J. Phys. Chem. 1902, 86, 3471-3478
HOO-, although ita ring system may lose activity. The possibility of hexagonal coordination for the cobalt ion (only ion in the present study) may allow the effective modification by the carrier through its fifth coordination site to be active at ita sixth coordination site. Okura et al? assumed that oxidized C e T P P easily reads with HOO(step 2). The face-to-face cobalt porphyrin has been reported to form Gc-superoxo)dicobaltcomplex, allowing the electrochemical reduction of molecular oxygen to HzOz.16 (16)Collman, J. P.; Denisevich, P.; Konai,Y.; Marrocco, M.; Koval, C.; Anaon, F. C. J.Am. Chem. SOC.1980,102,6027.
3471
The support may encourage such redox properties of the central metal ion through a strong interaction. A large enhancement by nickel oxide and alumina may suggest that p-type semiconduction of the carrier (accepting an electron from Co-TPP) may be favorable for such a catalyst activation, in contrast to the case of N&H2 reaction.€ In addition, the enlarged effective surface area of MTPP and the local acid-base and hydrophilic natures of the carrier surface should strongly influence the activity. Limited activity increase by silica-alumina may be due tc its high acidity, which is not favorable for the dissociation of hydrogen peroxide (step 1) near the surface.
Rate of Demlcelllzatlon from the Dynamlc Surface Tensions of Micellar Solutions E. Rlllaerto and P. Jooo' DePament Cdbmb, Unlversitake Instelling Antwerpen, Universiteitsplein 1. 2610 Wllr!lk, Belgium (Received: October 27, 1981; In Final Form: April 6, 1982)
The dynamic surface tensions of micellar surfactant solutions (Triton X 100, cetyltrimethylammoniumbromide (CTAB), cetylpyridiniumchloride (CPCl),and myristyltrimethylammonium bromide (MTAB)) were measured by using the oscillating-jetand flowing-film methods. The experimental data are discussed by the assignmeni of a dilatation on a surface element. The diffusion equation considering demicellization as a chemical reactior was solved by using the concept of a diffusion penetration depth. From these experiments rate constants foi demicellization are obtained. The rate constants are of the same order of magnitudes as those obtained b5 other investigators using more classical techniques for fast reactions.
Introduction Both the oscillatingjet a d the flowing film are suitable methods for measuring the dynamic surface tension of surfactant solutions.1-3 The flowing film is a method recently developed in our laboratory and consists of flowing a surfactant solution as a thin layer (thickness of the order of 1 mm) over an inclined plate. In both methods, at a variable distance from the orifice of the jet or the inlet of the flowing film. the surface tension is measured. Following H&sen' a surface element a t a distance x has a surface age t given by t = x / u , (u, = the velocity a t the surface at x ) . The resulting surface tension as a function of time is currently discussed by diffusion of surfactant molecules from the bulk to the surface, and in many cases it is found that the adsorption kinetics are diffusion controlled. For some surfactants however (diols),P e t r P gave evidence that diffusion is not the rate-determining step. Considering surfactant solutions at concentrations exceeding the cmc, first monomers are diffusing from the bulk to the new surface. Secondly, the bulk liquid near the surface is depleted from monomers, the concentration becomes less than the cmc, and monomers are supplied by the micelles. Hence, besides diffusion, another relaxation process, micellar breakdown, becomes operative and affecta the dynamic surface tension. This dynamic surface tension depends on the rate of demicellization. This demicellization enters as a source term in the diffusion equation. Turning around the dynamic surface tension (1) R. S. Hansen, J. Phys. Chem., 68, 2012 (1964). (2)R.Defay and G. Petr6, "Surface and Colloid Science", Vol. 3, E. Matijevic, Ed., Wiley, New York, 1971,p 27. (3) R. Van den Bogaert and P. Jooe,J. Phys.Chem., 83,2244(1979); 84, 190 (1980). (4)G. Petr6, Ph.D. Thesis, Brussels, 1970. 0022-3654/82/2086-3471101.25/0
of micellar solutions yields information about the rate ai which the micelles are broken and seems to be, besides the more CO~entionalmethods as T ,P j m P and Stopped flow a method to study demicellization kinetics.
