J. Phys. Chem. 1981, 85, 928-932
928
Nitrite Quenching of Terbium Luminescence in Sodium Dodecyl Sulfate Solutions Franr Grieser‘ Hahn-Meitner-lnsritut fur Kernforschung Berlin GmbH, Bereich Strahlenchemie, D- I000 Berlin 39, West Germany (Received: May 13, 1980; In Final Form: December 17, 1980)
Excited Tb3+,bound to sodium dodecyl sulfate (SDS) micelles, is quenched by NOT with an apparent rate constant of (1.1f 0.2) x IO7 M-’ s-l, a factor of -100 lower than in free solution. The quenching rate in the micellar solution is independent of the SDS concentration in the range of 0.02-0.1 M, implying that in this range all terbium ions are bound to the micelles. The addition of salt and partially water soluble alcohols increases the quenching rate constant. Some of the possible factors responsible for the enhancement are discussed.
Introduction Two inherent and important properties of ionic micellar solutions are their ability to solubilize hydrophobic substances and to bind counterions, to varying extents, to the micelle surface. The first of these properties has received considerable attention over the past several years both from a point of view of trying to understand the way hydrophobic species are solubilized by the micelle as well as utilizing the properties of solubilized molecules for studies of catalysis reactions,’ the micelle microenviornment,2 photoi~nization,~ energy and electron transfer: isotope enrichment: to name but a few. Such studies have yielded a large amount of information on the surface and core properties of micelles and on the interaction of molecules in reduced space dimensions. The study of ion binding to the micelle surface has perhaps not been as extensively studied, although a considerable amount of information on the surface binding of singly charged ions is available.6 Some attempts at quantifying the extent of more highly charged metal ions on negative surface micelles have also been made by using a variety of techniques, ESR? NMR? complex formation? and the reaction rate of the hydrated electron.‘O In the present paper another method is reported in studying Tb3+binding to anionic micelles. It is shown that the rate at which NO, quenches excited Tb3+can be used to determine the extent the metal ion binds to SDS micelles. It is also shown that the variation in the quenching constant with the addition of some inert reagents can be used to monitor the effect these additives have on the surface potential and on the counterion layer surrounding the micelle. Experimental Section The sodium dodecyl sulfate (SDS) used was BDH Chemicals Ltd. specially purified grade. The cmc measured by use of a fluorescence technique1’ was 6.0 X M. This value is a little lower than what is generally regarded as the best value; however, since rather large concentrations of additives were needed to obtain significant changes in the measured quantities of interest, further purification was considered unnecessary. Tb(N03)36H20was Ventron ultrapure (>99.9%). NaNOz was Merck pro analysis, and all other salts were Merck Suprapur grade. The sodium benzenesulfonate was Fluka recrystallized puriss grade (>99%). All the alcohols used were Merck pro analysis. Solutions were made with water obtained from a Millipore filtration system. It had a *Address correspondence t o the author a t the Department of Physical Chemistry, University of Melbourne, Parkville, 3052,Australia. 0022-3654/81/2085-0928$01.25/0
