Electric properties of macromolecules. XIII. Transient electric birefringence of sodium polyethylenesulfonate solutions

The electric birefringence of sodium polyethylenesulfonate in water has been studied. For a low molecular weight fraction, the electric field dependence followed the Kerr law quite closely. For a higher molecular weight fraction, the specific Kerr constant was much larger, and pronounced saturation of the electric birefringence was observed in fields of 15 kv./cm. The specific Kerr constant increased with decreasing polyelectrolyte concentration in pure water. On the other hand, it decreased on isoionic dilution. The saturation effect was the more marked, the lower the polyelectrolyte concentration. The saturation behavior resembled that of permanent dipole orientation, but this mechanism was not supported by the build-up of the birefringence. The magnitudes of specific Kerr constants of various types of macromolecules in solution are tabulated and discussed.     

Flow and electric birefringence in solutions of ladder polychlorophenylsilsesquioxane

Flow birefringence (FBR) and electric birefringence (EBR) have been investigated for dilute solutions of a number of fractions of cyclolinear (ladder) polychlorophenylsilsesquioxane (CLChPhS). FBR and EBR are negative in sign and their characteristic values increase with molecular weight in accordance with properties characteristic of kinetically and equilibrium—rigid chain polymers. In sinusoidal fields, dispersion of EBR characteristic of kinetically rigid chains was found: its dependence on molecular weight quantitatively agrees with the theory of relaxation and rotatory friction of rigid molecules. Analysis of experimental data confirms the validity of the molecular model of CIChPhS as a double-chain ladder cis-structure and permits us to obtain quantitative information concerning important molecular parameters such as the character of rotation of phenyl side groups the values of valence angles in chains and in oxygen bridges and dipole moments of the monomer unit of the chain and of the SiO bond.     

Electric birefringence of solutions of aromatic poly(amide hydrazide) in dimethyl sulphoxide

Birefringence in a pulsed electric field has been investigated for solutions of para-aromatic polyamid hydrazide (PAH) in dimethyl sulphoxide. The values of the specific Kerr constant K extrapolated to zero concentration have been determined. The experimental data are adequately described by the theoretical dependence of K on the contour length of the PAH molecules for kinetically rigid wormlike chains. The angle formed by the dipole moment of the monomer unit and the direction of the PAH chain was found to be 61.5 ± 1.5°. Comparison between relaxation times obtained from the curves of the decay of birefringence after the end of the electric pulse and the intrinsic viscosities of some PAH samples confirm the conclusion about high kinetic rigidity of PAH macromolecules.     

Anomalous Kerr effect relaxation in an alternating field

Perturbation theory is used to derive the complex harmonic components (stationary regime) arising in Kerr effect relaxation for an assembly of nonelectrically interacting, polar, and polarizable symmetric-top molecules acted on by a strong dc bias electric field superimposed on a weak ac electric field. The approach starts from a fractional kinetic equation written in configuration space and represents an extension of the Smoluchowski equation to fractional dynamics. This equation is solved in the context of a subdiffusive process characterized by an anomalous exponent alpha ranging from 0 to 1, the Brownian limit. By using a perturbation procedure restricted to the second order in the ac field strength, analytic expressions for the electric birefringence spectra representing the frequency dependence of the first (in omega) and the second (in 2omega) harmonic components are obtained. Various Cole-Cole-like diagrams are presented in order to illustrate the results so obtained and to emphasize the role played by the fractal parameter alpha in the anomalous diffusion collision process. A comparison of our theoretical model with experimental measurements of the ac Kerr effect response of a dilute polymer solution [poly(3-hexylthiophene)] appears to be quite satisfactory.     

Anomalous nonlinear dielectric and Kerr effect relaxation steady state responses in superimposed ac and dc electric fields

It is shown how the rotational diffusion model of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to anomalous nonlinear dielectric relaxation and the dynamic Kerr effect by using a fractional kinetic equation. This fractional kinetic equation (obtained via a generalization of the noninertial kinetic equation of conventional rotational diffusion to fractional kinetics to include anomalous relaxation) is solved using matrix continued fractions yielding the complex nonlinear dielectric susceptibility and the Kerr function of an assembly of rigid dipolar particles acted on by external superimposed dc E0 and ac E1(t)=E1 cos omegat electric fields of arbitrary strengths. In the weak field limit, analytic equations for nonlinear response functions are also derived.     

