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Thermodynamic studies on adsorption at interfaces
Thermodynamic Studies on Adsorption at Interfaces IV. Dodecylammonium Chloride at Water/Air Interface KINSI MOTOMURA, SHIN-ICHIRO IWANAGA, YOSHITERU HAYAMI, SHOZO URYU, AND RYOHEI MATUURA D e p a r t m e n t o f Chemistry, Faculty o f Science, K y u s h u University 33, Fukuoka 812, J a p a n
Received March 13, 1980; accepted June 27, 1980 The thermodynamic treatment of the adsorption at water/oil interface developed in the previous papers has been extended so as to be applied to the adsorption at water/air interface. The surface tension of the aqueous solution of dodecylammonium chloride (DAC) has been measured as a function of temperature and concentration. By applying the thermodynamic relations, the entropy of surface formation As and the surface density of DAC F H have been calculated. Further, we have shown that the energy of surface formation Au can be evaluated numerically. It has been observed that the values of As and Au decrease, while the value of F7 increases, with increasing concentration of DAC. It has been found that the adsorbed film transforms from a gaseous to an expanded state at a relatively low concentration, which has been proved thermodynamically. Such a behavior seems to be similar to that at water/hexane interface except for the phase transition. The mutual interaction between DAC molecules in the adsorbed film appears to be weakened by the presence of hexane. INTRODUCTION
where c~ is the concentration of component i expressed in number of moles per unit volume, the superscripts W and A indicate the aqueous and gaseous phases, respectively, and the subscripts w and a indicate water and air, respectively. Further, they showed that Eq. [2] can be approximated by the expression
The Gibbs adsorption isotherm given by Eq. [1] is commonly applied to measurements of the surface tension y of surfactant solution made at constant temperature T under atmospheric pressure: (O~lOtz,)r =
- Fxc ,
[ 1]
where /zl is the chemical potential of the surfactant and F~ is its surface excess per unit area referred to the dividing surface chosen so that the surface excess of water is zero (1). However, the application of Eq. [1] to such a case is incorrect from the thermodynamic viewpoint. Delay et al. (2) derived an exact equation which should be employed in place of Eq. [1] when the measurements are carried out in the presence of air (assumed to be one component) at constant pressure p:
(O~lO~,)~,p =
A w wC aA -- CwC ~ aw )], CwC 1 )/(Cw
[3]
under an ordinary condition. In the preceding papers (3-10), we have proved that the thermodynamic treatment based on the excess quantity defined by Hansen (I 1) is useful in clarifying the structure and properties of adsorbed film at oil/water interface. This approach may be expected to be developed for the case of adsorption at water/air interface, providing an equation analogous to Eq. [3]. In the present paper, the thermodynamic treatment of adsorption at water/air interface is described in a fashion similar to that
(o~//O~l)~,~ = - r ~ + r2 x [(cWc~-
- r7
[2] 32
0021-9797/81/030032-07502.00/0 Copyright© 1981by AcademicPress, Inc. All rightsof reproductionin any formreserved.
Journal of Colloid and Interface Science, Vol.80, No. 1, March 1981
THERMODYNAMIC STUDIES ON ADSORPTION, IV at water/oil interface. The surface tension of dodecylammonium chloride solution was measured as a function of temperature and concentration and the thermodynamic quantity changes associated with the adsorption were evaluated and compared with the corresponding changes at water/hexane interface. THEORETICAL Let our system be composed of air and aqueous solution of surfactant under atmospheric pressure. The air phase is saturated by the vapors of water and surfactant after the system attains equilibrium. In a homogeneous region in the gaseous phase at a great distance from the interface; therefore, there exists a G i b b s - D u h e m equation expressed in the form s A d T - d p + cAd/za + cwd/zw A
+ c~d/zl = 0,
[4]
where s is the entropy per unit volume. Here air has been treated as if it behaves like a pure component. In a manner similar to that in Part I of this series (3), thus, we can derive the equation which gives 3' as a function of the independent intensive variables T, p , and/x~: d3" = - s H d T
+ vHdp -- FHd/zl,
[5]
where s ~, v H, and F~ are, respectively, the surface excess entropy, volume, and number of moles of surfactant per unit area defined with respect to the two dividing planes which make the surface excess numbers of moles of air and water to be zero. This is the fundamental equation describing the adsorption of surfactant at water/air interface. Immediately we can obtain the expression r~ = -(Oy/O/Xl)r,p.
