Effective potential approach to bulk thermodynamic properties and surface tension of molecular fluids I. Single component n-alkane systems

The aim of this work is to develop spherically symmetric effective potentials allowing bulk thermodynamic properties and surface tension of molecular fluids to be predicted semiempirically by the use of statistical mechanical methods. Application is made to the straight chain alkane fluids from methane to decane. An effective Lennard-Jones potential is generated with temperature-dependent parameters fitted to the critical temperature and pressure and to Pitzer's acentric factor. Insertion of this potential into the generalised van der Waals (GvdW) density functional theory yields bulk properties in good agreement with experiments. The surface tension is overestimated for the longer alkane chains. In order to account for the surface tension, an independently adjustable attractive range of interaction is required and obtained through the use of square-well potentials chosen so as to leave the bulk thermodynamics unaltered while the attractive range is fitted to the surface tension at a single temperature. The GvdW theory, which includes binding energy, entropic and profile shape contributions, then generates surface tension estimates that are of good accuracy over the full range of available experimental data. It appears that, given a sufficiently flexible form, effective potentials combined with simple statistical mechanical theory can reproduce both bulk and non-uniform fluid data of great variety in an insighful and practically useful way.     

Separable unimolecular reaction rate theory

A new unimolecular reaction rate theory is derived on the basis of a classical model of the reaction. The fundamental assumptions are (i) instantaneous activation-deactivation events represented by a statistical transition probability, (ii) irreversible dissociation, and (iii) separability of internal and external dynamics. The third assumption is found to be satisfied when the statistical transition probability satisfies a generalized strong collision assumption and it leads to a rate theory which depends on internal molecular dynamics only through lifetime information for the isolated molecule. The new theory shows that the rate coefficient is non-Markoffian although the memory effects will not be apparent on the macroscopic time scales of traditional experiments. Thus Slater's “new approach to rate theory” is a special case of the separable rate theory when applied to slow reactions. New experimental techniques are predicted to have the capacity to resolve the memory effects in the rate coefficient and provide lifetime information which would then allow greatly improved accuracy in the prediction of rates for a wide range of unimolecular reactions.     

Numerical study of the effects of constitutive models on plastic buckling of plate elements

Compared with experiments, the J₂ deformation theory of plasticity is known to predict plastic buckling with better accuracy than the more accepted incremental J₂ flow theory. This paradox is commonly known as the ‘plastic buckling paradox’. In an attempt to analyse this discrepancy, the two mentioned constitutive models were implemented in a non-linear finite element code, along with a third non-associative J₂ flow theory. The latter model incorporates a vertex-type plastic flow rule. Using these three constitutive models, the buckling behaviour of plate outstand elements was investigated. Comparisons between the buckling strengths derived are presented. The non-linear static buckling simulations show that the instability introduced by the alternative flow rule of the non-associative model has substantial influence on the buckling behaviour. The acceptance of only small departures from normality was shown to reduce the predicted ultimate capacity of the plates. Furthermore, for plates with small plate slendernesses it was found that the imperfection sensitivity was significantly reduced when using the non-associative flow rule.     

Ergodic collision theory of intermolecular energy transfer

We present a simple theory of collisional energy transfer between molecules based on the assumption of ergodic collisions, i.e., the final state distri     

An efficient solution of weak-collision master equations in thermal unimolecular reaction rate theory

A new finite-basis-set method of solving the weak-collision master equation of thermal unimolecular reactions in the general pressure regime is presented. Consecutive sections of the equilibrium probability density are used as basis functions. Significant advantages in terms of efficiency and applicability are obtained. Representative calculations are performed to illustrate the method's convergence properties and storage requirements. Calculations of collisional efficiency factors in the low-pressure limit β₀ and weak-collision broadening factors F^WC(ω) are performed to offer a simple concise representation of weak-collision effects. It is noted that weak-collision effects can be incorporated into fall-off curves with an accuracy of within an order of magnitude by simple scaling of the strong-collision fall-off curves. However, for accurate representation of weak-collision effects the weak-collision broadening must be taken into account.     

Ground-state inversion method applied to calculation of molecular photoionization cross-sections by atomic extrapolation: Interference effects at low energies

The ground-state inversion method, which we have previously developed for the calculation of atomic cross-sections [ 29 ], is applied to the calculation of molecular photoionization cross-sections. These are obtained as a weighted sum of atomic subshell cross-sections plus multi-centre interference terms. The atomic cross-sections are calculated directly for the atomic functions which when summed over centre and symmetry yield the molecular orbital wave function. The use of the ground-state inversion method for this allows the effect of the molecular environment on the atomic cross-sections to be calculated. Multi-centre terms are estimated on the basis of an effective plane-wave expression for this contribution to the total cross-section. Finally the method is applied to the range of photon energies from 0 to 44 eV where atomic extrapolation procedures have not previously been tested. Results obtained for H₂, N₂ and CO show good agreement with experiment, particularly when interference effects and effects of the molecular environment on the atomic cross-sections are included. The accuracy is very much better than that of previous plane-wave and orthogonalized plane-wave methods, and can stand comparison with that of recent more sophisticated approaches. It is a feature of the method that calculation of cross-sections either of atoms or of large molecules requires very little computer time, provided that good quality wave functions are available, and it is then of considerable potential practical interest for photoelectron spectroscopy.     

Strong collision rate coefficients in unimolecular reaction rate theory

The traditional and a recently proposed renormalized approximation to the rate coefficient obtained from a strong collision master equation are derived and compared. It is shown that they deviate significantly when applied to the unimolecular reactions of large molecules with low activation energies at elevated temperatures. The derivation is extended to yield a method whereby the exact rate coefficient can be calculated without increasing the level of numerical effort. An analysis of the exact rate coefficient in the high and low collision frequency limits is found to verify the validity of the traditional approximate rate coefficient in these limits. The renormalized rate coefficient fails in the low frequency limit. Both approximations can be significantly in error at intermediate collision frequencies and the use of the exact expression is recommended.     

Unimolecular activation–deactivation: Impulsive collision theory

A theory of collisional energy transfer based on microcanonical relaxation in the limit of infinitesimal collision lifetimes is developed. In distinction to the recently formulated ergodic collision theory the potential energy is now frozen due to the short time scale, and only kinetic energy is available for redistribution. As a consequence, the rate of energy transfer is decreased, and agreement with experimentally based estimates generally improved.     

The use of computed tomography in non-destructive testing of polymeric materials, aluminium and concrete: Part 1—basic principles

In 1895 Wilhelm C. Röntgen discovered the X-ray as an important instrument for medical diagnosis. During the first 50 years of the 20th century X-ray technology developed slowly. It is only within the last decade that growth in imaging technology in the range of techniques available has been rapid. In the 1970s computed tomography (CT) was discovered by Cormack^1,2 and Hounsfield³. This article describes the principal differences between X-radiography and computed tomography.     

Dispersion of carbon black

Satisfactory dispersion of the carbon black is essential to the production of rubber compounds possessing the maximum possible resistance to wear, tensile strength and abrasion resistance. The methods used to measure/estimate the degree of dispersion are reviewed in this paper.Most current methods are based on some form of microscopy. Light microscopy (at small magnifications) of cryomicrotomed rubber specimens in transmitted light is used to some extent. However, the preparation of the specimen is too time-consuming to warrant the use of the method for routine inspection. This has led to the development of an instrument—the Dispergator—which employs split field microscopy of freshly-cut samples to reduce the total time of testing (including the time required for specimen preparation) to about 1 min.