Kinetic Control by Chemical Step at an AdsorptionBlocked Electrode Surface MUTSUO KODAMA and ROYCE W. MURRAY Department o f Chemistry, University of North Carolina, Chapel Hill, N. C.
b
Polarographic and chronopotentiometric studies have been conducted to elucidate the nature of the perturbing effect of adsorbed brucine on the electroreduction of copper(1l) in tartrate medium. Inhibition by brucine causes splitting of the single chronopotentiometric wave for copper tartrate into three waves. The current and tartrate concentration dependency of i71’2 for the first two waves shows that they are controlled by the rate of tartrate ligand dissociation in a chemical reaction prerequisite to electron transfer. The chemical reaction in the first wave corresponds to a dissociationof tartrate ligands to form the electroactive species CUT^-^. The third wave represents attainment of diffusion-controlled reduction of copper. Possible reasons for the chemical kinetic effect are discussed.
N
of perturbations in the behavior of an electroactive substance caused by the presence of an adsorbed film on the electrode surfbce have been reported. Polarographically, these alterations range from minor to major in extent and assume the form of split, irreversible, or sway-backed current potential waves, prewaves, distorted current-time curves of individual drops, etc. A variety of explanations have been given for such effects; current theories are formulated on the basis of rate processes. By a I) effect ( 7 ) , an adsorbed ionic species can alter the potential in the electrical double layer to increase or decrease the electron-transfer rate parameters. A different explanation for a lowering of reversibility is based on a physical decrease in the available electrode surface area; the enlarged current density makes greater demands on the electron-transfer rate ( 4 ) . This current density increase can also produce control by a chemical reaction coupled to electron transfer (8). I n addition, the rate-determining step might be connected with a penetration by the electroactive species through the adsorbed film to the metal surface (11). I n any given case, one or several of these mechanisms could be operative. An extensive review on adsorption effects has been published (14). I n the course of investigation of a new method for the electrochemical differentiation of optical enantiomers ( I S ) , it was observed that the surface UNEROCS INSTANCES
1638
ANALYTICAL CHEMISTRY
275 I5
activity of brucine causes a distortion of the polarographic wave of copper(I1) in tartrate medium. The present report concerns a detailed polarographic and chronopotentiometric examiaation of this effect. EXPERIMENTAL
A11 solutions were prepared from reagent grade chemicals and redistilled (from alkaline permanganate) water and were standardized by conventional procedures where necessary. Brucine was used as the sulfate salt (K. and K. Laboratories, Inc.). Solutions containing known amounts of d-tartartic acid, copper(II), and brucine mere adjusted to the desired pH with base just prior to use. d water-jacketed beaker cell with Teflon top was used for all experiments. The three-electrode chronopotentiometric and polarographic experiments employed a platinum wire auxiliary electrode and a commercial S.C.E. reference isolated by a KSOs salt bridge. The polarographic D.M .E. had the open circuit characteristics m = 1.680 mg./second and t d = 4.57 seconds in airfree 0.1M KC1 a t a column height of 50.0 cm. The chronopotentiometric working electrode was a hanging mercury drop electrode prepared by collection of mercury drops from the D.3I.E. with a Teflon scoop for transfer to a platinum (flush) tip electrode. The calibrated electrode area vas 3.32 X sq. cm. Blank solutions containing brucine were chronopotentiometrically “clean” in the potential region of concern. h small double wave exhibiting a fairly constant i7 was observed a t -1.0 volt (pH 4.80), followed by the brucine catalytic hydrogen wave a t - 1.45 volt. A Philbrick Researches, Inc., Model K7-Al0 operational amplifier manifold powered by a Model R-300 power supply was employed nith conventional passive circuitry for all experiments. Measurements were recorded with a Sargent Model SR recorder (polarograms), a Sanborn Model 151-100A single channel recorder with Model 150-1800 preamplifier (chronopotentiograms with 7 > 0.05 second), and a Tektronix Model 564 storage oscilloscope with C-12 camera (chronopotentiograms with 7 < 0.05 second). POLAROGRAPHIC RESULTS
