Influence of Erroneous Data on the Results of Calculations From Acid-Base Surface Free Energy Theories. IV. Solution of an Overdetermined Set in the Case of Homoscedastic Error

The van Oss-Chaudhury-Good theory (vOCGT) was checked for a large artificial set of the work of adhesion input data calculated for 15 solids and 300 liquids. Numerical values of LW component and acid (A) and base (B) parameters were assigned to 15 solids. These 15 solids were grouped in 5 sets of 3 solids each. Also numerical values of LW component and A and B parameters were assigned to 300 liquids (three sets of 100 liquids each). Data for these solids and liquids were especially selected to present real types of materials encountered in practice. For all 15 solids and 300 liquids the values of the work of adhesion were calculated and these values were assumed to be error-free. Next, new values of the work of adhesion were obtained by adding a random homoscedastic error of normal distribution (also called the Gaussian distribution - it is continuous probability distribution defined by two parameters: the mean and variance (standard deviation squared, sigma(2))) belonging to 8 distributions of a mean value equal to the error-free work of adhesion value and standard deviations of 0.5, 1, 2, 5, 7, 10, 15 and 20 mJ/m(2). The LW components and A and B parameters for these solids were back-calculated for each solid and error level. Liquids were grouped in sets of 10 liquids and overdetermined set of equations was solved for the 3 solids. It was found, that there existed a linear correlation between the RMSE (root mean square error) of the solution and the standard deviation of the work of adhesion data. This correlation was highly significant (with correlation coefficient higher than 0.9998) and existed separately for LW component, A and B parameters as well as for the total solution vector. The RMSE values of the total solution as well as separately for LW component and A and B parameters were correlated with the condition number of a given 10-equation overdetermined set. A very good correlation was found only for the total solution and worse for A parameter, and practically there was no correlation for B parameter and the LW component. Based on the correlation between the RMSE and the standard deviation of the work of adhesion it was possible to determine what should have been the maximal standard deviation of the work of adhesion when a calculated value of a given LW component or A or B parameter differed no more than 1 mJ/m(2) from an error-free (true) value. (C) Koninklijke Brill NV, Leiden, 2009