks. It is shown that this analogy can be used to realize approximately a given impedance function of an RC network.

Theory of the dynamical viscosity of polymer solutions

A dynamical theory of polymer viscosity in dilute polymer solutions is presented. This theory includes the internal chain dynamics and the full dynamics of the hydrodynamic interactions within a polymer chain. The formulation considers the full dynamical coupled equations describing the internal motions of the polymer, the hydrodynamic behavior of the fluid, the polymer-fluid coupling, and the random forces which are responsible for the Brownian motion of the chain. Thus, the theory would reduce to the generalized Kirkwood theory if the dynamics of the hydrodynamics were ignored and the explicit treatment of the polymer dynamics and the random forces were dropped in favor of the thermodynamic force of the Kirkwood theory. As illustrative examples, only the simplest hopping-type models for the polymer dynamics are considered; the nature of the random forces is elucidated by the use of the fluctuation dissipation theorem; and the preaveraged dynamical hydrodynamic interactions are incorporated (with a phenomenological description of excluded volume effects). When the internal dynamics of the chain is ignored along with the dynamics of the fluid, the standard Kirkwood-Riseman result for the intrinsic viscosity is recovered. But in the general case, the dynamics alters the relaxation spectrum. The internal chain dynamics (hopping of individual chain ``beads'') gives rise to the finite high frequency intrisic viscosity and its different molecular weight dependence than the low frequency case.

On the electric polarization of DNA.

AbstractDielectric dispersion of DNA was studied in the frequency range 100 Hz–100 kHz at four different temperatures (6–30°C). The dielectric increment ε0–ε∞ increased with the rise of temperature. The relaxation time, on the other hand, decreased. Both the increase in dielectric increment and the decrease in relaxation time could not be explained on the basis of the counterion polarization theory. Dipole moment was estimated from Kirkwood theory. It was found to decrease systematically with temperature. Even at 0°C there was a dipole moment of 104D.

Subunit structure of earthworm erythrocruorin

The subunit structure of earthworm erythrocruorin was studied. The native protein was found to have a sedimentation coefficient of 61.1 S and a molecular weight, as determined by sedimentation equilibrium, of 3.84 × 10 6. Dissociation of the 60 S molecule was observed at acid and basic pH. Calcium ion was found to prevent dissociation in the basic range. Dissociated species of 10.1, 3.5 and 2.3 S were isolated and their molecular weights determined to be 163 × 10 3, 41 × 10 3 and 22 × 10 3, respectively. On a molecular weight basis, the native molecule consists of twenty-four 10 S subunits, each of which is composed of four 3.5 S units, which are further divided into two 2.3 S units. The 2.3 S species contains a single heme per molecule. A model of the 60 S molecule, where the twenty-four 10 S subunits are arranged into four concentric layers of six subunits each, is proposed. Support for this arrangement is provided by the excellent agreement between the sedimentation coefficient of a 1 24 th unit calculated by the application of Kirkwood's (1954) theory with the experimentally determined sedimentation coefficient of the 10 S subunit. An 88 S aggregate observed at the transition pH of acid dissociation is attributed to a side-by-side association dimer of the 60 S molecule.

Dielectric relaxation and dipole interactions in a high temperature lattice

Dipole relaxation of a sphere and of a spherical region in surrounding dielectric are calculated by Zwanig's methods, using his assumed distribution function equation for Brownian motion and a modified one based on Kirkwood's transport theory. The latter is shown to give no new relaxation time from dipole forces and to give functions consistent with Glarum's relation but not with ones derived from cavity models.

Circular dichroism of (+)-2-butanol in the vacuum ultraviolet. A comparison of theoretical and experimental values

The circular dichroism and absorption spectra of (+)-(S)-2 butanol have now been measured to 1350 Å. Theoretical rotational strengths calculated using an independent systems approach are compared to the measured values. The results support use of the extended Kirkwood theory for calculation of rotational strengths. Our method for applying the theory is described in detail. Using a model in which the first three electronic transitions in simple alcohols are assigned as n → σOH*, n → σCO*, n → 3sO, we obtain good agreement in sign and magnitude between calculated and experimental rotational strengths. The importance of including the generally ignored gij type term of Kirkwood is clearly illustrated. It is expected to dominate for transitions which are both magnetically and electrically allowed when the static fields are small.