In 0.25M tartrate solution, copper (11) yields a polarogram with a sharp maximum of the first kind (Figure 1, curve A ) . The maximum is completely
suppressed by small concentrations of surface-active substances, such as 0.02mM brucine, which produce a well defined, diffusion-controlled wave (curve B ) . At pH 4.80, E1,2is -0.05 volt us. S.C.E. and the wave exhibits a nearly reversible behavior, as indicated by a slope of 34 mv. for a plot of potential us. log [ ( i d - i)/i]. These results are in accord with a previous report (12). Addition of larger concentrations of brucine produces a distortion of the polarographic wave which becomes more pronounced as the brucine concentration or solution pH is increased (Figures 1 and 2). At pH 4.80 and brucine concentrations of 6mM and below, the depression is restricted to potentials more positive than about -0.4 volt, beyond which the wave rises to its normal diffusion-controlled value. That the wave depression is due to an adsorption effect of brucine is immediately evident from the distortions produced in the current-time curves, samples of which are shown in Figure 3. With increasingly negative applied potential from -0.05 volt (where the i-t curves have a normal appearance), the i-t curves fairly abruptly become flattened a t the top, finally bending over to drop to zero (at about -0.25 volt), and then progressively returning through a qualitatively similar sequence to a normal pattern a t -0.45 volt. At -0.25 volt, the qualitative shape of the i-t curves (the current returns to zero at time 6) is suggestive of a diffusion-controlled coverage of the electrode surface by brucine surfactant which completely inhibits the electrode reaction. Examination of the dependency of 6 on C (the concentration of diffusing brucine) according to the appropriate equation (9, 16) 6 =
1.82
x
io6r,2
DCZ
(1)
where r, is the saturated surface excess in moles per sq. cm., produced a roughly linear plot of 6 us. C-2 with zero intercept. Comparison of the measured surface coverage of 1 A2/molecule ( D assumed as 1 X 10-6 sq. cm./sec.) with the estimated 100 size of a brucine molecule, however, indicates that factors other than simple diffusion control the inhibition of the electrode reaction by brucine a t this potential. The electrocapillary curves of Figure 4 show that brucine is adsorbed over a wide span of potential. The influences
10
U
.
i
10 4
I-
4
W
z a K
3
z I-
5
V
W
a 3
0
5
I
0 -0.5
0
-1.0
E , V.
I
Figure 2. copper(II)
0 -0.5
0
E
Figure 1 . copper (11)
-1.0
, V. v s .
S.C.E.
Effect of brucine on d.c. polarography of
2.00mM Cu, 0.25M tartrate, 0.20mM brucine Curves A-D: pH 4.80, 5.25, 6.50, and 8.60, respectively
of brucine concentration (above about lm-11) and pH on the values of t d are rather small. The pH region of 4.5 to 6.0 was selected for further study; a brucinetartrate salt tends to precipitate below p H 4.5, and the tartrate buffer capacity becomes poor above pH 6.0. CHRONOPOTENTIOMETRIC RESULTS
I
3.0
0
'
SEC.
2.00mM Cu, 12.00mM brucine, 0.25M tartrate, pH 4.80 Curves A-E: -0.10, -0.20, -0.25, -0.40, and 0.45 volt vs. S.C.E., respectively
-
served a t 0.1 and 0.5.V tartrate concentrations; values of 2.41 and 2.16 X ampere-sec.1/2, corresponding to D values of 4.49 and 3.61 x sq. cm./sec., were obtained, respectively. This change in diffusion coefficient was duplicated exactly in polarographic diffusion currents measured in the absence of brucine (Table 11). Diffusion coefficient changes of similar magnitude are common in other systems over ligand concentration regions spanning alterations in the average coordination number of relatively highly charged complexes, as can be seen from inspection of listings of polarographic diffusion current constants. The chronopotentiometric E1,4 value of -0.06 volt is in good agreement with the polarographic result. I n the presence of brucine, a chronopotentiogram for copper exhibits three clearly defined waves (Figure 5 ) . The chronopotentiograms have this appearance even a t brucine concentrations producing negligible polarographic de-
I
I
0
I
-0.5
-1
.o
Electrocapillary curves for brucine in 0.25M
Curve A: no brucine, pH 4.80 Curves B-E: 6.00mM brucine; pH 4.80, 5.25, 5.75, and 6.35, respectively
Figure 5. copper(II)
1.0
0.5 TIME
-1.5
E ,V.VS.S.C.E.
Figure 4. tartrate
I
Polarographic current-time
A
I 0
4.0
2.0
TIME
Figure 3. curves
S.C.E.
