Chain Polymer Molecules Research Articles

Theory of Excluded Volume Effect in a Chain Molecule Based on the Random Flights Model

The unperturbed distribution function of the distance between the i -th and j -th segments of a chain polymer molecule is assumed to be the distribution function of the | j - i | steps random flights. The expansion coefficient of the excluded volume effect of chain molecule is calculated with this distribution function by the method of cluster expansion. The number and types of clusters under consideration and the acquired asymptotic behavior of the expansion coefficient are identical with the previous report. The expansion coefficient is expressed in a closed from by the aid of the error function as \(\alpha^{2}{=}1+\frac{2+((1/c)-2)\mathrm{e}^{-\xi 2}\xi^{-2}\text{Erfc}^{-1}(\xi)}{1+\mathrm{e}^{-\zeta 2}Erfc^{-1}(\xi)/c}{=}3+O(\mathrm{e}^{-N}/N)\).

The physical properties of rigid chain polymer molecules in solution

Various features of the chemical structure of a polymer that can give rise to a high equilibrium rigidity of its molecular chains (interaction of side groups, the presence of rings in the main chain, a ladder structure, conjugation in the chain etc.) are outlined. It is shown how study of the hydrodynamic and optical properties of dilute solutions of a polymer enables quantitative information on the equilibrium flexibility of its molecules to be obtained. It is characteristic of chain molecules with high equilibrium rigidity that they also have high kinetic rigidity. The latter gives rise to a number of unique properties of rigid chain polymers that are essentially different from the properties of flexible chain polymers (high briefringence of solutions in mechanical and electrical fields, low frequency dispersion of dielectric polarization, the Kerr effect etc.). Study of the non-equilibrium dielectric and electro-optical properties of solutions of rigid chain polymers using appropriate theories, enables substantial information to be obtained on intramolecular mobility, optical anisotropy and on the magnitude and direction of the dipole moments of polar groups in the polymer molecules.

Possible existence of two classes of conformational changes in linear polymeric chain molecules

Possible existence of two classes of conformational changes in linear polymeric chain molecules

Possible existence of two classes of conformational changes in linear polymeric chain molecules

In the light of recent fluorescence depolarization and nuclear magnetic resonance measurements in solutions of linear polymeric chain molecules, it is porposed that the local conformational changes belong to two main classes which do and do not obey the diffusion limit, respectively. The implications for internal viscosity effects on flow birefringence and high frequency viscoelastic behaviour are discussed.

Time–temperature superposition of large‐strain shear properties of the ethylene–propylene copolymer system

AbstractThe principle of time temperature superposition for some mechanical properties of polymers is well known, particularly where strains are on the order of 1% or less. For large strains the simple data transformation techniques are not useful, probably because of morphological changes in the polymer. Morphological changes have the effect of changing the mechanical properties, thus necessitating a shift on the verticle axis as well as horizontal axis where mechanical properties are plotted on the ordinate and strain rate, e.g., is plotted on the abscissa. By the Rouse and Zimm theories of flexible chain polymer molecules a relationship is shown between a verticle shift and a horizontal shift, thereby making it unnecessary to determine the exact nature of morphological changes in the polymer when strained. Six polymers were strained to the fracture point and the shear modulus and fracture strength data were used to demonstrate the technique of simultaneous verticle and horizontal transformation of data.

Configuration-dependent properties of polymer chains

Abstract

Correlation and Distribution of Segments in a Chain Molecule

The singlet and the pair distribution functions of segments of a chain polymer molecule are evaluated at fixed center of gravity of the molecule, the former to the first order in the excluded volume effects and the latter to the zeroth order. The results are applied to the evaluation of the viscosity and other transport coefficients. The mutual relations of these segment distribution functions are discussed in comparison with the recent self-consistent field approach by Reiss and others to the excluded volume effects. Thus, the product assumptions on higher-order distribution functions are examined.

