Sensitive Absorption Spectrophotometry for Electrochemical Studies by a Continuous Specular Reflection Technique David
C. Walker
Chemistry Department, Uniuersity of British Columbia, Vancouver, Canada This paper describes a technique developed to distinguish by absorption spectrophotometry the possible precursors of hydrogen in the hydrogen electrode reaction. The technique involves directing a light beam from a continuous gas laser around a long, curved, polished, silver electrode surface so that the beam makes innumerable minute specular reflections. Small changes in the attenuation of the light during electrolysis are amplified by tuning the detector to the frequency of the a.c. field applied to the silver cathode. Attenuation of the light has been attributed to an absorbing species near the electrode surface and a calculation of the molar absorptivity, based on the equivalent optical cell, gives a lower limit which i s consistent with the species being the hydrated electron. The equivalent optical cell can be represented by the relationship I(abs)/lo= C Y C and ~ is not restricted to (YCZ> A so that Figure 3a is exaggerated and Figure 3b is even more so. The latter, however, permits an evaluation of b, the absorption path length of a ray initially distance x from the surface. In Figure 3b if U X represents such a ray, then X W j X Z represents the fraction of time within the absorbing region. From the congruent triangles X V W and X Z Y it follows, to a good approximation for x > 2X, that X W j X Z = X V . X Y / X Z 2 . Because X V = A, X Y = R , YZ = R - x and x 2X, b = IXj2x. [For x < X (representing the fraction X/r of the whole beam) b = I and for X < x < 2X (also representing the fraction Xjr) b 0.71.1 We can thus sketch an optical cell which is equivalent to the absorption path of the spiralling laser beam. This is shown in Figure 4. For any ray of infinitesimal thickness, dx, and absorption path length, 6, we can assume Beer's law to hold, I t = Zo104Cb, SO that I z (total) can be evaluated by integrating over the beam from x = 2X to x = r a n d adding the approximate correction 1.5 Zo(X~r)lO-acz for x < 2X. Thus
-
Ir
Zldx = Z,
L:
1 0 - u c x ~ ~dx 2z
+ 1.5 Io(X/r)lO-"c~
VOL. 39, NO. 8, JULY 1967
899
r
1.0
b Figure 5. Plot of loba/' against x for (I) a = 10-5,(11)a = 10-4, and (111) a = 2 X 10-4cm Area A is lightly shaded, area B is entire area below the u = lo-' cm line, area C is heavily shaded (The probable position of 2X is indicated for a =
10-4cm)
0.6
IO-Vx
L
0.2
. .
0
or
Thus we have established the relationship given in Equation
AI/I,, = 1
-J
10-a'Zdx
'
- 1.5 (X/r)
2h
4.
(3)
where AI = total intensity absorbed and a = crcX1/2 in Equation 3. The integral of Equation 3 can be transformed into the differenceof two Placzek Functions (8).
Lrn
,,-+-2.3
ay/Tdy
-
Lrn
z-1,-2.3aZ/2hdZ
and can be evaluated analytically for various values of a. Alternatively it is perhaps more informative to evaluate the integral of Equation 3 graphically. Thus lo-"/" is plotted against x from 0 to r in Figure 5 for values of a = 10-6, a = 10-4,and u = 2 X 10-4 cm (a probably being of this order of magnitude, although any value of u could be used). [N.B. r has a value of approximately 1 mm-about half the diameter of the laser beam.] For reasons presented previously (Z), based on the known reactivity and diffusion constant of e,, one would expect X to be about lo-' cm for e-*,. Thus Figure 5 marks the expected lower limit of the integral, 2X, for a = cm. It is evident then that the correction term for x < 2X is going to be small (it is not shown in Figure 5). At x = 2X b = 114 but changes rapidly to b = I as x 4 X and then remains constant as x + 0. Thus part of the dark shaded area C corresponds to transmitted light, and indeed, area C and the area given by l,5(X/r)10-~c'will be of comparable magnitudes and thus largely cancel each other. Furtherwhereas AZ/Io ,., the more, since X/r is probably corrections for x < 2h cannot be large and we can write