Theory
As already said, to a given surface element at a distance x from the orifice or the inlet, a surface age t is attributed t = x/u. (1:
On the other hand, one can consider, following Cerro a n d Whitaker,5 the whole system as being stationary. The mathematical analysis is very complicated; a major diffi. culty is that the hydrodynamic and (convective) diffusior equations are coupled. The fluid velocity of the surface at the inlet (at x = 0) is zero and attains a maximum value after a transition regime (strictly for x a). Among othei things, this transition regime depends on the kind oj surfactant in solution and its concentration. Apparent13 a gradient in velocity along the surface, dvJdx, occurs. Tht dilatation 0 is defined as 0 = du,/dx. This stretching 01 the surface, expressed by the dilatation, is the highest ai the inlet and becomes zero a t x m. At last, adsorption to an empty surface, as treated bj Ward and Tordai? is characterized by a relaxation timt being the same as that coming from longitudinal waw experiments.' This was corroborated by Loglio et al.'
-
-
(5)R.L. Cerro and S.Whitaker, Chem. Eng. Sci., 26,785(1971a);J Colloid Interface Sei., 37,33 (1971). (6)Ward and L.Tordai, J. Chem. Phys. (7) J. Lucassen and D. Giles, J. Chem. Soc., Faraday Trans. 1,71,21' (1975). (8)G. Loglio, E.Rherta, and P. Joos, Colloid Polym. Sci., 259,1221 (1980);G.Loglio, V. Tesei, and R. Cini, J . Colloid Interface Sci., 71,311 (1979).
0 1982 Amerlcan Chemical Society
3472
The Journal of Physical Chemistry, Vol. 86, No. 17, 1982
They showed that the adsorption to a surface can be described by the complex elasticity modulus. From this it becomes clear that the problem can be tackled along at least two separate ways. One can assign to a surface element at a distance x from the inlet a certain surface age; this is the method of Hansen, Defay, and Petr6. Or one can assign to this surface element a dilatation. An expression giving the dilatation as a function of x is yet unknown. For a simple diffusion process it can be approximated by 9 = (2t)-', t being the surface age. The problem of Ward and Tordai, allowing for demicellization, can be solved (see Appendix). Since the expression is rather involved, we prefer to follow the other way by assigning to a surface element a dilatation. For diffusion-controlled processes, the dynamic surface tension, for stationary conditions, as a function of the dilatation is given by the theory of Van Voorst Vader.g The subsurface concentration, C,, at this particular dilatation is C, = Co - I'(d/2D)'J2 (2) where Co = bulk concentration (mol ~ m - ~r) = , adsorption (mol cm-2), ?r = 3.14..., D = diffusion constant (cm2 s-l), and 9 = dilatation (s-'). The subsurface concentration is related to the surface tension by means of a suitable equation of state, e.g., the von Szyszkowski equation. Assuming small dilatations, the difference in subsurface concentrations is related through the difference in surface tensions : AC, = Co - C, = (dC/da)Aa (3) with Au = ud - uo, uo = surface tension at equilibrium, and a d = dynamic surface tension at the dilatation. From eq 2 and 3 one obtains
(4) The restriction that Au must be small to allow for eq 4 is not too severe. Assuming a relaxation between subsurface and adsorption of the Langmuir type, one finds for high concentrations
r-da dC
RTI"
e=-
-du d In r (1
1
+ 2r + 2 r 2 ) 1 / 2
(8)
where r is the Lucassen number given by 7
-(-)D
= dc
d r 2w For
7
>> 1, hence for low w, eq 8 becomes
) 5
€=-r--( du w dC
'1'
The modulus of elasticity is equal to the jump in surface tension, Au, if
9 = 2u/*
(11)
The dilatation 9 can be seen as a degenerated frequency. Returning now to micellar solutions, as already said, an additional source term must be added to the diffusion equation:
+
&/at = D ( d 2 c / d z 2 ) k(C0 - C)
(12)
where z is the coordinate normal to the surface, C is the monomer concentration, Co is the cmc, and k is the rate constant for demicellization. It is assumed that the demicellization follows a first-order reaction and that diffusion of the micelles may be neglected (see further). Moreover micelles are not surface active. Danckwerts" considered a diffusion equation of this type, and from his results an expression for the diffusion penetration depth is obtained: (aDt)'I2 6=
~
