- Email: [email protected]
Contact angles in thin liquid films. II. Contact angle measurements in Newton black soap films
Contact Angles in Thin Liquid Films II. Contact Angle Measurements in Newton Black Soap Films J. A. D E FEIJTER 1 AND A. VRIJ z Van 't Hoff Laboratory for Physical and Colloid Chemistry, University of Utrecht, Padualaan 8, Utrecht, the Netherlands Received April 22, 1977; accepted September 9, 1977 Contact angles of the very thin Newton black (NB) soap films stabilized by sodium dodecyl sulfate (NaDS) have been measured with the diffraction method of Princen and Frankel [J. Colloid Interface Sci. 35, 386 (1971)]; the indifferent electrolyte being NaC1 and Na~SO4. The absolute value of the interaction free energy, laF(he)l, calculated from the contact angle, was found to increase strongly with increasing salt concentration, c3, and with decreasing temperature, T. Below the CMC a slight decrease of IAF(he)fwith decreasing NaDS concentration, c2, was observed. Both IAF(he)] and its variation with c3 were found to be different for NaC1 and NaeSO4. From the variation of ~u~(he) with T the interaction entropy, AS(he), and the interaction energy, AU(he), were calculated. Their values show that the formation of the NB-films is energetically a very favorable process, but entropicaUy very unfavorable. From the variation of AF(he) with c2 and c3 we calculated the difference AF~ between the surface excess at the film- and the bulk surface for NaDS (AF2) and the salt (&F3), respectively, using the Gibbs-Duhem relation for films derived in paper I [J. Colloid Interface Sci. 64, 258 (1978)]. The surface excess of NaDS is slightly higher at the film than at the bulk surface, the difference being less than 1%. The surface excess of the salt is also higher at the film surface than at the bulk surface with z~F3 = + 1.34 x 10-r equiv/m2 for NaC1 at 23.5°C; AF3 decreases with increasing temperature. For Na2SO4 the value of AF3 is a factor of 1.28 higher than for NaCI. 1. INTRODUCTION
Among soap films stabilized by ionic surfactants two types can be distinguished: the common black films (CB-films), with a thickness, h, between 6 and 100 nm depending on the electrolyte concentration of the soap solution from which the film is drawn, and the Newton black films (NB-films), with h = 5 nm, almost independent of the electrolyte concentration? The latter type of film is formed when the electrolyte con' Present address: Unilever Research Laboratory, Olivier van Noortlaan, Vlaardingen, the Netherlands. 2 To whom requests for reprints should be addressed. 3 The terms "Newton black"- and "common black"films will be used instead of "second black"- or "Perrin"-film and "first black"-film; this in accordance with the recommendations of the IUPAC-commission on Colloid- and Surface Chemistry (4).
centration exceeds some critical value (1). The CB-films have been studied as model systems to test theories on interaction forces which govern the stability of hydrophobic colloids (2, 3). The behavior of NB-films is much less understood. Qualitative information on the composition of NBfilms stabilized by sodium dodecyl sulfate (NaDS) was obtained by Jones et al. (1), who investigated the influence of temperature, counterion type and neutral additives on the critical salt concentration, c3(crit), at which the transition takes place from CB- to NB-films. Ibbotson and Jones (5) studied the influence of the valency of the counterion on c3(crit) for films stabilized by tetra-decyl-trimethylammoniumbromide. Contact angle measurements of NB-films have been reported by several authors
269
0021-9797/78/0642-0269502.00/0 Journal o f Colloid and Interface Science, Vol. 64, No. 2, April 1978
Copyright © 1978 by Academic Press, Inc. All fights of reproduction in any form reserved.
270
D E F E I J T E R A N D V R IJ
(6-11). However, in most cases no attempt was made to interpret them, as they were used solely to illustrate a new measuring technique (6-9). A systematic study of the contact angles of NB-films stabilized by NaDS was published by Huisman and Mysels (12), who investigated the influence of various counterions at constant temperature (23°C). They made an attempt to interpret the results in terms of the theories of double-layer repulsion and van der Waals attraction. No correlation, however, was found with the theory. In order to obtain more quantitative information about the structure and properties of NB-films, we measured contact angles with the more recent and accurate technique of Princen (13, 14) using an apparatus built in our own laboratory. In this paper we describe contact angle measurements of NB-films formed from NaDS + NaC1 and NaDS + Na2SO4-solutions at different temperatures and electrolyte concentrations. The results will be interpreted in a new form, using the thermodynamic analysis given in (15) (paper I), in terms of the film composition and the interaction forces that act in such films. 2. E X P E R I M E N T A L M E T H O D S
1. Materials The sodium dodecylsulfate (NaDS) was a sample prepared and purified in our laboratory by Huisman (16). Within the experimental error of 0.2 mN/m, no minimum was found in the surface tension vs the NaDS concentration. This indicated that the surfactant did not contain detectable amounts of solubilizable surface active impurities. NaC1 and Na2SO4 were of analytical grade (Analar) and were used without further purification. All water used in the experiments was distilled twice in a quartz apparatus. 2. Methods Contact angle measurements were made both above and below the critical micelle concentration (CMC) of the surfactant. Journal of Colloid and Interface Science, Vol. 64, No. 2, April 1978
Above the CMC the diffraction method of Princen and Frankel (13, 14) was used. The optical part of the apparatus consisted of a 1.0 mW H e - N e laser (Spectra Physics 133, h = 632.8 nm) and a combination of two biconcave lenses which broadened the parallel laser beam to a diameter of 6 mm. The quality of this beam was improved by placing a pinhole in the focus plane of the first lense. The soap film was formed within a rectangular, double-walled, Perspex cell with inner dimensions 4 x 9 x I i cm, the temperature of the cell and its contents being kept constant, within 0.05°C, by the circulation of water from a thermostat through the cell walls. The parallel light beam transversed the cell through circular glass windows of a high optical quality (diameter, 2 cm) in the front and the rear faces of the cell. The liquid film was formed in a vertical, rectangular glass frame (3 x 3 cm) by drawing the frame partly from the surfactant solution contained in a rectangular Teflon cuvette, of dimensions 2 x 4 x 4 cm, filled to overflowing. A rectangular part of the center of the laser beam (0.3 x 0.5 cm) passed through the transition between the film and its plateau border. The intensity of the light diffracted downwards was measured by a photomultiplier fixed at the end of a motor driven arm of 1 m length. The arm pivoted at the film meniscus. A narrow horizontal slit and a sharp cut-off filter (laser line filter with half bandwidth of 3.0 nm) was placed in front of the photomultiplier; this enabled us to work in daylight. The rather large contact angles, 0, could be calculated from the location of the maxima and minima in the intensity vs diffraction angle curve (see Ref. (14) Eq. [8]). Such curves were sometimes smooth as predicted by theory but often showed sharp superimposed peaks probably due to multireflections of the glass windows (14). This had little effect on the accuracy,
271
C O N T A C T A N G L E S I N T H I N L I Q U I D FILMS. II