Effect of brucine on d.c. polarography of
2.00mM Cu, 0.25M tartrate, pH 4.80 Curves A-F: 0, 0.20, 2.00, 4.50, 6.00, and 12.00mM brucine, respectively
I n the absence of brucine, the chronopotentiometry of copper(I1) in tartrate reveals a diffusion-controlled and reversible character. I n 0.25X tartrate, pH 4.80, a 2mM copper solution produces an ir1j2value of 2.32 f 0.02 x ampere-sec.l'* with no trends over a transition time range of 0.0011 to 0.84 second. This corresponds to D = 4.16 X sq. cm./sec. -1similarly excellent constancy of i+/* was ob-
VS.
, SEC.
Effect of brucine on chronopotentiometry of
2.00mM Cu, 0.25M tartrate, pH 4.80, i / A = 6.02 X
lo-'
ampere/sq.
cm.
Curve A: 6.00mM brucine; curve B: no brucine
VOL. 37, NO. 13, DECEMBER 1965
1639
time properties of these waves are as follows: For the first wave, the value 25 of i711/2 decreases with increasing applied current and ultimately reaches a limiting value, ( i ~ ~l llm’, ~as)illustrated by the curves of Figure 6. Data summarizing the dependencies of the negative - i slopes and ( i ~ ~ ~ ’ ~ ) ]‘?w , ~ values for such curves on the various 5 solution parameters are given in Table r I. At brucine concentrations lower than m 6mM, an increase in concentration causes a gradual increase in the i ~- i ~ ~ ’ ~ slope but has no effect on (i~11’2)llm. ,4t higher brucine concentrations, ( i ~ ~ oh I 1’2)1,m also commences to decrease. In all cases in which a sufficiently long segment of the decreasing i 7 I 1 l 2 values was obtained to permit extrapolation to zero current, a value of (irll’z)o reI5 sulted which, within the uncertainty limits imposed by the long extrapola10 20 IO 40 50 W value obtion, agreed with the i CURRENT, /*A served in the absence of brucine. The second wave also exhibits a Figure 7. Transition time-current bedecrease in i721/2with increasing curhavior of second chronopotentiornetric rent density (Figure 7 ) ,but an ( i s 2 1 ’ 2 ) l , m wave for copper tartrate in presence could not be attained for this wave. of brucine - i slope 2.00mM Cu, 6.00mM brucine, pH 4.80 The dependency of the Curve A: 0.10M tartrate; curve E: 0.25M of Figure 7 on the solution parameters, tartrate; curve C: 0.50M tartrate; curve D: qualitatively the same as for the first 0.25M tartrate (no brucine) wave, is summarized in Table 11. Extrapolation to zero current could readily be accomplished and ( i 7 P ) o 2.31 & 0.01 X ampere-sec.1/2 a t agreed with the i + 2 values observed in pH 4.80 and copper, brucine, and the absence of brucine, showing the same tartrate concentrations of 2.00mM, trend of D vith tartrate concentration 6.00mJ1, and 0.2531, respectively, over exhibited by those values and by the a transition time range of 0.016 to 1.06 polarographic diffusion current, i d . Measurement of i ~&s a~ function ~ / ~seconds. This value is in excellent agreement with that observed in the of current revealed a constant value of absence of brucine under the same solution conditions. 4
\
0
I
I
1
I
I
10
PO
30
40
50
CURRENT
j
P A
Figure 6. Transition time-current behavior of first chronopotentiornetric wave for copper tartrate in presence of brucine 2.00mM Cu, 6.00mM brucine, pH 4.80 Curve A: 0.10M tartrate; curve E: tartrate; curve C: 0.50M tartrate
0.25M
pressions (0.2mX). S o effect of time of equilibration of the hanging mercury drop electrode with the solution could be observed beyond a 1-minute (stirred) waiting period. The first and second chronopotentiometric waves correspond approximately in potential t o the two “steps” of the polarogram for copper in the presence of brucine. The third chronopotentiometric wave has no polarographic counterpart, The current-transition
Table 1.
PH 4.80 4.80 4.80 5.25 5.75 4.80 4.80 4.80 Table
It.