where r" = saturation adsorption, a = the Langmuir-von Szyszkowski constant, and lI = surface pressure. Hence, assuming Rm" = 10, for a surface tension between 30 and 40 dyn cm-', r(du/dC) changes by a factor of 2.71. Hence, for diffusion-controlled adsorption kinetics the dynamic surface tension can be discussed as well by the theory of Ward and Tordai as by Van Voorst Vader's theory. The point is that in both cases the diffusion penetration depth, 6, must be equal. For the situation of Ward and Tordai, this penetration depth is given by the penetration theory (5) whereas, for the situation of Van Voorst Vader, film theory is used to obtain 6 = (aDt)'I2
+
erf (kt)'J2 exp(-kt)
(13)
[xD\'/~
1
This expression may be substituted into the equation for conservation of mass at the interface, under steady-state conditions (dI'/dt = 0)
yielding an expression for the dynamic surface tension (remembering eq 3)
(6)
6 = (aD/29)'/' From eq 1,5, and 6 one gets 9 = 1 / 2 t = u, / 2 x
(7)
If one plots the dynamic surface tension as a function of the square root of the dilatation, a linear relation must be ~
found, at least for small dilatations. For very high dilatations, of course, the surface tension of pure water should be found. It is noteworthy that the theory of Van Voorst Vader bears some analogy with elasticity measurements. According to Lucassen,'O the modulus of elasticity, e, at a given angular frequency w is given by
Making use of eq 7, eq 13 can be written as
2)
--Rmm2 a
Rillaerts and Joos
~~~
~~~
(9)F. Van Voorst Vader, Th. Erkelens, and M. van den Tempel, Trans. Faraday SOC.,60, 1170 (1964).
(16) equation 16 reduces to eq 4 for k = 0 as it should. A (10)J. Lucassen and M. van den Tempel, Chem. Eng. Sci., 27, 1283 (1972). (11)P.V. Danckwerta, Trans. Faraday SOC.,46, 300 (1950);47, 1014 (1951).
Dynamic Surface Tensions of Mlcellar Solutions
The Journal of phvsical Chemktty, Vol. 86, No. 17, 1982 3473
numerical calculation reveals that for k/26 1 1eq 16 approximates to
ud (dYne m-')
I
For submicellar solutions, the dynamic surface tension is proportional to whereas for micellar solutions it is proportional to 6. The rate of demicellization can be obtained. For doing this, we can perform an experiment a t a concentration just below or a t the cmc. Here the dynamic surface tension, ad*, (ad* = dynamic surface tension as a function of 6, at the cmc) follows eq 4, whence dad*/d6'/2 = -I'(da/dC) ( T / 2O)'l2
(18)
For micellar solutions one has from eq 17
where adM = dynamic surface tension of micellar solutions. For micellar solutions, as yet argued by Lucassen, the parameters r, du/dC, and, of course, D, are the same as those for a solution just below the cmc. The reason is that, by further increase of the total concentration, the monomer concentration is constant and only the concentration of micelles increases and that micelles are not surface active. Since both slopes d ~ r ~ * / d 6and ' / ~ dadM/d6are known, one can eliminate I'(dcr/dC)D-1/2yielding k.
a = -2[
(dad*/d6'12)
T
]
2
I
I
1
2
procedure can be followed. Using Gibbs' equation -da = RZT d In C (21) one gets for
-Rm2
=dC C and I?,at the cmc, is obtained from the equilibrium surface tension log concentration plot. For the diffusion constant D,one has to assume a reasonable value. Hitherto, we have neglected the diffusion of the micelles. For the dynamic surface tension one can consider three situations. (i) The demicellization rate k is small compared with the dilatation 6, and the dynamic surface tension obeys eq 3. (ii) The rate constant is of the order of magnitude of 6 and eq 16 must be used. (iii) The rate of demicellization is much faster than diffusion. As Lucass e d 2 has shown, this merely results in a diffusion-controlled mechanism with an effective diffusion constant much larger than the real one. At last it should be stated that the functional relationship between the dynamic surface tension and the dilatation gives information about the relaxation processes which are operative. If the dynamic surface tension is proportional to ell2, then only diffusion occurs. However, if the dynamic surface tension is proportional to 6, other mechanisms are operative. Here attention to micellar relaxation is stressed. But also similar processes as desolubilization and even PetrB's results for diols gave such a relationship.