conductivity of < X lo4 Q-l cm-l, and a pH of 5.7 after equilibration with air. Emission intensities were measured by using a Perkin-Elmer MPF 4 spectrophotometer. Absorption scans were made with a Varian Superscan 3 spectrophotometer. Emission lifetimes were measured by using a frequency doubled Korad KlQP ruby laser system.12 Conductivity measurements were made with a Philips PW 9501 conductivity meter with a PW 9514/10 conductivity cell (cell constant 1cm-’). The solutions for analysis were made from stock solutions of SDS added to standard flasks containing the desired weighed amount of salt or alcohol. With the higher alcohol concentrations the dilution of the SDS solutions was 55%. Solutions used for the quenching experiments were then made by taking the required amount of prepared SDS-additive or just SDS solution, injecting the appropriate amount of Tb3+ from a 0.1 M stock ~olution,’~ and then to 10-mL aliquots of this solution injecting microliter quantities of concentrated (1)See, for example, J. H. Fendler and E. J. Fendler, “Catalysis in Micellar and Macromolecular Systems”, Academic Press, New York, 1975. (2)Some of many are (a) H. J. Pownall and L. C. Smith, J . Am. Chem. Soc., 95, 3136 (1973). (b) M. Gratzel and J. K. Thomas in “Modern FluorescenceSpectroscopy”,E. L. Wehry, Ed., Vol. 2,Plenum Press, New York, 1976,p 169. (c) K. A. Zachariasse, Chem. Phys. Lett., 57, 429 (1978). (d) A. R. Watkins and B. K. Selinger, ibid., 64,250 (1979). (e) M. S. Fernandez and P. Fromherz, J . Phys. Chem., 81, 1755 (1977). (3)(a) S.C. Wallace, M. Gratzel, and J. K. Thomas, Chem. Phys. Lett., 23,359(1973);(b) J. K. Thomas and P. Picoulo, J. Am. Chem. SOC.,100, 3239 (1978);101,2502 (1979); (c) S.Alkaitis and M. Gratzel, ibid., 98, 3549 (1976). (4)For example, (a) M. Almgren, Photochem. Photobiol., 15, 297 (1972); (b) M. Almgren, F. Grieser, and J. K. Thomas, J. Am. Chem. SOC., 101,2021(1979);(c) N.J. Turro, M. Aikawa, and A. Yekta, ibid, 101,772 (1976);(d) S.A. Alkaitis, G. Beck, and M. Griitzel, ibid., 97,5723(1975); (e) S. A. Alkaitis, M. Grltzel, and A. Henglein, Ber. Bunsenges. Phys. Chem., 79,541 (1975). (5)N.J. Turro and B. Kraeutler, J. Am. Chem. Soc., 100,7432(1978). (6)See, for example, the following and references therein: (a) J. W. Larsen and L. J. Magid, J . Am. Chem. SOC.,96,5774 (1974);(b) F.H. Quina and H. Chaimovich, J. Phys. Chem., 83,1844 (1979). (7) (a) I. D. Robb, J. Colloid Interface Sci., 37, 521 (1971); (b) J. Oakes, J . Chem. SOC., Faraday Trans. 2, 69,1321(1973);(c) A. HaseJpn., 43, 3116 gawa, Y. Michihara, and M. Miura, Bull. Chem. SOC. (1970). (8)J. R. Escabi-Perez,F. Nome, and J. H. Fendler, J. Am. Chem. SOC., 99,7749 (1977). (9)J. Holtzwarth, W. Knoche, and B. H. Robinson, Ber. Bunsenges. Phys. Chem., 82, 1001 (1978). (10)M. Gratzel and J. K. Thomas, J. Phys. Chem., 78, 2248 (1974). (11)K. Kalyanasundaram and J. K. Thomas, J.Am. Chem. Soc., 99, 2039 (1977). (12)G. Beck, J. Kiwi, D. Lindenau, and W. Schnabel, EUF.Polym. J., 10, 1069 (1974). (13)When this stock solution was prepared, it was noticed that the pH changed from 5.7 to 4.4. This indicates that there is a negligible amount of hydrolysis of Tba+to Tb(OH)2+or Tb(OH)2+. The pH change can be used to calculate an approximate pK, of 8.0. This agrees quite well with that given in the literature, 8.16. (D. D. Perrin, “Dissociation Constants of Inorganic Acids and Bases in Aqueous Solution”, Butterworths, London, 1969,p 205.)
0 1981 American Chemical Society
The Journal of Physical Chemistry, Vol. 85, No. 7, 198 1 929
Nitrite Quenching of Terbium Luminescence
12 I
-
I
I
"
l
I
l
I
I
l
l
I
X
-;"
.LiCI 10.02N SDSI
6
f xu 4
2
0
0.2 0.4 0.6 Ionic strength
0.8
Flgure 1. Second-order rate constants for the quenching of excited Tb3+ by NOL as a function of ionic strength. The W points are from time-resolved quenching measurements. The 0 points are calculated from Stern-Volmer plots by using a lifetime of excited Tb3+of 390 /LS. Ionic strength values are due to contributions from mixed solutions of Tb(N0 )p5H20and NaNO,. The insert shows the luminescence decay to Tb3": (A) natural lifetime, (B) with 1 X M NaNO,, (C)with 2 X M NaNO,. The arrow shows the base line level, and the position of the laser pulse. The solutions were 0.1 M in Tb3+.
