Introduction

There is a convenient mathematical idealization which asserts that a cube of edge length, ℓ cm, possesses a surface area of 6ℓ2 cm2 and that a sphere of radius r cm exhibits 4πr2 cm2 of surface. In reality, however, mathematical, perfect or ideal geometric forms are unattainable since under microscopic examinations all real surfaces exhibit flaws. For example, if a ‘super microscope’ were available one would observe surface roughness due not only to voids, pores, steps, and other surface imperfections but also due to the atomic or molecular orbitals at the surface. These surface irregularities will always create a real surface area greater than the corresponding theoretical area.