Experimental Section The method for measuring the dynamic surface tension by flowing a surfactant solution over an inclined plate was (12)J. Lucasaen, Faraday Discuss. Chem. SOC. 59, 76 (1976).
I
I
3
I
I
L
5
(,+)
I
6
7
a
Flgure 1. Dynamic surface tension u,, (dyn cm-') of sodium laurate in 0.1 N NaOH (C = 1.52 X lod mol cm3) as a function of the square root of the dilatation 0 (si)(from ref 3)(inclined plate).
described previously. For measurements with the oscillating jet, Petre's apparatus was used. The wavelength is obtained by measuring the distance between the focal lines, visualized on a screen, using a traveling microscope (horizontal cathetometer). From the wavelength, the surface tension a was calculated by using Bohr's2 formula:
(dadM/d6)
If an experiment just below the cmc is not feasible, another
r-da
501
a=-
4 p F 1 + (37/24)(b2/a2) 6ah2 1 + (5/3)(7r2a2/Xz)
(23)
where p = density, F = flow rate, a = mean radius of the jet (a = 0.0208 cm), X = wavelength, and b = amplitude of the jet oscillation (b = 0.0014 cm). For pure water the right surface tension was found after the fourth wave. As surfactants we used a nonionic Triton X 100, purchased from Merck, which was not pure. The other surfactants were of Anal& grade. All experiments were performed a t room temperature (20 f 2 OC).
Results and Discussion The validity of eq 4 and 7 was checked experimentally for surfactant solutions below the cmc. As an example, Figure 1gives the results, published previously,3for sodium laurate using the flowing-film method, and Figure 2 gives the results for an octanol solution (oscillating jet). Good agreement is obtained, and the resulting diffusion coefficients are acceptable (D = 4 X lo* cm2 s-' for sodium laurate a t C = 1.52104 mol ~ m - D~ = , 6.7 X lo4 em2 s-' for odanol at C = 1.34 X lo* mol ~ m - ~These ). results can even well be dimmed as on the basis of Ward and Tordai's theory. Further evidence about the linear relationship between the dynamic surface tension and the square root of the dilatation is given by solution of Triton X 100, below the cmc (Figure 3). The cmc of Triton X 100 obtained from equilibrium surface tension measurements is 0.1 g L-'. The dynamic surface tension of this solution is given in Figure 3 and plotted vs. O1l2 (results obtained with the flowing film). Disregarding for a moment that our Triton X 100 sample was not pure, we will nevertheless try to get a diffusion coefficient. From eq 18 and 22
Here C is the concentration at the cmc (mol wt
- 647,
3474
The Journal of physical Chemlstiy, Vol. 86, No. 17, 1982
Riilaerts and Joos
/
f
701
' / /
/
/
/
I
Flgure 2. Dynamlc surface tension of octanol solutlon (C = 1.34 X lod mol cm4) as a function of the square root of the dilatation (oscillating Jet).
/
I
I
25
5
7:
Flgure 4. Dynamlc surface tension of T r b n X 100 at a concentratlon twice the cmc as a function of the dilatation (Inclined plate).
I
0
60
0 /, /
/
0
/ / -
0
Flgure 3. Dynamic surface tenslon of Triton X 100 at the cmc as a function of the square root of the dilatation (Inclined plate).
whence at the cmc C = 1.54 X mol ~ m - ~ From ). the equilibrium surface tension curve we obtain an adsorption I' = 2.7 X 10-lo mol cm-2. According to Herrmann and Kahlweit,I3 the cmc of Triton X 100 at 10 "C is 3 X ~~~
~
(13)C. V. Herrmann and (1980).