which was known to be _+3 min for 0 > 1 degree. After the cuvette was filled with a freshly prepared solution, the atmosphere within the cell was always equilibrated for at least 15 hr. Solutions older than 2 days were discarded. The contact angle was measured when the soap film had reached equilibrium. This took about 5 min for films with 0 > 5° and 0.5 hr or more for films with 0 as small as 1°. Below the CMC of the surfactant, 0 was m e a s u r e d with S h e l u d k o ' s e x p a n s i o n method (8, 17) using microscopic, circular films because o f lack of stability of the large vertical films. We modified the method slightly by keeping constant the hydrostatic pressure in the film, rather than the volume of the film plus plateau border. The experiments were carried out at 23°C. Film thicknesses were obtained from the intensity of a reflected light beam (18, 19). The surface tension of the bulk solution was measured with the Wilhelmy plate (accuracy _+0.2 mN/m) and the refractive index o f the solution with an Abbe refractometer. 3. E X P E R I M E N T A L R E S U L T S
Table I gives the interaction free energy, zkF(h~), for the large soap films of the
system 0.05% NaDS + NaC1. The temperature, T, was varied from 20.5 to 29.5°C and the NaC1 concentration, c3, from 0.19 to 0.50 mol/liter. The total NaDS concentration, c2~ = 0.05% = 1.74 x 10 -3 mol/liter, was above the CMC which varies from 0.7 to 0.5 x 10 -3 tool/liter when the NaC1 concentration is increased from 0.19 to 0.50 tool/liter (16). The interaction free energy, z~(h~), was calculated from the contact angle 0 (Ref. (15) Eq. [26]) with 2~(he) = 2o'~(cos 0 - 1),
[1]
where o-" is the surface tension of the bulk solution. We used the value o f o-~ measured at 23°C (see Table I), as within the experimental error no significant variation of o-~ with the temperature was found, i.e., Ido-"/dTI < 0.07 mN/m degree. This introduced an error of, at most, 1% for the highest temperature of 29.5°C. The variation of MT(he) with the NaC1 concentration and t e m p e r a t u r e is illustrated in Figs. 1 and 2. The results for the system 0.05% NaDS + Na2SO4 are tabulated in Table II and illustrated in Fig. 3. Also here the NaDS concentration, czt, was above the CMC, as the CMC of NaDS is quite insensitive to the nature o f the co-ion (20). When c2t was increased from 0.05 to 0.10% no significant
TABLE I Interaction Free Energy
AF(he) and
Surface Tension or" of the System 0.05% NaDS + NaC1 A F ( h e ) / m J m -2
ca (NaC1) (molfliter)
0.19 0.21 0.23 0.25 0.275 0.30 0.35 0.40 0.50
o"
20.5°C
22.0°C
23.5°C
25.0°C
26.5°C
28.0°C
-0.214 -0.328 -0.445
-0.102 -0.225 -0.330 -0.425 -0.565 -0.655 -0.840
-0.012 a -0.122 -0.233 -0.322 -0.455 -0.555 -0.740 -0.900
-0.011 a -0.021 -0.134 -0.224 -0.344 -0.435 -0.630 -0.810 - l. 10
-0.012 a -0.036 -0.138 -0.252 -0.360 -0.530 -0.700 -0.980
-0.011 a -0.010 ~ -0.063 -0.171 -0.260 -0.435 -0.595
-0.680 -0.765 -0.970
29.5oc
-0.011 ~ -0.0125 -0.083 -0.176 -0.354 -0.505
(raN/m) 23oc
33.1 32.8 32.6 32.4 32.2 32.0 31.6 31.4 31.1
C o m m o n black (CB)-film. Journal o f Colloid a n d Interface Science, Vol. 64, No. 2, April 1978
272
DE FEIJTER AND VRIJ - 1.0
AF(h.) ( m J / m -2)
/ _o°
/ / /
I/././././ I
0.20
0.25
I
,
.
I
,
,
,
,
I
0 40
0.30 0.35 c 3 ( N o C I ) ( rnol . I "1)
FIG. l. Interaction free energy AF(he) as a function of the salt concentration for the system 0.05% NaDS + NaC1. (Experimental points of the CB-films, as given in Table I, have been omitted for the sake of clearness.)
change in 2W(he) was observed, i.e., above the CMC the value of 2W(h~) is insensitive to variations in czt. Contact angles of the NB-films below the CMC could only be measured at rather high electrolyte concentrations. For c3 (NaC1) < 0.35 mot/liter and c3 (Na2SO4) < 0.40 equiv/liter the formation of the NBfilms was greatly delayed or did not even occur at all. This was also found by Kolarov et al. (8). When c2 was decreased below the CMC a slight decrease of 12W(he)l was obtained in most cases. It is not clear, however, whether the change in fia~(he) is significant as the experimental error was
rather large. The decrease o f [AF(he)[, was always smaller than 0.2 mJ/m 2 when c2 was decreased from the CMC to 1A × CMC. Within the experimental error of 0.1 nm, the thickness o f the NB-films was identical for NaC1 and Na2SO4 at the same salt concentration. The equivalent water thickness, hw, of the films, as obtained from the Rayleigh equation (21) when the film is assumed to be a homogeneous water layer with refractive index n = 1.333, was 4.4 nm for c3 (NaC1) = 0.3 tool/liter and 4.5 nm at 0.4 tool/liter. The same hw-values were found for the microscopic, circular films and the large vertical films.
_1.00 &F(hel (mJ m'21 " ¢ YO"°°/. / -1
-050
T (*C)
FIG. 2. Interaction free energy &F(he) as a function of the temperature for the system 0.05% NaDS + NaC1. (Experimental points of the CB-films have been omitted.) Journal of Colloid and Interface Science, Vol. 64, N o . 2, April 1978
CONTACT ANGLES IN THIN LIQUID FILMS. II
273
4. DISCUSSION OF RESULTS
TABLE II
The results as given in the previous section show that the interaction free energy, z~(he), of the NB-films stabilized by NaDS strongly depends on the salt concentration; both for the systems with NaCI and NazSO4. For the NB-films with NaC1 this was observed b y others before (6-9, 12-14). As a new result we find that AF(he) strongly depends on the temperature, the variation of AF(h~) with T being practically constant. For the films with NaC1 this is illustrated in Fig. 2. Our AF(h~)-values of the system 0.05% NaDS + NaC1 perfectly agree with the results of Princen and Frankel (14), who used the same technique. Agreement within 0.03 mJ/m 2 is found with the results of Prins (7), who measured the film tension directly with a microbalance. The same technique was used by Clint et al. (6). Their ]AF(h~)[-values are 0.01 to 0.08 mJ/m 2 larger than ours, whereas those measured by Huisman and Mysels (12), using the bubble-cap method, are 0.1 to 0.2 mJ/m 2 smaller. The differences between the data of the different authors are presumably caused by the fact that in most cases the temperature was not controlled accurately. Huisman and M y s e l s (12) found that 2uW(he) of the NB-films stabilized by NaDS strongly depends on the nature of the
Interaction Free Energy £xF(h~)and Surface Tension o-~ of the System 0.05% NaDS + Na2SO4 h F ( h e ) / m J m -2
ca(Na~SQ) equiv/liter
22.0°C
23.5°C
0.25 0.30 0.35 0.40 0.50
-0.032 -0.192 -0.330 -0.445 -0.641
-0.009 a -0.100 -0.235 -0.353 -0.538
25.0°C
tr ~
26.5°C
(raN/m) 23°C
-0.175 -0.330
32.8 32.2 31.9 31.6 31.4
-0.021 0.271 -0.416
Common black (CB)-film.
counterion. We find that 2u~(he) also depends on the nature of the co-ion. Figures 1 and 3 show that for a given T both the absolute value of AF(he) and its variation with the salt concentration c 3 is larger for the films with NaC1 than for those with Na2SO4. No difference i s found in the variation of 2UW(h~) with T for the two systems. Our data as given in Tables I and II also include some hF(h~)-values of c o m m o n black (CB)-films. For the salt concentrations and temperatures studied, the z2urr(h~)values of these films are quite small ( - - 0 . 0 1 mJ/m2). They are represented by the horizontal parts of the curves in Figs. 1-3. Although the number o f data is limited, it is clear that the variation of AF(he) with c3 and T is much smaller than for the NB-films. When for a given temperature the salt
-113 AF(he) (rnJ m-2)
-(35
0.2.5,
0.30
035
0.40
0.45 0 50 c3(No2SOd)(equiv U1)
FIG. 3. Interaction free energy 2xF(he)as a function of the salt concentration for the system 0.05% NaDS + Na,2SO4. J o u r n a l o f Colloid a n d Interface S c e n c e , Vol. 64 No. 2, April 1978
274
DE FEIJTER AND VRIJ 35
concentration was increased from 0.3 to 0.4 mol/liter.
