Nobuhisa Imai

Interaction between Rod-like Polyelectrolytes

A system of rod-like polyelectrolytes in a salt-free solvent is treated systematically. The force between two rods arranged parallel in their free volume is obtained, as a function of their charge density and the distance between them, by using the exact solution of the Poisson-Boltz-mann equation for this system and the general expression of force by Bell and Levine. Numerical examples are given under various conditions of charge and distance. At high charge, the force between charged rods is greatly depressed by counter ions around the rods even at the short mutual distance. Owing to the neutrality condition a force which we call the neutrality force appears between rods. This force makes stable the equidistant arrangement of many rods in the solution. Simpler models; plate, one rod, and pipe; are also treated and a general theory on the force in cylindrical coordinate systems is developed. As a result, the effect of counter ions on the force between charged particles is clearly understood.

The release of monovalent counterions by addition of divalent countemons to aqueous solutions of maleic acid copolymer

Divalent cation binding and the release of monovalent cations accompanying the cation binding were experimentally studied by ion-selective electrode methods in aqueous solutions of copolymer of maleic acid and ethyl vinyl ether. It was found that in the process of Ca2+ addition, all the Ca2+ added was bound to polyions and the initially condensed Na+ was released in proportion to the concentration of the added Ca2+ up to the critical concentration of added Ca2+ at which the condensation of Ca2+ ceases. Values of the structural charge density parameter xi(s), were determined from the end-points of condensation of Ca2+. The process of Na+ release by adding Ca2+ was analyzed on the basis of the counterion condensation theory by using these xi(s) values. In addition, the relationship between the activity coefficient gamma-- of Ca2+ and degree of neutralization alpha in salt-free solutions was obtained from the Manning theory. Agreement between the calculated and experimental values was excellent in both cases.

Crossover behavior for Brownian motion

The trajectories of molecular motions of polystyrene latex and bacteriophage T4, the latter of which was visualized by dye DAPI, were observed in solutions under light microscopes. The experimental plots of log L(r) vs log r, where L(r) is the trajectory length and r is the observation scale, showed a broad transition‐like behavior between the fractal states of the fractal dimension D=1 and D=2, when r is increased. We presented here an experimental formula of D(r) or L(r) which connected the two fractal states, and discussed this transition character on the basis of this formula.

Dynamic Light Scattering of Polystyrene Latex in the Ordered State

A Laue pattern is observed for the ordered array of polystyrene latex particle. The pattern is well corresponding to a fcc lattice. The time correlation of intensity of scattered light, g (1) (τ), is also measured and analyzed. The intensity fluctuation of Laue spot shows a long time-correlation which can be approximately expressed as g (1) (τ)∼(τ) -0.61 at longer correlation time. The fact that decay constants, \(\varGamma\), of g (1) (τ) show maximum at the half of the scattering angle of the Laue condition indicates that the movement of particle is correlated with each other.

Interaction between Polyions and Low Molecular Ions

The characteristic nature of ion-binding of much charged polyions has been investigated mainly on the basis of the Poisson-Boltzmann (P.B.) equation and partly through the conductance experiment. In general, the ion-binding can be classified into two types, the ψ-binding and the P-binding. The former is due to the electrostatic field around polyions, while the latter is due to the short-range interaction between ionized groups of polyions and salt-ions. Through the theoretical analysis of non-linear property of the P.B. equation, we have found, for every shape of polyions, the strong ψ-binding of counterions which greatly depresses the polyion-charge within a thin ion-condensation phase around the polyion. By exactly solving the two-dimensional P.B. equation, we have also obtained the ion-distribution around many rod-like polyions and found the two-step ion-condensation phenomenon; at the first step, counterions are condensed in the neighbourhood of the assembly of polyions, and at the second step, a simi...

The release of monovalent counterions by addition of divalent counterions in coulombic interaction system.