M. Kahlweit, J. Phys. Chem., 84, 1536
/
/
//
/
o
I
Lv
/ /
50
0
/
/
40v /
/
/
/
/
/
40
30
t
Flgure 5. Same as Figure 4 but plotted as a square root of the dilatation.
mol ~ m - ~Our . value (1.54 X lom7mol cm-? seems to be in agreement with this, considering our sample is not pure and our measurements were done at room temperature (about 22 "C). When these data are used, a diffusion coefficient D = 7 X lo-' cm2 s-l is obtained. This value is somewhat too low; this is due to impurities in our sample. In Figure 4 the dynamic surface tensions of a Triton X 100 at a concentration twice the cmc are plotted vs. 0. In agreement with eq 17 a linear relation is found except at low dilatations. Replotting the same data, but as a function of the square root of the dilatation shows that at low dilatations a linear relation is observed, sug-
The Journal of Physical Chemistty, Vol. 86, No. 17, 1982 3475
Dynamic Surface Tensions of Micellar Solutions
TABLE I: Demicellization Constants (k)a
ync em")
CT(cmc)
CT(cmc)
k , s-'
k, s"
Triton X-100 2 3 5 2.5 5 1.5 2.63 5.25
7.5 10
4.5 30.5 74.4
298 608
CTAB~ 10 15 20 CPCW 171 7.89 165 10.53 180 240 270
270 240 240 154 188
MTAB 6.25 9.37
828 1438
13.00 5568 18.75 18040 CT = total concentration. tk) = 240 s". T = 4.2 X 10-3. c tk) = 170 s - 1 . 7 = 5.9 x 10-3.
x x
X
x
X
I
I
I
5
10
15
(3.7
e
Figure 8. Dynamic surface tensions of micellar Triton X 100 soiutlon: (0)3 X cmc; (X) 5 X cmc; ( 0 )7.5 X cmc; ( 0 ) 10 X cmc.
gesting that in this time scale the adsorption process is controlled by diffusion (Figure 5). For this time scale the demicellization rate is fast and diffusion of micelles becomes more important. When one calculates from these data the diffusion coefficient, a value D = 3.7 X lo* cm2 s-l is obtained. This value is significantly larger than the one obtained a t concentrations below the cmc (D= 7 X lo-' cm2 s-l), indicating that diffusion of micelles cannot be neglected. Finally, the dynamic surface tensions of Triton X 100 at increasing concentrations are plotted as a function of the dilatation (see Figure 6). Again, the results are in agreement with eq 17. It should be stressed that the extrapolated surface tension at 0 0 from the curve does not yield the equilibrium surface tension. As suggested previously for a Triton X 100 concentration twice the cmc, in the low dilatation range diffusion of micelles becomes important, and the demicellization rate is fast. As outlined previously, the demicellization constant is calculated and results are given in Table I. Next, we investigated the dynamic surface tension of cationic micellar solutions. For cetyltrimethylammonium bromide (CTAB) we found a cmc of lo* mol cmT3,in agreement with literature data. From the equilibrium surface tension concentration curve, we calculated an adsorption at the cmc of 2I' = 5.7 X mol cm-2. The dynamic surface tension of a solution at the cmc was measured with the oscillating jet and the inclined plate; results are given in Figure 7 as a function of the square root of the dilatation. Again, the adsorption is controlled by diffusion, and, using eq 23, we obtained a diffusion coefficient D = 5.6 X lo* cm2 s-l. Results for micellar CTAB solutions, obtained by the oscillatingjet, are given in Figure 8; eq 17 is again confirmed. The demicellization constants obtained are given in Table I and are rather independent of the concentration. The
-
Flgure 7. Dynamic surface tension of CTAB at the cmc as a function of the square root of the diiatatlon: (0)inclined plate; (X) oscillating jet.
relaxation time 7 for demicellization defined at 7 = k-' is 4.2 X s. As already observed for Triton X 100, the extrapolated surface tensions for 0 0 are below the equilibrium value. One can turn around and define, somewhat arbitrarily, a critical dilatation Bo where the dynamic surface tension becomes equal to the equilibrium surface tension. For dilatations below Bo the micellar breakdown is fast, and the dynamic surface tension is controlled by the diffusion of micelles. Apparently this diffusion is so fast that the dynamic surface tension does not differ from the equilibrium value. The results for cetylpyridinium chloride are similar to those for CTAB and are given in Figure 9 and Table I. The mol cm-2. For a CPCl solution at the cmc was 9.5 X cmc dcd*/dB'I2 was 2.8 dyn s1I2 cm-', yielding a diffusion
-
3476
The Journal of Physicel Chemistry, Vol. 86, No. 77, 1982
Rillaerts and Joos
c
70 1
50
Flgure 8. Dynamic surface tension of micellar CTAB solutions as a function of the dilatatkm: (1) 2.5 X lo-', (2) 5 X lo", (3) 7.5 X lo", (4) (5) 1.5 X and (6) 2 X mol ~ m (osciilating - ~ jet).
