Index of content:
Volume 17, Issue 3, 01 March 1949
Thermodynamics of Crystallization in High Polymers. IV. A Theory of Crystalline States and Fusion in Polymers, Copolymers, and Their Mixtures with Diluents17(1949); http://dx.doi.org/10.1063/1.1747230View Description Hide Description
The configurational entropy of a mixture of solvent and polymer molecules composed of segments connected by flexible bonds has been derived for the case in which the lattice they occupy contains limited regions of perfect order (i.e., the crystallites), which are reserved for occupancy by polymer segments exclusively. Although the derivation is carried out primarily for polymer chains of uniform length, modifications required for the treatment of heterogeneous polymers are included. An expression for the free energy of fusion ΔFf of the semicrystalline mixture of polymer and solvent is derived assuming a vanLaar heat of mixing term.
The equilibrium (average) crystallite length ζ e , derived by differentiation of ΔFf , depends principally on the ``nucleation parameter'' D which, though it evades explicit evaluation from theory, represents the relative ease with which the first layer of a crystallite tends to form; ζ e may depend to a lesser extent on the degree of crystallinity. The equilibrium degree of crystallinity, similarly deduced, depends primarily on the temperature. Fusion is predicted to occur over a range of temperatures, but the temperature Tm (the ``melting point'') at which crystallinity totally disappears is sharply defined. The melting range is predicted to be narrower the greater the chain length. If the degree of polymerization is greater than 100, the range (depending on the heat of fusion) for equilibrium melting should be quite narrow, as much as 75 percent of the fusion occurring within a few degrees of Tm . The dependence of the melting point on chain length is expressed approximately by a proportionality between the temperature depression given by ΔTm=Tm 0—Tm , where Tm 0 is the melting point for infinite chain length and the reciprocal of the degree of polymerization.
Incorporation of a diluent should markedly broaden the melting range. If the degree of polymerization is very great, ΔTm should be proportional to the number of moles of diluent per unit volume.
Extension of the treatment to random copolymers yieldswhere hu is the heat of fusion, μ′ is the heat of mixing parameter, and XA and v A are the ``mole'' fraction and volume fraction, respectively, of the crystallizingstructural unit in the copolymer. This expression is the exact analog of the freezing point relationship for ``regular'' binary mixtures of monomeric substances. Crystallinity in an ordered copolymer (the partial analog of an ``irregular'' solution) in which the structural units of a given type are arranged in long sequences should disappear at a temperature only slightly below Tm for the pure polymer. The phase rule cannot be applied to the crystal‐amorphous transformation in polymers since the free energy per unit amount of the amorphous ``phase'' is not a unique function of the composition. Copolymers should melt over a wider temperature range and their crystallinity‐temperature relationship is predicted to be sigmoid in character.
17(1949); http://dx.doi.org/10.1063/1.1747231View Description Hide Description
The spectrum of ethylene oxide was investigated from the visible down to about 600A, with high resolution in the vacuum region. No discontinuous absorption was found above 1713A. Two Rydberg series, beginning at 1435 and 1382A were found, which converge to the same ionization potential at about 10.81 ev. Two non‐Rydberg transitions were found, with origins apparently at 1713.4 and 1572.4A. An analysis and discussion is made of the spectrum. It is concluded that the Rydberg transitions arise by excitation from a molecular bonding orbital, very similar to one responsible for Rydberg series in ethylene and related compounds.
17(1949); http://dx.doi.org/10.1063/1.1747232View Description Hide Description
A method of setting up the vibrational secular equation for polyatomic molecules of ``Urey‐Bradley field'' type is described. By this method the vibration frequencies of CCl4, CBr4, CH4, CD4, CCl3Br, CCl2Br2, CClBr3, CCl3H, CCl2H2, CClH3, CCl3D, CCl2D2, CClD3, CH3D, CH2D2, and CHD3 molecules have been calculated. The 102 fundamental frequencies calculated using 28 distinct force constants are in satisfactory agreement with the observed, with a mean deviation of 1.4 percent.
17(1949); http://dx.doi.org/10.1063/1.1747234View Description Hide Description
The assumption of equal force constants in the potential functions of cis‐ and trans‐forms leads to a product rule for the planar vibrations of rotational isomers.
The rotational isomers of symmetrical dichloro‐ and dibromoethane are trans‐ and ``gauche.''
17(1949); http://dx.doi.org/10.1063/1.1747235View Description Hide Description
From the variation of the intensities of infra‐red bands with temperature the value of ΔH 0 for the reaction C2h dichloroethane →C2 dichloroethane is found to be 1250±50 cals. per mole. The probable energy difference between the isomers is 1100±50 cal. per mole. A tentative assignment of all the fundamentals has been made.
Peak intensities and integrated intensities yield the same results within the limits of the experimental error. The ratio of the number of C2 molecules to the number of C2h molecules at room temperature is 0.29.
