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Integral equation theory applied to polar molecular fluids


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Fraser, KJ 1986 , 'Integral equation theory applied to polar molecular fluids', PhD thesis, University of Tasmania.

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This thesis is an examination of the application of integral
equation theory to the study of polar molecular liquids. The integral
equation used as the basis for this work is the site-site OrnsteinZernike
(SSOZ) equation coupled with the hypernetted chain (HNC)
approximation as the closure. The numerical solution of the SSOZ
equation using Gillan's method is examined in detail, and in
particular for liquid systems with Coulombic interactions. A method is
presented for the symmetry reduction of the Jacobian matrix to
facilitate the numerical solution for larger molecular systems. This
method is not based on the individual analytic reduction of the matrix
integral equation for molecules of particular symmetries, but is a
simple procedure within the numerical solution algorithm itself. This
allows its general use for molecules of arbitrary symmetry.
It is demonstrated analytically for a non-linear triatomic model
with charges on the end sites, that the SSOZ-HNC equation effectively
decouples, with the decoupling being dependent on the difference
between the multiplicative and additive means of the radial
distribution functions involving only charged sites. This decoupling
has the consequence that the structural effe~ts due to the dipolar
interactions cancel each other out. This results in the dipolar
interactions having little or no effect on the calculated structure
The numerical solution to the SSOZ-HNC equation is obtained for a
series of hard and soft sphere, non-linear, dipolar, triatomic models.
The results obtained show that the dipolar interactions have a very
significant effect on the liquid structure but that this is not
reflected in the corresponding structure factor due to the effective
decoupling of the integral equation.
This effective decoupling phenomenon is predicted to apply to a
range of dipolar molecular liquids. To test this, the SSOZ-HNC
equation is solved for an interaction site potential model for the
highly dipolar, but non-hydrogen bonded liquid, acetonitrile. The
radial distribution functions obtained show that the dipolar
interactions have a significant effect on the liquid structure.
However, as predicted, there is very little effect on the calculated
scattering function. Also, there is very good agreement between the
calculated and experimental neutron scattering, coherent differential
cross section. Comparison of the SSOZ-HNC radial distribution
functions and internal energies with molecular dynamics simulation
results from the literature f~r the same potential showed overall,
very good agreement. From these results, it was also concluded that
there are two dominant, nearest neighbour orientations in liquid
acetonitrile due to the dipolar interactions.

Item Type: Thesis - PhD
Authors/Creators:Fraser, KJ
Keywords: polar molecular fluids
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