Characteristics of First Chronopotentiornetric Wave in Presence of Brucine
[CUI, mM 2.00 2.00 2.00 2.00 2.00 1.00
2.00 2.00
[Brucine], mM 6.00 6.00 6.00 6.00 6.00 6.00
2.00 12.00
[Tartrate], M 0.10
0.25 0.50 0.25 0.25 0.25 0.25 0.25
-Slope sec.112’
0.474 1.49 3.16 1.90 3.86 1.55 1.04 3.14
(i~,’”)1im, amp. X 106 1.11
0.665 0.379 0.506
-
0.285 0.675 0.348
Characteristics of Second Chronopotentiornetric Wave in Presence of Brucine pH = 4.80
[Tartrate], -Slope, sec.li2 x (iT1”)O/idt M 102 2.10“ 2.37 6.00 0.10 2.00 2.10Q 0.25 5.75 2.00 6.00 2.12= 0.50 9.94 2.00 6.00 2.10 0.25 5.79 1.oo 6.00 2.12 0.25 5.42 2.00 2.00 ... 0.25 14.5 2.00 12.00 a Essentially the same numbers were obtained for i ~ l ’ ~ / i(brucine d absent). [CUI, mM
1640
[Brucine], mM
ANALYTICAL CHEMISTRY
ELECTRODE REACTION MECHANISM I N PRESENCE OF BRUCINE
Interpretation of the above results in terms of a detailed mechanism for the reaction of copper tartrate in the presence of brucine is complicated by the considerable variety of possible blocking modes of brucine. The expected properties of a number of possible mechanisms were examined for consistency with the experimental results. An encouraging degree of consistency with certain proposals was evident, particularly for the first chronopotentiometric wave, discussion of which follows. In a general sense, an i ~ decreas~ ~ ing with increasing applied current implies replacement of the diffusional mass transfer step preceding electron transfer with another, slower kinetic process. Such a process, of which the slope of the i ~ ~ 1 ’-2 i curves is a qualitative rate measure, can assume two forms : a slow rate of penetration of the surfactant layer by the electroactive species, or control of the supply of electroactive species by the rate of a
’
~
chemical reaction. Presence of the latter rate process is clearly demonstrated by the rate dependency on tartrate concentration shown in Table I, the direction of which is consistent with a chemical reaction involving a loss of tartrate ligand(s) as a prerequisite to electron transfer :
-+ chem
CUT,
CUT,-,
+
electron transfer
mT (2) .Use, control by a chemical reaction rate implies that, at sufficiently high currents, rate control can revert to diffusion of the equilibrium quantity of the species capable of undergoing electron transfer. CUT,...,, negligible amounts of this species being chemically supplied from CUT, before the transition time is reached. Occurrence of this event is indicated by attainment of an (iT11/2)11m whose value is tartrate At least in concentration-dependent. its simplest form, control of the value of r1 by a physical penetration rate process would not be expected to exhibit either of these experimental characteristics. Inquiry into the mechanism by which brucine invokes control of T i by Reaction 2 leads to consideration of three forms of brucine involvement: a current density effect caused by lowering of electrode surface area by adsorbed brucine, an inhibition (of an unspecified nature) of reduction of CUT, coupled with a surface chemical reaction, and the presence of copper-tartrate-brucine mixed complexes in the bulk solution which exhibit slow rates of tartrate dissociation. The latter one of these was especially scrutinized in view of its strong relevance to a related study of electrode asymmetry effects (IS) and is clearly demonstrated to be absent on the basis of the following observations: ~ )independent of Values of ( i ~ ~l,m~ ’are the bulk brucine concentration at 6m J I brucine and lower. At constant brucine Concentration, the ir11’2 - i slopes are independent of the copper/ brucine concentration ratio. Distortion of the polarographic i-t curves suggests the presence of a surface type of inhibition. The visible absorption spectrum of copper tartrate solutions is independent of the brwine concentration. These facts exclude significant direct participation of brucine in Reaction 2 , a t least in the solution phase. Each of the former two mechanistic proposals provides considerable agreement of expected with observed behal-ior of the first wave; the pertinent features of each follow: A. This mechanism presumes a large increase in the effective current density at the electrode surface as a result of lowering of free surface area by adsorbed, impenetrable brucine. This large current density imposes demands