[61
By comparing Eq. [6] with Eq. [3], we are led to the conclusion that the surface tension measured at constant temperature under atmospheric pressure gives not F~, but F1H. Making use of the molality of surfactant in the aqueous solution, rn w, when the sur-
33
factant dissociates completely into v+ positive ions and v_ negative ions, instead of/~1 as the thermodynamic variable, Eq. [6] is rewritten in the form F~ =
-
(O3"lOm w)r,pl (v+ + v _ ) ( O ~ . l a m W ) T , p
[7]
where/~+_ is the mean chemical potential of surfactant, if c w is assumed to be negligibly small. Further, we can obtain As :
-(03"laT),,m~,,
[8]
where As is the entropy of surface formation defined by As = s H - F1Hs W 1,
[9]
Sl being the partial molar entropy of surfactant. It should be noted that Eqs. [7] and [8] are identical in form to Eqs. [III.16] and [III. 14] applied to the adsorption at water/oil interface in Part III (5), respectively. Denoting the corresponding energy and volume by Au and Av, respectively, we have the relation (3) [10] Let us now consider a phase transition which takes place in the adsorbed film at water/air interface. Supposing the adsorbed film of ionic surfactant to be comprised of two phases c~ and fl in equilibrium, its state can be described by the relations A u = 31 + T A s - p a y .
d3" = - A s ~ d T
+ Av~dp
- (v+ + v_)r~'%Otz+lOmW)r,~dm w
[11]
and d3" = - A s ° d T
+ Av~dp
- (v+ + v_)F~'°(Ol~+_/OmW)r,pdrn w,
[12]
where the superscripts a and fl indicate the phases a and fi, respectively. Eliminating the variable m w between Eqs. [11] and [12] at constant pressure, we obtain ( 03"/ O T )~q
=
-(AsO/F~,~ - As~IF~,~)/ ( l / r ~ ,~ -
Journal of Colloid and Interface Science, Vol.
l/r~,~),
[13]
80, No. 1, Ma r c h 1981
34
MOTOMURA ET AL.
where the superscript eq means that the two phases coexist in equilibrium. Alternatively, elimination of 3' yields the relation (Omwl/OT)~ q = - ( A s ~ - As~)/(~+ + v_)
r~,'9(o~+_/OmW)~,p.
× (r~,~ -
~
-E [14]
These equations show what thermodynamic quantities decide the 3' vs T and m w vs T curves of the system in which two adsorbed phases coexist under atmospheric pressure. MATERIALS AND METHODS
Dodecylammonium chloride was synthesized and purified by the method described previously (9). Water was distilled triply from alkaline permanganate. Surface tension was measured by the dropvolume technique using a glass dropping tip. The drop was formed in a saturated atmosphere of the aqueous solution. The volume of drop was determined by the procedure that the drop was developed rapidly to about 95% of its final volume, allowed to stand for about 10 min until the adsorption equilibrium was established, and then turned off slowly. The value of surface tension was calculated by use of the relation
o
I
50 - ¢ ' ~ : ~ ¢ - ~
z 45 E 40
3 4
~ ~
6
o--.~..~ 35
2
~
7
I
I
i
i
i
290
295
300
305
310
FIG. lb. Surface tension vs temperature c u r v e s at c o n s t a n t concentration u n d e r a t m o s p h e r i c pressure: (1) m w = 5.09 m m o l e kg-1; (2) 5.60; (3) 6.17; (4) 7.11; (5) 8.10; (6) 9.02; (7) 9.97; (8) 11.1.
