Polymer Chains In Solution Research Articles

Conformations of macro-zwitterions in solution

In order to calculate the degree of dissociation of macro-zwitterions a function has been derived for the distribution of distances between oppositely charged ends of a macro-zwitterion chain, bearing in mind the coulombic interaction and the conventional statistics of polymer chains in solution. Numerical integral values of the distribution function were tabulated to enable dissociation constants to be calculated bearing in mind the type of polymer chain, solvent polarity and chain length. It was shown that the relation between calculated dissociation constants and chain length approximates to the relationship predicted merely on the basis of a simple thermodynamic study of fairly long chains.

On the transport of compact particles through solutions of chain-polymers

The problem is discussed of providing a theoretical explanation for the empirical equation of Laurent, Bjork, Pietruszkiewicz & Persson (1963) which relates the relative retardation of the sedimentation of compact particles in solutions of hyaluronic acid to the radius of the particle and the concentration of hyaluronic acid. From published and original data, the same relation is shown to apply also to sedimentation and diffusion in solutions of a number of linear and branched chain-polymers. Of several approaches to the problem, only one, based on the stochastic model of diffusional migration, yields the empirical relationship, and predicts a value of the numerical constant close to that observed. This treatment is shown to apply to other forms of migration, including the case where the chain-polymer is itself migrating. The theory is tested by calculation, from migration data, of the effective radii of the polymer chains. The results are consistent and comparable with values deduced from equilibrium experiments.

Observations on Deformation of Drops in Polymer Solutions

Observations have been performed of liquid drops suspended in several chain polymer solutions with respect to their small deformation individually.Two flow systems have been set up in which the drops or bubbles are subject to streaming with pure shear and to uniform streaming at low constant speed. In the first case, the theoretical formula derived by Taylor is compared with the experimental results, which show that though the deformation is always linear with the applied shear, both larger and smaller deformations than those expected theoretically take place. It has become evident that there are other important factors than the shear rate, interfacial tension and viscosity, i. e. concentration of the solution, C, and the degree of polymerization of the solution, n for the same kind of liquid system. The diagrams of the dimensionless deformation vs. shear rate indicate that they contribute to the drop deformation in the form Cn.For the second case of uniform streaming, gas bubbles deform into various shapes. Qualitative interpretation of the shape is also possible in terms of Cn.

Dimensions of branched and linear polymer chains in solution: Modifications of flory's theory

AbstractIt is pointed out that a theory proposed by Vrij for the expansion of a linear polymer chain in solution beyond its unperturbed size is also applicable formally to branched chains. The theory predicts the temperature at which the chain obeys random‐flight statistics to be lower for a branched chain than for a linear one (for a polymer–solvent system exhibiting the usual upper critical consolute point). Vrij's derivation follows a well‐known procedure of Flory, but refines it to take account of the variation of the time‐averaged segment density with distance from the center of mass of the chain. This modification in combination with a somewhat different derivation is shown to lead to a similar result. Yet another scheme for “correcting” Flory's theory is outlined. Some reasons are advanced for questioning the physical significance of these small modifications of Flory's theory, all of which depend on the retention of previously ignored terms in power series expansions.

Boson representation of rayleigh scattering by chain polymers

The effect of excluded volume on the particle scattering factor ( P) of a linear polymer chain in solution is described in terms of the boson formalism introduced by Fixman. P is calculated with the lowest order boson approximation to the equilibrium distribution, which gives a modified Gaussian function. The results obtained show the variation of P with the excluded volume parameter ( z). They are compared with those from other theories.

Stereospecific Polymerization of Trityl, Diphenylmethyl and Benzyl Methacrylates

Polymerizations of trityl (TMA), diphenylmethyl (DMA) and benzyl (BMA) methacrylates were carried out mainly by n-butyllithium (n-BuLi) and the tacticities of the polymers were studied by NMR spectroscopy. Polymerization of TMA by n-BuLi gave a highly isotactic polymer in toluene as well as in tetrahydrofuran (THF). The polymer obtained in radical polymerization by AIBN catalyst had about 60% isotacticity in triads. From these results the growing-chain-controlled mechanism was proposed to this polymerization. In the polymerization of DMA by n-BuLi a highly isotactic polymer was obtained in toluene at lower temperatures and a highly syndiotactic one in THF. The radical polymerization gave a predominantly syndiotactic polymer. Temperature dependence of the NMR signal-width of the isotactic polymer indicates that the conformational arrangement of the polymer chain in solution is much rigid up to a fairly higher temperature. These results suggest that the growing-chain-controlled mechanism may contribute to some extent to the stereoregulation of DMA in toluene. BMA behaved very similarly to methyl methacrylate in the polymerization by n-BuLi. Probably the same polymerization mechanisms can be applied for both monomers. Polymerization of TMA, DMA and BMA by phenylmagnesium bromide or diethylaluminum diphenylamide was also investigated.

