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Langmuir 1996, 12, 1688-1689
Notes Temperature Dependence of Gas Permeability of Newton Black Films Rumen Krustev, Dimo Platikanov,* and Michael Nedyalkov Department of Physical Chemistry, University of Sofia, 1126 Sofia, Bulgaria Received August 23, 1995. In Final Form: November 20, 1995
Introduction Recently we presented1 experimental results about the dependence of the gas permeability coefficient K (cm/s) of Newton black films (NBF) on the surfactant concentration C at four different temperatures. We discussed the results using our assumption2 that K can be presented as a sum of background permeability coefficient K0 of the hole-free area of the film and the corresponding coefficients Ki of the holes of i molecular vacancies.
K ) K0 +
∑i Ki ) K0 + ∑i aiC-i
(1)
According to the nucleation theory of hole-mediated stability and permeability of surfactant bilayers,3-5 the NBF being a bilayer is populated by molecular vacancies as well as holes (clusters of i vacancies). This theory derives expression for the coefficients ai. In ref 1, we fitted the theoretical equations3-5 to the experimental results and found an interesting difference: while for the lower temperatures (23 and 25 °C) the fitted curve coincides well with the experimental points also in the concentration range where K is constant, for both higher temperatures (27 and 30 °C) the experimental points in the same C range lie above the fitted curve. We called Kp1 the K value obtained experimentally from the K(C) curve plateau at C > cmc, and we assumed the constant K value of the horizontal part of the fitted theoretical curve is K0. Hence for both lower temperatures Kp1 ≈ K0 while for both higher temperatures Kp1 > K0. When we presented the temperature dependencies of K0 and Kp1 in Arrhenius coordinates, we obtained a straight line with constant slope for ln K0(1/T), but a straight line with a kink for dependence ln Kp1(1/T), the slope being smaller in the range 27-30 °C than the slope in the range 23-27 °C. This change in the slope is an indication for a change in the mechanism of gas permeation through the bilayer film. The following preliminary hypothesis has been assumed in ref 1. According to the theory,3-5 more and more holes of larger size i are likely to form with increasing temperature. Hence there is a significant constant number of holes in the bilayer film although the surfactant concentration is above cmc. The theory requires2-5 the number of holes to decrease with increasing C, and at a * E-mail:
[email protected] (1) Nedyalkov, M.; Krustev, R.; Stankova, A.; Platikanov, D. Langmuir 1992, 8, 3142. (2) Nedyalkov, M.; Krustev, R.; Kashchiev, D.; Platikanov, D.; Exerowa, D. Colloid Polym. Sci. 1988, 266, 291. (3) Kashchiev, D.; Exerowa, D. J. Colloid Interface Sci. 1980, 77, 501. (4) Kaschiev, D.; Exerowa, D. Biochim. Biophys. Acta 1983, 732, 133. (5) Exerowa, D.; Kashchiev, D. Contemp. Phys. 1986, 27, 429.
given characteristic concentration Cch, Ki becomes negligible, i.e. K ) K0 for C > Cch. It seems that at lower temperatures Cch < cmc and K ) K0 in our case. With increasing temperature both Cch and cmc change so that above certain temperature Cch > cmc, and in our case the hole-mediated permeability noticeably contributes to the gas permeation, i.e. K ) K0 + ∑Ki. However the measurements at four temperatures only were not sufficient to get more reliable conclusions, as well as to determine the temperature point at which the mechanism changes. Here we present a detailed study of the temperature dependence of K of NBF at C > cmc. Experimental Section In the present study we used a new procedure for determination of K from the experimental data, which provides better accuracy than that used in refs 1 and 2. The new procedure allows determination of K of NBF with small contact angle θ between the film and bulk while the procedure in refs 1 and 2 is suitable at θ > 7°. We used the same experimental apparatus as in ref 1, the so-called “diminishing bubble method” described in ref 2. The temperature has been kept constant by thermostatic microscope stage with accuracy of (0.1 °C. The NBF radius r as well as the bubble radius Rb of a small gas bubble floating on the solution surface was simultaneously measured at fixed time intervals during the spontaneous diminishing of the bubble. In the new procedure we again used the definition6,7
K ) -(dN/dt)(∆Cg/A)
(2)
∆Cg ) (2σ/Rb)(1/RT)
(3)
with
Since the gas can be treated as ideal, the number of moles N(t) of gas in the bubble as a function of time t is given by
N(t) ) (Pat + 2σ/Rb)4πRb3/3RT
(4)
The film area A(t), however, is given now by the approximation
A(t) ) πr2
(5)
The integration of eq 2 with eqs 3 and 4 yields
K ) [(Pat/2σ)(R04 - Rt4) + (8/9)(R03 - Rt3)]/
∫r
t 2
0
dt (6)
where R0 ≡ Rb(0), Rt ≡ Rb(t), Pat is the atmospheric pressure, and σ is the solution surface tension, measured separately by the Wilhelmy method. The integral in the denominator of eq 6 is calculated numerically using the Newton rule from the experimental data (one example is shown in Figure 1 for a bubble at 25 °C). The measurements have been carried out with only one aqueous solution of sodium dodecyl sulfate (SDS): 2.0 mM SDS plus 0.5 M NaCl. The SDS used has been prepared by Henkel GmbH (Germany) especially for scientific research; the sodium (6) Princen, H. M.; Mason, S. G. J. Colloid Sci. 1965, 20, 353. (7) Princen, H. M.; Overbeek, J. Th. G.; Mason, S. G. J. Colloid Interface Sci. 1967, 24, 125.
