Solid surface tension components and their error limits induced by contact angle measurement in application of the van Oss–Chaudhury–Good approach

Abstract

The square roots of solid surface tension components/solid surface tension components (SQSSTCs/SSTCs) and their error limits, that is, maximum absolute errors (MAEs) and maximum relative errors (MREs) obtained from the van Oss–Chaudhury–Good (vOCG) approach were evaluated for various liquid triplets. The parameters were considered as functions of contact angles and the errors thereof. The valid domain of contact angles was defined from the physical nature of the problem as a domain composed of contact angles leading to positive LW SQSSTC and non-negative AB SQSSTCs. A sufficient broad common range of SQSSTCs/SSTCs determinable by various liquid triplets assures the validity of the vOCG approach. On the valid domain, both MAEs and MREs depend on contact angles, so the vOCG approach estimates different SSTCs at different accuracy with a given triplet. Using the smallest condition number triplets, most SSTCs can be evaluated at reasonable accuracy under the assumption of Δθi = 1° (i = 1, 2, 3). The SQSSTCs/SSTCs are monotone functions of contact angles of each contact angle provided the other two are kept fixed and the MRE in each SQSSTC/SSTC increases monotonically with a decreasing parameter. The opposite monotonicity of SQSSTCs/SSTCs and their MREs reveals the underlying reasons for disputable problems in application of the vOCG approach, for example, negative SQSSTCs. A comparison between the ranges of SQSSTCs/SSTCs and the valid domains of contact angles of diverse liquid triplets explains the general cause of liquid selection criteria.