Polymer Chains In Solution Research Articles

Osmotic Pressure of Moderately Concentrated Polymer Solutions

By two methods, a linearization and a variational principle, the Born-Green-Kirkwood equation for the radial distribution function is solved approximately and the osmotic pressure of chain polymer solutions computed at arbitrary concentration. The gaussian intermolecular potential energy of Flory and Krigbaum is used, and this restricts the range of validity of the theory to volume fractions less than one-tenth. It is shown how the distribution of polymer molecules in the solvent becomes random as the concentration is increased. For good solvents, the quantity [(P/c2)—RT/Mc], where P is the osmotic pressure and M the molecular weight, is predicted to increase rapidly with concentration c, and then to level off rapidly, the whole effect being accomplished at quite low concentrations as the molecules are forced to overlap. Some experimental corroboration is displayed. Severe doubt is cast on the practicality of the virial expansion of P, and possibly on the validity, beyond quite low concentrations.

Theory of Dilute Polymer Solution. III. Heterogeneous Polymer

The second virial coefficients of osmotic pressure and light scattering of heterogeneous chain polymer solutions are calculated to the double-contact approximation. Two types are assumed for the molecular weight distribution: the Schulz distribution, and the distribution with two deltalike peaks. Then, the heterogeneity corrections for intrinsic viscosity are evaluated on the assumption of the Schulz distribution. On the basis of the results obtained, a tentative attempt is made at interpreting the proportionality between the intrinsic viscosity at the Θ temperature and the square root of the molecular weight without discarding the hydrodynamic scheme, and the relation between the hydrodynamic and statistical radii of heterogeneous polymer coil is also examined. Finally, the relation between the second virial coefficient A2 and intrinsic viscosity [η] is discussed somewhat in detail. And it is shown that the initial curvature of the curve of [η]/[η]θ — 1 vs A2Mw/[η]θ is concave upward for ordinary fractionated samples, where [η]θ is the intrinsic viscosity at the Θ temperature, and Mw is the weight-average molecular weight. This statement is verified by comparison with experiment.

Problems of the statistical thermodynamics of dilute polymer solutions

AbstractThe current status of the statistical thermodynamics of dilute solutions of chain polymers is reviewed, with particular attention to the interactions between single chain molecules and solvents and to the mutul interactions of two chains.With respect to the problems of one and two chains, the following topics are considered: the potential of mean force between chain segments and its dependence on the slevent; relationship between latice and continuum theories; comparison between machine calculations and analytical theories of chain dimensions; exact series and approximate or semi‐empirical theories of the osmotic second virial coefficient, and comparison with the experimental data; effects of polydispersity; behavior in mixed solvents. Higher virial coefficients and phase separation are also briefly discussed.

Polymer NSR spectroscopy. I. The motion and configuration of polymer chains in solution

AbstractMany polymers in solution exhibit well‐resolved NSR spectra, in contrast to the broad peaks observed for the solid state. The peaks for polystyrene dissolved in carbon tetrachloride are not very much broader than those of cumene and other small organic molecules. When segmental motion is restricted or prevented, polymer peaks may become very broad even in solution. This is observed for poly‐γ‐benzyl‐L‐glutamate in trichloroethylene, in which it probably exists as large aggregates of α‐helices. It is shown that the α‐helical conformation itself is not responsible for this broadening. Many proteins also show poorly resolved spectra in the native state, but well‐resolved peaks in the unfolded state. Large “anomalous” shifts observed in the positions of the proton peaks in the NSR spectra of polystyrene and substituted polystyrenes are interpreted in terms of a π‐current model of the benzene ring. It is concluded that where sequences of 10 or more phenyl groups are present on a polymer chain, they tend to cluster together in a quasi‐crystalline arrangement.

Dimension of polymer chains in solution

Journal of Polymer ScienceVolume 35, Issue 129 p. 553-555 Letter to the Editor Dimension of polymer chains in solution Edward F. Casassa, Edward F. Casassa Mellon Institute, Pittsburgh 13 PennsylvaniaSearch for more papers by this authorT. A. Orofino, T. A. Orofino Mellon Institute, Pittsburgh 13 PennsylvaniaSearch for more papers by this author Edward F. Casassa, Edward F. Casassa Mellon Institute, Pittsburgh 13 PennsylvaniaSearch for more papers by this authorT. A. Orofino, T. A. Orofino Mellon Institute, Pittsburgh 13 PennsylvaniaSearch for more papers by this author First published: March 1959 https://doi.org/10.1002/pol.1959.1203512929Citations: 13AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume35, Issue129March 1959Pages 553-555 RelatedInformation

Theory of Dilute Polymer Solutions (III) Intrinsic Viscosity

A theory of the intrinsic viscosity [η] of chain polymer solutions is developed on the basis of the Kirkwood and Riseman scheme, taking some modifications concerning the excluded volume effect into account. If the volume effect is represented by the linear expansion factor α of the root mean square radius of gyration, it is concluded that [η] is proportional to α 2 for the free-draining molecule and α 2.43 for the non-free-draining molecule. This implies that the effective hydrodynamic radius of the polymer coil is not proportional to the statistical one in the limit, where the rigid sphere model is asymptotically valid; in other words, the more the polymer chain is expanded, the deeper the solvent molecules penetrate into the polymer coil.

Theory of Dilute High-Polymer Solutions (the Pearl Necklace Model)

A theoretical expression for the second virial coefficient A2 of chain polymer solutions is derived. This accounts for the empirical relation between A2 and molecular weight M, according to which A2 is proportional to M—α. α has a value of about 0.23 over a suitable range of molecular weight. According to the theory, α≈½—¾· (log1.684x), when x, a variable proportional to the square root of M, becomes very large. The temperature variation of A2 is also explained. Krigbaum and Flory's data on the molecular weight and temperature dependence of A2 are discussed.

Statistical Mechanics of Polymer Solutions. Parts I and II

Some contributions are made to the refining of the lattice model theory of Flory of chain polymer solutions by introducing the idea used in the recent theory of regular assembly that combinatory factor constructed in terms of multiple site clusters can be properly used to take long-range correlations between a given site and its far distant neighbors into account. In Part I, the combinatory factors of Flory and others in current use are reconstructed to exemplify the pseudo-assembly method which has been presented by Kikuchi and the present authors for an easy construction of combinatory factors of higher-order approximation for regular assembly, and to give a thorough understanding of the succeeding uses in Part II. In Part II, a refined theory of chain polymer solutions is developed. The final expressions for the entropy of dilution and the osmotic pressure depend on the flexibility and the degree of branching of the polymer chain, and give a better agreement with observed data even at high dilution.

Viscoelastic Properties of Dilute Polymer Solutions

The viscoelastic properties of dilute solutions of chain polymers have been measured at frequencies in the range from 200 cps to 60 kc. The data are compared with theoretical curves calculated from the steady-flow viscosities of the solution and solvent, the molecular weight and concentration of the polymer, and the absolute temperature; this calculation made use of equations obtained from a recently developed theory. The equations contain no adjustable constants. The theory is shown to be at least a good first approximation to the viscoelastic properties of the solutions studied. The agreement of the data and the theory implies that, up to 60 kc at least, the viscoelastic properties of dilute solutions of polystyrene and polyisobutylene are the result of the thermal motions of the segments of the polymer molecules. These segmental motions coordinate with one another to produce changes in the configurations of the molecules. The configurational changes have associated with them a series of relaxation times. These relaxation times are shown to depend upon molecular weight of the polymer, concentration, type of solvent, and viscosity of solvent.