NaNOz solution. This procedure was followed to ensure that each aliquot contained the same amount of Tb3+;the dilution of the SDS solution by the Tb3+and NaN02 addition was negligible. Addition of Tb3+to an SDS solution initially caused a precipitate to form, presumably a terbium dodecyl sulfate compound, which quickly redissolved on stirring if the concentration of the SDS solution was sufficiently high.14 For 0.02 M SDS, which was used in most of the experiments, the maximum amount of Tb3+that could be solubilized was between 3 and 4 mM. The terbium in solution was excited at 367 nm and the emission observed at 545 nm. With the high sensitivity conditions generally needed to observe the Tb3+*emission (at low Tb3+ concentrations of = 2 mM) scattered light from the micelle solution overlapped the terbium emission. To correct for this, solutions of identical composition without Tb3+ present were illuminated and the scatter intensity recorded, thereby giving the true amount of the Tb3+ emission intensity. Apparent second-order quenching constants (k,) were derived from standard Stern-Volmer plots, using a measured luminescence lifetime of 390 ps, Micelle aggregation numbers were determined by using the method described by Turro and Yekta.15 The values were calculated by using a R ~ ( b p y ) concentration ~~+ of 5 X lov5M and concentrations of 9-methylanthracene of 1.5 X and 3 X M for the 0.02 M SDS solutions, and 3X and 5 X M for the 0.05 M SDS solutions. All micellar solutions made were allowed to equilibrate for a few hours, and all measurements, using these solutions, were generally made within 12 h of preparation. Measurements were made at room temperature, 22 f 2 "C. Results and Discussion Tb3+*Quenching in Micellar Solutions in the Absence and Presence of Salt. A large number of negatively charged ions were tried in order to quench the terbium luminescence; of these NO, was the only one found that showed any significant effect. The quenchingle was found (14) This behavior has been observed for other metal ions and studied in some detail; e.g., S. Kratohvil, K. Shinoda, and E. Matijevic, J. Colloid Interface SOC.,72,106 (1979); D.Meisel, M. S.Matherson, and J. Rabani, J. Am. Chem. SOC.,100,117 (1978). (15) N. J. Turro and A. Yekta, J.Am. Chem. SOC.,100,5951 (1978).
[additive] /mol d ~ n - ~ Flgure 2. The influence of salt on the apparent quenching constant of excited Tb3+ by NO2- in SDS solutions. The points W and V are for NaBr and NaNO,, respectively, in 0.02 M SDS. The Tb3+ concentration was 2 mM.
to be dynamic in nature and the rate constant dependent on the ionic strength of the solution (see Figure 1). The quenching of Tb3+* in micellar solutions was studied in the range of 0.02-0.1 M SDS. Within experimental accuracy, the slopes of the Stern-Volmer plots were linear and constant, giving a quenching constant of (1.1 f 0.2) X lo7 M-l s-l. This value was confirmed by timeresolved measurements with the laser system, which gave a quenching constant of (1.0 f 0.2) X lo7 M-l s-l for the same surfactant range. With the addition of salt to the micellar solution an enhancement of the quenching constant was observed. The extent of the increase was dependent on the micelle concentration and on the kind of salt used, as can be seen in Figure 2. To explain the above results we found it significant to consider the equilibrium of Tb3+ between the micelle surface and the bulk water phase. From purely electrostatic considerations the bound Tb3+ions can be expected to reside predominantly in the Stern layer and to a smaller extent in the diffuse counterion layer surrounding the micelle.4b An equilibrium constant1' can be defined as K = [Tb3+lb/([M1[Tb3+lf) (1) where the subscripts b and f denote micelle bound, and free terbium ions, respectively, and [MI is the total micelle concentration. The total emission from excited terbium is then a sum of the bound and unbound ions. In the volume region where Tb3+is boundls there is a high counterion density and a strong repulsive field for negative ions. Both these factors would contribute to the apparent reduction of the Tb3+*-N02- quenching rate, compared to the bulk intermicelle phase. The observation that the quenching rate constant, in the absence of added salt, is constant over the surfactant range (16) The actual mechanism is not known but may involve an energy transfer step. The triplet energy of NOz- is -53 kcal mol (A. Treinin and E. Hayon, J.Am. Chem. SOC., 98,3884 (1976)) an that of the Tb*+ 5D4state r 5 8 kcal/mol (ref 4b). (17) A derivation of the equilibrium constant for hydrophobic molecules binding to micelles is given by C. L. Kwan, s.Atik, and L. A. Singer J. Am. Chem. SOC.,100,4783 (1978). The method is equally applicable to micelle bound ions. Note: in this derivation it is assumed that the volume of the micelle phase is negligible compared with the bulk water phase. (18) Due to the nature of the experimental measurements, bound ions are defied as those that reside between the micelle surface and to a point in the diffuse layer where the repulsive potential energy between NO, and the micelle is equal to the thermal energy of the system; the repulsive potential corresponds to about 25 mV at this point.
