Studies on dilute solutions of rodlike macroions. II. Electrostatic effects

A group of rodlike polymers soluble only in strong protic acids was studied using light scattering and viscosity techniques. These include poly(1,4-phenylene benzobisoxazole), poly(1,4-phenylene benzobisthiazole) and poly(1,4-phenylene terephthalamide). The solution properties were dependent on the ionic strength of the acid used as solvent. In a low ionic strength acid such as chlorosulfonic acid, the polymer solutions exhibited decreased unpolarized scattering, an extremely small translational diffusion coefficient, and high viscosity. All of these effects could be eliminated by the addition of a salt such as lithium chlorosulfonate, which increased the ionic strength of the solvent. The effects were attributed to a pseudo ordering of the polymer solvent system caused by electrostatic repulsions between protonated polymer chains effective over large distances (ca. 100 Å) in the low ionic strength solvent. This type of ordering is distinct from actual anisotropic phase formation, which occurs at higher concentrations in these systems. Analysis of data at infinite dilution gave a persistence length of at least 45 nm for poly(1,4-phenylene terephthalamide), larger than previous experimental results, but in accord with recent rotational isomeric state calculations and similar to experimental data for poly(p-benzamide).     

Properties of cellulose acetate in solution. I. Light scattering,osmometry, and viscometry on dilute solutions

Light-scattering, osmotic pressure, and viscometric studies on fractions of cellulose acetate (degree of substitution 2.45) in three solvents are described. The data yield the dependence of the mean-square radius of gyration 〈s²〉, the second virial coefficient Γ₂, and the intrinsic viscosity [η] on molecular weight M and temperature. The results are interpreted to show that excluded volume effects on 〈s²〉 are negligible, even though Γ₂ is large and dΓ₂/dT is positive. The large experimental value of d In [η]/d In M is interpreted in terms of partial draining effects. Data on 〈s₂〉 and [η] for other cellulose esters in the literature are similarly interpreted. Significant aggregation found in solutions of cellulose acetate in many solvents is discussed.     

Correlation of counterions with rodlike macroions as assessed by anomalous small-angle X-ray scattering

We consider the analysis of a rodlike synthetic polyelectrolyte in solution by anomalous small-angle X-ray scattering (ASAXS) in order to elucidate the correlation of the counterions with the highly charged macroion. ASAXS can be applied to these systems because the absorption edge of typical counterions, for example, bromine or iodine ions can be attained by synchrotron radiation. Model calculations using the Poisson–Boltzmann cell model show that ASAXS furnishes two terms caused by the anomalous dispersion of the counterions. The leading terms is a cross-term between the ordinary scattering amplitude of the polyelectrolyte and the real part of the scattering length f ′ of the counterions. A second term refers solely to the anomalous contribution of the counterions, i.e., to f ′ and f ′′ ( f ′′: imaginary part of scattering length). Preliminary data obtained from rodlike synthetic macroions having iodine counterions corroborate the theoretical deductions. They demonstrate that ASAXS is capable of furnishing information that is not available by the ordinary SAXS experiment. Received: 11 December 2000/Accepted: 22 February 2001     

Nematic ordering in dilute solutions of rodlike polyelectrolytes

Quantitative theory of orientational behavior of rodlike polyelectrolytes in dilute solution is developed. We find that in salt-free solutions many-body Coulomb interactions between macro- and counterions favor nematic ordering. It is shown that the orientationally isotropic phase of the solution becomes unstable toward nematic ordering at polymer concentration smaller than the overlap concentration. Our predictions are consistent with experimental observations for synthetic polyelectrolytes poly(p-phenylene)sulfonates in aqueous solutions.     

Light scattering from polymer films having optically anisotropic rodlike texture. III. Inter-rod interference

Effects of interparticle interference on depolarized light scattering from polymer films having nonspherulitic (rodlike, disklike, or fibrous) crystalline superstructures are explored, both theoretically and experimentally. Discrepancies between the observed “rodlike scattering” and the predicted scattering based on “single-rod” theory are pointed out and accounted for in terms of various types of aggregation models for polymeric solids and solutions.     