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Langmuir, Vol. 12, No. 6, 1996 1689
Figure 1. One example experimental data film radius r vs time t used for calculation of the integral in the denominator of eq 6 for a bubble at 25 °C. Table 1. Experimentally Obtained Mean K Values Together with Their Standard Errors ∆ t, °C K, 10-3 cm/s ∆, 10-3 cm/s
22
23
25
26
27
29
30
31
32
25 2
28 1
34 3
38 2
41 1
49 2
55 4
56 2
62 3
chloride p.a., recrystallized, has been roasted at 600 °C to eliminate organic impurities.
Results and Discussion The surfactant concentration C ) 2 mM used in the present measurements corresponds to the middle of the plateau in the K(C) curves (Figures 1 and 2 in ref 1) and in the whole temperature range C > cmc. That means the measured K value for each temperature coincides with the corresponding Kp1. That is why in the present paper we avoid the subscript “pl”. Each mean K value has been obtained from 10 to 20 single measurements. All experimental data are presented in Table 1 together with the standard errors, ∆. The experimental data from Table 1 are presented in Arrhenius coordinates8,9 in Figure 2. It is clear that the experimental points do not follow a straight line with constant slope in the whole temperature range. We assume there is a kink in the ln K(1/T) dependence, i.e. there are two straight lines with different slopes. We applied the following procedure to find the cross point of these straight lines. The slopes of the straight lines successively fitted to the three, four, five, etc. points beginning from the lowest temperature have been calculated. The same has been done beginning from the highest temperature. It has been found that in both cases the slope noticeably decreases, (8) Retardation of Evaporation by Monolayers: Transport Processes; LaMer, V. K., Ed.; Academic Press: New York, 1962. (9) Barnes, G. T. Adv. Colloid Interface Sci. 1986, 25, 89.
Figure 2. Temperature dependence of the gas permeability coefficient of NBF in Arrhenius coordinates.
or respectively increases after the experimental point for 26 °C. Hence we fitted the straight line 1 to four experimental points (22-26 °C) and another straight line 2 to six experimental points (26-32 °C). In the lower temperature interval an activation energy E ) 73 ( 4 kJ/mol has been calculated from the slope of the straight line 1 and E ) 63 ( 3 kJ/mol, from the slope of straight line 2 in the higher temperature range. The difference between the E values in the lower and higher temperature range is an indication that at about 26 °C there is a change in the mechanism of gas permeation through these NBFs. The activation energy of 73 kJ/mol is very close to the E value calculated1 from the ln K0(1/T) dependence for the background permeation. Above 26 °C the activation energy is smaller. The present results are in favor of our preliminary hypothesis1 that at higher temperature (26-32 °C) in addition to the background permeability K0 through hole-free bilayer there is also a hole-mediated permeability Ki, i.e. below 26 °C K ) K0 and above 26 °C K ) K0 + ∑Ki. It is interesting to note that at temperatures close to 26 °C phase transition has been established in the system SDS + water.10,11 In general, if a phase transition would occur in the bilayer film, the binding energy Q of a molecule in the bilayer will be smaller at temperatures above the transition point. The smaller the value of Q, the larger the number of holes that will occur in the bilayer.3-5 This is in qualitative agreement with the above-presented interpretation of the experimental results. Acknowledgment. The authors acknowledge with thanks the financial support of the Bulgarian National Fund “Scientific Research”, contract no. X-220. LA950711O (10) Kekicheff, P.; Grabielle-Madelmont, C.; Ollivon, M. J. Colloid Interface Sci. 1989, 131, 112. (11) Kekicheff, P. J. Colloid Interface Sci. 1989, 131, 133.