A simulation model for the study of the motion of random-coil polymer chains

A lattice model of the dynamical behavior of a random-coil polymer chain in solution is described. Simulation of the model by a high-speed digital computer is discussed. The model appears especially suitable for the study of the effects of excluded volume interactions upon the motions of random-coil polymer chains.

Infrared spectra of polymer solutions. I. Conformational stability of isotactic polymer chains in solution

AbstractThe infrared spectra of isotactic polystyrene, polypropylene, and poly‐p‐chlorostyrene were measured in dilute solutions or gels at various temperatures ranging from room temperature to −100°C. For isotactic polystyrene and polypropylene, all the absorption bands characteristic of the helical conformation of the molecules increase in intensity with decreasing temperature, and show intensities at low temperature as strong as in the highly crystallized samples. This suggests that the molecules can assume very regular conformations even in solution. Similar temperature dependence of the spectra was observed for a homogeneous gel of isotactic poly‐p‐chlorostyrene, which is believed to be noncrystalline. These experimental facts lead to the conclusion that the stability of the TG type helical conformation of these isotactic polymers may be ascribed to the intramolecular forces within a molecule. The fact that these spectral changes are reversible has permitted a thermodynamic treatment of the conformational regularity in solution on the basis of the infrared data. The temperature dependence of the absorption intensities has been interpreted quantitatively by a simple statistical mechanical model, and the enthaply and the entropy differences between the helical and the random states of the monomeric residue in the molecular chain have been estimated.

Calculation of the Mean-Square-Displacement Function for the Slow Motion of Long-Chain Molecules and Its Application to Neutron Diffusion

We calculate the mean-square-displacement function for the motion of a polymer chain in solution. The motion is described by means of coupled Langevin equations. The peculiar behavior in square root of time obtained by de Gennes is rederived here. It is shown, however, that it is restricted to a certain time interval which depends on the number of beads and rank of the beads at which the mean-square displacement is computed. Implications for a neutron-scattering experiment are discussed. It is also seen that for infinite polymers the influence of inertial effects is entirely negligible, thus showing that the Bueche and Rouse models are equivalent in this respect.

Specific Effects in Acid Catalysis by Polymeric Sulfonic Acids in the Hydrolysis of Some Carboxylic Esters

Abstract The catalytic effects of polymeric sulfonic acids in ester hydrolysis in aqueous acetone were inferior to that of hydrochloric acid. However, the hydrolysis rate was accelerated by increasing the water content of acetone-water mixtures, and, in a water solution, polymeric sulfonic acids were much more effective catalysts. Furthermore, the catalytic efficiency of polymeric sulfonic acid in ester hydrolysis in water increased with the length of the ester molecule. The polymeric sulfonic acid with a strong hydrophobic character was more effective; 69% sulfonated polystyrene-sulfonic acid, for example, hydrolyzed methyl hydrogen azelate in water over five times more rapidly than hydrochloric acid. The specificity thus obtained suggests that, in the hydrolysis of electrically-neutral esters in water, ester molecules are concentrated in the neighborhood of the polymer by the hydrophobic interaction between catalyst and substrate. Besides, in the hydrolysis of aliphatic esters catalyzed by polyvinylsulfonic acid in 50% aqueous acetone, there was a linear relationship between the reciprocal of the rate constant and the intrinsic viscosity of the polymer, while in the case of polystyrenesulfonic acid hardly such any relationship was found. These remarkably different behaviors of the two kinds of polymer catalysts should be attributed to the difference in the expansion of the polymer chain in solutions.

Correlation of Shear Behavior of Solutions of Polyisobutylene

New data are presented for the shear behavior of solutions of polyisobutylene in toluene at 25°C. Five samples (viscosity-average molecular weight range of 105 to 5×106) were studied at shear rates from 1.0 to 3×105 sec−1. Both Couette and capillary viscometers were used in the investigation. The results are correlated by a standard reduced variable plot and compared with earlier data. A method for predicting the viscosity of straight chain polymer solutions from minimal data is discussed.

Dynamics of Polymer Chains

A general formalism is presented to serve as a basis for the calculation of dynamic properties of chain-polymer solutions. The polymer model which is adopted restricts the applicability of the formalism to dilute or moderately concentrated solutions.