T(°C)
5. EVALUATION OF THERMODYNAMIC INTERACTION PARAMETERS 2~
L
0.20
0125
I
0~30 0.35 c3(cr}t) (equiv. 1-1)
FIG. 4. Relation between the transition temperature and cz(crit) for the system 0.05% NaDS + NaC1 and 0.05% NaDS + Na2SO4. concentration is increased, the transition from CB- to NB-films takes place at the salt concentration where the slope of AF(he) vs cz suddenly increases (see Figs. 1 and 3). This is the critical salt concentration, cz(crit), where AF(he), and consequently also the film tension 3', are equal for the two film types; for ca = c3(crit) the CB- and NB-film type can coexist in one film. Figure 4 shows the relation between the transition temperatures and cz(crit) as obtained from Figs. 1-3. Thus c3(crit) is found to increase with increasing temperature; i.e., the NBfilms are most easily formed at low temperatures. At a given temperature it is smaller for the films with NaC1 than for those with Na2SO4. The c3(crit)-values for the films with NaC1 agree within 0.01 mol/liter with those of Jones et al. (1) who visually determined the salt concentration where CB- and NB-film type occur in one film. The thickness o f NB-films is quite insensitive to changes in c3 and T (1, 22). Our values for the equivalent water thickness, hw, of the NB-films are 0.2 nm smaller than those measured by Bruil (22) and 0.7 nm smaller than the ones reported by Jones et al. (1). T h e y also found a slight increase of hw with increasing c3. The h~-values reported by Prins (7) are 0.2 nm smaller than ours. H e found a small decrease of 4.3 to 4.2 nm when the NaC1 Journal o f Colloid andl/tterface Science, Vol. 64, No. 2, April 1978
In paper I (15) we have shown that the contact angle, 0, of a film not only gives the interaction free energy, ~ ( h e ) , but also the change in the surface entropy, A~s, and in the surface excess o f the solutes, AF,, caused by the interaction between the film surfaces. From Eq. [35] o f paper I it is seen that the difference between the surface excess entropy o f the film surface and the bulk surface, A~s = ,s s - ' s % is obtained from the variation of AdZ(he) with temperature T (at constant disjoining pressure, II, and chemical potentials o f the solutes, /z0. In practice ASs is not a very convenient quantity, as it is quite difficult to keep the chemical potentials ~ constant when T is changed. Both from a theoretical and practical point of view it is much more convenient to use the interaction entropy, AS(he), obtained from the variation of AF(he) with T at constant composition of the bulk solution and disjoining pressure II:
AS(he) =-- -dAF(he)/dT.
[2]
Figure 2 shows that the plots of AF(he) vs T o f the NB-films o f the system 0.05% NaDS + NaC1 are practically straight. Thus, the interaction entropy AS(he) is practically independent of T. The plots for different c3 being parallel shows that for a given value o f AF(he) the interaction entropy is independent of the salt concentration. Both for the NB-films with NaCI and with Na2SO4 we find: A S ( h e ) = - 0 . 0 6 6 -+ 0.003 mJ/m 2. For the CB-films o f the same systems the absolute value o f AS(he) is at least a factor of 50 smaller (see Table I). Hence, the formation of an NB-film from two bulk surfaces (and also from a CB-film) is exothermic. Qualitatively, this was already concluded by Jones et al. (1). When AF(he) and AS(he) are known, one
275
CONTACT ANGLES IN THIN LIQUID FILMS. II
can calculate the interaction energy AU(he) with: aU(he) = zXF(he) + T'AS(he).
[3]
In the temperature range studied (20.529.5°C) the value of T,SS(he) is - 2 0 ___ 1 mJ/m 2, both for the NB-films with NaC1 and NaeSO4. The 2uF(he)-values of these films range from - 0 . 0 0 9 to - 1 . 1 mJ/m 2 (see Tables I and II). Thus the value of the interaction energy AU(he) must be approximately - 2 0 mJ/m 2. The accuracy of the experimental results is not sufficiently large for us to determine whether the variation of 2uF(he) with ca is caused by a variation of AU(he) or o f AS(he) or both. From the above results it follows that the formation of an NB-film of the systems NaDS + NaC1 and NaDS + Na2SO4 is energetically a highly favorable process, but, on the other hand, entropically highly unfavorable, with the quantities AU(he) and - T AS ( h e) tending to compensate each other. The difference, AFt, between the surface excess o f c o m p o n e n t i at the film- and the bulk surface is obtained from the variation AF(he) with the composition of the bulk solution by using Eq. [35] of paper I. For the system N a D S ( = 2 ) + salt(=3) at constant temperature the equation reduces to: d[AF(h~) + IIh~] = -2AF~d/x2 - 2AF3d/x3 + hdII,
[4]
where/x2 and/x3 are the chemical potentials of NaDS and the salt, respectively. In our experiments the disjoining pressure II at the transition between the film and the plateau border was small and almost constant, with I1 -~ 25 N/m S. In the NB-films the llhe-term is about 10 -4 mJ/m 2 and can be neglected with respect to flaW(he). T h e n we have at constant 17: dAF(he) = -2AF2d/x2 - 2AF~d/za.
[5]
In the systems studied by us the chemical potentials Ix2 and Ix3 are interrelated, as the surfactant NaDS and the salts NaC1 and
Na2SO4 have one ion in common. In our case the salt concentration c3 is always at least a factor of 1000 larger than the surfactant m o n o m e r concentration c2; the change in /za upon a variation of c2 can then be neglected. The variation of/z2 and /z3 with changing c2 and ca is then given by: NaDS:
d/x2 = R Td lnf2c2 + R Td lnf2ca,
NaCI:
d/x3 = R Td In (f3ca)2 = RTd lna~,
Na2SO4:
[6]
d/z3 = R Td In (f3c3)~/2 = R Td In as,
where f2 and fa are the mean ion activity coefficients o f NaDS and the salt, respectively (c3 in equiv/liter). W h e n b e l o w the CMC the N a D S monomer concentration c2 is changed at constant T, 17 and ca, we have: dAF(he) = -2AF~d/xz = -2AFz(RTd lnf2c~).