on the rate of Reaction 2 , which then exerts a kinetic influence not discernible a t the lower current densities accessible at brucine-free surfaces. Higher brucine concentrations accentuate this effect through a larger surface coverage, causing the decrease in apparent rate shown in Table I. At sufficiently lox current densities, control by Reaction 2 diminishes, and extrapolation of i ~ , to ” ~ zero current provides the diffusion-controlled condition observed in the absence of brucine. I t might be superficially expected that the extrapolated (irl”*)o should be lower than the “no brucine” according to the fractional area reduction by adsorbed brucine, rather than the experimentally observed equality of these two quantities. A more detailed consideration of the area effect, however, shows that the observed extrapolation must be expected. While the free surface area may be reduced by brucine adsorption, the solution volume from which diffusion occurs to the “holes” is unchanged, Thus. when the time of diffusion is short, the most appropriate area is the free area, but at longer times the diffusion layer around each hole will assume partial (henii-) spherical character, and the effective diffusional area will be larger than the free area. At sufficiently long times, the diffusion layers emanating from each hole will merge, and when the combined diffusion layers are much deeper than the distances between holes, the gross diffusion profile will again revert to a linear form for which the total electrode area is now appropriate. The extrapolated value of (ir11’2)o is thus seen to be justified. This area effect is analogous to, but opposite in direction from, that of electrode surface roughness, discussed previously by Reinmuth ( I , 15). In terms of the required flux density of electroactive reactant CUT,-, for an applied current in the region of decreasing iTi1’2, the above area considerations also indicate that demands on the rate of Reaction 2 will be severely increased in the region of a hole as compared to the outermost fringes of the diffusion layer. The exact mathematical formulation of this situation in terms of a kinetically controlled r1 must be correspondingly complex. However, for the purpose of semiquantitative comparison of tartrate concentration rate effects a t constant brucine an concentration, assumption of averaged flux density and utilization of a conventional uniform flux relation (3) hold possibilities for a useful first approximation. B. This mechanism assumes that copper complexes of stoichiometry other than CUT,-, are unable to undergo direct electron transfer a t the brucine-
covered surface a t the potential of the first wave, either by virtue of very slow physical penetration processes or because of slow rates of electron transfer. At high currents, only the equilibrium quantity of CUT,-, governs the value of rl,as reflected in the constant ( i ~ ~ ~ ’ attained a t such currents. At lower currents, Reaction 2 can supply additional CUT,-, until ultimately a completely diffusion-controlled condition of (ir11’2)ois reached. To account for the effect of brucine concentration on the rate (in1l2 - i slope) of Reaction 2 , remembering that participation of solution phase brucine has been ruled out, this mechanism implies that Reaction 2 occurs on the electrode surface (is of heterogeneous type) and involves the participitation of adsorbed brucine. Examples of forms this participation might take would be coordination of surface brucine to CUT,-,, or a significant effect of a brucine-determined I) potential on the surface rate of tartrate dissociation. This surface reaction mechanism necessarily involves a higher level of speculative content than that of the more conventional mechanism &I,Because of its equal consistency with the available experimental observations, however, it must remain as an alternative mechanism until further investigations of chronopotentioinetric blocking effects provide a inore substantial background for its evaluation. In the mathematical formulation of this type of surface kinetic process, application of the reaction layer concept may be appropriate. h previous reaction layer treatment ( 2 ) of the effects of a preceding chemical reaction in chronopotentiometry produces an equation of the same general form as that obtained by a purely diffusional approach ( 3 ) . Insight into the stoichiometric aspects of Reaction 2 requires information on the equilibrium composition of the solution. Copper forms a variety of complexes, depending on the solution pH and the tartrate to copper ratio. At pH > 6 and low ratios, mixed hydroxy-tartrate complexes have been reported (I?’). Higher ratios and pH can produce polynuclear mixed complexes ( I O ) . Low pH may form CuHTT ( 5 ) . At pH < 6, a series of complexes CUT, is expected where 2 = 1 to 4. The stepwise log formation constants for this series have been reported (potentiometric) as 3.20, 1.91, -0.34, and 1.71 (6). Predominant solution components expected under the present conditions are accordingly those of 2 = 2 and 4. The extent to which the higher z complexes may be protonated is not clear. For both mechanisms -4 and B, the value of ( i ~ ~ 1 ’ 2 ) , , , represents the solution concentration of the species VOL. 37, NO. 13, DECEMBER 1965
1641
~ ) 1 , ~
