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Volume 35, Issue 1, 01 January 1964
 SPECIAL SECTION ON HIGH‐POLYMER PHYSICS


Normal Stress Effects in Second‐Order Fluids
View Description Hide DescriptionIn the general theory of the behavior of simple fluids with fading memory in slow deformations, the constitutive equation of those fluids called second‐order fluids gives to the equation of Newtonian fluids a correction for viscoelasticeffects that is complete to within terms of order greater than two in the time scale. The hydrodynamical behavior of incompressible second‐order fluids is determined by three material constants: η_{0}, β, γ, besides the density. We show here that not only the viscosity η_{0}, but also the constant γ which governs certain normal stress effects, is determined by the shear‐relaxation modulus of classical infinitesimal viscoelasticity. This result enables us to show that in a slow Couette flow the viscoelastic contribution to the difference in normal thrusts on the inner and outer cylindrical walls has a sign opposite to that of the inertial contribution. We also suggest several practicable methods for measuring β and γ.

Nuclear Magnetic Resonance in Poly (Normal α‐Olefins)
View Description Hide DescriptionThe spin‐lattice nuclear magnetic resonance relaxation has been measured in a series of poly(normal α‐olefins) in which the side chains ranged in length from methyl to hexadecyl. The studies were carried out as a function of temperature, from −160° to 150°C, and as a function of the radiofrequency, specifically at 10, 20, 30, and 50 Mc/sec. The dependence of the NMR relaxation upon temperature and frequency shows that increase in the length of branches contributes to increased segmental mobility. Effects of thermal history are examined. The rate of side‐chain crystallization of polydodecene can be measured from the time dependence of the spin‐lattice relaxation.

Sonic Degradation of Polyisobutylene in Solution
View Description Hide DescriptionNarrow, well‐defined molecular weight fractions of polyisobutylene were irradiated in n‐hexadecane as 3% concentrations by a 10‐kc/sec sonic oscillator. The irradiatedpolymers were recovered by precipitation and evaporation; the molecular weight distributions were determined by column chromatographic fractionation. Narrow fractions for study had viscosity molecular weights of 15 100, 40 000, 74 400, and 137 000. The changes in distribution are compared with those from a broad distribution polymer with a molecular weight of 40 000. The limiting degree of polymerization below which degradation will not take place is at least as low as 200, and probably 100, for polyisobutylene in solution, considerably lower than the 1000–2000 reported for several polymers.

Temperatures Generated by the Flow of Liquids in Pipes
View Description Hide DescriptionIn the development of molecular theories of liquid and polymer structure, great importance is attached to stress and time dependences of the apparent viscosity of materials and their solutions. Some of these dependences can be accounted for by the heating of the fluid which is a consequence of the flow. In this report, solutions for the time and space distributions of the temperature in an incompressible fluid flowing steadily in a capillary with isothermal walls are presented. A comparison of the computed temperature changes with observed changes in apparent viscosity of some lubricating oils suggests that the temperature effect is significant. The possible usefulness of the solutions for understanding the origin of turbulence in flow and the heating of a cylindrical rod loaded in torsion is also discussed.

Stress—Strain Curves of Rubbers in Simple Shear
View Description Hide DescriptionIt has been stated in a brief report that a gum rubber Hevea stock exhibited a linear stress—strain relationship in two‐dimensional shear up to 300% shear. The experimental procedures and results are reported here in detail. Detailed results are reported also of a series of dynamic stress—strain measurements with the St. Joe Flexometer, briefly referred to in 1940. These dynamic shear—shear stress curves are linear within a given stress range. Whenever the greatest previous stress is exceeded, a new linear curve is obtained, of lower modulus.
Nonreversible crystallinity has been generally neglected in theories of rubber hysteresis and in experimental efforts to obtain truly reversible stress—strain curves.

