Bernal’s road to random packing and the structure of liquids

Abstract

Until the 1960s, liquids were generally regarded as either dense gases or disordered solids, and theoretical attempts at understanding their structures and properties were largely based on those concepts. Bernal, himself a crystallographer, was unhappy with either approach, preferring to regard simple liquids as ‘homogeneous, coherent and essentially irregular assemblages of molecules containing no crystalline regions’. He set about realizing this conceptual model through a detailed examination of the structures and properties of random packings of spheres. In order to test the relevance of the model to real liquids, ways had to be found to realize and characterize random packings. This was at a time when computing was slow and in its infancy, so he and his collaborators set about building models in the laboratory, and examining aspects of their structures in order to characterize them in ways which would enable comparison with the properties of real liquids. Some of the imaginative – often time consuming and frustrating – routes followed are described, as well the comparisons made with the properties of simple liquids. With the increase of the power of computers in the 1960s, computational approaches became increasingly exploited in random packing studies. This enabled the use of packing concepts, and the tools developed to characterize them, in understanding systems as diverse as metallic glasses, crystal–liquid interfaces, protein structures, enzyme–substrate interactions and the distribution of galaxies, as well as their exploitation in, for example, oil extraction, understanding chromatographic separation columns, and packed beds in industrial processes.

Keywords:

• liquid structure
• random packing
• Voronoi polyhedra

Acknowledgements

Bernal’s laboratory work was made possible by the imagination and expertise of the members of the liquids team that Bernal assembled over a period of perhaps three decades. In alphabetical order these unsung heroes include G. Atkinson, I.A. Cherry, S. King, K.R. Knight, K.P.N. Kutty, J. Mason and J. Wilkinson. I am also much indebted to the late John Ziman for discussions and inspiration – not all of which had to do with liquid state physics.