Kerr Effect of Xanthan/DTAB Aqueous Solutions

The Kerr effect of the Xanthan (charged polyelectrolyte; 113 ppm)/DTAB (surfactant) mixture in aqueous solution was studied. The static Kerr constant (B) and mean relaxation times (τ) values as a function of surfactant concentration (C_DTAB ) were determined. The observed birefringence (Δn) is not a linear function of the electric applied field (E ²). For small E values Δn grows with E ² and at a certain field value the birefringence tends to saturate. The addition of small quantities of DTAB lowers B values with respect to the Kerr constant of Xanthan (113 ppm) aqueous solution. The relaxation time of the mixtures is linearly dependent on the applied field and it decreases when DTAB concentration increases. The importance of the equivalent point is signalled. It is supposed that the initial rigidity of the polyelectrolite decreases because of the surfactant addition. Conductivity (σ) values as a function of surfactant concentration are presented.     

Electrical and dynamooptical properties of Frechet dendron-modified polystyrene molecules in solutions

The electrooptical, dynamic, and dielectric characteristics of polystyrene modified by the Frechet dendrons of 1–4 generations have been studied in benzene, chloroform, and THF solutions. It has been shown that the Kerr constant and the shear optical coefficient for all the studied polymers coincide in sign and their absolute values increase with the dendron generation number. The intrinsic optical anisotropy of the repeating unit of dendronized polystyrene molecules is negative in sign, and its absolute value tends to grow with an increase in the generation number of dendrons. The frequency dispersions of the Kerr constand and of the dielectric polarization have been discovered for solutions of the modified polymer. The ratio between the times of relaxation characterizing the dispersion of dielectric permittivity and of the Kerr constant of solutions and the times of a rise and decay of electric birefringence measured on the onset and termination of the rectangular-pulsed field does not obey the longitudinal relaxation theory for polar macromolecules. The relaxation times of dielectric polarization and of electric birefringence tend to increase with the dendron generation number.     

Transient electric birefringence of wormlike macromolecules in electric fields of arbitrary strength: a computer simulation study

We have studied the birefringence decay of linear models of macromolecules for two different types of flexibility, the broken-rod chain and the wormlike chain, using a computer simulation of a transient electric birefringence experiment. We have paid particular attention to the influence of the intensity of the orienting field, including two orienting mechanisms, the induced dipole, and the permanent dipole. We have compared wormlike and broken-rod models of the same radius of gyration, finding that they present a different decay curve under the influence of the same intensity of the field. We have seen that these differences are due to the faster relaxation times (smaller in the wormlike chain model) and amplitudes, because, regardless of the type of flexibility, the overall size of a molecule (measured by the radius of gyration) essentially determines the longest relaxation time. We have also analyzed how the relaxation process is affected by the degree of flexibility, the orientation mechanisms, and the intensity of the field. Studying a different aspect, we have paid attention to the deformation of a molecule in a transient electric birefringence experiment as a source of information. In this work we have developed equations to characterize this deformation in terms of one of the components of the gyration tensor, if a dynamic light scattering experiment under the influence of an electric field could be performed. To develop this work we have simulated the Brownian dynamics of the different models, relaxing after the removal of an orienting external electric field of arbitrary strength. A comparison with other methods such a the rigid body treatment or the correlation analysis of Brownian trajectories has also been included. We have seen that differences between the two Brownian dynamics methods are small and that the rigid-body treatment is only an acceptable approximation to obtain the longest relaxation time.     

Kerr effect in solutions of carbosilane dendrimers with terminal mesogenic groups

First results of investigations of electro-optical properties of liquid crystalline (LC) dendrimers in solution are presented. Measurements of electric birefringence (Kerr effect) and dielectric polarization of first generation carbosilane dendrimers with different ester linked terminal mesogenic groups (cholesteryl, cyanobiphenylyl and 4-methoxyphenyl benzoate) have been carried out using dilute solutions in CCl4. The results show that the dielectric polarization is proportional to the second power of the electric field in accordance with Kerr law. The Kerr constants calculated are close to those of the low molar mass analogues of the corresponding mesogenic groups. Thus the electric birefringence of the LC dendrimer solutions is mainly determined by the electro-optical properties of their terminal mesogenic groups oriented in the electric field independently of the main chain.     

The electric birefringence of polyelectrolytes: an electrokinetic approach

We discuss the Kerr constant of a polyelectrolyte solution in the dilute regime. We show that the birefringence induced in a suspension of nonspherical polyelectrolytes by an external electric field probes the electrokinetic properties of the suspension. This is because the Kerr constant is directly connected to the electric torque exerted on the particles, and therefore contains information on the induced dipole, similarly to the other electrokinetic techniques. The article is a guideline for the development of an electrokinetic theory of the electric birefringence of polyelectrolytes. We compare two different methods to derive the Kerr constant of the polyelectrolyte solution. The first method uses an expression for the electric torque which is obtained through electrostatics, and yields a Kerr constant which has the same frequency dependence as the anisotropy of the real part of the polarizability of the dressed particle (that is, of the particle plus surrounding ions). The second method assigns an effective value of the induced electric dipole per particle by using the theory of the dielectric enhancement, and gives a Kerr constant proportional to the anisotropy of the real part of the dielectric constant of the suspension. The two methods give a considerably different frequency dependence of the Kerr constant: we suggest that the expression obtained by the second method is more capable of correctly describing the main features of the experimental results obtained with polyelectrolytes having small shape anisotropy.     