The flexibility of rodlike micelles in aqueous solutions and the crossover concentrations among dilute,semidilute, and concentrated regimes

A flexibility parameter, the persistence length, has been evaluated from the radii of gyration and the contour lengths for rodlike micelles of heptaoxyethylene alkyl ethers (C _n E₇,n=12, 14, 16) and tetradecyldimethylammonium chloride (C₁₄DAC) and bromide (C₁₄DAB) at the observed crossover concentrations between dilute and semidilute regimes. The persistence length range is 43–73 nm, except for C₁₂E₇, for which it is 32 nm. The crossover concentrations between dilute and semidilute regimes for the semiflexible rodlike micelles calculated according to Ying and Chu as a function of the molecular weight, the contour length, and the persistence length are consistent with the observed values. The crossover concentration between semidilute and concentrated regimes was, on the other hand, calculated by using the same micelle parameters, including the value of thickness of cross-section of the rodlike micelles. The obtained values are at variance with the observed values. This means that rodlike micelles in semidilute and concentrated solutions might differ in size and/or flexibility from those in dilute solution.     

Light scattering studies on solutions of chlorinated rubber

Summary Measurements have been made of the depolarisation factors _u , _v , _h, and the intensity of scattering in the horizontal transverse direction, in the case of solutions of four different samples of chlorinated rubber in carbon tetrachloride. The size, shape and molecular weight of the micelles have been deduced by the application of the light scattering theories of Gans, Vrklajan and Katalinic and Debye. The extent to which the degradation of the rubber molecule occurs on chlorination has also been assessed.

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Zusammenfassung Für Lösungen von vier verschiedenen Proben von chloriertem Kautschuk in Tetrachlorkohlenstoff wurden Messungen der Depolarisation und der Lichtstreuung durchgeführt. Größe, Gestalt und Molekulargewicht wurden unter Verwendung der Theorien der Lichtstreuung von Gans, Vrklajan, Katalinic und Debye abgeleitet. Die Stärke des Abbaues, dem die Kautschukmoleküle bei der Chlorierung unterworfen sind, wurde abgeschätzt.

     

Light scattering from polymer films having optically anisotropic rodlike texture. A quantitative test of theories

The light scattering intensity distribution from rodlike crystalline superstructures is quantitatively investigated theoretically and experimentally. The arithmetic average of theoretical H_v scattered intensities at azimuthal angle μ = 0° and μ = 45° is shown to decrease with increasing scattering angle θ in proportion to W^?1 at high scattering angles for a system composed of a random assembly of rodlike superstructure having very small lateral dimensions relative to the length. The quantity W is defined as 2π(L/λ) sin θ where L is the length of the rod, and λ is the wavelength of light in the medium. A method is proposed to estimate the length L by using the W^?1 dependence. Effects of internal heterogenity, polydispersity in rod length, and finite lateral dimensions of the rodlike superstructure are considered to account for experimental deviation of the scattered intensity distributions from the W^?1 dependence. The effect of finite lateral dimensions turns out to be the most important.     

Effect of solvent on depolarized light scattering in dilute polymer solutions

An optical model of a system in which both polymer segments and solvent molecules are described as point dipoles has been used to calculate the intensity of light depolarized in scattering. The final expression consists of six terms, the physical meaning of which is briefly discussed. An approximation procedure has been worked out for the calculation of two interaction terms due to deviations of the local field in solution from the Lorentz–Lorenz field; the terms have been calculated for simple models of flexible and rigid molecules. Their dependence on molecular weight appears to be approximately the same as the intrinsic anisotropy of the polymer molecule; their contribution is nonzero even for a solvent isorefractive with the polymer.     

Light scattering investigation of interaction between polymers in dilute solution

Parameters characterizing the interaction of nonidentical polymer molecules in dilute solutions of mixtures of two polymers have been defined on the basis of Stockmayer's theory of light scattering in multicomponent systems. Various procedures for evaluation of the interaction parameters from experimental data have been compared. Specific features of the investigation of such interactions are demonstrated with the scattering behavior of the system polystyrene-poly-(methyl methacrylate)-dioxane.     

Effect of flow on solutions of rodlike molecules

A flow field imposed on a solution of rodlike particles tends to align the rods owing to friction between the fluid and the rods. The potential energy of rods in a steady-state, homogeneous, and irrotational flow is superposed on the equilibrium Gibbs free energy of the quiescent solution to obtain the total free energy. The exact lattice treatment of Flory and Ronca is used in formulating the problem. Effects of flow on the orientational distribution function of rods and phase separation are analyzed with particular reference to elongational and pure shear flows. Calculations carried out for various compositions and flow characteristics reveal the presence of a region where the order parameter is sensitive to changes in prevailing flow conditions. Experimental determination of orientation by measuring flow birefringence is discussed.     

