228 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 4 



A 



pj. 



C 



4-42. Vibrating Capacitor 



The surface potential or contact potential 1 between two electrodes 

 varies with the chemical and physical structure of the electrode 

 surfaces; the observation of the variations of the potential of an 

 electrode versus that of a constant-reference electrode can furnish 

 information of a chemical or physical process taking place at the 



-\ surface. Surface layers are some- 

 times vulnerable, so that meas- 

 urements of the contact potential 

 must be carried out without 

 touching the surface. 



A system suitable to measure 

 such potential differences was 

 first described by Zisman 2 and is 

 illustrated in Fig. (4-4)3. It con- 

 sists of two electrodes A and B 

 which together form a capacitor 

 C . The surface of one electrode 



M 



B 



^ 



^ 



R\ 



Hsy 



■►WWvVS 



Fig. (4-4)3. Vibrating capacitor: C, 

 capacitor; A, fixed, and B, vibrating 

 electrode driven by motor M; excursion 

 of the vibrating electrode is 25. 



may be altered by applying the 

 material to be investigated to it. 

 If E c is the potential difference between the electrode surfaces, Q = 

 C E C is the charge of the capacitor. Any change of capacitance 

 will cause a current (neglecting R) of 



• dQ F 



l= Tt =E < 



dC« + c dE c 



dt 



dt 



(1) 



Under steady-state condition (E c = constant), the second term in 

 Eq. (1) vanishes. 



A driving mechanism M causes one electrode to oscillate with a 

 frequency/ (angular velocity co = 2tt/) by an amount ±d about its 

 middle position. If d is small compared to the average distance d, 

 the capacitance can be expressed by 



and the current is 



C = C Q I 1 — - sin cot 



■E c coC - cos cot 

 d 



1 For nomenclature see A. A. Frost, Rev. Sci. Instr., 17, 266 (1946). 



2 W. A. Zisman, Rev. Sci. Instr., 3, 367 (1932). 