Electric dipole moments in polar solvents. I. Audiofrequency measurement with slightly conducting solutions

Audiofrequency methods were used to measure dielectric constants of dilute solutions containing electrolytes up to free-ion concentrations of 10−4M. Using a calibrated transformer bridge, capacitance was measured with an accuracy of 0.03 pF at a conductance of 100 μmho and within 0.3 pF at 800 μmho. Evaluation of the double-layer capacitance from the frequency dependence of the data is discribed. The effect of the free ions on the dielectric constant is found to be relatively large and in reasonable agreement with the prediction of the Debye-Falkenhagen theory. The calculation of the electric dipole moment for polar solutes, including ion pairs, is discussed in terms of Kirkwood's theory. Experimental tests are described for finding out whether possible deviations of Kirk-wood's correlation factors from unity may be neglected. These tests involve changing the solvent and the temperature. The tests were satisfied for the ion pairs of tetraisoamylammonium nitrate and for nitrobenzene in chlorobenzene and acetic acid.

Application of the Kirkwood theory of transport in polymer solutions to rigid assemblies of beads

The Kirkwood general theory of irreversible processes in polymer solutions is reformulated to give correct translational and rotatory diffusion coefficients for highly symmetric, rigid molecules which may be represented by rigid assemblies of beads. This provides an elementary description of the physical meaning of the Kirkwood approximation, and gives simple criteria to judge whether Kirkwood's incorrect formulas are or are not exactly valid for a given system. Following the formulation presented here, translational and rotatory diffusion coefficients of rigid rods and rigid rings are also evaluated.

Viscoelastic Properties of Dilute Aqueous Solutions of Carbohydrate

The viscoelastic properties of dilute aqueous solutions of sodium alginate at ultrasonic frequencies were investigated by means of a torsional method with crystal resonators. The new type resonators such as a huge crystal resonator and a jointed resonator used in this study enabled us to cover the frequency range from 26KHz to 131KHz.In order to examine the configuration of carbohydrate in an aqueous solution, the complex intrinsic rigidity which was obtained from the present data by extrapolation to zero concentration was quantitatively compared with those obtainable from the existing molecular theories at infinite dilution. In this study, the concentration dependence of the normalized loss shear moduli was found to be non-linear, so that Fuoss-Strauss equation was used to obtain the intrinsic values.In an aqueous solution of sodium alginate which is assumed to take a "stringlike" configuration, the measured values and their frequency dependences could not be predicted by any of the existing theories. However, with the addition of NaCl, the experimental values approached the theoretical curves given by the Kirkwood's theory for "rodlike" polymer. It was supposed that some electrostatic structures, which can be dissociated with the addition of urea, were formed in the presence of NaCl.

The Friction Coefficient Formalism in the Statistical Mechanics of Transport Processes

Kirkwood's theory for the friction coefficient in Brownian motion relates the transport coefficients to the microscopic properties of a system through the time integral of a force autocorrelation function. The expression is useful subject to the validity of certain assumptions on the form of the autocorrelation function. These restrictions and the predicted diffusion coefficients have been examined using the method of molecular dynamics. It is shown that the assumptions are invalid and that when Kirkwood's expression is evaluated exactly it gives negative self-diffusion coefficients. This leads to the conclusion that the friction coefficient approach to transport in simple systems is physically unreasonable and should no longer be used.

A statistical approach to the Onsager and Kirkwood dielectric theory for liquids of rigid dipoles

A discussion of the Kirkwood and Onsager theory for the electric permittivity of pure liquids consisting of non-polarizable molecules is presented. Using classical statistical mechanics it is shown that in the Kirkwood treatment the mean moment of a molecule i in the liquid, under the influence of an external field, is evaluated neglecting short-range interactions between the molecules in the neighbourhood of i, whereas the remaining ones are treated as a statistical continuum. In the Onsager theory short-range interactions between i and all molecules of the system have been neglected.

Blast wave propagation in an inhomogeneous atmosphere

The Brinkley–Kirkwood theory (1947) is modified to determine the law of propagation of a blast wave in an arbitrary inhomogeneous medium for spherically and cylindrically symmetric cases. The shock path is obtained in terms of a simple quadrature. The numerical results for the shock path and the entire flow region behind the shock, propagating in an exponential atmosphere, show excellent agreement with the exact numerical solution.