4515
Langmuir 1996,11, 4515-4518
The Adsorption of Triton X-100 at the Air-Aqueous Solution Interface B. Janczuk,i J. M. Bruque," M. L. Gonzalez-Martin, and C. Dorado-Calasanz Departamento de Fisica, Universidad de Extremadura, 06071 Badajoz, Spain Received October 19, 1994. I n Final Form: August 14, 1995@ Measurements ofthe surface tension of aqueous solutions of Triton X-100(TX-100) were made at different temperatures. Isotherms and thermodynamic adsorption parameters were determined from the surface tensions. Also, the equation of state for the monolayer film of TX-100at the water-air interface was analyzed. A linear dependence was found between log r and log C in the region of low concentration of TX-100in solution,and three differentmethods used to calculatethe free energy of adsorptiongave slightly different results. In the region of low concentration the ll(A - Ao) values were equal to 1kT. At high concentration,there were attractive Lifshitz-van der Waals forces between the apolar parts of the TX-100 molecules and repulsive acid-base forces between the heads of the TX-100molecules in the adsorbed monolayer film.
Introduction Nonionic surfactants have a wide applicability theoretically and technologically. The mechanism of adsorption of nonionic surfactants, especially at the liquid-air interface, and the orientation and interaction of their molecules in the interface region have been the subject of study over recent decades.ls2 It is currently well established that surfactants form monolayer films at the solution-air interface. The nature of these interfacial monolayers is elucidated by applying a rigorous thermodynamic treatment to the interfacial tension data which are considered as a function ofdifferent thermodynamic variables. Thermodynamic studies of aqueous solutions of Triton X-100are important for understanding the apolar and polar interactions between Triton X-100 and water molecules. The standard thermodynamic adsorption parameters can be determined from the surface tension data for very dilute solutions of surfactants, where the reduction in surface tension varies linearly with the molar concentration of the surfactant in bulk. Unfortunately, good surface tension data in this region are difficult to obtain, and in the literature there are few studies on the low concentration range, because investigations ofthe effect of surfactants on the surface tension of solvents have generally been restricted to the region where the reduction of the surface tension is important. The surface tension data in the region of low surfactant concentration can also be useful in the study of the equations of state for monolayer surfactant films at the air-liquid and liquid-liquid interfaces. On the basis of these data, it is possible to establish the limiting value of the product rL4 (IT is the difference between the surface tensions of solution and pure solvent, andA is the surface area per molecule) and the region of A values where the intermolecular interactions between surfactant molecules influences appreciably the surface tension of the solution. Thus the purpose of this present work was to measure the surface tension of aqueous solutions of TX-100 at * T o whom all correspondence should be sent. E-mail:
j
[email protected] .es.
' On sabbaticalleavefrom the Departmentof Physical Chemistry, Faculty of Chemistry, Maria Curie-Skiodowska University, 20031 Lublin, Poland. Abstract published in Advance A C S Abstracts, November 1, @
1995. (1)Rosen, J. M. In Surfactants and Interfacial Phenomena; Wiley Interscience: New York, 1989. (2) Chatoraj, D. K.; Birdi, K. S. In AJsorption and Gibbs Surface Excess; Plenum: New York, 1984.
different temperatures, particularly at low concentrations. We also evaluated standard thermodynamic adsorption parameters and tested the equation of state in terms of Lifshitz-van der Waals and acid base (Lewis) intermolecular interactions.
