# Free Surface Energy and Hansen Solubility Parameter Vector Field. Interface Thickness
## 4 Conclusions  
The Hansen vector field model established in this paper allows us, among other things:1. To link, for the first time, the cohesion energy of substances with their free surface energy, as surface or interfacial tension. 2. To calculate the surface tension and free energy of thousands of substances by knowing their Hansen solubility parameters, which are easily obtained from the molecular structure of substances. Likewise, it is possible to determine the interfacial tension between them with a simple vector calculation. 3. To theoretically calculate and accurately estimate contact angles that would, in many cases, be hard to experimentally determine. This vector field model saves experimental work and time. Furthermore, this model allows us to empirically prove that the interface between two substances is not a mathematical surface with no thickness (as suggested by the [PERSON] hypothesis), but indeed has a small-scale thickness, as proposed by [PERSON]. The said thickness is approximately half of the Bohr radius. Further research is needed to explore the application of the Hansen vector space for other interactions such as polymer swelling, the chemical resistance of coatings, cracking, suspension stability, covering penetration, biological membrane penetration, absorption, adsorption, etc. Formal analysis, R.B.-M.; investigation, R.B.-M. and A.S.A.A. ; methodology, R.B.-M. and A.S.A.A. ; resources, R.B.-M. and A.S.A.A. ; visualization, R.B.-M. and M.A.B.-R.; writing--original draft, R.B.-M. and M.A.B.-R.; writing--review and editing, R.B.-M., M.A.B.-R. and A.S.A.A. All authors have read and agreed to the published version of the manuscript. This research received no external funding. This article does not contain any studies with human participants or animals performed by any authors. Not applicable. Data Availability Statement: The data that support the findings of this study will be available in the cited references. This work has been carried out as part of the research of the doctoral thesis of [PERSON], directed by [PERSON]. The doctoral thesis belongs to the Doctoral Program in Chemistry of the University of Granada (codes ISCED 1 Chemistry and ISCED 2 Physical, Chemical, Geological Sciences). Escuela Internacional de Postgrado of Universidad de Granada. The authors declare no conflicts of interest. The \"Ref\" column indicates the origin of the surface tension data. When Ref is 1, it means that the data have been directly measured by the authors using the Harkins and Brown droplet weight method. When Ref is 2, it indicates that the data have been published by [10]. In some cases, surface tension data of the same substance, with Ref = 1 and Ref = 2 are shown in order to test the (always small) variability in both references. Moreover, the [PERSON] solubility parameters are included according to the values published in the second edition of his manual [5]. Likewise, the calculated squares of interaction vectors like 4\(d_{D}\)\({}^{2}\) + \(d_{P}\)\({}^{2}\), the surface tensions calculated after linear regression and the absolute error between the calculated and experimental or bibliographic values are shown. When Ref is 1, it means that the surface tension values have been determined in a laboratory by the authors using the Harkins and Brown droplet weight method. The data with Ref = 2 are provided by [10], those with Ref = 3 are taken from [21], and those with Ref = 4 are from [22]. The solubility parameters data obtained by [5] are also shown. The calculated surface tension and absolute error with regard to the experimental or bibliographic values are also shown.