Ultimate Tensile Properties of Elastomers. II. Comparison of Failure Envelopes for Unfilled Vulcanizates
View Description Hide DescriptionThe tensile stress‐at‐break σ_{ b } (based on the initial cross‐sectional area) and the corresponding ultimate extension ratio λ_{ b } of unfilled vulcanizates of silicone, hydrofluorocarbon (Viton B), butyl (both sulfur‐cured and resin‐cured), and natural rubber were determined at many strain rates and temperatures; the latter ranged from slightly above the glass transition temperature T_{g} , up to a temperature somewhat below that at which chemical degradation affected the results. For each vulcanizate except natural rubber, data obtained over an extended temperature range superposed to give a time‐ and temperature‐independent failure envelope on a plot of log(σ_{ b }273/T) vs log(λ_{ b }−1), where T is the test temperature in °K; for natural rubber, data obtained between 90° and 120°C superposed, but those at lower temperatures did not because of strain‐induced crystallization. For each vulcanizate, data at elevated temperatures gave, or tended toward, a line of unit slope on a plot of log (λ_{ b }σ_{ b }273/T) vs log(λ_{ b }−1), where λ_{ b }σ_{ b } is the breaking stress based on the cross‐sectional area at the moment of rupture. The position of each line corresponded to the equilibrium modulus E_{e} derived from stress—strain curves. Failure envelopes previously obtained for two styrene—butadiene vulcanizates, which had different crosslink densities, superposed to give a master failure envelope on a plot of log(λ_{ b }σ_{ b }273/T) vs logE_{e} (λ_{ b }−1). On this type of plot, failure envelopes for all the vulcanizates except silicone and natural rubber were found to be essentially identical. At a given value of λ_{ b }σ_{ b }, silicone had a smaller λ_{ b } and natural rubber a somewhat larger λ_{ b } than the vulcanizates of the three other rubbery polymers.

Molecular Theory for the Tensile Strength of Gum Elastomers
View Description Hide DescriptionThe tensile strength and ultimate elongation properties of any given amorphous elastomer can be described by a characteristic failure curve. It is shown in this paper that the failure curve can be predicted from a knowledge of the creep curve of the elastomer together with the data from a Mooney‐Rivlin plot. The theory relating the ultimate properties to the viscoelastic properties of the elastomer is based upon the idea of a propagating crack, the rate of propagation being limited by viscoelastic mechanisms. Data for the failure curves and creep response for EPR and SBR elastomers are presented and shown to support the theory. Literature data for butyl rubber are also shown to confirm the theory.

A Theory of Orientation Correlations in Crystalline Polymeric Solids
View Description Hide DescriptionThe scattering of light from crystalline polyolefins results principally from a correlation in crystal orientation described by an empirical Debye‐Bueche correlation function f(r)=exp(−r/a) for crystals separated by distance r. A one‐dimensional theory is developed in which neighboring crystals may differ in orientation by a small angle ±δ. A random‐walk theory results in the exponential correlation function where the correlation distance is given by a=Kd/δ^{2} for crystals separated by distance d. K is a numerical factor which is ½ for crystals confined to a plane and ⅔ for crystals permitted to orient about a cone of apex angle δ with respect to the preceding crystal. The extension to two dimensions is proposed by means of a computer simulation of the lattice, and preliminary results of such an analysis are presented.

Relationship between Morphology and Deformation Mechanisms of Polyolefins
View Description Hide DescriptionThe birefringence of polyolefins undergoes a change from an initial negative value at low elongation to a positive value at higher elongations. The extent of the negative contribution depends upon time after quenching the sample and upon temperature. The changes result from a change in the mode of crystal orientation. A model involving spherulite deformation and reorientation of crystals within the spherulite is proposed. Changes with time and temperature are ascribed to changes in a parameter γ describing the mobility of crystals within the spherulites. The model is also used to account for variation in the dynamic birefringence with straining frequency.