17(1949); http://dx.doi.org/10.1063/1.1747236View Description Hide Description
The potential energy as a function of azimuthal angle has been computed on the basis of an inverse fifth power of the distance law for the energy of interaction. Suitable corrections for second order interactions were also made. A three minima potential curve is obtained of the formThe barrier is computed to be 2.81 K cal./mole.
The Thermodynamics of High Polymer Solutions. IV. Phase Equilibria in the Ternary System: Polymer—Liquid 1—Liquid 217(1949); http://dx.doi.org/10.1063/1.1747238View Description Hide Description
Two approximate methods of calculating equilibrium phase diagrams in ternary systems of polymer and mixed liquids have been compared with exact phase diagrams based upon the Flory‐Huggins equations. Both a ``single liquid approximation'' and a ``complete immiscibility approximation'' are worthless except for the crudest qualitative considerations. Analytical expressions for the plait points of such ternary systems (a maximum of ten) have been derived. A consideration of the solubility of polymers in mixed solvents leads to the conclusion that a polymer may be completely soluble in certain mixtures of non‐solvents if its internal pressure (cohesive energy density) lies between those of the two liquids and if the two liquids are themselves completely miscible. The position of the phase boundary is nearly independent of the molecular weight of the polymer for molecular weights above 10,000. Osmotic pressures in mixed solvents are discussed, and Gee's suggestion that the osmotic pressure is zero at the critical solubility limit is confirmed.
The Thermodynamics of High Polymer Solutions. V. Phase Equilibria in the Ternary System: Polymer 1—Polymer 2—Solvent17(1949); http://dx.doi.org/10.1063/1.1747239View Description Hide Description
A thermodynamicanalysis of phase equilibria similar to that developed in Part IV when applied to the ternary system of two polymers and a solvent leads to an explanation of the usual incompatibility of different high polymers in solution. Unless their heat of mixing is virtually zero or negative, two high polymers are always immiscible in the absence of a solvent; the primary role of the solvent is non‐specific, merely one of diluting the polymer mixture and decreasing the heat of interaction of the polymers. The recent experiments of Dobry and Boyer‐Kawenoki show reasonable agreement with these theoretical conclusions. Osmotic pressures of mixed polymers are discussed; such measurements would permit determination of μ12, the interaction constant of the two polymers.
17(1949); http://dx.doi.org/10.1063/1.1747240View Description Hide Description
The thermal decomposition of propylene was investigated for temperatures ranging from 680°C up to 870°C and with percentages of decomposition from 0.01 percent up to about 2 percent. The reaction was shown to be a homogenous gas reaction of the first order, the first‐order constant being given by an expression 1.1·1013 exp—(72,000/RT). Two mechanisms are discussed, both of which account for the observed kinetics and products of decomposition. It is demonstrated that the first step in the thermal decomposition of propylene is the splitting of the C–H bond leading to the formation of H atoms and allyl radicals. The problem of the value of D(C–H) in propylene is discussed in the light of the two suggested mechanisms. An attempt is made to account for the variety of the reactions between H atoms and propylene molecules as observed by various investigators.
17(1949); http://dx.doi.org/10.1063/1.1747241View Description Hide Description
The thermal decomposition of isobutene was found to be a homogeneous gas reaction of the first order. The first‐order constant is 0.5·1013 exp(67,000/RT). The products of the decomposition included H2, CH4, and allene. The experimental results are explained in terms of a chain mechanism, the initiating step being the decomposition of the isobutene molecule into an H atom and a [Complex chemical formula] radical. The most probable value of the D(C–H) in isobutene is 76 kcal./mole. This estimate is based on certain assumptions concerning the frequency factors.
17(1949); http://dx.doi.org/10.1063/1.1747242View Description Hide Description
The triplet‐singlet emission of benzene at 3400A in a rigid glass‐solution has been obtained and measured more accurately than in previous work. An assignment is proposed accounting for all the important bands observed. The analysis of the vibrational structure indicates the presence of the 703 cm−1 b 2g fundamental, showing that in the triplet‐singlet transition, the triplet level combines in the same manner as a 1 B 1u state for electric dipole radiation. This will lead to a definite assignment of the symmetry of this triplet level when the theoretical rules for intercombinations in polyatomic molecules are derived. The analysis supports a hexagonally symmetric planar model for this triplet state.
17(1949); http://dx.doi.org/10.1063/1.1747243View Description Hide Description
The average configuration of polymer molecules in solution is markedly influenced by the obvious requirement, ordinarily disregarded in problems relating to molecular configuration, that two elements of the molecule are forbidden from occupying the same location in space. The influence of spatial ``interferences'' between different segments of the molecule on its average configuration has been investigated by statistical and thermodynamic methods.