[7]
Thus, 2xFz can be calculated from the variation of AF(he) with cz, below the CMC, at constant salt concentration. From the experimental results given in sect. 3 we find that AFz is presumably positive with AF2 ~< 5 X 10 .8 mol/m ~ (=3 x 1016 molecules/mZ), both for the films with NaC1 and Na2SO4. For the range of salt concentrations studied the surface excess F~" o f NaDS at the bulk surface is 4.2 x 10 -6 mol/m 2 (23-25). Thus the surface excesses F2~ and F2s of NaDS at the bulk- and the film surface, respectively, are equal within 1%. This is in agreement with the findings of Jones and Ibbotson (23) who measured F2~ and F2~ directly with a radio tracer method. The difference, AF.~, between the surface excess of the salt at the film- and the bulk surface can now be derived from the variation of 2xF(he) with the salt concentration c3. When c3 is varied at constant Journal of Colloid and Interface Science, Vol. 64, No. 2, April 1978
276
DE F E I J T E R A N D VRIJ
/
-1.0
~ F ( h e) ( m J rn " 2 )
-0.5
/'/
/://: ///:/, ,/e
I
-1.5
0.3 I
I
I ~--~ l o g
0.4 I
05 I
L
.110
C3 (tool 1-1) ,
a3(NoCI)
FIG. 5. fiJF(he) vs log aa(NaC1), with a,3 = (f3c3) z.
total NaDS concentration, the chemical potentials /z2 and /z3 vary simultaneously (see Eq. [6]). Above the CMC the NaDSm o n o m e r concentration cz can be equated to the CMC. The CMC of NaDS depends on the salt concentration; when c3 >> CMC, as in our experiments, the two quantities are interrelated by the experimental relation (26, 27) d In CMC = kd In c3.
dNF(he) = -(0.32AF2 + 2AFa)d/~8 -AG(3)d/zz --= - Z~G(3). [2RTd In f3cg], and for Na2SO4:
dAF(hD = -(0.42&F2 + 2hF3)d/z3 _= - AG(3)d/z 3 --- - A G ( 3 ) . [3/2RTd lnf3e3].
[8]
For the system NaDS + NaC1 the value of k is about - 0 . 6 8 (16). The same value can be used for NaDS + Na2SO4 as the co-ion has only a minor influence on the CMC (20). Substituting Eqs. [6] and [8] into Eq. [5] and assuming that f2 = fa, we find, for the system with NaC1, at constant total surfactant concentration c2t (=0.05%): -10 AF(h e) (mJ m - 2 )
[9]
[10]
The quantities AG(3) are obtained from the plots of 2u~(h~) vs log aa as given in Figs. 5 and 6 for NaC1 and Na2SO4, respectively. The activity coefficients f3 of NaC1 and Na2SO4 were obtained from Ref. (28). The fact that the plots are straight indicates that, both for NaC1 and Na~SO4, AG(3) is independent of the salt concentration. For the system with NaCI the contribution of the AF2-term to AG(3) is found to be less than 6% and for Na2SO4 less than 8%. When the AF2-term is neglected, T A B L E III
- Q5
/4~A9,'-
AFz o f the Salt for the NB-Films of the Systems NaDS + NaC1 (I) and NaDS + Na~SO4 (II) AF3 × 107/equiv m -2
- 2i.0
FiG. 6. ~ ( h ~ )
i -1.5 log G3(No2SO 4 )
vs log a3(Na~SO4), with as = (f3c3) 3/2.
Journal of Colloid and Interface Science, Vol. 64, No. 2, April I978
(1) (II)
20.5°C
22.0°C
23.5°C
25.0°C
26.5°C
29.5°C
1.39
1.35 1.72
1.34 1.71
1.33
1.29
1.22
CONTACT ANGLES IN THIN LIQUID FILMS. II
we have: AG(3)= 2AF3. The AF3-values thus obtained are tabulated in Table III. For the NB-films of the system 0.05% NaDS + NaC1 at 23.5°C we then find: AF3 = +1.34 x 10-7 mol/m 2, with AF3 decreasing with increasing temperature. The AF3-value for Na,2SO4, expressed in equiv/ m2, is larger by a factor of 1.28, the film thicknesses being equal in the two cases. From the results of our contact angle experiments it can thus be concluded that for the NB-films stabilized by NaDS more salt is adsorbed at the film surface than at the bulk surface. Qualitatively, the same conclusion was arrived at by Jones et al. (1). It is in agreement with what one should expect from the diffuse double-layer theory. This theory predicts that indifferent electrolyte is repelled from a charged surface in contact with an electrolyte solution, i.e., that F3" is negative. In a film where the double layers of the two surfaces interact the volume from which the salt is expelled decreases. As a consequence the absolute value of F3 decreases, i.e., FJ is less negative than F3~ or A F 3 - - = F J - F 3 ~ is positive (29-31). In a following paper we will attempt to interpret the herefound values of AFa in terms of the electrical double-layer theory. Further we will use the obtained values of Z~(he), AS(he) and AU(he) to draw conclusions concerning the nature of the interaction forces in the very thin NB-films. ACKNOWLEDGMENTS This work was part of the research programme of the "Stichting voor Fundamenteel Onderzoek der Materie" (FOM) with financial support from the "Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek" (ZWO). REFERENCES 1. Jones, M. N., Mysels, K. J., and Scholten, P. C., Trans. Faraday Soc. 62, 1336 (1966). 2. Sheludko, A., Advan. Colloid Interface Sci. 1, 39 (1967).
277
3. Clunie, J. S., Goodman, J. F., Ingram, B. T., in "Surface and Colloid Science," Vol. 3, p. 167. Wiley (Interscience), New York, 1971. 4. Everett, D. H., Pure Appl. Chem. 31, 581 (1972). 5. Ibbotson, G., and Jones, M. N., Trans. Faraday Soc. 65, 1146 (1969). 6. Clint, J. H., Clunie, J. S., Goodman, J. F., and Tare; J. R., Nature 223, 291 (1969). 7. Prins, A., J. Colloid Interface Sci. 29, 177 (1969). 8. Kolarov, T., Sheludko, A., and Exerowa, D., Trans. Faraday Soc. 64, 2864 (1968), 9. Huisman, H. F., Mysels, K. J., and Razouk, K. J., J. Phys. Chem. 70, 1339 (1966). 10. Clunie, J. S., Corkill, J. M., Goodman, J. F., and Ingram, B. T., Spec. Discuss. Faraday Soc. 1, 30 (1970). 11. Ingram, B. T., J.C.S. Faraday 1 68, 2230 (1972). 12. Huisman, H. F., and Mysels, K. J., J. Phys. Chem. 73, 489 (1969). 13. Frankel, S., and Princen, H. M., J. Phys. Chem. 74, 2580 (1970). 14. Princen, H. M., and Frankel, S., J. Colloid Interface Sci. 35, 386 (1971). 15. De Feijter, J. A., Rijnbout, J. B., and Vrij, A., J. Colloid Interface Sci. 64, 258 (1978). 16. Huisman, H. F., thesis, Utrecht, 1964. 17. Sheludko, A., Radow, B., and Kolarov, T., Trans. Faraday Soc. 64, 2213 (1968). 18. Duyvis, E. M., thesis, Utrecht, 1962. 19. Lyklema, J., and Mysels, K. J., J. Amer. Chem. Soc. 87, 2539 (1965). 20. Corrin, M. L., and Harkins, W. D., J. Amer. Chem. Soc. 69, 63 (1947). 21. Born, M., and Wolf, E., "Principles of Optics." Pergamon, Elmsford, N.Y., 1959. 22. Bruil, H. G., thesis, Wageningen, 1970. 23. Jones, M. N., and Ibbotson, G., Trans. Faraday Soc. 66, 2394 (1970). 24. Wilson, A., Epstein, M. P., and Ross, J., J. Colloid Sci. 12, 345 (1957). 25. Weil, I., J. Phys. Chem. 70, 133 (1966). 26. Mukerjee, P., Advan. Colloid Interface Sci. 1, 243 (1967). 27. Mijnlieff, P. F., J. Colloid Interface Sci. 33, 255 (1970). 28. Robinson, R. A., and Stokes, R. H., "Electrolyte Solutions" 2nd ed., Butterworth, London, 1959. 29. Schofield, R. K., Nature 160, 408 (1947). 30. Bolt, G. H., and Warkentin, B. P., Kolloid-Z. 156, 41 (1958). 31. De Haan, F. A. M., J. Phys. Chem. 68, 2970 (1964).