d
930
The Journal of Physical Chemistry, Vol. 85, No. 7, 1981
Grieser
p
studied and about 100 times lower than in free solutionlg implies that essentially all the Tb3+is bound to the micelles. The linearity of the Stern-Volmer obtained is also consistent with this conclusion (see Appendix I). The strong binding of Tb3+precludes an exact calculation of K , however, a lower limit for the binding constant can be estimated. If one assumes that the quenching technique is sensitive to,say, 10% “free” Tb3+at the lowest SDS concentration (2 X M), one obtains a value of 5 X lo4 M-l, as a lower limit. The high binding constant of Tb3+ suggested by the present work20 also supports the interpretation given to the electron reaction data for Eu3+ binding to SDS micelles, for which a lower limit for K of lo5 M-’ was estimated.21 Further information may also be obtained from the apparent quenching constant by expressing it in the form
k, = phi exp(\k/25.6)
71
-.-
2 I
‘0
0.1
(2)
Here, ki is the second-order ionic-strength-dependent quenching constant, which takes into account the high localized counterion concentration around the micelle where the Tb3+*-N0c interaction occurs. The exponential term,22 from the Boltzmann equation, corrects for the actual NOz- concentration in the negative potential (\k) region of quenching. A steric factor, 6, is included since Tb3+* is associated with the micelle and therefore the encounter with NO, is dimensionally restricted compared to a bulk solution interaction. Taking an ionic strength23of 0.5 M for the Stern layer region, ki N 3 X lo8 M-l s-l (from Figure l),k, = 1.1X lo7 M-l s-l, and /3 = 1/2,24one calculates \k N -67 mV. This value is considerably lower than the -130 mV surface potential given by Fernandez and Fromherz,%which they obtained using a completely micelle bound probe. The lower value calculated here most probably reflects the greater width of the distribution of bound Tb3+around the micelle, compared with the probe used by the aforementioned authors. Consider now the results showing the influence of salt on K, in the micellar system. The general increase in k, with added salt may, from a simplistic analysis, be attributed to a lowering of the surface potential. There are, however, certain aspects of the data which are not in complete accord with this idea. In Figure 2 it can be seen that the addition of Na+ enhances the value of k, to a greater extent than does the same amount of Li+. Yet, Li+ and Na+ reduce the surface potential of SDS micelles equally.2e Furthermore, at the relatively high concentra(19) Considering the ionic strength of the solution a t 0.02 M SDS and 2 mM Tb(N0 )3, one would expect a quenching constant of approximately 109 M-* s-1. (20) A distribution constant of 500 M-’ for Tb3+binding to SDS micelles is given in ref 8. This value is incorrect. The total Tb3+ concentration added was used as the “free” Tb3+concentration in the calculation. I am indebted to a referee for pointing this out. (21) F. Grieser and R. Tausch-Treml, J. Am. Chem. SOC.,102, 7258 (1980). (22) The observed first-order quenching constant, divided by the actual NOz‘ concentration in the region of the quenching, equals phi. The NOz- concentration a t the surface of the micelle is found from the Boltzmann equation, using the added [NO,-] as the concentration in the bulk phase. (This is a valid assumption because the micelle pseudo phase is only a small percentage of the solution.) (23) This value was determined for Br- around hexadecyltrimethylammonium bromide micelles (M GrBtzel, K. Kalyanasundaram, and J. K. Thomas, J . Am. Chem. SOC.,96, (1974). Since this micelle has about the same surface potential (positive), aggregation number, and degree of ionization as SDS, the ion density should be about the same. Even if the ion density was overestimated by a factor of 2 or 3 , 4 is still more positive than -100 mV. (24) This value is somewhat arbitrarily chosen; see dicussion on the steric factor in ref 4b.