3" = ( V A d g / r ) F ,
[15]
where V is the volume of drop, /~d the difference in density between aqueous solution and humid air, g the acceleration of gravity, r the radius of dropping tip, and F the correction factor which is a function of r / V 113 (12, 13). The value of F was taken from the correction table of Lando and Oakley (14). The density of pure water was used instead of that of the aqueous solution, because the concentration is sufficiently low. The density of humid air d Awas evaluated by d a = (1.293/3.67T)(1 - 0.375pw/760),
[16]
where Pw is the saturated vapor pressure (in atmosphere) of water (15). The error estimated for the value of surface tension was less than 0.06 mN m -1. Temperature was kept constant by immersing the cell in a thermostat.
70 Z
E 65
60 ~
1
RESULTS AND DISCUSSION
2
i
i
290
295
i
300 TJK
i
305
I
310
FIG. la. Surface tension vs temperature constant concentration u n d e r a t m o s p h e r i c (1) m w = 0 m m o l e kg-1; (2) 0.316; (3) 0.524; (5) 1.11; (6) 1.34; (7) 1.61; (8) 1.95; (9) 2.17; (11) 2.73; (12) 3.14.
curves at pressure: (4) 0.811, (10) 2.49;
Journal of Colloid and Interface Science, Vol. 80, No. 1, March 1981
The surface tension of the aqueous solution of dodecylammonium chloride (DAC) was measured as a function of temperature at a given molality under atmospheric pressure. In Figs. la and b, the values of 3' are plotted against T at various concentrations. It is seen from these figures that the 3' vs T
35
T H E R M O D Y N A M I C STUDIES ON ADSORPTION, IV
0.15 0.10 ? E
"--
0.05 0
- 0.05
-0.10 i
2.0
h
i
~
4.0 6.0 8.0 rnlW/m tool kg-1
i
10.0
FIG. 2. Entropy of surface formation vs molality curves at constant temperature under atmospheric pressure: (1) 288.15°K; (2) 298.15°K; (3) 308.15°K.
curve has a distinct minimum at higher concentrations, while it is a m o n o t o n o u s l y decreasing curve, like that of pure water, at lower concentrations. This b e h a v i o r resembles that of DAC at w a t e r / h e x a n e interface (9). The o c c u r r e n c e of such a minimum indicates that the surface tension vs concentration curves at different t e m p e r a t u r e s intersect each other and the e n t r o p y of surface formation b e c o m e s zero at the minimum point. By applying Eq. [8] to the experimental data shown in Figs. l a and b, one can evaluate the entropy of surface formation of DAC numerically. The values of As obtained at the temperatures 288.15,298.15, and 308.15°K are drawn as a function of m w in Fig. 2. As expected, As decreases with increasing m w and ultimately b e c o m e s negative. Further, we note that As decreases with rising T and its decrease is p r o n o u n c e d at a higher concentration. This b e h a v i o r seems similar to that at water/hexane interface (9). Inspecting Fig. 3 in m o r e detail, h o w e v e r , we find some differences b e t w e e n the As vs m w curve at water/air interface and that at water/ hexane interface at 298.15°K. The f o r m e r has a higher value of As, and it exhibits a discontinuous change, although small, at a relatively low concentration. This is the most characteristic for water/air interface. The
adsorbed film at water/air interface appears to display a phase transition at this concentration. The phase transition is examined well by estimating the surface density o f D A C . Selecting the values of surface tension at a given t e m p e r a t u r e f r o m Figs. l a and b, we can obtain the plot of 7 against m w at constant T under atmospheric pressure, which is illustrated in Fig. 4. Figure 4 also shows how the 7 vs m w curve varies with temperature. As expected, the curves are found to intersect each other. It is of great importance to note that a b r e a k point is observed on the c u r v e and its concentration is in a g r e e m e n t with the one at which the As vs m w c u r v e changes discontinuously. Assuming the aqueous solution of DAC to be ideal and with v + = v - = 1, the surface density F H can be evaluated b y means of Eq. [III. 17]: [17]
F H = -(mW/2RT)(OT/OmW)T,p.
