Free Surface Energy and Hansen Solubility Parameter Vector Field. Interface Thickness

In this paper, a three-dimensional vector field model is proposed, whose dimensions are the Hansen Solubility Parameters: dispersion parameter (δD), polarity parameter (δP), and hydrogen bonding parameter (δH). The vector space that defines the field has the peculiarity of having a dispersion vector with a magnitude of 2 as its base vector, while the polarity and hydrogen bonding vectors have a magnitude of 1. A substance is characterised as a position vector, and the interaction between two substances is determined by calculating the vector difference of both, known as the interaction vector. The interaction among substances may involve solubility, swelling, cracking, surface tension, interface tension, and any physical phenomena where the intermolecular energies of dispersion, polarity or hydrogen bonding come into play. This paper studies free surface energy (surface and interfacial tension). It has been found that free surface energy is directly proportional to the square of the magnitude of the interaction vector. The proportionality constant, τ, is expressed in length units, has a value of 0.025 nm, and does not depend on the chemical nature of the substance or state of matter (solid, liquid or gas). The constant value τ appears universal and aligns with the thickness of interfaces, thereby supporting Guggenheim’s hypothesis. This hypothesis asserts that interfaces possess actual thickness and are not merely mathematical surfaces, as originally postulated by Gibbs. Moreover, it also has been found that the interface thickness, τ, is approximately equal to half of the Bohr radius, a0, which is defined by universal constants. Because the solubility parameters of thousands of substances are known and can be easily determined from their molecular structure, a good approximation of the surface and interfacial tension of any given substance can now be calculated. It has also been found that the contact angles of sessile droplets in three-phased systems can be calculated from the interaction vectors of the implicated substances.