Approaches to determine the surface tension of small particles: Equation-of-state considerations |
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| Authors: | R P Smith D R Absolom J K Spelt A W Neumann |
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| Institution: | 1. State Key Laboratory of Separation Membranes and Membrane Processes, School of Environment and Chemical Engineering, Tianjin Polytechnic University, 399 Binshui West Road, Tianjin 300387, P. R. China;2. State Key Laboratory of Inorganic Synthesis and Preparative Chemistry, College of Chemistry, Jilin University, Changchun 130012, P. R. China;3. Tianjin International Joint Research Centre of Surface Technology for Energy Storage Materials, College of Physics and Materials Science, Tianjin Normal University, Tianjin 300387, P. R. China |
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| Abstract: | The primary purpose of this paper is a clarification of the question how sensitive five approaches to the determination of solid surface tensions are to the form of the equation of state for interfacial tensions, which is used in the interpretation of the experimental results. The five approaches are (1) adhesion, (2) phagocytosis, (3) sedimentation volumes, (4) solidification front, and (5) contact angles. Three equation-of-state-type relations, i.e., that due to Neumann et al., the unmodified Good equation, and Antonow's rule, are considered. The first three techniques depend on thermodynamic models in a way that requires of the equation of state only symmetry, γ12 = f(γ1v, γ2v) = f(γ2v, γ1v), and zero as the minimum interfacial tension, γ12 = f(γ1v, γ2v) = 0 when γ1v = γ2v. All three equations (and many similar ones, which one might consider) satisfy these requirements and hence produce identical results. In other words, the validity of these three techniques and the results which they produce are not sensitive to details of the equation of state used. The last two techniques, the solidification front technique and the contact angle method, present more stringent requirements for the equation-of-state relation used. The solidification front technique eliminates Antonow's rule from further consideration because of this equation's intrinsic inability to predict particle rejection by advancing solidification fronts, a frequent experimental observation. This technique also eliminates those equation-of-state relations which violate the minimum interfacial tension condition. Finally, the contact angle technique is the most discriminating tool with which to study the merit of equation-of-state relations. Of the relations considered here, only that due to Neumann et al. yields, in conjunction with contact angle data, values for the solid surface tension which are in agreement with those obtained from the other techniques. |
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