Application of Eq. [17] to the curves in Fig. 4 gives the F H vs m w plots at 288.15,298.15, and 308.15°K. The results are drawn in Fig. 5. It is seen that the value of F~ increases with an increase in concentration and changes discontinuously at the concentration corresponding to the b r e a k point. It is also found that the F~ vs m w c u r v e is shifted d o w n w a r d with a rise in t e m p e r a t u r e . H e r e we again note the difference of the a d s o r p -
0.15 0.10
E 0.05 (.9
0 -0.05 -0.1~
i
2.0
h
i
4.0 6.0 8.0 m~/mmol kg-1
i
10.0
FIG. 3. Entropy of surface formation vs molality curves at 298.15°K under atmospheric pressure: (1) water/air interface; (2) water/hexane interface. Journal of Colloid and Interface Science, Vol. 80, No. 1, March 1981
36
M O T O M U R A E T AL.
70
¥
1
60
Z
E
~5o 40
30
i
2.0
i
i
i
i
4.0 6.0 8.0 10.0 rr~/mmol ko-I
FIG. 4. Surface tension vs molality curves at constant temperature u n d e r atmospheric pressure: (1) 288.15°K; (2) 298.15°K; (3) 308.15°K.
tion b e h a v i o r with that at water/hexane interface (9). Evidently the discontinuous change of F~ p r o v e s that a transformation occurs b e t w e e n phases of the a d s o r b e d film. When the 7 vs m w curves in Fig. 4 are c o m p a r e d with the corresponding curves of octadecanol at hexane/water interface (7), the variation in the concentration of b r e a k point with t e m p e r a t u r e is o b s e r v e d to be rem a r k a b l y small. Such a b e h a v i o r m a y be accounted for b y Eq. [ 14], which in the present case is written as
with temperature. By substituting the a b o v e numerical values into Eq. [13], on the other hand, we can evaluate the slope of the surface tension of b r e a k point vs t e m p e r a t u r e curve. Thus we obtain (O3"/OT)~ q = - 0 . 1 6 m N m -1 K - L It is now explicable by this result that a b r e a k point has not been o b s e r v e d on any y vs T curve in Figs. la and b. These findings support the view that the a d s o r b e d film of D A C at water/air interface displays the phase transition. It is v e r y important to k n o w what kinds of phases participate in the transformation. F o r this purpose, the surface pressure vs area curve of adsorbed film seems m o s t useful. By use of Figs. 4 and 5, we can plot the surface pressure defined b y 7r = 3 , ° -
%
[19]
3'0 being the surface tension of pure water, against the area per DAC molecule given b y A = 1/NAF~,
[20]
NA being A v o g a d r o ' s number. The plot of ~r vs A at 298.15°K is shown b y curve 1 in Fig. 6. This curve is found to be quite similar in shape to a typical curve of insoluble film attended by a phase transition. Taking into
5.0 f l f 2
i
( a m W l OT)~ q = -(mW/2RT)(As
~' "3
4.0
~ -
As~)/
(F n,~ - r~,~).
% [18]
The right side of Eq. [18] can be calculated by making use of the a b o v e results. On substituting the n u m e r i c a l v a l u e s m w = 1.40 m m o l e kg -1, As ~ = 0.156 mJ K -~ m -2, As s = 0.150 mJ K -I m -2, F~ "~ = 0.74 tzmole m -2, and F H'o = 1.40 /zmole m -2 estimated from Figs. 2 and 5 at 298.15°K, we now obtain (OmW/OT)~ q = 2.6 tzmole kg -1 K - L It is easily understood that this small value explains the observation that the b r e a k point does not shift appreciably
"6 3.0 E :::L
2.0
1.0
/ i
0
0
2,0
i
i
i
i
4.0 6.0 8.0 I0,0 rnW/rnmol kg-I
FIG. 5. Surface density vs molality c u r v e s at c o n s t a n t temperature u n d e r a t m o s p h e r i c pressure: (1) 288.15°K; (2) 298.15°K; (3) 308.15°K.