Experimental Section Triton X-100(TX-100) is a p-( 1,1,3,3-tetramethylbutyl)phenoxypoly(ethy1eneglycol)containing an average of 9.5oxyethylene units per molec~le.~ It was supplied by Merck with a high grade of purity (they vs log C curve showsno minimum near the critical micelle concentration (cmc)region). The solutions were prepared with doubly distilled and deionized water from a Milli-Qsystem. Its surface tension was always tested before preparing the solutions. The surface tension of the TX-100aqueous solutions was measured at 15,25,and 35 "C,under atmospheric pressure, by the ring method. The apparatus was controlled by a computer which also analyzed the results. This allowed the measurement process to be repeated, once the maximum pull on the ring was reached, without taking the ring out of the solution. The temperature was controlled within fO.1 "C with thermostated water (from a Haake-Cthermostat)circulating through a jacket surrounding the vessel containing the solution sample. In all cases, more than 10 successivemeasurements were carried out. The standard deviation of the surface tension for 10 measurements on different samples at the same concentration ofTX-100 depends on that concentration, ranging from f0.05mN/m at low concentrations to f 0 . 2 mN/m for concentrations near the cmc. However, for the same sample the standard deviation of 10 determinations of the surface tension from the maximum pull on the ring was f0.014 mN/m. Results and Discussion Surface tensions ( y ) measured as a function of the concentration of the solution (C) for TX-100solutions at 15,25,and 35 "Care presented in Figure 1. The shapes of the y vs log C curves are the same for 15,25,and 35 "C. Near the cmc the relationship between y and log C is linear. At a given concentration, the surface tension decreases with increasing temperature. The cmcvalues determined from the data shown in Figure 1 are presented in Table 1. They decrease from 2.88 mol L-l through 2.63 mol L-l to 2.14 mol L-l for 15,25,and 35 "C, respectively. Adsorption Isotherms. On the basis of a plot of the surface tension as a function of the equilibrium concen(3) Biozelli, C. J.; Millar, D. B. Biophys. Chem. 1976, 3, 355.
0743-7463/95/2411-4515$09.00/00 1995 American Chemical Society
Janczuk et al.
4516 Langmuir, Vol. 11, No. 11, 1995
0 0 0 0 0 0 0
.......:OOO e 0 e 0
0 0 0 0
O 8
8
.*
eo
.
oo
eo.
0 0:*00 0.0.
-
0
O *OO
60
E 0
Z
.. 0
E
0
\
k 50
.
e o
. .. ..
0
0
.....
00000
40 -
0 0 0 0 0
15 25 35
0
"c "c "c
~
e o
-
e o
0 0
30-
15 25 35
i'i'
'
2.7 2.6 2.5
2.88 2.63 2.14
O'Omo
I
I
61.6 64.3 66.8
41.16 40.84 39.79
tration of TX-100 in water, the amount of surfactant adsorbed at the water-air interface, r, and the area occupied per molecule, A, can be determined using the Gibbs equation of adsorption. mol L-' or less) containing For dilute solutions only one nondissociated surface-active solute, the Gibbs equation can be written in the form'
dy = -R7T d In C or
The values of dyldC were determined by fitting the y vs C data with the polynomial y = a,CR
+ an-lCn-l+ ... + a,C + a,
(2)
It was impossible to obtain only one smooth curve approximating the y vs C data over the whole range of C from 0 to the cmc. Therefore, eq 2 was used to fit the data only in the range of C from 0 up to the concentration corresponding to the first point of saturation of TX-100 at the water-air interface (the point at which A reaches a constant value, equal to the minimum area per molecule, Am).
I
I
I
oirl
0
.
where N is Avogadro's number. Table 1 presents the values of the maximum r, T,, the minimum A, A,, and the surface pressure at the cmc, Ifmax. From Table 1,it is clear that Tm and nmax decrease and A, increases, as the temperature is raised. It should be stressed that, for all the temperatures investigated, TX-100shows a higher surface activity (the cmc is smaller and the n,,, higher) than other ionic surfactants, such as SDS.' The Standard Thermodynamic Functions. There are different equations which may be used to evaluate the free energy of adsorption, AG;,, of TX-100at the waterair interface. According to the concept of Langmuir, if the adsorbed molecules are immobile and adsorbe on "sites" in the interface, the areaA per adsorbed molecule will be related to the bulk concentration of the surfactant, and AGid will satisfj+
A@ - A,) = C/oexp-(AGidlRT)
(4)
where A0 is the "excluded area", Le., the area of the interface unavailable to one molecule due to the presence of another, and w is the number of the moles of water per dm3. However, in the absence of intermolecular interactions between molecules of surfactant in the film, the adsorbed molecules at the water-air interface become perfectly mobile. Then, any previously occupied site at the water(4) Haydan, D. A,; Tayler, F. H. Philos. Trans. R. SOC.London, Ser. A 1960,252, 225.
Langmuir, Vol.11, No. 11, 1995 4517
Adsorption of TX-100
[$)c+
= a (Traubes's constant)
For this concentration range, the standard free energy of adsorption can be calculated from the following equation:'
AG;, = -2.303RT
-47L -.-.-. -9
+
.-.-.