70
i I
1
I
I
(4-1)
100 200 e Flgurs 9. Dynamic surface tension of CPCl as a function of the dilatation: (1) 2.5 X lo-', (2) 5 X 10" (3) 7.5 X lo-', and (4) mol ~ m (oscillating - ~ jet).
100
150 e(s-1)
Flgure 10. Dynamic surface tension of MTAB in 0.05 M KBr as a function of the dilatation: (1) 2.5 X lo-', (2) 3.75 X lo", (3) 5 X lo-', and (4) 7.5 X lo-' mol omF3(oscillating jet).
coefficient D = 8.6 X lo4 cm2s-l (r = 5 X 10-lomol cm-2). As for CTAB the demicellization constant is independent of concentration and the relaxation time 7 = 5.9 X s. Last, we studied the demicellization rate of myristyltrimethylammonium bromide (MTAB). The cmc was 3.5 X lo4 mol ~ m - ~ The . dynamic surface tension plotted as a function of the square root of the dilatation gives a straight line with a slope dad*/dO'/' = 1.15; the adsorption at the cmc was found to be 5.2 X 10-lo mol cm-2. From these data a diffusion coefficient D = 4.5 X lo4 cm-2s-l is calculated. However, the time scale of our apparatus was not appropriate to study demicellization rates. Therefore, to MTAB 0.05 M KBr was added; the cmc is now 4 X mol cmW3. With the oscillating jet and for this concentration, no significant decrease in surface tension was observed. For this we were forced to calculate the slope dud*f dullZ= 10.1. Results for micellar MTAB solutions are given in Figure 10;the rate constants for demicellization are given in Table I. In contrast with the other cationics these rate constants strongly depend on concentration. It was our aim not to study the rate of demicellization but to investigate how the dynamic surface tension of surfactant solutions is affected by the presence of micelles. It is evident that only the slow relaxation time is observed. Further, it should be stressed that our method deals with quite large deviations from equilibrium between micelles and monomers. Nevertheless, it is expected that the rate constants coming out of this work are comparable with results of other investigators. The relaxation times for cationics were measured by Kresheck et and by Inoue et al.15 and compared with ours. We found that, for CTAB (14) G. C. Kresheck, E. Hamori, G. Garyport, and H. A. Scheraga, J. Am. Chem. SOC.,88,246 (1966). (15)T. Inoue,R.Tashiro, Y. Shibuya, and R. Shimozawa, J. Colloid
Interface Sci., 73,105 (1980).
Dynamic Surface Tensions of Micellar Solutions
and CPC1, the relaxation time did not depend on the concentration of micelles. Inoue et all6 investigated the relaxation times for sodium alkyl sulfates and observed that the relaxation time was independent of concentration. Adding some minor components yielded a relaxation time which was concentration dependent. However, they stated that this feature may not be generalized. Our data for CTAB and CPCl are in agreement with this. For Triton X 100 and MTAB (containing 0.05 M KBr) the relaxation time depends on concentration. As already said, our Triton X 100 sample was not pure. For MTAB the relaxation time was concentration dependent; we do not know whether this is proper for MTAB or is due to the addition of KBr or to impurities in our sample. Herrmann and Kahlweit13studied the relaxation time for Triton X 100 by P and T jump. Their highest slow rate constant was 30 s-l at concentrations ranging from 2 to 5 times the cmc. For this concentration range our data are comparable with theirs. Lucassen12performed elasticity measurements on micellar solutions of nonionics. In his theory, Kresheck's relation was used, and therefore his results are not strictly comparable with ours. For a series of nonionics the rate constants at a concentration 10 times the cmc ranged from k = 70 s-l to k = 2000 s-l. Our rate constant for Triton X 100 at a concentration to times the cmc falls into this range (k N 600 s-l). The dependence of the relaxation time on concentration is explained by the theory of Aniansson and co-worker~.'