37
T H E R M O D Y N A M I C S T U D I E S ON A D S O R P T I O N , IV
40
3O
¥ z
20
10
i
0
1.0
0
i
i
2.0 3,0 A /nrn 2
i
4.0
FIG. 6. Surface pressure vs area curves at 298.15°K under atmospheric pressure: (1) water/air interface: (2) water/hexane interface.
account that the transition area is fairly large compared with that of the expanded s t a t e condensed state transformation, we may conclude that the phase transition of the adsorbed film of DAC takes place from a gaseous state to an expanded state. This is in accord with the fact that the value of (0y/ OT)~ q is appreciably different from that of octadecanol at hexane/water interface (7). It is also important to consider the temperature dependence of As. As we have seen previously, the value of A s decreases with increasing T. It also decreases with increasing m w and, consequently, with increasing FIH. Using a method similar to that in Part I (3), we can correlate As to F~n by the relation
observation. Thus we may say that the difference between g~ and s w is magnified by a rise in temperature, which might be accounted for by a change in the properties of water with temperature. Such a result has been obtained in the case of the adsorption of DAC (9) and also of sodium dodecylsulfate (5) at water/hexane interface. L e t us now evaluate the energy of surface formation Au. In terms of Eq. [10], Au is related to other thermodynamic quantities. Since the values of 7 and As are known already, the value of Av is required for the evaluation of Au. Thermodynamically, Av is given by the derivative of surface tension with respect to the pressure of air phase in equilibrium with the surfactant solution: [22]
Av = (Oy/Op)r, ml w',
which is derived in a similar way as Eq. [8]. It seems reasonable to assume that the value of Av is of the order of the value at nitrogen/water interface. The latter one can be estimated by using the data of Massoudi and King (16). Thus, we obtain Av = - 0 . 8 2 0 mm 3 m -2, which y i e l d s p h v = -0.0831 mN m -1. Therefore, we may conclude that the value o f p S v is negligibly small as compared with the values of 7 and T A s and accord-
120 ~
...........
100 80
AS
I -I =ra(Sa
-
-
I -I Sa~)+ rw(Sw
Sw)
+ Fa(S~ n - H - sW),
[21]
where gi represents the mean partial molar entropy of c o m p o n e n t i and the superscript I denotes the quantity to be inherent in the interface. Accordingly, a decrease in As implies that the mean partial molar entropy change gln - s w has a negative value. On the other hand, the value of FIa decreases as T rises. Therefore, the value of As should increase with rising T, if g~ - s w is independent of T. This is in conflict with the
~ 60 E \
.~ 4o
-
20
'
0
1.0
'
'
2.0 3.0 r ~ / ~ m o t m-~
'
4.0
FIG. 7. Energy of surface formation vs surface density curves at 298.15°K under atmospheric pressure: (1) water/air interface; (2) water/hexane interface. Journal of Colloid and Interface Science, Vol. 80, No. 1, March 1981
38
MOTOMURA ET AL.
ingly Eq. [10] reduces to A u = 3, + T A s .