Relationship between Molecular Weight, Radial‐Growth Rate, and the Width of the Extinction Bands in Polyethylene Spherulites
View Description Hide DescriptionTo test theories of the twisting or correlated orientation of crystallites along the radial arms of sperulites, we measured the radial growth rates (G) and the extinction spacings (s) of a series of molecular weight fractions of linear polyethylene. At equivalent degrees of supercooling the radial growth rate is faster for the lower molecular weight fractions. Comparison with earlier measurements shows that the critical free energy for the formation of a growth nucleus is essentially the same for a single crystalgrowing from dilute solution as for a spherulite crystallizing from the melt. The data are not consistent with the hypothesis that s is directly proportional to the parameter δ=D/G, but indicate an additional factor that has the temperature dependence of a nucleation process.

Investigation of the Morphology Associated with the Dissolution Process of Polymer Single Crystals
View Description Hide DescriptionThe morphological changes accompanying the dissolution of polyethylene single crystals in solvent have been correlated with the temperature of annealing. By this method, the solution temperatures of crystals of finite thicknesses were accurately determined. Based on these results, a surfacefree energy of 58 ergs/cm^{2} was calculated for the fold surface of polyethylene lamellae crystallized at 80°C from dilute solution. In addition, several novel morphological features were observed at intermediate stages of crystal dissolution which may aid in the understanding of folded‐chain crystallization.

Morphology of Isothermally Bulk‐Crystallized Linear Polyethylene
View Description Hide DescriptionThe internal morphology of isothermally bulk‐crystallized fractions, and of whole polymer, Marlex 50 polyethylene is revealed by fracture experiments. Three distinctly different types of lamellae are then observable if one uses suitable electron microscopic techniques: (1) regular or type I lamellae which are similar in appearance to solution‐grown lamellae, (2) narrow or type II lamellae which have finite widths, and (3) extended‐chain or type III lamellae which have step heights approximately equal to fully extended chain lengths calculated from viscosity‐average molecular weights. The type I and II lamellae appear to consist of folded chains. The step heights of the type I and type II lamellae are shown to increase from about 150 to 350 Å with increasing crystallization temperature. The widths of the type II or narrow lamellae vary directly with temperature from 350 to 800 Å. However, the step heights of the type III lamellae, which range from 150 to 1050 Å, are essentially independent of temperature but do vary with molecular weight. The melting points of these different types of lamellae are shown to be consistent with presently existing theories and the relationship between morphological parameters of these lamellae and reported low‐angle x‐ray periodicities are discussed.

Evaluation of Small‐Angle X‐Ray Scattering of Polymers
View Description Hide DescriptionThe influence of the particle factor and lattice factor on the positions of the small‐angle reflections of polymer crystalline samples is investigated. Since a single‐crystal cake or a polymersolid crystallized from melt supposedly consists of stacks of nearly parallel plate‐like lamellae, one may describe the scattering behavior of polymer crystals based on a periodic step function with fluctuating periods (linear paracrystal). In this model the particle factor as well as the lattice factor may shift the scattering maxima out of the positions given by the Bragg equation. Good agreement with the observation that the first order leads to a larger spacing than the second one may be obtained by introduction of an unsymmetrical distribution function for the lamellar thickness.

Secondary Crystallization and Annealing of Polyethylene
View Description Hide DescriptionAnnealing of single crystals and of single‐crystal cakes of polyethylene leads to an increase in density because the growth of crystal thickness with time reduces the area of the density deficient surface regions. When the same process is applied to the isothermal crystallization and to the annealing of bulk samples, one has to consider the long period distribution of the crystals due to their varying age and thermal history; then one is able to reproduce sufficiently well the experimental data. In particular, starting with inhomogeneous athermal nucleation and uniform three‐dimensional growth (n = 3), one obtains a higher initial value of the Avrami exponent (n′ = 3.7), i.e., a faster density increase as a consequence of the relatively rapid decrease of the surface mass defect contribution to the density of the crystals in the first stage of their thickness growth. The extremely slow reduction of this contribution with growing age of the crystals also explains the long tail of secondary crystallization and annealing curves where the crystallinity, although slowly approaching, never reaches unity. The early drop of crystallinity below the calculated values and particularly the observed transition from primary to secondary crystallization, however, being much gentler than predicted by the theory, have to be explained by additional effects, i.e., mainly by impurity rejections during crystallization by negative pressure relaxation developing in areas completely blocked by growing spherulites and by tied molecules partly included in two different crystals so that the intervening loops from pure geometrical reasons are prevented from further crystallization.