-8
-.--./, -7
-5
-6
-4
-3
log (C/mol I-')
Figure 2. Dependence of AG:d (calculated from eq 5) on log C at 15, 25, and 35 "C. Table 2. Values of the Standard Thermodynamic Parameters of Adsorption at the Water-Air Interface, AG&p A& and A&, for TX-100
15
43.8" 45.46 44.5c 45.3a 47.1b 46.2c 46.6a 48.5b 48.W
25 35
a
5.9
0.175
5.9
0.175
5.9
0.175
From eq 5. From eq 6. From eq 7.
air interface may become free and hence available for adsorption due to the lateral displacementof the molecule to another site. A statistical correction to eq 4 for this lateral motion has been introduced by de Boer.5 The modified equation may be written as f01lows:~ A0
A-A,
exp-
A0
A-A,
-w
Values of the free energy of transfer of TX-100 molecules from the bulk phase to the water-air interface evaluated from eq 5 are presented in Figure 2. For the calculations, A was determined from eq 3 and A0 = 35.7 Figure 2 shows that AGid decreases with the increase of temperature from 15 to 35 "C. For each temperature, in the region of low TX-100 concentration the values of AGi, are constant (these constant values are presented in Table 2);from log C equal to about -7 there is a small decrease and then a sharp increase of AGid with log C. It is evident that for log C higher than -7 there are attractive and repulsive interactions between the TX-100 molecules adsorbed in the monolayer. At first, the attractive interactions are greater than the repulsive, but at higher concentrations the repulsive interactions become considerably larger than the attractive ones. It must be noted that, since TX-100 is a nonionic surfactant, the repulsive forces are only of the acid-base type. Also, it is clear that the major increase of AGid appearing in the concentration region where A = A, may be because eq 5 is not valid in that range. For very dilute solutions of surfactant (ll = y - yo = 0-0.3 mN m-l), the reduction in the surface tension of the solution varies nearly linearly with the concentration of surfactant in the bulk phase and
A2.
( 5 ) de Boer, J. H.In The Dynamic Character ofAdsorption; Oxford University Press: Oxford, 1953.
log(^), an
Using the values of y determined from eq 2 in the region of concentrations less than mol L-l, the AGid values were calculated from eq 6 and are presented in Table 2. One observes that these values of AGid are 1.6-1.9 kJ mol-l lower than those calculated from eq 5. Rosen and Aronson6 have suggested a new method of calculating the standard free energies of adsorption on the aqueous solution-air interface, using the surface tension data in the vicinity of the cmc. In this method, the standard free energy of adsorption for nonionic surfactants, at concentrations less than mol L-l, can be calculated from the expression
AGO,, = RT In C/W- 6.023IL4,
(7)
Of course, eq 7 is valid only in the range where there is a linear dependence of y on log C . Using eq 7, the standard free energy of TX-100 adsorption was evaluated at different temperatures. The results are listed in Table 2. One observes that AGid is negative and decreases with increasing T. These values of AGI, are 0.7-1.4 kJ mol-l lower than those calculated from eq 5. However, the difference between the AGad values determined on the basis of Traube's rule (eq 6 )and from Rosen and Aronson's concept (eq 7) does not exceed 0.9 kJ mol-' (1.9%), and one can say that there is agreement between the two sets of values. It should also be stressed that the differences between the values of AG,d determined by using eqs 5,6, and 7 at a given temperature do not exceed 1.9 kJ mol-l. Given also that TX-100 is not a pure monocomponent ~hemical,~ the agreement between the values of AGad determined using the different methods is good. This means that using experimentaldata from the region where the reduction in surface tension varies linearly with the molar concentration of the bulk phase and where the intermolecular interactions between surfactant molecules do not influence the ll values, it is possible to determine a standard free energy of adsorption for TX-100 whose values are close to those calculated using experimental data from the region of A where the intermolecular interactions between TX-100 molecules do influence the surface tension of the solution. From the values of AGid at different temperatures, the change in the standard entropy of TX-100 adsorption, A s i d , may be obtained from the relation
Aso,, = -a(AG$)/aT
(8)
and the change in the standard enthalpy of adsorption of TX-100, M i d l may be calculated on the basis of the thermodynamic relation
The resulting values of Midand Asid are presented in Table 2. They of course do not depend on the temperature and are both positive. This implies that bond breaking predominates in the adsorption process and the system becomes more random aRer adsorption. (6) Rosen, M. J.;Aronson, S.Colloids Surf. 1981, 3 , 201
Janczuk et al.