undergoing electron transfer (CUT,-, of Reaction 2) and should vary with tartrate concentration in the same manner as the concentration of that species. Table I11 compares calculated equilibrium concentrations of the various copper tartrate complexes with experimental (ir1112)lim values. Only the concentration of the species CUT^-^ varies in a manner compatible with (i711/2)llm, furnishing positive identification of the electrode reactant for the first chronopotentiometric wave. Determination of the tartrate reaction order (m)of Reaction 2 involves analysis of the dependency of the reaction rate, as represented by the ir1li2 - i slopes, on tartrate concentration. If the viewpoint of mechanism A is taken and the assumption of an averaged flux is made, the pertinent relation applicable to a single first-order reaction preceding electron transfer (S), for the condition of sufficiently large (k, kb)’” +I2,is
+
where e = [ K ( k f kJ1’2]-1, k f and kb are the forward and back first-order chemical rate constants, and K is the equilibrium ratio of the chemical reaction product and reactant. Reaction 2 can be formulated as CuTn2- 2n
+ mH+ CuTz-’
+ mHT-
(4)
+ mT-’
(5)
or CUT,‘ - ‘n
CUTZ-’
sentially diffusion-controlled character a t potentials cathodic of -0.4 volt. The 8 2 values of Table I V are influenced to an uncertain extent by the fact that the kinetically controlled r1 is included in the rz measurement. Suspicion that the variation of irZ1I2 with current might be simply a reflection of the kinetic features of 71-i.e., that the second wave is actually diffusion controlled-is dispelled by the observation that the variation of i n 1 / 2 persists even when the first wave attains the diffusionllm. controlled condition of The third chronopotentiometric wave represents a further removal of the kinetic effect of brucine to the point that a completely diffusion-controlled condition is attained. This is indicated both by the constancy of i@ and its equality with the value observed in the absence of brucine. The potential separation of the second and third chronopotentiometric waves from the first wave can be rationalized in a variety of ways consistent with the mechanisms A and B proposed for the first wave. All of these involve suppositions as to the nature of the reducible species of waves two and three. The only conclusion which can be drawn in this respect, however, is that, because of the existence of a tartrate dissociation effect, direct reaction of the CUT*+ species in the second wave seems unlikely. It is not necessary to assume that waves two and three do not involve the CuTz-2 species as the electrode reactant. For example, in mechanism A a reorientation of adsorbed brucine a t -0.4 volt to cover a smaller fraction of the total surface area could permit Reaction 2 to provide additional CUT^-^ for the second wave. [An abrupt desorption of brucine to produce the same effect cannot be inferred from the smooth electrocapillary curve, (Figure 4).] In mechanism B a potential-determined enhancement of the surface reaction rate could yield the same result. Finally, it is clear that the chronopotentiometric technique can provide an invaluable complement to classical polarography for the investigation of surfactant effects on electrode reactions. It js equally clear that while a number of general features and a few specific details of the blocking mechanism in the present system could be deduced, many other features could be accounted for only in a tentative manner, and further study of a broadened scope is indicated for their evaluation.
Inasmuch as the solution has sufficient buffer capacity and excess tartrate, these reactions can be considered as pseudo first order. By appropriate substitutions of the equilibrium constants for Reactions 4 and 5 and of tartaric acid dissociation constants, and assuming that kb >> k f , 0 can be shown to be proportional to [HT-]“/2/ [H+]” and [HT-]m/2/[H+]”’2 for the two reactions, respectively. The i711/2 - i slopes for the two reactions (01) have the same functional dependency on [HT-]; a comparison of the experimental and calculated relative values of 61 a t constant brucine concentration is given in Table IV. A fair correspondence to m = 2 is apparent. This result indicates that the chemical Table 111. Comparison of ( i n 1 1 2 ) l i , reaction occurs as a stepwise process in with Concentration of Copper Tartrate which loss of a second ligand (from Complexes CuTab4)is the slower step and displays a degree of consistency with the above pH = 4.80, [CUI = 2.00mM, [brucine] = determination of n - m = 2 in that the 6.00mM predominant precursor of CuT2+ is [Tar[CUTZ-’I [ C U T ~ - ~ I suggested as CUT^-^, a major solution trate], @la component, that the intermediate M (ir11’2)iim (ir1”2)iim ( i n ” 2 ) i i m CUTS-~ is present in small equilibrium 0.10 0.021 0.136 0.0061 concentrations,