Crystallization and Melting Behavior of Polyethylene Oxide Copolymers
View Description Hide DescriptionThe course of isothermal crystallization of a series of high molecular weight polyethylene oxide copolymers was studied with a microdensity balance. The comonomers, butylene and styrene oxides, ranged from 0.2 to 4 mole%; several examples of different polymerization conditions were also studied. The consequence of adding noncrystallizing components to a presumably linear polymer was observed in both melting point depression and the shape of the crystallization isotherm. From the melting points obtained on the experimental copolymers, the heat of fusion appeared to be lowered by the addition of noncrystallizable sequences. Inasmuch as the shape of the crystallization isotherm is changed when different amounts of comonomers are present in a random copolymer, an estimate can be made of the amount of noncrystallizing polymer acting like a block from the crystallization kinetics data and the melting point depression.

Glass Transition and Ionic Conductivity in Cellulose Acetate
View Description Hide DescriptionFor many polymers an effective glass transition can be defined via a change in slope of logσ[Ω^{−1}cm^{−1}] vs T ^{−1}[°K^{−1}]. Measurements for dry cellulose acetate (CA), previously doped by soaking (48 h) in 0.1M alkali‐chloride solutions, indicate that depends on ion and polymer properties. A model based on fluctuation theory and ``free volume'' concepts is developed. The main assumptions are: (1) ions partially fill void space reducing the available local free volume; and (2) reduction in local free volume about an ion can be accounted for in the statistical expression by subtracting an effective ion volume V_{i} from the total volume (per mole) V of a reference aggregation of particles of most probable volume V _{0}. (B is the bulk modulus,R the gas constant.) With simplified distribution functions, we obtained the expressions T_{g}≈Bδ^{2}/6RV _{0} and , where a = B/6V _{0} R, W_{i} is ionic volume (per mole) from x‐ray measurements on crystals, m = V_{i}/W_{i} , and δ is a measure of free volume. For CA, the best fit is corresponding to a fractional free volume f_{g}≈δ/V _{0}, which may be as much as 12%. Below , activation energies for conduction by alkali‐chloride‐doped CA were found to be given by E_{b} [kcal / mole]≈ 15+0.7W_{i} ≈16.1+2.45(10^{24}α), where α[cm^{3}/ion] is the electronic polarizability of the ion. Above , the energy E_{a} was approximately 29 kcal/mole, independent of the ion. Alternative interpretations in terms of internal pressure and polarization effects are discussed.

Theory and Measurements of the Glass‐Transformation Interval of Polystyrene
View Description Hide DescriptionEquations for the apparent heat capacity in the glass‐transition interval as functions of temperature, heating rate, and thermal history have been developed and programmed for computation. The hole theory of liquids was used as basis for the analysis of the glass transition. Experimental information was derived from dynamic differential thermal analysis, DDTA, on polystyrene.
The maximum of the apparent heat capacities found experimentally agrees with the theory. The peak temperatures T_{m} can be expressed over four decades of heating rates by logq = A′ − B/T_{m} , where q is the heating rate, A′ is an approximate constant, and B is the activation energy for hole formation. Higher cooling rates lead to higher activation energies on subsequent heating, indicating the need to recognize a hole size distribution.
The minimum in the heat capacity that precedes the maximum on heating through the glass‐transition interval could be detected on quenched samples. Mathematical expressions for the minimum temperature and magnitude were developed.
The temperature of ``half‐freezing'' on cooling, equivalent to Tool's ``fictive temperature,'' was found experimentally to occur at constant q·τ, where τ is the relaxation time (q·τ = 6.6° for polystyrene). From the ``half‐freezing'' temperatures as a function of cooling rate one can determine the properties of a ``mean hole.'' For polystyrene the activation energy of the mean hole is 157 600 cal/mole of holes.

50°C ``Transition'' in Polystyrene
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