Large-scale supramolecular structure in solutions of low molar mass compounds and mixtures of liquids: I. Light scattering characterization

Static and dynamic laser light scattering were used to bring evidence of large-scale supramolecular structure in solutions of low molar mass electrolytes, nonelectrolytes, and mixtures of liquids. It was shown that solutes are distributed inhomogeneously on large length scales. Regions of higher and lower solute concentration exist in solution and give sufficient scattering contrast for experimental observation. A detailed light scattering study showed that these regions can be characterized as close-to-spherical discrete domains of higher solute density in a less dense rest of solution. These domains do contain solvent inside and can be therefore characterized as loose associates (giant clusters, aggregates). Their size distributions are significantly broad, ranging up to several hundreds of nanometers. Characteristic sizes of these inhomogenities thus exceed angstrom dimensions of individual molecules by several orders of magnitude. The number of solute molecules per domain varies approximately in the range 10(3)-10(8). Phenomena described were observed in a very broad range of solutes and solvents. Among others, selected data on most common substances of great chemical and biological importance such as sodium chloride, citric acid, glucose, urea, acetic acid, and ethanol are presented.     

Solvation phenomena in dilute multicomponent solutions I. Formal results and molecular outlook

We derive second-order thermodynamically consistent truncated composition expansions for the species residual partial molar properties--including volume, enthalpy, entropy, and Gibbs free energy--of dilute ternary systems aimed at the molecular account of solvation phenomena in compressible media. Then, we provide explicit microscopic interpretation of the expansion coefficients in terms of direct and total correlation function integrals over the microstructure of the corresponding infinite dilution reference system, as well as their pressure and temperature derivatives, allowing for the direct prediction of the species partial molar properties from the knowledge of the effective intermolecular interactions. Finally, we apply these formal results (a) to derive consistent expressions for the corresponding properties of the binary system counterparts, (b) to illustrate how the formal expressions converge, at the zero density limit, to those for multicomponent mixtures of imperfect gases obeying the virial equation of state Z = 1 + BPkT, and (c) to discuss, and highlight with examples from the literature, the thermodynamic inconsistencies encountered in the currently available first-order truncated expansions, by pinpointing the mathematical origin and physical meaning of the inconsistencies that render the first-order truncated expansions invalid.     

Relative molecular weight distributions of cis-polybenzoxazole/polyphosphoric acid rodlike liquid crystalline polymer solutions from dilute solution rheometry

The molecular weight for a dilute solution of cis-polybenzoxazole (PBO) in polyphosphoric acid (PPA) was determined by fitting the rheological data with a semiempirical polydisperse hybrid theory. The hybrid theory models a semiflexible rigid rod as an elastic cylinder. The cylinder has both a rotational relaxation spectrum given by an ideal rigid rod and an internal bending relaxation spectrum spaced in accord with the relaxation time spectra of a flexible coil with fully developed hydrodynamic interactions. The model was fitted to rheological data collected for a 0.05 weight percent solution with intrinsic velocity (one-point determination) of 320 ± 10 cc/g. The model predicts a number-average molecular weight near 12800 ± 400 g/mol with a polydispersity index of 2.5 ± 0.1. By using the Yamakawa-Yoshizaki equation the intrinsic viscosity is calculated for the model molecular weight distribution as 310 cc/g.     

The cluster structure of dilute aqueous-alcoholic solutions and molecular light scattering in them

The structures, equations of state, and character of fluctuations of dilute water-glycerol solutions are discussed. Two or three glycerol and about ten water molecules were found to form a fairly stable molecular complex. We call this complex elementary cluster (pseudoparticle). In a certain region of state parameters, the system could be considered a solution of pseudoparticles (clusters). Its properties were modeled by the van der Waals equation. The character of interactions between clusters was analyzed. An anomalous increase in concentration and molecular light scattering fluctuations was caused by the approach to the solution “pseudospinodal.” The experimental data were found to be in quite satisfactory agreement with theoretical estimates.     

Light scattering characterization of thermodynamic interaction of polymers in dilute solution. Effect of experimental error and temperature

Interaction between non-identical polymer molecules in a dilute solution of a mixture of two polymers is quantitatively characterized by the interaction parameter A₂₄, which is the second virial coefficient for interaction of unlike species. The value of A₂₄ may be experimentally obtained by light scattering. The determination of A₂₄ is very sensitive to experimental error in the input data, particularly for mixtures in which one polymer is greatly in excess, and for mixtures of polymers having molecular weights differing by orders of magnitude. A slight rise in A₂₄ with temperature has been observed for solutions of mixtures of polystyrene and poly(methyl methacrylate) in diethyl malonate in the range 25–100 C. This change in A₂₄ reflects the increased mutual miscibility of the polymers in solution at elevated temperatures.