A technique was devised for obtaining rate laws and kinetic parameters which describe the thermal degradation of plastics from TGA data. The method is based on the inter-comparison of experiments which were performed at different linear rates of heating. By this method it is possible to determine the activation energy of certain professes without knowing the form of the kinetic equation. This technique was applied to fiberglass-reinforced CTL 91-LD phenolic resin, where the rate law - (1/we)(dw/dt) = 1018e−55,000/RT [(w - wf)/w0,]5, nr.−1, was found to apply to a major part of the degradation. The equation was successfully tested by several techniques, including a comparison with constant temperature data that were available in the literature. The activation energy was thought to be correct within 10 kcal.

Kinetics of thermal degradation of char-forming plastics from thermogravimetry. Application to a phenolic plastic

It is shown that by the application of Borel’s method of summation to the later terms of an asymptotic expansion, the ‘sum’ of such terms can normally be replaced by an easily calculable series involving ‘basic converging factors’. As particular consequences, [i] the remainder in a truncated asymptotic expansion can be written down once the general term in the expansion is known; [ii] the converging factor for a given asymptotic expansion can conveniently be calculated from the basic converging factors; and [iii] the Stokes phenomenon is simply expressed in terms of discontinuities in these basic quantities. Formulae and tables are given for the basic converging factors.

Asymptotic Expansions and Converging Factors. I. General Theory and Basic Converging Factors

The interactions of a point charge and of a point dipole with a hydrogen atom are investigated. Interaction energies, dipole and quadrupole moments are calculated using exact perturbation theory. Spheroidal coordinates are necessary to solve the differential equations which arise, and wave functions for the atom in these coordinates are seen to be the correct zero-order ones to use. The exact form of the perturbing potential is employed, giving results with both polynomial and exponentially decreasing terms. These are compared with the simpler but less accurate results obtained when the expanded form of the perturbation is used.

Wave Functions for the Hydrogen Atom in Spheroidal Coordinates II: Interaction with a Point Charge and with a Dipole

A perturbation calculation, valid in the limit of large separations, of various properties of the 2p$\pi $ state of HeH$^{2+}$ is carried out. The total energy and the kinetic and potential energies are calculated to the fifth order, the dipole moment to the third order and the quadrupole moments to the second order and the results compared with those obtained using exact and variationally determined two-centre wave functions. Some results are also given for the 2p$\pi \_{u}$ and 3d$\pi \_{g}$ states of H$_{2}^{+}$ and the influence of nuclear symmetry at large separations is briefly discussed.

C.A. Coulson

Papers

LXXX. Some new values for the exponential integral