~ This theory, which is now widely accepted, considers demicellization as a steady flow of aggregates through a narrow passage of intermediate aggregates and includes the Kresheck equation14 as a special case. Anyhow, our data for Triton X 100 and MTAB do not obey the equation of Kresheck. The equation of Aniansson et al. contains parameters not known to us, and we are not confident enough with their theory to discuss our data. We have proved experimentally that for micellar solutions the dynamic surface tension is a linear function of the dilatation, whereas for submicellar systems it is proportional to The reason for this is that micellar breakdown must be accounted for in the diffusion equation and this second relaxation mechanism becomes operative. We think that this is general. If adsorption kinetics are diffusion controlled, the jump in surface tension, Au (Au = Ud - u,, 6, = equilibrium surface tension), is plotted as a function of the dilatation on a log-log scale, and the slope is 0.5. A higher slope indicates that another relaxation mechanism occurs. This will be supported by two examples. First, one can expect that desolubiliiation of a minor component should give a similar relation. Therefore, we added dodecanol to a sodium dodecyl sulfate (SDS)solution at a concentration above the cmc. After some time the solution became clear, indicating that dodecanol is incorporated into the micelles. Using the inclined plate, we measured the dynamic surface tension of this solution. In all of the cases that we studied, results plotted on a log-log scale (log AT vs. log e) yield an initial slope exceeding 0.5. An example is given in Figure 11 (slope = 1). Secondly, using the oscillating jet, Petri5 studied adsorption kinetics of dial~ohols.~ He observed a diffusion coefficient which was far too low and postulated an adsorption barrier. This adsorption barrier is due to molecular rearrangements in the surface. We plotted PetrB's results (an example is (16)T.Inoue, Y.Shibuya, and R. Shimcnewa, J.Colloid Interface Sci., 65,370 (1978). (17)E.A. G. Anianaaon and S. N. Wall, J. Phys. Chem., 78, 1024 (1974);M.Almgren, E.A. G. Anianason,and K. Holmaker, Chem. Phys., 19,l(1977).
The Journal of Fhyslcal Chemistry, Vol. 86, No. 17, 1982 3477
I
I
0.5
1
(e: 3-1) log e
-
Figure 11. Dynamic surface tension (Au = u,, ue)as a function of the dllatatbn (log-log scale) for a micellar SDS (C = 2 X lo-' mol cm3) dodecand (C = 6 X lo-' mol an3)solution. EquHibrkrm surface tension u, = 30.6 dyn cm-' (inclined plate) (slope = 1).
log& n o
0-
-0.25-
- 0.5 -
-0.75 -
tI
-l
(e: 4 4 ) 1.5
2.0
439
Figure 12. Dynamic surface tension of a 1/10 decanediol solution (C = 2.5 X 10" mol cm3) as a function of the dilatation plotted on a log-log scale. u, = 56.4 dyn cm-' (slope = 1); Au = ud- u,: ?ro = surface pressure, u, - ue (u, = surface tension of water).
given in Figure 12) on a log-log scale, the slope being always larger than 0.5. This seems to be in agreement with PetrB's explanation that diffusion is not the rate-determining step and that another mechanism is present. On the other hand, Van Voorst Vader, using similar substances, observed that the kinetics of adsorption was ruled by diffusion. These facts are not conflicting since for both experiments the time scales are entirely different (Petr6, s; Van Voorst Vader, 100 s). 1 X 10-3-10 X
J. Phys. Chem. 1982, 86,3470-3403
3478
-
-
Acknowledgment. Dr. Petr6 of the University of Brussels is acknowledged for the help with the oscillating-jet apparatus. E.R. is greatly indebted to the Belgian I.W.O.N.L. for financial support during the course of this work.