It is shown that if the average linear dimension of a polymer chain is to be taken proportional to a power of the chain length, that power must be greater than the value 0.50 previously deduced in the conventional ``random flight'' treatment of molecular configuration. This power should approach 0.60 for long chain molecules in good solvents. With increase in size of the solvent molecule, the influence of interference on molecular configuration diminishes, vanishing entirely in the extreme case of a solvent which is also a high polymer. The effect of a heat of interaction between solvent and polymer may also be incorporated quantitatively in the theory. A positive heat of mixing (poor solvent) tends to offset the expansive influence of interference, and the exponent referred to above tends to approach 0.50. The results are of foremost significance in the interpretation of the intrinsic viscosity and its dependence on the polymer constitution and on the solvent. It is pointed out that the spatial dimensions of the irregularly coiled polymer molecule cannot be correlated directly with hindrance to rotation about chain bonds, unless the expansion of the configuration due to interference and the effects of the heat of dilution are first of all taken into account.
17(1949); http://dx.doi.org/10.1063/1.1747244View Description Hide Description
A theory is presented which accounts approximately for the apparently anomalous difference between the thermal diffusion coefficients of an ion in the presence and in the absence of other electrolytes; the theory is based on the existence of an electric field parallel to the thermal gradient in the electrolyte as a consequence of the variation in mobility among the various ions present. It is pointed out also that some data on the behavior of electrolytes in a Clusius column are at variance with the Debye exponential law concerning the steady‐state distribution of solute.
17(1949); http://dx.doi.org/10.1063/1.1747245View Description Hide Description
Burning velocities of nitrogen‐oxygen‐butadiene−1,3 and helium‐oxygen‐butadiene−1,3 have been measured at atmospheric and reduced pressures. At atmospheric pressure the ratio of 3.7:1 for the maximum burning velocities was obtained for helium compared to nitrogen as the inert gas. Reduction of pressure caused an increase then a decrease in burning velocity for helium‐oxygen‐butadiene−1,3. The maximum value of the burning velocity occurred at 300 mm pressure. Calculations of the equilibrium concentrations of H, O, and OH for the gas mixtures used have been made. Assuming that the controlling factor in the burning velocity is the back‐diffusion of H‐atoms, good agreement between calculated and experimental burning velocity ratios is obtained.
17(1949); http://dx.doi.org/10.1063/1.1747246View Description Hide Description
A number of simplifying hypotheses concerning the distribution of molecular electrons are discussed. On the basis of these hypotheses, the contribution of electrostatic forces to the interaction energy between two non‐adjacent covalent bonds in a molecule has been estimated by expansion of the electrostatic potential in inverse powers of the distance. The expansion is carried as far as the quadrupole term. A discussion is given of the magnitudes to be expected for quadrupole moments of covalent bonding distributions. It is found that the electrostatic interactions, when extended to the quadrupole approximation, are sufficient to account for potential barriers hindering internal rotation in ethane, methylamine, methyl alcohol and dimethylacetylene. Using reasonable assumptions concerning the distribution of unshared electron pairs, the unsymmetrical configuration of hydrogen peroxide is found to be stable, in agreement with experiment. Extension of the treatment to the more complex molecules propane, isobutane, and neopentane indicates that the interaction between non‐adjacent groups is not negligible. A relation between bondquadrupole moments and interatomic distance is given, and possible refinements to the treatment are discussed.
17(1949); http://dx.doi.org/10.1063/1.1747247View Description Hide Description
The effect of droplet size on surface tension is given theoretical consideration with the help of results of the Gibbs thermodynamic theory of capillarity and of previous results of the author as to the sign and magnitude of superficial densities. It is concluded that surface tension can be expected to decrease with decrease in droplet size over a wide range of circumstances. In addition, approximate figures are obtained for the rate at which such decreases may be expected. The decreases become significant for very small drops. The results are of interest in view of the important role of surface tension in determining the behavior of small droplets.
17(1949); http://dx.doi.org/10.1063/1.1747248View Description Hide Description
A general statistical mechanical theory of interfacial phenomena is developed and expressions are derived relating the surface tension and other superficial thermodynamic functions to the potential of intermolecular force and molecular distribution functions. On the basis of a reasonable approximation to the superficial density of molecular pairs, the Lennard‐Jones potential and the Eisenstein‐Gingrich radial distribution function, the surface tension,surface energy, and the superficial density of matter, referred to the surface of tension, are calculated for liquidargon at 90°K and compared with experiment. The positive value which is obtained for the superficial density, referred to the surface of tension, confirms the results of Tolman's quasi‐thermodynamic theory and leads to the conclusion the surface tension of small drops decreases with increasing curvature.
- LETTERS TO THE EDITOR
17(1949); http://dx.doi.org/10.1063/1.1747249View Description Hide Description