Journal of Colloid and Interface Science, Vol, 64, No. 2, April 1978
Among soap films stabilized by ionic surfactants two types can be distinguished: the common black films (CB-films), with a thickness, h, between 6 and 100 nm depending on the electrolyte concentration of the soap solution from which the film is drawn, and the Newton black films (NB-films), with h = 5 nm, almost independent of the electrolyte concentration? The latter type of film is formed when the electrolyte con' Present address: Unilever Research Laboratory, Olivier van Noortlaan, Vlaardingen, the Netherlands. 2 To whom requests for reprints should be addressed. 3 The terms "Newton black"- and "common black"films will be used instead of "second black"- or "Perrin"-film and "first black"-film; this in accordance with the recommendations of the IUPAC-commission on Colloid- and Surface Chemistry (4).
centration exceeds some critical value (1). The CB-films have been studied as model systems to test theories on interaction forces which govern the stability of hydrophobic colloids (2, 3). The behavior of NB-films is much less understood. Qualitative information on the composition of NBfilms stabilized by sodium dodecyl sulfate (NaDS) was obtained by Jones et al. (1), who investigated the influence of temperature, counterion type and neutral additives on the critical salt concentration, c3(crit), at which the transition takes place from CB- to NB-films. Ibbotson and Jones (5) studied the influence of the valency of the counterion on c3(crit) for films stabilized by tetra-decyl-trimethylammoniumbromide. Contact angle measurements of NB-films have been reported by several authors
269
0021-9797/78/0642-0269502.00/0 Journal o f Colloid and Interface Science, Vol. 64, No. 2, April 1978
Copyright © 1978 by Academic Press, Inc. All fights of reproduction in any form reserved.
270
D E F E I J T E R A N D V R IJ
(6-11). However, in most cases no attempt was made to interpret them, as they were used solely to illustrate a new measuring technique (6-9). A systematic study of the contact angles of NB-films stabilized by NaDS was published by Huisman and Mysels (12), who investigated the influence of various counterions at constant temperature (23°C). They made an attempt to interpret the results in terms of the theories of double-layer repulsion and van der Waals attraction. No correlation, however, was found with the theory. In order to obtain more quantitative information about the structure and properties of NB-films, we measured contact angles with the more recent and accurate technique of Princen (13, 14) using an apparatus built in our own laboratory. In this paper we describe contact angle measurements of NB-films formed from NaDS + NaC1 and NaDS + Na2SO4-solutions at different temperatures and electrolyte concentrations. The results will be interpreted in a new form, using the thermodynamic analysis given in (15) (paper I), in terms of the film composition and the interaction forces that act in such films. 2. E X P E R I M E N T A L M E T H O D S
1. Materials The sodium dodecylsulfate (NaDS) was a sample prepared and purified in our laboratory by Huisman (16). Within the experimental error of 0.2 mN/m, no minimum was found in the surface tension vs the NaDS concentration. This indicated that the surfactant did not contain detectable amounts of solubilizable surface active impurities. NaC1 and Na2SO4 were of analytical grade (Analar) and were used without further purification. All water used in the experiments was distilled twice in a quartz apparatus. 2. Methods Contact angle measurements were made both above and below the critical micelle concentration (CMC) of the surfactant. Journal of Colloid and Interface Science, Vol. 64, No. 2, April 1978
Above the CMC the diffraction method of Princen and Frankel (13, 14) was used. The optical part of the apparatus consisted of a 1.0 mW H e - N e laser (Spectra Physics 133, h = 632.8 nm) and a combination of two biconcave lenses which broadened the parallel laser beam to a diameter of 6 mm. The quality of this beam was improved by placing a pinhole in the focus plane of the first lense. The soap film was formed within a rectangular, double-walled, Perspex cell with inner dimensions 4 x 9 x I i cm, the temperature of the cell and its contents being kept constant, within 0.05°C, by the circulation of water from a thermostat through the cell walls. The parallel light beam transversed the cell through circular glass windows of a high optical quality (diameter, 2 cm) in the front and the rear faces of the cell. The liquid film was formed in a vertical, rectangular glass frame (3 x 3 cm) by drawing the frame partly from the surfactant solution contained in a rectangular Teflon cuvette, of dimensions 2 x 4 x 4 cm, filled to overflowing. A rectangular part of the center of the laser beam (0.3 x 0.5 cm) passed through the transition between the film and its plateau border. The intensity of the light diffracted downwards was measured by a photomultiplier fixed at the end of a motor driven arm of 1 m length. The arm pivoted at the film meniscus. A narrow horizontal slit and a sharp cut-off filter (laser line filter with half bandwidth of 3.0 nm) was placed in front of the photomultiplier; this enabled us to work in daylight. The rather large contact angles, 0, could be calculated from the location of the maxima and minima in the intensity vs diffraction angle curve (see Ref. (14) Eq. [8]). Such curves were sometimes smooth as predicted by theory but often showed sharp superimposed peaks probably due to multireflections of the glass windows (14). This had little effect on the accuracy,
271
C O N T A C T A N G L E S I N T H I N L I Q U I D FILMS. II
which was known to be _+3 min for 0 > 1 degree. After the cuvette was filled with a freshly prepared solution, the atmosphere within the cell was always equilibrated for at least 15 hr. Solutions older than 2 days were discarded. The contact angle was measured when the soap film had reached equilibrium. This took about 5 min for films with 0 > 5° and 0.5 hr or more for films with 0 as small as 1°. Below the CMC of the surfactant, 0 was m e a s u r e d with S h e l u d k o ' s e x p a n s i o n method (8, 17) using microscopic, circular films because o f lack of stability of the large vertical films. We modified the method slightly by keeping constant the hydrostatic pressure in the film, rather than the volume of the film plus plateau border. The experiments were carried out at 23°C. Film thicknesses were obtained from the intensity of a reflected light beam (18, 19). The surface tension of the bulk solution was measured with the Wilhelmy plate (accuracy _+0.2 mN/m) and the refractive index o f the solution with an Abbe refractometer. 3. E X P E R I M E N T A L R E S U L T S
