Compressibility, the measurement of surface tension, and particle size in molecular or nuclear matter

It is shown that the interface shrinkage resulting from the capillary pressure difference between both sides of a curved interface is the product of a "standard shrinkage" kappa gamma (kappa is the isothermal compressibility, gamma the interfacial tension) by a dimensionless factor that depends only on the shape of the sample of matter under study. The behaviour of the standard shrinkage in the critical domain shows that it cannot be a measure of the thickness of the liquid-vapour interface in that domain. The standard shrinkage of classical liquids somewhat above triple point is usually near to 0.048v(c)(1/3) (v(c) is the critical molecular volume); exceptions to this rule are discussed. The variation of the standard shrinkage along the liquid-vapour coexistence curves of water and argon is presented; the effect of the interface shrinkage on the measured surface tension of liquids can become important within about 15% of the critical temperature. The standard shrinkage of solids is less than that of the corresponding liquids, and is of no consequence when measuring the surface tension of solids. The standard shrinkage of the nuclear fluid is 0.23 fm = 0.09v(c)(1/3). The saturation density of infinite nuclear matter is about 9% less than its value in atomic nuclei, and a term proportional to A(1/3) (A is the mass number) must be added to the nuclear binding energy formula. (c) 2005 Published by Elsevier Inc.