Benzylolcohol 10.02M SDSI
Ethanol (0.02M SDSI
0.2 0.3 0.L 0.5 [Alcohol1/ mol dmq3
0.6
Flgure 3. The influence of alcohol on the apparent quenching constant of excited Tb3+ by NO,- in SDS solutions. The Tb3+ concentration was 2 mM.
. I
b
10
-
X
‘5
-
99
0
0.1 0.2 0.3 0.L 0.5 0.6 IAlcohol] /mol dm-3
Flgure 4. The variation in conductivity of 0.02 M SDS solution as a function of some n-ailphatlc and aromatic alcohols.
tions of added salt, compared to the SDS concentrations used, the change in the surfactant concentration would not be expected to influence the surface potential of the micelle to any significant extent. These points make it clear that the increase in k, cannot be solely explained in terms of a decrease in the micelle’s surface potential with added salt. It may be added that this is so even if one takes into consideration a broadening of the distribution of bound Tb3+ as the surface potential is lowered. A possible interpretation of the results is that added Na+ and Li+,apart from lowering the surface potential, compete with Tb3+for surface sites, thereby lowering the amount of Tb3+bound in the Stern layer. Based on related results obtained by others25this explanation seems plausible. One final point to note in Figure 2 is the somewhat greater affect of NaBS in increasing k, than the other sodium salts. Since there is no other related information available a definitive explanation for this result cannot be given. However, it is worth noting that if there is some association of BS- with the micelle, the larger k, values (25) I t has been shown that the strength of binding to SDS micelles increases in the order Li+ < Na+ < K+ (ref 6a), therefore Na+ would be more effective than Li+ in displacing surface bound Tba+. The binding of Mnz+to SDS micelles was reduced by the addition of M)NaN03, and KNOs (ref 7c), the effect being greater for KNOB. The displacement of Cu2+bound to poly(vinylsu1fate) was shown to be more efficient for Na+ than Li+ (C.D. Jonah, M. S. Matheson, and D. Meisel, J. Phys. Chem.,81,1805 (1977)). The displacement of Tb3+ from the Stern layer will cause a general shift in the ion distribution. However, it is expected that the amount of “free” Tb3+ is still small. If there was a substantial amount of “free” Tb3+*,the Stern-Volmer plots would be nonlinear (see Appendix 1). This was not found.
Nitrite Quenching of Terbium Luminescence
The Journal of Physical Chemlstty, Vol. 85, No. 7, 1981 931
TABLE I: Aggregation Numbers o f Surfactant and Alcohol Molecules in “Mixed” Micelles 103. [free
monosolution
1-pentanol (0.05 M SDS)
1-pentanol
(0.02 M SDS)
mer],a [alcohol], mol m o l d m - 3 dm-3
0 0.1 0.2 0.3 0.4 0 0.05 0.1 0.2 0.27
6.0 2.3 1.3 0.8 0.7 6.0 3.6 2.3 1.3 0.8
surfactant molecules/ micelleb
66* 3 54 + 2 37 f 2 31 f 1 36* 2 65 f 2 52+ 1 32* 2 27 f 1 26+ 2
alcohol molecules/ micelle‘
32 43 58 102 22 28 43 62
67 f 2 56* 3 18 47 + 1 28 39 2 1 35 30+ 1 40 22i 1 48 ethanol 0 6.0 65 + 2 (0.02 0.25 5.6 63+ 2 0.5 5.2 63i 2 M SDS) Calculated based on the data of ref 31 and 32. See Calculated by using the m e t h o d described in ref 33. Appendix 11. 1-butanol
(0.02 M SDS)
0 0.1 0.2 0.3 0.4 0.6
6.0 4.1 3.0 2.3 1.9 1.2