Molecular conformations,hydrodynamics and optics of ladder polymers

Hydrodynamic (diffusion, sedimentation, viscosity), dynamo-optical and electro-optical properties of several ladder polysiloxanes with different substituents in the side groups have been investigated.In accordance with the theories of hydrodynamic properties of worm-like chains, the equilibrium rigidity of the main chain of these macromolecules was evaluated quantitatively. High equilibrium rigidity of ladder polysiloxanes is a direct consequence of the double-chain structure of their molecular chains.Values of reduced birefringence in electrical and mechanical fields in solutions of ladder polysiloxanes increase with molecular weight but tend to a limit, which is characteristic for semirigid macromolecules.Birefringence in an electrical field for solutions of all ladder polymers investigated is by two orders higher than the value of electro-optical effect in polymers with flexible chains and its sign (negative) coincides with that of flow birefringence. In a variable (sinusoidal) field in the region of high frequencies, strong frequency dependence of birefringence is characteristic for all samples. Unique electrooptical properties in constant and variable fields prove that, in contrast to polymers with flexible chains, highly organized orientational long-range order exists in ladder macromolecules, moreover, it is not only an axial order but also a polar one. The occurrence of long-range correlation in the orientation of polar groups and bonds of the molecular chain gives rise to high total moment of the macromolecule, which is responsible for its rotation in an electrical field. The direction of this dipole moment coincides with the long axis of the molecule since the Kerr effect is of the same sign as flow birefringence.     

Electric birefringence of dispersions of platelets

This paper describes the electro-optic response of a suspension of disk-like colloids. We have considered aqueous suspensions of Gibbsite platelets and measured the electrically induced birefringence in the broad frequency range 10(2)-10(8) Hz. When simply dispersed in an electrolyte solution, these particles orient with their major axis parallel to the electric field at all frequencies. The spectral dependence of their Kerr coefficient features three regimes: an electrokinetic α-relaxation within the kHz range, a conductive Maxwell-Wagner-O'Konski (MWO) relaxation having characteristic frequency in the 1-10 MHz range, and a nonzero high frequency asymptote. We quantitatively analyze the MWO spectral component and the high-frequency asymptote on the basis of a model developed for oblate particles. This analysis enables us to obtain the relevant particle properties: surface conductivity, zeta potential, and intrinsic Gibbsite birefringence. When the particles are dispersed in a mixture that also contains smaller spherical particles that have a charge of the same sign, their electric birefringence becomes negative at low frequency. This anomalous orientation of the platelets is analogous to that observed in mixtures of prolate and spherical particles, and demonstrates the anomalous birefringence as a universal property of suspensions of nonspherical particles when surrounded by smaller charged particles.     

A theoretical analysis of the effect of solvent on the Kerr constant of dilute polymer solutions

A new model in which solvent molecules are regarded as discrete particles is used for investigating the influence of solvent orientation near a polymer chain and of the anisotropy of the internal electric field on the Kerr effect in a polymer solution. The relation derived for the Kerr constant consists of two parts containing nine terms each in the general case (the physical meaning of the terms is briefly discussed). Relations for the above effect in a nonpolar isotropic solvent, and explicit calculations of the Kerr constant for a simple model of a rigid polymer molecule are given.     

An instrument for measuring the oscillatory electric birefringence properties of polymer solutions

An instrument for measuring the oscillatory electric birefringence properties of synthetic polymer dissolved in organic solvents has been designed and constructed. Novel features of the design include an in situ variable inter-electrode spacing Kerr cell and a double-beam optical train. The accessible frequency range extends from below 1 Hz to at least 100 kHz, with electric fields variable up to approximately 6000 V cm^?1 (peak-to-peak). Measurements are made with a powerful computerized data acquisition and processing system, based on an approach previously used for viscoelastic and oscillatory flow birefringence experiments. Preliminary results on a viscous liquid, Aroclor-1248, indicate that time-temperature superposition holds to reduced frequencies of at least 100 MHz. Comparison with theoretical predictions for rigid rod suspensions suggests that this liquid exhibits relaxation behavior with a time constants of ca. 6 ns at 25.00°C.     