Table I gives the interaction free energy, zkF(h~), for the large soap films of the
system 0.05% NaDS + NaC1. The temperature, T, was varied from 20.5 to 29.5°C and the NaC1 concentration, c3, from 0.19 to 0.50 mol/liter. The total NaDS concentration, c2~ = 0.05% = 1.74 x 10 -3 mol/liter, was above the CMC which varies from 0.7 to 0.5 x 10 -3 tool/liter when the NaC1 concentration is increased from 0.19 to 0.50 tool/liter (16). The interaction free energy, z~(h~), was calculated from the contact angle 0 (Ref. (15) Eq. [26]) with 2~(he) = 2o'~(cos 0 - 1),
[1]
where o-" is the surface tension of the bulk solution. We used the value o f o-~ measured at 23°C (see Table I), as within the experimental error no significant variation of o-~ with the temperature was found, i.e., Ido-"/dTI < 0.07 mN/m degree. This introduced an error of, at most, 1% for the highest temperature of 29.5°C. The variation of MT(he) with the NaC1 concentration and t e m p e r a t u r e is illustrated in Figs. 1 and 2. The results for the system 0.05% NaDS + Na2SO4 are tabulated in Table II and illustrated in Fig. 3. Also here the NaDS concentration, czt, was above the CMC, as the CMC of NaDS is quite insensitive to the nature o f the co-ion (20). When c2t was increased from 0.05 to 0.10% no significant
TABLE I Interaction Free Energy
AF(he) and
Surface Tension or" of the System 0.05% NaDS + NaC1 A F ( h e ) / m J m -2
ca (NaC1) (molfliter)
0.19 0.21 0.23 0.25 0.275 0.30 0.35 0.40 0.50
o"
20.5°C
22.0°C
23.5°C
25.0°C
26.5°C
28.0°C
-0.214 -0.328 -0.445
-0.102 -0.225 -0.330 -0.425 -0.565 -0.655 -0.840
-0.012 a -0.122 -0.233 -0.322 -0.455 -0.555 -0.740 -0.900
-0.011 a -0.021 -0.134 -0.224 -0.344 -0.435 -0.630 -0.810 - l. 10
-0.012 a -0.036 -0.138 -0.252 -0.360 -0.530 -0.700 -0.980
-0.011 a -0.010 ~ -0.063 -0.171 -0.260 -0.435 -0.595
-0.680 -0.765 -0.970
29.5oc
-0.011 ~ -0.0125 -0.083 -0.176 -0.354 -0.505
(raN/m) 23oc
33.1 32.8 32.6 32.4 32.2 32.0 31.6 31.4 31.1
C o m m o n black (CB)-film. Journal o f Colloid a n d Interface Science, Vol. 64, No. 2, April 1978
272
DE FEIJTER AND VRIJ - 1.0
AF(h.) ( m J / m -2)
/ _o°
/ / /
I/././././ I
0.20
0.25
I
,
.
I
,
,
,
,
I
0 40
0.30 0.35 c 3 ( N o C I ) ( rnol . I "1)
FIG. l. Interaction free energy AF(he) as a function of the salt concentration for the system 0.05% NaDS + NaC1. (Experimental points of the CB-films, as given in Table I, have been omitted for the sake of clearness.)
change in 2W(he) was observed, i.e., above the CMC the value of 2W(h~) is insensitive to variations in czt. Contact angles of the NB-films below the CMC could only be measured at rather high electrolyte concentrations. For c3 (NaC1) < 0.35 mot/liter and c3 (Na2SO4) < 0.40 equiv/liter the formation of the NBfilms was greatly delayed or did not even occur at all. This was also found by Kolarov et al. (8). When c2 was decreased below the CMC a slight decrease of 12W(he)l was obtained in most cases. It is not clear, however, whether the change in fia~(he) is significant as the experimental error was
rather large. The decrease o f [AF(he)[, was always smaller than 0.2 mJ/m 2 when c2 was decreased from the CMC to 1A × CMC. Within the experimental error of 0.1 nm, the thickness o f the NB-films was identical for NaC1 and Na2SO4 at the same salt concentration. The equivalent water thickness, hw, of the films, as obtained from the Rayleigh equation (21) when the film is assumed to be a homogeneous water layer with refractive index n = 1.333, was 4.4 nm for c3 (NaC1) = 0.3 tool/liter and 4.5 nm at 0.4 tool/liter. The same hw-values were found for the microscopic, circular films and the large vertical films.
_1.00 &F(hel (mJ m'21 " ¢ YO"°°/. / -1
-050
T (*C)
FIG. 2. Interaction free energy &F(he) as a function of the temperature for the system 0.05% NaDS + NaC1. (Experimental points of the CB-films have been omitted.) Journal of Colloid and Interface Science, Vol. 64, N o . 2, April 1978
CONTACT ANGLES IN THIN LIQUID FILMS. II
273
4. DISCUSSION OF RESULTS
TABLE II
The results as given in the previous section show that the interaction free energy, z~(he), of the NB-films stabilized by NaDS strongly depends on the salt concentration; both for the systems with NaCI and NazSO4. For the NB-films with NaC1 this was observed b y others before (6-9, 12-14). As a new result we find that AF(he) strongly depends on the temperature, the variation of AF(h~) with T being practically constant. For the films with NaC1 this is illustrated in Fig. 2. Our AF(h~)-values of the system 0.05% NaDS + NaC1 perfectly agree with the results of Princen and Frankel (14), who used the same technique. Agreement within 0.03 mJ/m 2 is found with the results of Prins (7), who measured the film tension directly with a microbalance. The same technique was used by Clint et al. (6). Their ]AF(h~)[-values are 0.01 to 0.08 mJ/m 2 larger than ours, whereas those measured by Huisman and Mysels (12), using the bubble-cap method, are 0.1 to 0.2 mJ/m 2 smaller. The differences between the data of the different authors are presumably caused by the fact that in most cases the temperature was not controlled accurately. Huisman and M y s e l s (12) found that 2uW(he) of the NB-films stabilized by NaDS strongly depends on the nature of the
Interaction Free Energy £xF(h~)and Surface Tension o-~ of the System 0.05% NaDS + Na2SO4 h F ( h e ) / m J m -2
ca(Na~SQ) equiv/liter
22.0°C
23.5°C
0.25 0.30 0.35 0.40 0.50
-0.032 -0.192 -0.330 -0.445 -0.641
-0.009 a -0.100 -0.235 -0.353 -0.538
25.0°C
tr ~
26.5°C
(raN/m) 23°C
-0.175 -0.330
32.8 32.2 31.9 31.6 31.4
-0.021 0.271 -0.416
Common black (CB)-film.
counterion. We find that 2u~(he) also depends on the nature of the co-ion. Figures 1 and 3 show that for a given T both the absolute value of AF(he) and its variation with the salt concentration c 3 is larger for the films with NaC1 than for those with Na2SO4. No difference i s found in the variation of 2UW(h~) with T for the two systems. Our data as given in Tables I and II also include some hF(h~)-values of c o m m o n black (CB)-films. For the salt concentrations and temperatures studied, the z2urr(h~)values of these films are quite small ( - - 0 . 0 1 mJ/m2). They are represented by the horizontal parts of the curves in Figs. 1-3. Although the number o f data is limited, it is clear that the variation of AF(he) with c3 and T is much smaller than for the NB-films. When for a given temperature the salt
-113 AF(he) (rnJ m-2)
-(35
0.2.5,
0.30
035
0.40
0.45 0 50 c3(No2SOd)(equiv U1)
FIG. 3. Interaction free energy 2xF(he)as a function of the salt concentration for the system 0.05% NaDS + Na,2SO4. J o u r n a l o f Colloid a n d Interface S c e n c e , Vol. 64 No. 2, April 1978
274
DE FEIJTER AND VRIJ 35
concentration was increased from 0.3 to 0.4 mol/liter.