may be due partly to reasons similar to those discussed in the following section. Effect of Micelle-Solubilized Alcohols on k The addition of some aliphatic and aromatic alcoh& to SDS solutions resulted in an increase in k,, see Figure 3. The initial steepness of the slopes increases in the same order as the water solubility of the alcohol decreases.26 This observation suggests that micelle bound alcohol is responsible for the observed change in k,. In order to explain and to use the results of Figure 3 more fully, we made some additional related experiments to gain a greater insight into the effect of the solubilized alcohol on the micelle itself. The conductivity of the SDS solution was measured with increasing concentration of alcohol, and found to have the behavior seen in Figure 4. It can be noted that the initial slopes follow the same order as those for the k , measurements (Figure 3). This type of behavior has been observed before and explained in terms of the solubilization of the alcohol at the micelle-water interface, resulting in the liberation of bound Na+ ions.27 Lawrence and PearsonZ7 also made the suggestion that, even though there are more ionized surface groups when alcohol is solubilized, there is little change in the surface charge density because the ionized groups are spread over a greater area. A reduction in the surface charge density is possible, however, if the number of surfactant molecules per micelle is changed. Since this is an important point, the aggregation numbers for some of the present systems were determined by using the method described by Turro and Yekta.15 These results are given in Table I, along with the average number of alcohol molecules per mixed micelle. Drawing all this data together, a qualitative description to account for the behavior seen in Figure 3 can be given. At low amounts of added alcohol, relative to the saturation (26) “Lange’s Handbook of Chemistry”,revised 10th ed, McGraw-Hill, New York, 1967. (27) (a) J. T. Pearson and A. S. C. Lawrence, Trans. Faraday SOC., 63, 488 (1967); (b) A. S. C. Lawrence and J. T. Pearson, ibid., 63,495 (1967).
limit, there is a decrease in the number of surfactant units per mixed micelle and an increase in the ionization of the S04-Na+groups. Since k increases, signifying a decrease in the surface potential:l it must be concluded that the decrease in the surface charge density, due to the first factor mentioned above, outweighs the effect of increased ionization of the micelle. Approaching the saturation limit, as illustrated by the pentanol data, the ionization of the micelle has virtually ceased and the number of surfactant units per mixed micelle remains about the same. The surface charge density, however, continues to decrease because of the separation of the SO4- groups by surfacesolubilized alcohol, and consequently k, increases. This description of events is still a very simple overview of the changes occurring around the micelle surface as increasing amounts of alcohol are added to the solution. The solubilized alcohols will, of course, change the hydration of the micelles, therefore affecting the dielectric properties of the surfacem and, consequently, the surface potential. The distribution of bound terbium ions around the micelle surface will also be altered, as the solubilized alcohol lowers the surface potential. Unfortunately, the degree that these factors influence k is not known, since a quantitative assessment of the resdts is not possible at present. Appendix I In the steady-state experiment, the total emission quantum yield (P)will be a sum of the emission from Tba+* in the bulk solution, and Tbb3+*bound to the micelles, i.e.
P
= (1- (r)lp
+dbo
(3)
where a is the fraction of the total Tb3+ bound to the micelles. In the presence of a quencher (Q), which reacts with both bound and free Tb3+*,albeit at different rates, the quenching in the two domainsw can be expressed as
I p / I f = 1+ k i ~ [ Q ] Ib0/Ib
1
+ k,’.[Q]
(4)
(5)
If eq 3-5 are combined, the observed change in the total emission yield as a function of the quencher concentration is
P _ --
(1- (r)Ip + d b 0
+ where I = (1 - a ) I f+ d b . I
+ a I b o ( l + k , ’ ~ [ Q ] ) -(6) l
(1- c~)Ip{l k i ~ [ Q ] ) - l
For the Tb3+/SDS system experiments indicate that I?
