Journal of Adhesion Science and Technology, Vol.23, No.6, 799-813, 2009
Influence of Erroneous Data on the Results of Calculations From Acid-Base Surface Free Energy Theories. III. Solution of a Three-Equation Set in the Case of Homoscedastic Error
The van Oss-Chaudhury-Good theory (vOCGT) was checked for a large artificial set of 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 in each. Also numerical values of LW component and A and B parameters were assigned to 300 liquids (three sets of 100 liquids in each). Data for these solids and liquids were especially selected to represent real types of materials encountered in practice. For all 15 solids and 300 liquids the work of adhesion values 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 (A vector of random variables is homoscedastic if it has the same finite variance.) of the 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 error level. Two different methods for the solution of a 3-equation set were used and they gave practically the same results irrespective of the error level and liquids and solids used. 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 a correlation coefficient higher than 0.999) and was true separately for LW component, A and B parameters as well as for the total solution vector (i.e., combinedly for the LW component, A and B parameters). The RMSE values of the total solution vector (having as elements values of the LW component, A and B parameters) as well as separately for LW component and A and B parameters were correlated with the condition number of a given 3-equation set. A very good correlation was found only for the total solution, much worse for A or B parameters, and practically there was a lack of correlation for 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 if the calculated value of a given LW component or A or B parameter did not differ by more than 1 mJ/m(2) from an error-free (true) value. (C) Koninklijke Brill NV, Leiden, 2009