Salt Effects in Mucin Lubrication

Animal joints are lubricated by two complementary mechanisms. Weeping lubrication carries most of the joint load hydrostatically, leaving only a small fraction of the total to be carried by rubbing of the solid “skeletons” of the two cartilages. This rubbing is, in turn, lubricated by the synovial mucin; i.e., by long chain polymer molecules dissolved in the joint fluid. There is good evidence that the mucin molecules adsorb to the surfaces and provide boundary lubrication. In this paper we examine further this adsorption processs using a bearing whose two surfaces are rubber and glass, respectively. It is found that the lubricating ability of the mucin is good if it is applied to the bearing in a solution with about physiological salt concentration. At higher salt concentrations the lubrication is comparatively poor, while at zero salt concentration it is very bad indeed. If, on the other hand, the mucin is applied at physiological salt concentration, and then the salt and unadsorbed mucin are washed away with distilled water the lubrication remains good, and has, on occasion, even improved. Once the mucin has been adsorbed the entire range of salt concentration can be explored, with the lubrication becoming worse at high salt concentration and then recovering in greater or lesser degree when the salt is washed off. It seems, then, that the salt concentration affects lubrication in two ways. It can upset the adsorption of the lubricating film, and it can change the lubricating effectiveness of the film once it is adsorbed.

Ellipsoidal Model for Non-Newtonian Intrinsic Viscosity of Chain Polymer Solution

In order to discuss the non-Newtonian intrinsic viscosity of polymer solutions, the authors adopt an improved ellipsoidal model for the polymer molecule. Chikahisa's rigid ellipsoid model theory gives a good explanation of the shear-rate dependence of the intrinsic viscosity but his theory neglects the micro-Brownian motion of the chain polymer molecule. The authors establish a theory considering that the molecule may change its shape due to the micro-Brownian motion. The axial ratio of the deformed ellipsoid is obtained and the shear-rate dependence of the viscosity is calculated by Saito-Scheraga's theory. The region of the shear gradient where the viscosity reduction occurs is discussed comparing with Chikahisa's theory. There are two mechanisms to cause the non-Newtonian viscosity: the orientation of the polymer molecule and the deorientation of it. Which of these is more dominant in the non-Newtonian viscosity depends on the nature of polymer systems.

Random-Walk Model of Adsorption of a Chain-Polymer Molecule on a Long Rigid-Rod Molecule

A lattice model of adsorption of a flexible chain molecule on a rodlike molecule is investigated. The rodlike molecule is represented by the lattice sites on the z axis of a simple-cubic lattice; sites which are nearest neighbors to the z axis are adsorbing sites. The dimensionless adsorption energy per monomer unit is θ = ε/kT. The problem of enumerating polymer-chain configurations taking into account the increased probability of occupying adsorbing sites and the zero probability of occupying z-axis sites is formulated and solved as a random-walk problem. This model is a natural generalization of a random-walk model of adsorption on a plane solution surface. The average fraction of monomer units in adsorbing sites fR(θ) is computed in the limit in which the number of monomer units in the polymer chain approaches infinity. There is a critical value of the adsorption energy θc = ln (6/5) such that for θ<θc, fR(θ) = 0. For θ>θc, fR(θ) is an increasing function of θ with all derivatives equal to zero at θc = ln (6/5). In the analogous simple-cubic model of adsorption of a polymer-chain molecule at a plane solution surface, the same value of the critical energy has been obtained. For θ<ln (6/5) the average fraction of monomer units in adsorbing surface sites is zero, i.e., fS(θ) = 0. For θ>ln (6/5), fS(θ) is an increasing function of θ whose right-hand slope is 25 at θ = ln (6/5).

The second virial coefficient of polymer solutions

AbstractA theoretical calculation of the temperature dependence of the second virial coefficient of polymer solution is carried out, assuming the Lennard‐Jones potential, φ(S) = φ0[(S0/S)12 − 2(S0/S)6], between two molecular segments of chain polymer molecules in the solution. The result gives a good explanation for the experimental relation between the second virial coefficient, A2 and the temperature, T: A2 = a + (b/T), where b > 0 for good solvents and b < 0 for poor solvents. According to this calculation, the theta point, θ, at which the second virial coefficient vanishes is given by the relation, φ0/kθ = 0.292., and the temperature gradient of A2 at this point is determined by another molecular parameter, SM, where M0 represents the molecular weight of the segment. The theoretical value of the second virial coefficient agrees well with the experimental data of Krigbaum and Flory for polyisobutylene in benzene near the theta point, and it gives a value of about S0 = 10 A. for the dimension of a segment consisting of seven monomer units in the solution. Another method for calculation of the molecular parameters, which employs the experimental data of the second virial coefficient is described. Application of this method to the light scattering data of Outer, Carr, and Zimm, permits calculation of the molecular paramenters of polystyrene in several solvents.