= I b o , thus eq 6 reduces to
P / I = l/[(l- a)(1+ k i ~ [ Q ] ] -+’ ay(1+ ki’~[Q])-’] (7) The above equation predicts that if (1 - a) 1, then the measured quenching constant will be equal to the bulk quenching constant at the appropriate ionic strength. If a 1, the measured quenching constant will be equal to k ( , the apparent quenching constant for bound excited (28) The dissociation of TbS+from the micelle surface was also considered, however, from the data and arguments given in ref 27a this is not expected to be significant. The linear Stern-Volmer plots obtained in the present work are also in accord with this conclusion. (29) Addition of benzyl alcohol to SDS solutions was found to increase the dielectric constant at the micelle surface: K. Kalyanasundaram and J. K. Thomas, J.Phys. Chem., 81,2176 (1977). (30)For the case where quenching of a probe at the micelle surface is considered negligible see F. H. Quina and V. G. Toscano, J. Phys. Chem., 81,1750 (1977).
932
Additions and Corrections
The Journal of Physical Chemistry, Vol. 85, No. 7, 1981
ions. For the case where (1- a)is comparable to a,(with ki and k[ significantly different) then a plot of P/Z vs. [Q] would be nonlinear, showing two limiting gradients at low and high [Q], identifiable with k[ and ki.
Appendix I1 To complement the values in Table I the average number of alcohol molecules per mixed micelle was also calculated. To do this a somewhat complex procedure had to be used because the distribution constant K , (ratio of mole fraction of the solute in the micelle phase, x,, to that in the water phase, xBq)is dependenta on the concentration of added alcohol. Since there is very little information available in the literature on the variation in K, over a wide range of alcohol concentrations, it was assumed35that K , was linearly dependent on log (x,) between x, N 0.05 (31)(a) K. Hayase and S. Hayano, Bull. Chem. SOC.Jpn., 50, 83 (1977); (b) J. Colloid Interface Sci., 63, 446 (1978). (32)K. Shirahama and T. Kashiwabara, J. Colloid Interface Sci., 36, 65 (1971). (33) In using the Turro and Yekta method it is assumed that both static quenching and Poisson statistics are still valid for mixed micelles. For the I-pentanol/SDS system time-resolved measurements support this Almgren and J. E. Lafroth, to be published). The surassumption (M. factant aggregation numbers they obtained were in agreement with those in Table I. (34) M. Almgren, F. Grieser, and J. K. Thomas, J. Chem. SOC.,Faraday Trans. 1, 75,1674 (1979). (35) The basis of this assumption comes from the work of S. J. Dougherty and J. C. Berg, J. Colloid Interface Sci., 48,110 (1974).
(where values have been measured31)and x, at saturation (which were determined). Intermediate values of K , could then be used to calculate the concentration of alcohol in the micelle phase36 and, together with the aggregation numbers, the average number of alcohol molecules per micelle. The saturation limits determineds7were 0.35 (K, = 125) and 0.51 M (K, = 146) for 1-pentanol in 0.02 and 0.05 M SDS, respectively, and 1.25 M (K, = 32) for 1-butanol in 0.02 M SDS. The K , values agree reasonably well with that given in ref 34 for 1-pentanol ( K , N 150) and with those that can be calculated from the data in ref 27b, K , = 43 for 1-butanol and 152 for 1-pentanol in 0.069M SDS. were The K , values used a t low alcohol con~entrations~l 720 and 300 for 1-pentanol and 1-butanol, respectively. The number of alcohol molecules per micelle calculated with the above data are given in Table I. Acknowledgment. I thank Mats Ahngren and one of the reviewers for their helpful comments and constructuve criticism. (36) The alcohol concentrations were calculated by using eq 1-3 of ref 31a. (37)The saturation limit was taken as the point when the solution became opaque and on standing separated into two phases. At the saturation limit it was assumed that the concentration of alcohol in the water phase was the same as the solubility limit in pure water. This seems a reasonable assumption to make in view of the relative consistency of K , for different SDS concentrations.
ADDITIONS AND CORRECTIONS 1980, Volume 84
Eva Meirovitch and Jack H. Freed*: ESR Studies of Low Water Content 1,2-Dipalmitoyl-sn-glycero-3phosphocholine in Oriented Multilayers. 1. Evidence for Long-Range Cooperative Chain Distortions. Page 3281. Table I1 contains a typopgraphical error for values of R I , the rotational diffusion tensor component for the case of CSL in the biaxial phase. The correct values are as follows: T,"C 10-6Rl, S" 70
5.5
40
2.0
25
1.1
The value should also be lo6 s-l in the abstract. The correct value does appear in Figure 7.