[23]
N o w Au is calculated numerically b y use of Figs. 3 and 4. The Au vs F~ c u r v e obtained is drawn as curve 1 in Fig. 7. It appears that the value of Au decreases with increasing F~. This fact indicates that the adsorption process is an energetically favorable one in the case of the adsorption of DAC at water/air interface. Comparing the results at water/air interface with those at water/hexane interface, invaluable information m a y be e x p e c t e d regarding properties of the adsorbed film. Let us first consider the energy of surface formation. The 2~u vs F~ curves are compared in Fig. 7. It is found that the a d s o r b e d film at water/air interface has a higher value when c o m p a r e d at the same F~. H o w e v e r , the shapes of curves are similar as a whole except for the phase transition. It is obvious from Fig. 3 that this is the case for the entropy of surface formation. These facts m a y indicate that the D A C molecules b e h a v e similarly in both the adsorbed films at water/ air and water/hexane interfaces. L e t us next c o m p a r e the 7r vs A curves which are shown in Fig. 6. It is seen that the curves are rem a r k a b l y different. Thus we m a y say that the difference in the state of adsorbed film is best revealed b y the 7r vs A curve. On examining Fig. 6, the curve at water/hexane interface is supposed to c o r r e s p o n d to that which is o b s e r v e d at a t e m p e r a t u r e a b o v e the critical temperature. Therefore, it is inferred from analogy with the insoluble film that the DAC molecules in the adsorbed film at water/hexane interface m a y b e h a v e as though their mutual interaction could be w e a k e n e d by the p r e s e n c e of hexane. A similar explanation was 0ffele~ b y Scho= field and Rideal (17) for the difference in the adsorption of butylic acid between
Journal of Colloid and Interface Science, Vol. 80, No. 1, March 1981
water/air and water/benzene interfaces. H o w e v e r , it must be kept in mind that the adsorbed film is a two-dimensional solution c o m p o s e d of three c o m p o n e n t s , of which the surface densities are not determined experimentally except the surfactant. REFERENCES 1. Gibbs, J. W., "Collected Works," Vol. 1, p. 219. Dover, New York, 1961. 2. Defay, R., Prigogine, I., and Bellemans, A., "Surface Tension and Adsorption" (D. H. Everett, Transl,), p. 89. Longmans, London, 1966. 3. Motomura, K., J. Colloid Interface Sci. 64, 348 (1978). 4. Motomura, K., Matubayasi, N., Aratono, M., and Matuura, R., J. Colloid Interface Sci. 64, 356 (1978). 5. Motomura, K., Aratono, M., Matubayasi, N., and Matuura, R., J. Colloid Interface Sci. 67, 247 (1978). 6. Motomura, K., Advan. Colloid Interface Sci. 12, 1 (1980). 7. Matubayasi, N., Motomura, K., Aratono, M., and Matuura, R., Bull. Chem. Soc. Japan 51, 2800 (1978). 8. Matubayasi, N., Dohzono, M., Aratono, M., Motomura, K., and Matuura, R., Bull. Chem. Soc. Japan 52, 1597 (1979). 9. Aratono, M., Yamanaka, M., Matubayasi, N., Motomura, K., and Matuura, R., J. Colloid Interface Sci. 74, 489 (1980). 10. Ikenaga, T., Matubayasi, N., Aratono, M., Motomura, K., and Matuura, R., Bull. Chem. Soc. Japan 53, 653 (1980). 11. Hansen, R. S., J. Phys. Chem. 66, 410 (1962). 12. Harkins, W. D., and Brown, F. E., J. Amer. Chem. Soc. 4i, 499 (1919). 13. Wilkinson, M. C., J. Colloid Interface Sci. 40, 14 (1972). 14. Lando, J. L., and Oakley, H. T., J. Colloid Interface Sci, 25, 526 (1967). 15. Chemical Society of Japan, Ed., "Kagaku Benran," Part II, p. 667. Maruzen, Tokyo, 1975. 16. Massoudi, R., and King, A. D., Jr.,J. Phys. Chem. 78, 2262 (1974). 17. Schofield, R. K., and Rideal, E. K., Proc. Roy. Soc. London A 109, 57 (1925).