Effect of Velocity Gradient on the Radial Distribution of Polymer Molecules in Dilute Solution

A differential equation which determines the time dependence of the radial distribution function of polymer molecules in dilute solution is derived. The equation is represented in a form of a diffusion equation. For a case in which the solution is flowing with the constant velocity gradient, and the system is at a steady state, a calculation is carried out, adopting a Gaussian intermolecular potential between free draining chain polymer molecules. The result shows that the velocity gradient in solution causes the radial distribution function to be deformed into a non-spherical symmetry, and this deformation is increased with the increase of the velocity gradient and the molecular weight of polymer.

Mutual solubility of polymers and properties of their mixtures

AbstractHeats of mixing of polymers with each other have been measured, the behavior of the mixtures of solutions of various polymers has been studied, and the dependence of mechanical properties of polymer mixtures on the ratio of components has been investigated. It has been shown that mixing of polymers with each other is usually an endothermic process and, therefore, leads to formation of macroscopically homogenous, but actually microheterogenous, systems with an extremely high degree of dispersion. These microheterogenous polymer mixtures are formed because of the enormous viscosity of polymer mixtures, which prevents macroscopic separation into phases but does not hinder the considerable mobility of the segments of flexible chain molecules. It has been shown that the dependence of mechanical properties of microheterogenous polymer mixtures on the ratio of polymers in the mixture have sharp maxima or minima which cannot be found in the case of true polymers in polymer solutions. It has been found that the behavior of some polymer pairs is anomalous, in that exothermal mixing is supplemented by separation of the solution mixture into phases and by the appearance of maxima or minima in the dependences of the properties of polymer mixtures on the ratio of polymers in the mixture. This anomaly has been attributed to the effect of loose packing of the molecules of the polymers which show anomalous behavior. It has been shown that, in these systems, there necessarily exists a lower critical temperature of mixing whose value can be decreased by adding low‐molecular solvents to the loosely packed polymer. Attention has been drawn to the fact that, although mixing of amorphous polymers should be considered on a thermodynamic basis to be a mutual solution of two liquid phases, the large dimensions and the flexibility of polymer chain molecules require a critical revision of the possibility of formal application of the basis thermodynamic concepts and relations to a theoretical analysis of the behavior of polymer mixtures.

On the Ring Opening Reaction of ε-Caprolactam Derivatives

Abstract The ring-chain equilibria, (Remark: Graphics omitted.) were investigated experimentally for ε-caprolactam derivatives and their results could be analyzed by the method similar to that for ε-caprolactam. For the monomethyl derivative the equilibrium shifts to the ring-form and ΔH has been estimated to be 2.3 kcal/mol. which is smaller than ΔH(=3.5 kcal/mol.) for the unsubstituted. For dimethyl and N-methyl or -methylol derivatives equilibria shift too much to the ring-form to give polymers at high temperatures. The average unit of the Brownian motion of polymer chain molecules, i. e. the segment, for the monomethyl derivative is 13.3 skeleton atoms which is smaller than 19 skeleton atoms for unsubstituted polycapramide; the substitution makes it easier for chain molecules to be kinky.

Viscosity of Dilute Solutions of Long Chain Polymer Molecules

An expression for the relative viscosity ηr has been obtained on the basis of the ``theory of rate processes'' using an ``equivalent sphere'' model, which relates ηr to parameters such as the shearing force, absolute temperature, and the volume fraction of the polymer. In the limit of zero rate of shear, a relation between the Flory constant φ and Huggin's constant k″ has been obtained. Some important applications of the derived equations have been discussed.