Effect of external electric fields on membrane proteins: The bacteriorhodopsin

One of the possible mechanisms of the effect of external electric fields on biological systems is through their membrane proteins. At present, contradicting reports exist about the effect of external electric fields on the behaviour of the bacteriorhodopsin, the only protein molecule in the purple membrane fragments. Complex electro-optic studies (electric light scattering; electric dichroism and electric birefringence) and detailed investigations of the electric field strength dependence of the electro-optic effects on different fractions of purple membranes provide no evidence of alterations in the behaviour of bacteriorhodopsin. The effects observed are explained well by the orientations of the whole purple membrane fragments. The faster process detected in the electric light scattering decay curve could be attributed to changes in the form and/or the volume of purple membrane aggregates. The importance of these studies in understanding the dependence of the membrane properties on the variation of the transmembrane potential, which are essential for membrane pumping and channel behaviour, is discussed. Further possibilities of the application of the methods described in the study of other membrane proteins and other membrane problems are also discussed.     

Electric birefringence of discotic benzene-hexa-n-heptanoate in isotropic solution phase

Abstract

The electric birefringence of solutions of oblate discogen and prolate nematogen in dioxane has been examined. Discotic benzene-hexa-n-heptanoate (BH7) exhibits negative birefringence, while nematic 5CB and MBBA exhibit positive birefringences at low concentrations. Possible modes of solute orientation, compatible with the observed birefringence sign, are discussed. For BH7, it is suggested that the in-plane axes with larger optical polarizabilities align perpendicular to the field direction. The dependence of the specific Kerr constant on the solution concentration is also reported.     

Electrooptics of beta-FeOOH Particles in Aqueous Media

Reversing-pulse electric birefringence (RPEB) of a nearly monodisperse iron(III) hydroxide oxide sample in the beta-form (beta-FeOOH) was measured at 25 degrees C and at a wavelength of 633 nm in aqueous media in the presence of NaCl. The concentrations of beta-FeOOH and added NaCl varied between 0.00111 and 0.0555 g/L and 0.03 and 2.0 mM, respectively. Except for the suspensions with high salt concentrations, each RPEB signal showed a dip or minimum in the reverse process upon electric field reversal, together with a smooth rise in the buildup and a fall in the decay process. The observed signals were analyzed with a new RPEB theory, which takes into account not only the permanent electric dipole moment (μ) but also the root-mean-square ionic dipole moment ((1/2)) due to the ion fluctuation in ion atmosphere, in addition to the field-induced electronic (covalent) dipole moment Deltaalpha' E. The results showed that the slowly fluctuating moment of (1/2) is by far the most predominant one for the field orientation of the beta-FeOOH particle, though the permanent dipole moment μ may not be completely excluded. The rotational relaxation time of the whole particle was evaluated from the decay signal, while the relaxation time for fluctuating ions was estimated from RPEB signal fitting. The sign of the steady-state birefringence for beta-FeOOH suspensions was positive without exception under the present conditions. The birefringence signals in the steady state (delta/d) were proportional to the second power of the applied field strength (E) in the low field region; thus, the Kerr law was verified to hold for beta-FeOOH suspensions. The specific Kerr constant was evaluated for each suspension by extrapolating the values of delta/d to zero field (E-->0). Copyright 2000 Academic Press.     

On the electrical polarization of polymer single crystals in suspension

A model is proposed for the electrical polarization that causes the orientation and, hence, the electric birefringence of a suspension containing single crystals of a poly(ethylene oxide)–polystyrene diblock copolymer or a poly(ethylene oxide) homopolymer. It serves to describe how an electric dipole moment lying in the plane of the single crystal can be induced by protons migrating in poly-(ethylene oxide). The resulting Kerr effect is calculated up to saturating fields, and the observed dispersion of the polarization in high frequency fields is explained as a space charge relaxation phenomenon. The estimated relaxation time agrees satisfactorily with published experimental data.     

Conformational, optical, and electrooptical properties of cellulose pelargonates in solutions

Newly prepared cellulose pelargonate samples of various molecular weights were studied in dioxane and chloroform solutions by isothermal translation diffusion, high-speed sedimentation, flow birefringence (Maxwell effect), electric birefringence (Kerr effect), and viscometry. The conformational, hydrodynamic, optical, electrooptical, and dynamic characteristics of the polymer were determined.     

A theory of field-induced birefringence applicable to systems of large molecules

We consider a molecule in an external constant field interacting with a linearly polarized photon. When the field is chosen to be magnetic and directed along the wave vector of the photon (longitudinal), we find that the time dependence of the state function implies a rotation of the plane of polarization of the photon characteristic of the Faraday effect. Similarly when the field is transverse, the time evolution of the state corresponds to the Kerr effect in the case of an electric, and the Cotton—Mouton effect in the case of a magnetic field. The theory is applicable to a dilute system of freely oriented molecules of any size: the long-wavelength approximation is not invoked. The general procedure for averaging over all molecular orientations is carried out explicitly in the case of the Faraday effect.