Received March 13, 1980; accepted June 27, 1980 The thermodynamic treatment of the adsorption at water/oil interface developed in the previous papers has been extended so as to be applied to the adsorption at water/air interface. The surface tension of the aqueous solution of dodecylammonium chloride (DAC) has been measured as a function of temperature and concentration. By applying the thermodynamic relations, the entropy of surface formation As and the surface density of DAC F H have been calculated. Further, we have shown that the energy of surface formation Au can be evaluated numerically. It has been observed that the values of As and Au decrease, while the value of F7 increases, with increasing concentration of DAC. It has been found that the adsorbed film transforms from a gaseous to an expanded state at a relatively low concentration, which has been proved thermodynamically. Such a behavior seems to be similar to that at water/hexane interface except for the phase transition. The mutual interaction between DAC molecules in the adsorbed film appears to be weakened by the presence of hexane. INTRODUCTION
where c~ is the concentration of component i expressed in number of moles per unit volume, the superscripts W and A indicate the aqueous and gaseous phases, respectively, and the subscripts w and a indicate water and air, respectively. Further, they showed that Eq. [2] can be approximated by the expression
The Gibbs adsorption isotherm given by Eq. [1] is commonly applied to measurements of the surface tension y of surfactant solution made at constant temperature T under atmospheric pressure: (O~lOtz,)r =
- Fxc ,
[ 1]
where /zl is the chemical potential of the surfactant and F~ is its surface excess per unit area referred to the dividing surface chosen so that the surface excess of water is zero (1). However, the application of Eq. [1] to such a case is incorrect from the thermodynamic viewpoint. Delay et al. (2) derived an exact equation which should be employed in place of Eq. [1] when the measurements are carried out in the presence of air (assumed to be one component) at constant pressure p:
(O~lO~,)~,p =
A w wC aA -- CwC ~ aw )], CwC 1 )/(Cw
[3]
under an ordinary condition. In the preceding papers (3-10), we have proved that the thermodynamic treatment based on the excess quantity defined by Hansen (I 1) is useful in clarifying the structure and properties of adsorbed film at oil/water interface. This approach may be expected to be developed for the case of adsorption at water/air interface, providing an equation analogous to Eq. [3]. In the present paper, the thermodynamic treatment of adsorption at water/air interface is described in a fashion similar to that
(o~//O~l)~,~ = - r ~ + r2 x [(cWc~-
- r7
[2] 32
0021-9797/81/030032-07502.00/0 Copyright© 1981by AcademicPress, Inc. All rightsof reproductionin any formreserved.
Journal of Colloid and Interface Science, Vol.80, No. 1, March 1981
THERMODYNAMIC STUDIES ON ADSORPTION, IV at water/oil interface. The surface tension of dodecylammonium chloride solution was measured as a function of temperature and concentration and the thermodynamic quantity changes associated with the adsorption were evaluated and compared with the corresponding changes at water/hexane interface. THEORETICAL Let our system be composed of air and aqueous solution of surfactant under atmospheric pressure. The air phase is saturated by the vapors of water and surfactant after the system attains equilibrium. In a homogeneous region in the gaseous phase at a great distance from the interface; therefore, there exists a G i b b s - D u h e m equation expressed in the form s A d T - d p + cAd/za + cwd/zw A
+ c~d/zl = 0,
[4]
where s is the entropy per unit volume. Here air has been treated as if it behaves like a pure component. In a manner similar to that in Part I of this series (3), thus, we can derive the equation which gives 3' as a function of the independent intensive variables T, p , and/x~: d3" = - s H d T
+ vHdp -- FHd/zl,
[5]
where s ~, v H, and F~ are, respectively, the surface excess entropy, volume, and number of moles of surfactant per unit area defined with respect to the two dividing planes which make the surface excess numbers of moles of air and water to be zero. This is the fundamental equation describing the adsorption of surfactant at water/air interface. Immediately we can obtain the expression r~ = -(Oy/O/Xl)r,p.
