A concise, self-contained introduction to solid polymers, the mechanics of their behavior and molecular and structural interpretations. This updated edition provides extended coverage of recent developments in rubber elasticity, relaxation transitions, non-linear viscoelastic behavior, anisotropic mechanical behavior, yield behavior of polymers, breaking phenomena, and other fields.

Mechanical properties of solid polymers

Intrinsic viscosities and unperturbed dimensions of long chain molecules

Structure and elasticity of non-crystalline polymer networks

On the estimation of unperturbed dimensions from intrinsic viscositiesxcin

Solution properties of branched dextrans

Intrinsic viscosities of polystyrene and polyisobutylene fractions in good and in “ideal” solvents have been examined from the point of view of their dependence on molecular weight. A compilation of results is presented which covers exceptionally wide ranges, from several thousand to several to million, in molecular weight. The intrinsic viscosity in an “ideal” solvent (i.e., cyclohexane at 34°C. for polystyrene, or benzene at 24° for polyisobutylene) is remarkably well fitted over the molecular weight range cited above by the relation: 






where K is a constant, independent of molecular weight, for a particular polymer at a given temperature. The molecular expansion factor α3 which applies in good solvents (e.g., toluene for polystyrene and cyclohexane and diisobutylene for polyisobutylene) as calculated from: 






increases with molecular weight approximately in accordance with the relationship: 






However, the quantity (α5 − α3)/M1/2 changes appreciably with M in some cases. This is particularly true for molecular weights below 50,000. Results of an examination of the effect of rate of shear on the viscosity of polystyrene in benzene at 25° and in cyclohexane at 34°, and of the intrinsic viscosity-molecular weight relation for polystyrene in benzene at 25°, are reported.

Molecular weight dependence of the intrinsic viscosity of polymer solutions. II

Melting point depressions were determined by dilatometric and microscopic measurements for polyacrylonitrile in dimethylformamide and in γ-butyrolactone. These data give for the glass transition and melting point of the pure polymer 104 and 317°C., respectively. Both the heat and entropy of fusion are low. This suggests that the high melting point of polyacrylonitrile is due to its extended molecular conformation rather than to strong attractions between the molecules in the crystalline state.



Average crystallization rates measured dilatometrically indicate that the optimum temperature for crystallization from solutions in the concentration range 17–27% is only 21°C. above the glass transition temperature. On either side of the optimum temperature the rate decreases sharply, and although crystallization then continues for a longer time the amount of crystallinity finally developed is less.



For 15–20% solutions the viscosity increases abruptly as the glass transition is approached, and decreases rapidly at about 25°C. below the true melting point. The shear dependence is large at low temperatures but appears to vanish at 25°C. below the melting point. As the temperature is raised a narrow region is observed for each concentration in which the viscosity exhibits an anomalous increase. These temperatures stand in good agreement with the optimum temperature for crystallization as determined dilatometrically. The foregoing observations suggest the presence of molecular aggregates which are held together by regions of small and imperfect crystallites.



In addition to the low entropy of fusion, additional evidence for the extended shape of polyacrylonitrile molecules is provided by estimates based on dilute solution measurements. The interaction between nearest-neighbor nitrile dipoles was investigated in an attempt to correlate large unperturbed dimensions with the molecular structure. This dipolar interaction is repulsive, and its magnitude depends upon the rotational position of the two nitrile groups. By adding a further contribution representing the steric repulsion the total rotational potential is estimated for isotactic and syndiotactic sequences. The dipolar interaction is much larger than the steric repulsion, and the rotation about successive chain bonds must be cooperative to avoid certain high energy conformations. This requirement probably explains the low flexibility and high extension of polyacrylonitrile molecules. The total rotational potential for an isotactic sequence favors the same helical conformation observed in crystalline isotactic polyolefins, while for a syndiotactic sequence some type of helical conformation appears to be preferred rather than the extended planar zigzag.

Melting point depression study of polyacrylonitrile

Data are reported for the temperature coefficient of the retractive force for a natural rubber sample which had been crosslinked by irradiation. These measurements differ from those previously reported in allowing a longer interval for the attainment of equilibrium, in covering a wider range of elongations, and in a somewhat greater precision of the tension measurement. The Mooney equation constants for the tension at 45°C. are 2C1 = 2.617 kg./cm.2 and 2C2 = 0.876 kg./cm.2. The latter, although smaller than the values reported by other workers for similar samples, is far from vanishing. A comparison is given of (∂f/∂T)V,L as evaluated from the measured (∂f/∂T)V,L according to various proposals. Approximately 20% of the total force arises from the internal energy contribution, fe, when the relative elongation, α, is near unity. The fe/f ratios calculated from our measurements stand in good agreement with those obtained from Ciferri's data, despite the fact that the latter correspond to a much larger C2 value. Furthermore, both sets of data indicate that fe/f decreases with increasing α. The entropy component of the force, when fitted to the Mooney equation, yields C1s ≅ C1 but C2s < C2. This suggests that the C1 term is primarily due to entropy effects, whereas the internal energy makes a larger contribution to C2. The nonvanishing C2 and the variation of the fe/f ratio with α, represent deviations from the gaussian model treatment of Flory, Hoeve, and Ciferri. Criferri and Flory have expressed the opinion that finite C2 values arise solely from the failure to attain mechanical equilibrium. However, the cubic lattice model treatment of Krigbaum and Kaneko indicated that although the two discrepancies cited above may be accentuated by nonequilibrium effects, they can only be expected to vanish under equilibrium conditions in the limit of infinite chain length between crosslinks.

The contribution of internal energy to the elastic force of natural rubber

There are investigated the relations between the liquid compositions in the two phases formed when a polymer equilibrates in a mixed solvent. By imposing the simplifyng constraint that all of the polymer be located in one of the two phases, an expression for the equilibrium composition ratio, R = (φ1/φ2)/(v1/v2), is obtained through use of the customary expressions for the free energy of polymer solutions: 


(1)



Here subscripts 1, 2, and 3 refer to the two liquids and the polymer, respectively, χ is a free energy parameter, l is the ratio V1/V2 of the molar volumes of the two liquids, φ and v represent the volume fraction in the ternary and binary phases, respectively, and ϵ is an auxiliary variable relating φ and v for the two liquid components. Certain consequences of the equilibrium composition relationship are examined, and there are suggested possible applications to diffusion, light scattering, and solubility. The results of analysis of the two phases formed when crosslinked natural rubber equilibrates with the mixed solvent pairs: benzene–nitromethane and m-xylene–nitromethane confirm the form of the equilibrium composition relationship, and the values for the free energy parameters required to represent the data for these ternary systems appear to be reasonable.

W. R. Krigbaum

Papers

Molecular weight dependence of the intrinsic viscosity of polymer solutions. II

Melting point depression study of polyacrylonitrile

The contribution of internal energy to the elastic force of natural rubber

Phase equilibria in polymer–liquid 1–liquid 2 systems

Relationships between [η] or (R2) 3/2 and the second virial coefficient