A calculation of the unperturbed mean‐square end‐to‐end distance of isotactic and syndiotactic vinylic polymer chains in solution

AbstractThe results of a detailed conformational analysis given in a previous paper11 are briefly summarized in order to calculate the physical parameters which characterize the most probable conformations of an isotactic and syndiotactic polymer chain in an unperturbed solution. Moreover, a mathematical method of calculation of the mean‐square end‐to‐end distance, which also uses the matrix method of KRAMERS and WANNIER, and has advantages in some cases, is described, either for the isotactic or for the syndiotactic chain; the resulting values are given as a function of the physical parameters previously calculated. The calculated expression of the mean‐square end‐to‐end distance for an isotactic vinylic polymer is compared with an experimental value given for polystyrene10: the resulting value of ΔE (extra‐energy at a joint between segments spiralized in opposite sense) and Z (degrees of freedom in the same joint with respect to a (TG) or (GT) monomer unit) are in good qualitative agreement with the figures assumed by us.

The optical effect of the shape of rigid polymer chains in solutions—II. experimental : V. N. Tsvetkov, Vysokomol. soyed. 5: No. 5, 747–753, 1963

The optical effect of the shape of rigid polymer chains in solutions—II. experimental : V. N. Tsvetkov, Vysokomol. soyed. 5: No. 5, 747–753, 1963

The optical effect of the shape of rigid polymer chains in solutions—I theory : V. N. Tsvetkov, Vysokomol. soyed. 5: No. 5, 740–746, 1963

The optical effect of the shape of rigid polymer chains in solutions—I theory : V. N. Tsvetkov, Vysokomol. soyed. 5: No. 5, 740–746, 1963

The optical effect of the shape of rigid polymer chains in solutions—II. Experimental

The optical effect of the shape of rigid polymer chains in solutions—II. Experimental

The optical effect of the shape of rigid polymer chains in solutions—I. Theory

The optical effect of the shape of rigid polymer chains in solutions—I. Theory

Studies on the configuration and conformation of vinyl‐type polymers. II. Temperature dependence of the infrared spectrum of polyvinyl chloride in solution and stereoregularity

AbstractThe temperature dependence of the infrared spectra of polyvinyl chlorides in concentrated cyclohexanone solution has been studied. It is found that the absorbance ratio of the band at 696 cm.−1 to the band at 616 cm.−1, D696/D616, decreased as the measuring temperature was raised. This experimental finding has been interpreted as due to the reversible conformational change of the chain in the syndiotactic sequences of PVC. The syndiotacticity α of PVC was estimated to be in the range of 0.86 to 0.52 with varying of the polymerization temperature from −60°C. to 50°C. The stable conformations of the polymer chain in solution were also discussed.

Molecular weight of polymers from electrical resistivity of solutions

AbstractAn investigation has been carried out to further establish the usefulness of electrical resistivity techniques for the study of polymerization kinetics, and to determine the extent of molecular weight dependence of electrical resistivity. The resistivity increment, (p − p0)/p0, which may be regarded as the fractional increase in resistivity of a system due to the presence of polymer, was found to be directly proportional to the concentration of polymer in solution. Based on the assumption that conductance in polymeric systems occurs by migration of ionic impurities, the resistivity increment was shown to be identical to the specific local viscosity. A marked dependence of (p − p0)/p0 upon molecular weight was found. The relationships observed provide expressions for determination of molecular weight from resistivity data in the systems: polystyrene‐styrene, polystyrene‐cyclohexane, and poly(methyl methacrylate)‐benzene. Furthermore, these relationships indicate the existence of a “critical packing volume” for the polymer chains in solution. This effect permits a determination of the unperturbed end‐to‐end chain dimension of the polymer (polystyrene) which agrees reasonably well with the published value.

Concentration Dependence of Polymer Chain Configurations in Solution

On the basis of the theory of fluids and of the fashion prevailing in the statistical thermodynamics of dilute chain polymer solutions, the segment distribution functions are formally derived as a power series in concentration. The mean-square radius of gyration and end-to-end distance at finite concentrations are calculated by using the general equations derived and introducing the modified random flight model. Evaluation is carried out up to the linear term in concentration. The coefficients of the linear terms are obtained as a power series in the excluded volume parameter, and also appropriate closed forms for those are proposed, which might be properly applied to good solvent systems. The results show that the polymer chain dimension decreases with increasing concentration. Then the concentration-dependent term in the intramolecular intensity function in light scattering is evaluated. It is pointed out that the separation of this term and the intermolecular correlation leads to the possibility of estimation of the polymer chain dimension at finite concentrations by light-scattering measurements. Finally, the Huggins constant k′ in the viscosity-concentration relation is phenomenologically calculated. The concentration dependence of polymer chain dimensions proves to explain satisfactorily the effect of solvent power on the k′ constant.