The additivity rule of counterion activity or osmotic pressure in rodlike polyelectrolyte solutions has been discussed on the basis of the Fokker-Planck and Poisson equations in relation to the fluctuation of counterion distribution. This new theory has concluded that the additivity rule of counterion activity is less applicable than that of osmotic pressure due to the electric expansion force acting on the free-volume surface resulting from the fluctuation of counterion distribution. The theory has introduced an approximate relation between the counterion activities in the mixture solution of divalent and monovalent counterions, such that Deltaa+ = DeltaC++ - Deltaa++, in which Deltaa+ represents the increase of activity of monovalent counter-ions resulting from the addition of divalent counterionsDeltaC++, (in molar) to the solution, and Deltaa++ means the increase of the divalent counterion activity (in molar) in this process. This relation has been experimentally examined for Na-PSS solutions in the process of Cu2+ ion addition by the use of Na+ and Cu2+ sensitive electrodes, and it has been turned out that the relation is established in the low charge state of polyion.

Dielectric increment in polyion solutions due to the distortion of counterion distribution

A theory of DC dielectric increment, delta, has been constructed based on the Fokker- Planck and Poisson equations on the mechanism of the distortion of spatial counterion distribution around a rodlike polyion under the applied electric field, E, perpendicular to the polyion lod. The DC dielectric constant of polyion solutions can be obtained analytically in the both cases of absence and presence of counterion-flow. The nonlinearity of the Poisson-Boltzmann equation in the absence of E has given the interesting behaviors of delta. The calculation in the absence of counterion-flow has shown the delta-values having the same order of magnitude as the experimental data at the higher frequency range (around 100 kHz), and the importance of this mechanism has been pointed out.

Rotational diffusion constant of microcrystals of Wolfram oxide (WO3) in suspension

Abstract Rotational Brownian motion of Wolfram oxide (WO 3 ) colloids having rectangular-platelike shapes has been analyzed by means of a direct microscopic observation. By using a video-recording system and a time averaging method on the trace of each colloid in its polydispersed suspension, the rotational diffusion constants have been obtained as a function of its particle size. The rotational diffusion constants thus obtained have been compared with Perrins expression for rotational diffusion of general ellipsoidal particles, by assuming that a WO 3 colloid has approximately an ellipsoidal shape with three different axes. The order of the magnitude of rotational diffusion constant, D r , about the longest axis, c , has been found to be about 10 −3 /sec for c around 5 μm. The agreement with the theory has been numerically satisfactory, and the linear dependence of —log D r on c seen in the theory in this c range has been nearly established in the experiment.

Electroviscosity of polyelectrolyte solutions

A theoretical expression for the electroviscous effect in polyelectrolyte solutions, caused by the distortion of counterion-distribution and counterion flow around a polyion under a velocity gradient of solvent flow, was obtained to elucidate the characteristic behaviour of the viscosity of highly charged polyelectrolyte solutions observed at low salt concentration. The derivation of the theory was performed on the basis of the Navier-Stokes-Onsager equation, Poisson equation, and diffusion equations for low molecular ions by the use of a cell model (free-volume model) for a polyion. Energy dissipation was obtained without directly solving these equations. It was found that the derived expression of viscosity explained the experimental results satisfactorily, and that the streaming potential effect caused by the counterion flow played an essential role in the increase in viscosity of polyelectrolyte solutions at finite polymer concentration and low salt concentration ranges.

The charge effects of the self-diffusion constant of bovine mercaptalbumin

The charge effect on the translational self-diffusion constant, D, of polyelectrolytes has been quantitatively analyzed based on dynamic light scattering experiments. Perfectly monodisperse bovine mercaptalbumin has been used at low pH as a positively charged polyelectrolyte sample. Completely linear plots of log{g2(t)-1} vs. time t have been obtained for uncharged states of the protein, for the cor relation function of the scattered light intensity, g2(t). The plots deviate from linearity as polyions bear the charges. The D values for various ionic states, obtained from the initial slopes of the plots, have been analyzed using the simple theory of Imai and Mandel (N. Imai and M. Mandel, Macromolecules 15 (1982) 1562) derived based on the Onsager-Navier-Stokes equation for solvent flow with counterion distribution around a polyion. It has turned out that the experimental D values coincide well with the theory and that the characteristic nature of D can be elucidated principally from the charge effect.