T(°C)
5. EVALUATION OF THERMODYNAMIC INTERACTION PARAMETERS 2~
L
0.20
0125
I
0~30 0.35 c3(cr}t) (equiv. 1-1)
FIG. 4. Relation between the transition temperature and cz(crit) for the system 0.05% NaDS + NaC1 and 0.05% NaDS + Na2SO4. concentration is increased, the transition from CB- to NB-films takes place at the salt concentration where the slope of AF(he) vs cz suddenly increases (see Figs. 1 and 3). This is the critical salt concentration, cz(crit), where AF(he), and consequently also the film tension 3', are equal for the two film types; for ca = c3(crit) the CB- and NB-film type can coexist in one film. Figure 4 shows the relation between the transition temperatures and cz(crit) as obtained from Figs. 1-3. Thus c3(crit) is found to increase with increasing temperature; i.e., the NBfilms are most easily formed at low temperatures. At a given temperature it is smaller for the films with NaC1 than for those with Na2SO4. The c3(crit)-values for the films with NaC1 agree within 0.01 mol/liter with those of Jones et al. (1) who visually determined the salt concentration where CB- and NB-film type occur in one film. The thickness o f NB-films is quite insensitive to changes in c3 and T (1, 22). Our values for the equivalent water thickness, hw, of the NB-films are 0.2 nm smaller than those measured by Bruil (22) and 0.7 nm smaller than the ones reported by Jones et al. (1). T h e y also found a slight increase of hw with increasing c3. The h~-values reported by Prins (7) are 0.2 nm smaller than ours. H e found a small decrease of 4.3 to 4.2 nm when the NaC1 Journal o f Colloid andl/tterface Science, Vol. 64, No. 2, April 1978
In paper I (15) we have shown that the contact angle, 0, of a film not only gives the interaction free energy, ~ ( h e ) , but also the change in the surface entropy, A~s, and in the surface excess o f the solutes, AF,, caused by the interaction between the film surfaces. From Eq. [35] o f paper I it is seen that the difference between the surface excess entropy o f the film surface and the bulk surface, A~s = ,s s - ' s % is obtained from the variation of AdZ(he) with temperature T (at constant disjoining pressure, II, and chemical potentials o f the solutes, /z0. In practice ASs is not a very convenient quantity, as it is quite difficult to keep the chemical potentials ~ constant when T is changed. Both from a theoretical and practical point of view it is much more convenient to use the interaction entropy, AS(he), obtained from the variation of AF(he) with T at constant composition of the bulk solution and disjoining pressure II:
AS(he) =-- -dAF(he)/dT.
[2]
Figure 2 shows that the plots of AF(he) vs T o f the NB-films o f the system 0.05% NaDS + NaC1 are practically straight. Thus, the interaction entropy AS(he) is practically independent of T. The plots for different c3 being parallel shows that for a given value o f AF(he) the interaction entropy is independent of the salt concentration. Both for the NB-films with NaCI and with Na2SO4 we find: A S ( h e ) = - 0 . 0 6 6 -+ 0.003 mJ/m 2. For the CB-films o f the same systems the absolute value o f AS(he) is at least a factor of 50 smaller (see Table I). Hence, the formation of an NB-film from two bulk surfaces (and also from a CB-film) is exothermic. Qualitatively, this was already concluded by Jones et al. (1). When AF(he) and AS(he) are known, one
275
CONTACT ANGLES IN THIN LIQUID FILMS. II
can calculate the interaction energy AU(he) with: aU(he) = zXF(he) + T'AS(he).
[3]
In the temperature range studied (20.529.5°C) the value of T,SS(he) is - 2 0 ___ 1 mJ/m 2, both for the NB-films with NaC1 and NaeSO4. The 2uF(he)-values of these films range from - 0 . 0 0 9 to - 1 . 1 mJ/m 2 (see Tables I and II). Thus the value of the interaction energy AU(he) must be approximately - 2 0 mJ/m 2. The accuracy of the experimental results is not sufficiently large for us to determine whether the variation of 2uF(he) with ca is caused by a variation of AU(he) or o f AS(he) or both. From the above results it follows that the formation of an NB-film of the systems NaDS + NaC1 and NaDS + Na2SO4 is energetically a highly favorable process, but, on the other hand, entropically highly unfavorable, with the quantities AU(he) and - T AS ( h e) tending to compensate each other. The difference, AFt, between the surface excess o f c o m p o n e n t i at the film- and the bulk surface is obtained from the variation AF(he) with the composition of the bulk solution by using Eq. [35] of paper I. For the system N a D S ( = 2 ) + salt(=3) at constant temperature the equation reduces to: d[AF(h~) + IIh~] = -2AF~d/x2 - 2AF3d/x3 + hdII,
[4]
where/x2 and/x3 are the chemical potentials of NaDS and the salt, respectively. In our experiments the disjoining pressure II at the transition between the film and the plateau border was small and almost constant, with I1 -~ 25 N/m S. In the NB-films the llhe-term is about 10 -4 mJ/m 2 and can be neglected with respect to flaW(he). T h e n we have at constant 17: dAF(he) = -2AF2d/x2 - 2AF~d/za.
[5]
In the systems studied by us the chemical potentials Ix2 and Ix3 are interrelated, as the surfactant NaDS and the salts NaC1 and
Na2SO4 have one ion in common. In our case the salt concentration c3 is always at least a factor of 1000 larger than the surfactant m o n o m e r concentration c2; the change in /za upon a variation of c2 can then be neglected. The variation of/z2 and /z3 with changing c2 and ca is then given by: NaDS:
d/x2 = R Td lnf2c2 + R Td lnf2ca,
NaCI:
d/x3 = R Td In (f3ca)2 = RTd lna~,
Na2SO4:
[6]
d/z3 = R Td In (f3c3)~/2 = R Td In as,
where f2 and fa are the mean ion activity coefficients o f NaDS and the salt, respectively (c3 in equiv/liter). W h e n b e l o w the CMC the N a D S monomer concentration c2 is changed at constant T, 17 and ca, we have: dAF(he) = -2AF~d/xz = -2AFz(RTd lnf2c~).
[7]
Thus, 2xFz can be calculated from the variation of AF(he) with cz, below the CMC, at constant salt concentration. From the experimental results given in sect. 3 we find that AFz is presumably positive with AF2 ~< 5 X 10 .8 mol/m ~ (=3 x 1016 molecules/mZ), both for the films with NaC1 and Na2SO4. For the range of salt concentrations studied the surface excess F~" o f NaDS at the bulk surface is 4.2 x 10 -6 mol/m 2 (23-25). Thus the surface excesses F2~ and F2s of NaDS at the bulk- and the film surface, respectively, are equal within 1%. This is in agreement with the findings of Jones and Ibbotson (23) who measured F2~ and F2~ directly with a radio tracer method. The difference, AF.~, between the surface excess of the salt at the film- and the bulk surface can now be derived from the variation of 2xF(he) with the salt concentration c3. When c3 is varied at constant Journal of Colloid and Interface Science, Vol. 64, No. 2, April 1978
276
DE F E I J T E R A N D VRIJ
/
-1.0
~ F ( h e) ( m J rn " 2 )
-0.5
/'/
/://: ///:/, ,/e
I
-1.5
0.3 I
I
I ~--~ l o g
0.4 I
05 I
L
.110
C3 (tool 1-1) ,
a3(NoCI)
FIG. 5. fiJF(he) vs log aa(NaC1), with a,3 = (f3c3) z.
total NaDS concentration, the chemical potentials /z2 and /z3 vary simultaneously (see Eq. [6]). Above the CMC the NaDSm o n o m e r concentration cz can be equated to the CMC. The CMC of NaDS depends on the salt concentration; when c3 >> CMC, as in our experiments, the two quantities are interrelated by the experimental relation (26, 27) d In CMC = kd In c3.
dNF(he) = -(0.32AF2 + 2AFa)d/~8 -AG(3)d/zz --= - Z~G(3). [2RTd In f3cg], and for Na2SO4:
dAF(hD = -(0.42&F2 + 2hF3)d/z3 _= - AG(3)d/z 3 --- - A G ( 3 ) . [3/2RTd lnf3e3].