Theory of Dilute Polymer Solutions

Assuming the pearl necklace model for a chain polymer molecule in a solution, the theoretical expressions for the mean intermolecular potential and the radial distribution function of polymer molecules are derived. The methods in the theory of Born and Green, which is based on the superposition approximation, are conveniently applied to the case of solution. The results show that the mean intermolecular potential is nearly approximated by the Gaussian function, and it depends on the molecular weight and the temperature; the radial distribution function is also dependent on the molecular weight as well as on the temperature. At critical temperature where the second virial coefficient vanishes, the mean intermolecular potential vanishes and the radial distribution function assumes the constant value which is equal to unity. Theoretical expressions for the second and third virial coefficients are also given.

Studies of Rubberlike Polymers by Nuclear Magnetism

Abstract The actual width of the proton resonance line in uncured natural rubber has been determined at room temperature to be 0.06 gauss. Curing of polymers increases the line width at a given temperature. The small increase in natural rubber is possibly compatible with a physical bonding rather than the usually assumed cross-linking. For a butadiene-styrene copolymer, the increase of line width due to cure is somewhat larger. Carbon-black loading increases the line width to a lesser degree than does cure. This is compatible with the concept of physical bonding between the blacks and the polymer chain molecules. Variations of line width caused by changes in chemical composition and copolymerization were also investigated. Polypropylene and polypropylene oxide of roughly the same average molecular weight are compared. The polypropylene oxide exhibits a greater degree of “rotation” about its C—O bonds than polypropylene does about its C—C bonds. Two butadiene-acrylonitrile copolymers also have been studied as a function of temperature. Finally, spin-lattice relaxation time vs. temperature studies are reported for a butadiene-acrylonitrile copolymer and for raw Butyl, over the temperature range from −50° to 70° C. Estimates of the magnitude of the barriers hindering “rotation” are made.

Breakage of rubber‐filler linkages and energy dissipation in stressed rubber

AbstractThe stress–strain behavior of reinforced rubber is discussed in respect of the softening with applied stress and accompanying dissipation of energy. The concept of linkage strength factors X for attachments between rubber molecules and filler particles is shown to have wide application and usefulness, and to be related to the energy dissipated in breaking the linkages. The strength factors are a function of the prestress when the linkages break, and also the corresponding extension ratio and residual stiffness; and for a variety of fillers and considerable range of values they can be roughly converted to energies of breakage in calories per unit change in modulus by multiplying by η = 0.013. The range of strengths of these secondary linkages due to fillers may be expressed in terms of X by one distribution parameter K common to widely different rubber compounds. Energy data suggest that they are formed by physical attachments involving a number of chemical groups in the long chain polymer molecules. Presumably the strength distribution is mainly due to differences in the number of groups involved. The particle diameter of the filler has little or no importance in determining the energy dissipated in breaking secondary linkages, or their number as judged by stiffening action; yet it is a major factor in reinforcement as judged by tensile strength, tearing, and abrasion. Considerations of secondary linkages in conjunction with particle diameter show no prospect of explaining the differences in reinforcing action between types and grades of filler. An appreciation of the presence of some of strong‐type (primary) linkages due to carbon black is apparently necessary to understand the wide differences between fillers in the energy dissipated on breaking secondary linkages by a fixed prestress.

Studies of Rubberlike Polymers by Nuclear Magnetism

The actual width of the proton resonance line in uncured natural rubber has been determined at room temperature to be 0.06 gauss. Curing of polymers increases the line width at a given temperature. The small increase in natural rubber is possibly compatible with a physical bonding rather than the usually assumed cross linking. For a butadiene-styrene copolymer the increase in line width due to cure is somewhat larger. Carbon black loading increases the line width to a lesser degree than cure. This is compatible with the concept of physical bonding between the blacks and the polymer chain molecules. Variations in line width caused by changes in chemical composition and copolymerization were also investigated. Polypropylene and polypropylene oxide of roughly the same average molecular weight are compared. The polypropylene oxide exhibits a greater degree of ``rotation'' about its C–O bonds than polypropylene does about its C–C bonds. Two butadiene-acrylonitrile copolymers also have been studied as a function of temperature. Finally, spin-lattice relaxation time vs temperature studies are reported for a butadiene-acrylonitrile copolymer and for raw butyl, over the temperature range from −-50°C to 70°C. Estimates of the magnitude of the barriers hindering ``rotation'' are made.