Making now the long-time approximation, k t >> 1, erf (kt)'I2 1,exp(-kt) 0, and considering C, as a constant, then eq A.2 and A.3 approximate to
Appendix It will be shown that the assignment of a surface age to a surface element (the method of Hansen, Defay, and Pet$ yields substantially the same result. If one uses the Laplace transformation on eq 1 2 and accounts for the conservation of mass at the surface
AC = r[r/(4Dt)I1/' (k 0) (-4.5) The corresponding jump in surface tension is for micellar solutions
(A.1)
d r / d t = D(dC/&),
AC = I'/[(kD)1/2t]
-
and for simple diffusion
results, after rather tedious calculations, in
r=,
( 2
2k1I2
s,
t1/2
(-4.7) exp(-kt)] -
:)'jz
If one compares relation A.6 with eq 17, it is seen that 9 = l / t rather than 9 = 1/2tas for simple diffusion. From eq A.6 and A.7 it follows that
C,(t - 7 ) e-kr d7lI2 -
k=
(k7)'I2 d71/2
It is shown that eq A.2 reduces for k of Ward and Tordai:
-
0 to the relation
c,(t - 7 ) d71/2 ( ~ - 3 )
-[ 4
it1" C, (t erf 7)71/2
64.4)
T
da*/d(l/t1/2) da/d(l/t)
]
2
(A.8)
Hence, k calculated from eq A.8 differs only by k obtained from eq 20 by a numerical factor (k from eq 20 is a factor 2 too small as calculated from eq A.8). The introduction of the concept of diffusion penetration depth simplifies much of the mathematical analysis and gives results at least of the correct order of magnitude.
Photoionization of Aromatic Amino Acids in Aqueous Solutions. A Spin-Trapping and Electron Spin Resonance Study Magdl M. Mossoba, Kelsuke Maklno, and Peter Rlesr" Laboratory of PathophysMogy, National Cancer Instltote, Natbnal Instnotes of Health, Bethesda, Maryland 20205 (Received: February 26, 1982; In Flnal Form: May 3, 1982)
The wavelength dependence (280-334 nm) of the photoionization of tryptophan (Trp), tyrosine (Tyr), and phenylalanine (Phe) in aqueous solution was investigated by means of ESR and spin trapping. Chloroethanol, glycine (Gly), and alanine (Ala) were used to scavenge the hydrated electrons in the pH range 7-10. The dechlorination radical from chloroethanol and the deamination radicals from glycine and alanine were spin trapped with 2-methyl-2-nitrosopropane(MNP) and identified by ESR. From these observations it was inferred that photoionization could occur at 280 f 10 and 313 f 7 nm but not at 334 f 10 nm.
Introduction The photochemistry of the aromatic amino acids plays a dominant role in the inactivation of enzymes by UV light.lP2 Continuous irradiation and flash photolysis studies of tryptophan (Trp) below 275 nm indicate that an efficient initial process consists of ejecting an electron which results in the formation of a radical ~ a t i o n l that -~ could deprotonate giving a neutral r a d i ~ a l . ~A flash photolysis study of Trp with 300-360-nm radiation by Pailthorpe et al.e indicated fission of the N-H bond of (1) Grossweiner, L. I. Curr. Top. Radiat. Res. Q. 1976, 11, 141. (2) Vladimirov, Yu. A.; Roshchupkin, D. I.; Fessenco, E. E. Photochem. Photobiol. 1970, 11, 227. (3) Amouyal,E.; Bemas, A.; Grand,D. J. Phys. Chem. 1977,81,1349. (4) Bangher, J. F.; Grwweiner, L. I. Photochem. Photobiol. 1978,28, 175. (5) Santus, R.; Grossweiner, L. I. Photochem. Photobiol. 1972,15,101.
indole followed by rearrangement to the neutral 3-indolyl radical. In an investigation by Amouyal et al.3 of the photoionization of Trp in deaerated neutral aqueous solutions as a function of wavelength, in which nitrous oxide was used as the solvated electron (eaq-)scavenger and the N2 yield was monitored by gas chromatography, it was concluded that a photoionization threshold exists at 275 nm. In contrast, a study by Steen,' in which Trp solutions containing ferrous sulfate and oxygen were irradiated and the Fe3+yield was measured spectrophotometrically, revealed that the e, - yield was observed up to 300 nm. The yield markedly aecreased around 260 nm and was constant in (6)Pailthorpe, M. T.; Nicholls, C. H. Photochem. Photobiol. 1971,14, 135. (7) Steen, H. B. J. Chem. Phys. 1974, 61, 3997.
This article not subject to US. Copyright. Published 1982 by the American Chemical Society