[8]
For the system NaDS + NaC1 the value of k is about - 0 . 6 8 (16). The same value can be used for NaDS + Na2SO4 as the co-ion has only a minor influence on the CMC (20). Substituting Eqs. [6] and [8] into Eq. [5] and assuming that f2 = fa, we find, for the system with NaC1, at constant total surfactant concentration c2t (=0.05%): -10 AF(h e) (mJ m - 2 )
[9]
[10]
The quantities AG(3) are obtained from the plots of 2u~(h~) vs log aa as given in Figs. 5 and 6 for NaC1 and Na2SO4, respectively. The activity coefficients f3 of NaC1 and Na2SO4 were obtained from Ref. (28). The fact that the plots are straight indicates that, both for NaC1 and Na~SO4, AG(3) is independent of the salt concentration. For the system with NaCI the contribution of the AF2-term to AG(3) is found to be less than 6% and for Na2SO4 less than 8%. When the AF2-term is neglected, T A B L E III
- Q5
/4~A9,'-
AFz o f the Salt for the NB-Films of the Systems NaDS + NaC1 (I) and NaDS + Na~SO4 (II) AF3 × 107/equiv m -2
- 2i.0
FiG. 6. ~ ( h ~ )
i -1.5 log G3(No2SO 4 )
vs log a3(Na~SO4), with as = (f3c3) 3/2.
Journal of Colloid and Interface Science, Vol. 64, No. 2, April I978
(1) (II)
20.5°C
22.0°C
23.5°C
25.0°C
26.5°C
29.5°C
1.39
1.35 1.72
1.34 1.71
1.33
1.29
1.22
CONTACT ANGLES IN THIN LIQUID FILMS. II
we have: AG(3)= 2AF3. The AF3-values thus obtained are tabulated in Table III. For the NB-films of the system 0.05% NaDS + NaC1 at 23.5°C we then find: AF3 = +1.34 x 10-7 mol/m 2, with AF3 decreasing with increasing temperature. The AF3-value for Na,2SO4, expressed in equiv/ m2, is larger by a factor of 1.28, the film thicknesses being equal in the two cases. From the results of our contact angle experiments it can thus be concluded that for the NB-films stabilized by NaDS more salt is adsorbed at the film surface than at the bulk surface. Qualitatively, the same conclusion was arrived at by Jones et al. (1). It is in agreement with what one should expect from the diffuse double-layer theory. This theory predicts that indifferent electrolyte is repelled from a charged surface in contact with an electrolyte solution, i.e., that F3" is negative. In a film where the double layers of the two surfaces interact the volume from which the salt is expelled decreases. As a consequence the absolute value of F3 decreases, i.e., FJ is less negative than F3~ or A F 3 - - = F J - F 3 ~ is positive (29-31). In a following paper we will attempt to interpret the herefound values of AFa in terms of the electrical double-layer theory. Further we will use the obtained values of Z~(he), AS(he) and AU(he) to draw conclusions concerning the nature of the interaction forces in the very thin NB-films. ACKNOWLEDGMENTS This work was part of the research programme of the "Stichting voor Fundamenteel Onderzoek der Materie" (FOM) with financial support from the "Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek" (ZWO). REFERENCES 1. Jones, M. N., Mysels, K. J., and Scholten, P. C., Trans. Faraday Soc. 62, 1336 (1966). 2. Sheludko, A., Advan. Colloid Interface Sci. 1, 39 (1967).
277
3. Clunie, J. S., Goodman, J. F., Ingram, B. T., in "Surface and Colloid Science," Vol. 3, p. 167. Wiley (Interscience), New York, 1971. 4. Everett, D. H., Pure Appl. Chem. 31, 581 (1972). 5. Ibbotson, G., and Jones, M. N., Trans. Faraday Soc. 65, 1146 (1969). 6. Clint, J. H., Clunie, J. S., Goodman, J. F., and Tare; J. R., Nature 223, 291 (1969). 7. Prins, A., J. Colloid Interface Sci. 29, 177 (1969). 8. Kolarov, T., Sheludko, A., and Exerowa, D., Trans. Faraday Soc. 64, 2864 (1968), 9. Huisman, H. F., Mysels, K. J., and Razouk, K. J., J. Phys. Chem. 70, 1339 (1966). 10. Clunie, J. S., Corkill, J. M., Goodman, J. F., and Ingram, B. T., Spec. Discuss. Faraday Soc. 1, 30 (1970). 11. Ingram, B. T., J.C.S. Faraday 1 68, 2230 (1972). 12. Huisman, H. F., and Mysels, K. J., J. Phys. Chem. 73, 489 (1969). 13. Frankel, S., and Princen, H. M., J. Phys. Chem. 74, 2580 (1970). 14. Princen, H. M., and Frankel, S., J. Colloid Interface Sci. 35, 386 (1971). 15. De Feijter, J. A., Rijnbout, J. B., and Vrij, A., J. Colloid Interface Sci. 64, 258 (1978). 16. Huisman, H. F., thesis, Utrecht, 1964. 17. Sheludko, A., Radow, B., and Kolarov, T., Trans. Faraday Soc. 64, 2213 (1968). 18. Duyvis, E. M., thesis, Utrecht, 1962. 19. Lyklema, J., and Mysels, K. J., J. Amer. Chem. Soc. 87, 2539 (1965). 20. Corrin, M. L., and Harkins, W. D., J. Amer. Chem. Soc. 69, 63 (1947). 21. Born, M., and Wolf, E., "Principles of Optics." Pergamon, Elmsford, N.Y., 1959. 22. Bruil, H. G., thesis, Wageningen, 1970. 23. Jones, M. N., and Ibbotson, G., Trans. Faraday Soc. 66, 2394 (1970). 24. Wilson, A., Epstein, M. P., and Ross, J., J. Colloid Sci. 12, 345 (1957). 25. Weil, I., J. Phys. Chem. 70, 133 (1966). 26. Mukerjee, P., Advan. Colloid Interface Sci. 1, 243 (1967). 27. Mijnlieff, P. F., J. Colloid Interface Sci. 33, 255 (1970). 28. Robinson, R. A., and Stokes, R. H., "Electrolyte Solutions" 2nd ed., Butterworth, London, 1959. 29. Schofield, R. K., Nature 160, 408 (1947). 30. Bolt, G. H., and Warkentin, B. P., Kolloid-Z. 156, 41 (1958). 31. De Haan, F. A. M., J. Phys. Chem. 68, 2970 (1964).
Journal of Colloid and Interface Science, Vol, 64, No. 2, April 1978