the base line is considerably improved, and finally a differential pulse voltammogram synchronized to a DME in which the dc contribution is not important. Charging Current Due to Pulse Application. The current required to charge the double layer after the sudden rise in potential caused by the application of the pulse is given by ( 3 ) :
where R is the cell resistance, C is the double layer capacitance, and t is the time after the pulse was applied. This current decays rapidly to zero, so that if the pulse period is sufficiently long, this component will be negligible. If we assume C = 4 MF,R = 1 K, AE = 25 mV, and t = 40 msec, then ic,pulse = 1 PA. Under normal conditions, the double layer capacitance current arising from the pulse application can be ignored. The need for sufficiently long pulses to minimize ic,pulse limits the scan rates used in this technique. A reasonable compromise between fast scan rates and sufficient points on the potential-current curve enabled us to use potential scan rates of up to 200 mVlsec.
CONCLUSIONS Fast sweep differential pulse voltammetry at a DME has much to recommend itself as an analytical technique by being able to combine the dual advantages of speed (&)
dx
258
initial sweep potential (volts)
ACKNOWLEDGMENT Stimulating discussions with James F. Leathrum are gratefully acknowledged.
APPENDIX
where B ( x ) is the probability density function of x . 4) Superscript -1 indicates matrix inversion. 5) Superscript T indicates matrix transposition. For equations pertaining to the models of the electrochemical systems, the following notation holds: i = current (amperes) n 3 equivalents/mol A 3 electrode area (cm2) D =diffusion coefficient (cm2/sec) u = sweep rate (V/sec)
radius of HMDE (cm)
t =time (sec) f' activity coefficient (M-1)
RECEIVEDfor review March 14, 1975. Accepted October 27, 1975. Presented in part at the 168th National Meeting, American Chemical Society, Atlantic City, N.J., September 1974. This work was supported by the University of Delaware Research Foundation.
ANALYTICAL CHEMISTRY, VOL. 48, NO. 2, FEBRUARY 1976
