The quartz crystal microbalance; radial/polar dependence of mass sensitivity both on and off the electrodes

The response of AT-cut quartz crystal microbalances is analysed theoretically to show how mass sensitivity varies over the electroded and bare quartz areas. Analytical solutions are presented for the radial and polar dependence of mass sensitivity as a function of the electrode areal density for both planar and plano-convex crystals. In many surface science applications it is desirable to minimise the off-electrode sensitivity of the QCM, so as to make the fractional on-electrode response as close to unity as possible. This fractional response is shown to increase with the electrode mass, but to be in the range 0.90 to 0.94 for the planar crystals in common use. On the other hand, for plano-convex crystals this response readily exceeds 0.99. To check the accuracy of the calculations a simple method has been devised to deposit small dots of well defined mass at points on the crystal surface. These measurements show that the derived expressions for mass sensitivity are correct to within the measurement accuracy. The dots are deposited using a permanent marker pen giving a mass per dot of 0.21 mu g. After measurement, the dots are readily removed by solvent washing leaving the crystal calibrated and ready for other studies.