bonded network of water, attached ion, and counter ion. Water added to a resin containing large amounts of water goes primarily into a water-like environment and therefore does not change the correlation time or relaxation time significantly. This work shows that the relaxation properties of ion exchange resins can be studied easily by pulsed NMR techniques, and that the relaxation times give information on the molecular structure of the resins.
distortion of electric field gradients around the Z3Na nucleus and improving the quadrupolar coupling. From the data, it is not possible to decide whether change in the correlation time or in the quadrupole coupling constant is more important in the relaxation mechanism. CONCLUSIONS
Relaxation times for both water protons and 2aNacounter ions indicate that their environment is independent of crosslinking for water contents below 6 water molecules per ion exchange site. This environment has an increased correlation time, indicating a structure which becomes more rigid as the water content decreases. This model is in agreement with that proposed by Zundel (Z6), who postulates a hydrogen-
ACKNOWLEDGMENT
Thanks are extended to M. Schwartz for assistance with the spectrometer and signal averaging system. RECEIVED for review August 30, 1971. Accepted January 6, 1972. This work was supported in part by Grant AT(11-1)1082, from the Atomic Energy Commission.
~
(16) G. Zundel, “Hydration and Intermolecular Interactions,” Academic Press, New York, N.Y., 1969.
Self-Balancing Bridge for Differential Capacitance Measurements Dale H. Chidester and Ronald R. Schroeder Department of Chemistry, Wayne State Unicersity, Detroit, Mich. A self-balancing capacitance bridge has been designed and constructed utilizing electromechanical servo control of a capacitance multiplier to achieve balance. Using a 60-Hz signal of less than 10 mV peak to peak, capacitances in the range of 0.25 to 2.0 mF can be measured with a precision of +l%. Differential capacitance measurements of mercury electrodes were made using aqueous solutions of several different electrolytes and were compared with data found in the literature. A study of the adsorption of camphor at a hanging mercury drop electrode was conducted to confirm the instrument’s ability to function in systems with strongly adsorbed species.
To DATE, BRIDGE TECHNIQUES for measuring differential capacitance of mercury electrodes have been tedious and slow. Most work has been based on the techniques developed by Grahame (Z-3). Accuracy in such measurements depends on measuring the time at which a null of a capacitance bridge is achieved. The goal of this work has been to develop an automated bridge which can obtain continuous capacitance data as a function of time. THEORY OF OPERATION
A major difficulty in automating a capacitance bridge has been the lack of variable capacitors in the microfarad range and the further lack of a simple method of varying capacitance over even one order of magnitude in the microfarad region. The availability of good quality operational amplifiers has now simplified this problem and made possible the construction of capacitance multipliers which can operate over a decade range with values in the one microfarad region. Balance of the bridge is maintained by adjustment of the capacitance multiplier with an electromechanical servo system. The signal to control the servo is obtained by compar(1) D. C. Grahame, J. Amer. Chem. SOC.,63, 1207 (1941). (2) Zbid., 68, 301 (1946). (3) Zbid., 71, 2975 (1949).
ing the phase of the cell and reference signals, E, and E,, with a demodulator circuit. Figure 1 provides an overall block diagram of the instrument. The Bridge. The heart of this instrument is a modified Wien bridge circuit, one arm of which contains an electrolysis cell and the other arm contains a capacitance multiplier circuit. The condition for bridge balance (Figure l a ) is that the reference signal, E,, equals the cell signal, E,, in both amplitude and phase. Since the C,, R,, and C, portion of the circuit is electrically identical to a resistor and capacitor in series, the series resistances add algebraically, the bridge circuit can be represented by the circuit Figure l b where
and (3
From this circuit
+ + +
+
E, - 1 - RljwCz RARI R W C z 2 - 1 (R1 Rt)’m2Cz2 Es
(4)
and
+
+
E, R,(Rz R,)w2Cm2 - 1 - R2jwC, 1 (RP R,)2~2Cm2
E8
+
+
(5)
In the actual circuit R1 = RBIR 3 = R 4 , and R, and Rd are typically less than 100 ohms so R ,
