## Averaging Measurements with Many Drops and Many Liquids

The Fta32 software provides databases to store test liquid parameters, contact angle measurements, and surface energy method results. These are arranged in a flexible way so that contact angle data can be re-used many times in different sets or with different surface energy methods. The databases are standard Access 97 databases so the information in them can be captured by other Windows programs and used as you wish.

The general method of using the calculator in the software is to

Measure one or more contact angles with a liquid described in the Liquids.mdb database. You can easily add entries to this database if you use a liquid not already in it.

Transfer the contact angle data to the Angles table of the Solids.mdb database. You can do this by point-and-click or by typing the value in the Angles table. The parameters of the liquid you used will already have been transferred, or you can manually transfer liquid parameters by another mouse point-and-click.

Once you have your contact angles, open a new row in the Energies table of the Solids.mdb. Again by mouse clicks, you can associate as many contact angles (which are rows in the Angles table) to this surface energy calculation. Finally, assign one of the surface energy methods to the row and click Calc. The calculated surface energy values will be displayed and entered into the Energies row. You can have as many different Energies rows as you wish, each looking at the data in a different way. All results are saved in the Solids.mdb database.

The software will automatically do the following for you:

If there are more than one contact angle data for the same liquid, the angles will be averaged before the surface energy calculation is made. This averaging, of course, is only for the angles you selected into the Energies row being calculated.

If there are too many different liquids for the selected method, a regression is performed to get the best overall answer using the liquids you chose. For example, the Owens-Wendt method requires two different liquids. If you provide contact angles from three or more different liquids, the regression provides the best answer over the entire set. This is called an "over-determined" set of equations.

Over-determined equations are robust chemically, you are probing the surface with a number of differing chemistries, but are not robust numerically. This means in general there will not be a "perfect" solution to the equations. Therefore the "residual," the remaining RMS error, is reported to guide you as to how good the answer, or fit, was. The residual is reported in units of mN/m, just as any other surface tension or surface energy value. As a rule of thumb, residuals less than 1.0 are good and those above, say, 5.0 indicate a very poor fit. Over-determined equations were added in Build 154.