4518 Langmuir, Vol. 11, No. 11, 1995 Frank and Evans7have pointed out that, in the process of dissolving a hydrocarbon compound in water, microscopic %ebergs” are found around the apolar portion of the molecule. Therefore, it seems that the breaking up of the ordered “icebergs” and the desolvation of the TX100 molecules dominate the formation of the structure of the interface. Equation of State. Tests of the equation of state are commonly employed to investigate the properties of the adsorbed molecules at the air-aqueous solution interface. A considerable amount of experimental data have been accumulated on the change ofthe surface tension ofwater due to the addition of organic and nonorganic solutes.s If the interactions between the molecules of surfactant adsorbed in the monolayer do not influence its surface pressure, the equation of Volmer,’ originally derived for a two-dimensional gaseous film, can be used to investigate the properties of the adsorbed monolayer. Volmer’s equation is
II(A -A,) = kT
I
2.5 2.0
-
-- - - 1 5°C 2 5°C - -35Y
a
___
r: 1 .o
v
!
1
0.5 9 0.0-
-0
-7
-5
-6
-4
-3
log (C/moi I-’)
Figure 3. Dependence of TIL4 - Ao) on log C at 15,25, and 35 “C.
I
1
/
, /
(10)
where A0 is the “excluded area”, as defined above. In eq 10, the role ofAo is essentially analogous to the term “b” in the three-dimensional van der Waals equation of state for a real gas. It is obvious that for a pair of molecules, the center of one cannot get nearer than the distance 2r to the center of the other, so that the excluded area should be
A, = ~ ( 2 r ) ~=/ 22nr2
30
(11)
i.e., A0 is twice the cross-sectional area of one molecule. This treatment may be termed the “hard-disk twodimensional gas model”. When the largest cross-sectional area for TX-100 is taken to be that corresponding to n-propanol (r = 2.385 A), the A0 value calculated from eq 11 is about 35.7 Az. When this A0 value and the I’I and A values determined from the y vs C data were employed, the n(A -Ad values were calculated for TX-100 solutions at 15,25, and 35 “C and are shown in Figure 3. From this figure, one observes that, in the region of low concentration of TX-100 in the bulk phase, eq 10 is valid. However, in the concentration range from about 8.5 lo-* up to 1.6 mol L-l, a small drop of the II(A - Ao) values to below lkTis observed. Next, there is a nonlinear increase of n(A - Ao) up to a concentration corresponding to A = A,, and then, of course, a linear increase of n(A - Ao) becomes evident. To show more clearly the deviation of the experimental data from eq 10, we evaluated nd, I l k , and nd - nk as a function of log C for TX-100 solutions a t 15 “C,where nd = y - yo, and n k was evaluated by assuming it to be equal to n in eq 10. The values obtained are plotted in Figure
4. (7) Frank, H. S.; Evans, M. W. J . Chem. Phys. 1945, 13, 507. (8)Davies, J. T.; Rideal, E. In Interfacial Phenomena; Academic Press: New York, 1961.
.
2’
/
/
/
-1
-9
-E
-6
-7
log (C/mol
Figure 4. Dependence of I&, solutions a t 15 “C.
-5
-4
-3
I-’)
nk,and AH on log c for ‘l?x-100
One observes in this figure that, in the region of low concentration, nd = nk and then eq 10 is fulfilled; in the range of log C between -8.6 and -7.6, small negative values of nd - nk are observed; and, above this concentration region, the increase of nd - nk is evident and is linear against log C for C above mol L-I. The small negative values of lid - ilk indicate that, in the region of log C between -8.6 and -7.6, the attractive forces between TX-100 molecules in the adsorbed monolayer film are greater than the repulsive ones, but at higher concentrations there are strong repulsive forces between the polar heads ofthe TX-100 molecules. Thus the equation of state for a nonionic surfactant should be written in the form
(II, - HA - H,)(A - A,) = kT
(12)
where IIAis the part of II corresponding to the attractive Lifshitz-van der Waals forces between the apolar part of the surfactant and the attractive acid-base forces, and HRis the part of ll corresponding to the repulsive acidbase forces between the heads of TX-100 molecules in the water phase.
Acknowledgment. One of the authors (B.J.) very much appreciates the support obtained from the Spanish Ministerio de Educaci6n y Ciencia for his sabbatical stay at the Departamento de Fisica, Universidad de Extremadura, Spain. Financial support for this work by DGICYT under Project No. PB89-0519 is gratefully acknowledged. LA9408174