[61
By comparing Eq. [6] with Eq. [3], we are led to the conclusion that the surface tension measured at constant temperature under atmospheric pressure gives not F~, but F1H. Making use of the molality of surfactant in the aqueous solution, rn w, when the sur-
33
factant dissociates completely into v+ positive ions and v_ negative ions, instead of/~1 as the thermodynamic variable, Eq. [6] is rewritten in the form F~ =
-
(O3"lOm w)r,pl (v+ + v _ ) ( O ~ . l a m W ) T , p
[7]
where/~+_ is the mean chemical potential of surfactant, if c w is assumed to be negligibly small. Further, we can obtain As :
-(03"laT),,m~,,
[8]
where As is the entropy of surface formation defined by As = s H - F1Hs W 1,
[9]
Sl being the partial molar entropy of surfactant. It should be noted that Eqs. [7] and [8] are identical in form to Eqs. [III.16] and [III. 14] applied to the adsorption at water/oil interface in Part III (5), respectively. Denoting the corresponding energy and volume by Au and Av, respectively, we have the relation (3) [10] Let us now consider a phase transition which takes place in the adsorbed film at water/air interface. Supposing the adsorbed film of ionic surfactant to be comprised of two phases c~ and fl in equilibrium, its state can be described by the relations A u = 31 + T A s - p a y .
d3" = - A s ~ d T
+ Av~dp
- (v+ + v_)r~'%Otz+lOmW)r,~dm w
[11]
and d3" = - A s ° d T
+ Av~dp
- (v+ + v_)F~'°(Ol~+_/OmW)r,pdrn w,
[12]
where the superscripts a and fl indicate the phases a and fi, respectively. Eliminating the variable m w between Eqs. [11] and [12] at constant pressure, we obtain ( 03"/ O T )~q
=
-(AsO/F~,~ - As~IF~,~)/ ( l / r ~ ,~ -
Journal of Colloid and Interface Science, Vol.
l/r~,~),
[13]
80, No. 1, Ma r c h 1981
34
MOTOMURA ET AL.
where the superscript eq means that the two phases coexist in equilibrium. Alternatively, elimination of 3' yields the relation (Omwl/OT)~ q = - ( A s ~ - As~)/(~+ + v_)
r~,'9(o~+_/OmW)~,p.
× (r~,~ -
~
-E [14]
These equations show what thermodynamic quantities decide the 3' vs T and m w vs T curves of the system in which two adsorbed phases coexist under atmospheric pressure. MATERIALS AND METHODS
Dodecylammonium chloride was synthesized and purified by the method described previously (9). Water was distilled triply from alkaline permanganate. Surface tension was measured by the dropvolume technique using a glass dropping tip. The drop was formed in a saturated atmosphere of the aqueous solution. The volume of drop was determined by the procedure that the drop was developed rapidly to about 95% of its final volume, allowed to stand for about 10 min until the adsorption equilibrium was established, and then turned off slowly. The value of surface tension was calculated by use of the relation
o
I
50 - ¢ ' ~ : ~ ¢ - ~
z 45 E 40
3 4
~ ~
6
o--.~..~ 35
2
~
7
I
I
i
i
i
290
295
300
305
310
FIG. lb. Surface tension vs temperature c u r v e s at c o n s t a n t concentration u n d e r a t m o s p h e r i c pressure: (1) m w = 5.09 m m o l e kg-1; (2) 5.60; (3) 6.17; (4) 7.11; (5) 8.10; (6) 9.02; (7) 9.97; (8) 11.1.
3" = ( V A d g / r ) F ,
[15]
where V is the volume of drop, /~d the difference in density between aqueous solution and humid air, g the acceleration of gravity, r the radius of dropping tip, and F the correction factor which is a function of r / V 113 (12, 13). The value of F was taken from the correction table of Lando and Oakley (14). The density of pure water was used instead of that of the aqueous solution, because the concentration is sufficiently low. The density of humid air d Awas evaluated by d a = (1.293/3.67T)(1 - 0.375pw/760),
[16]
where Pw is the saturated vapor pressure (in atmosphere) of water (15). The error estimated for the value of surface tension was less than 0.06 mN m -1. Temperature was kept constant by immersing the cell in a thermostat.
70 Z
E 65
60 ~
1
RESULTS AND DISCUSSION
2
i
i
290
295
i
300 TJK
i
305
I
310
FIG. la. Surface tension vs temperature constant concentration u n d e r a t m o s p h e r i c (1) m w = 0 m m o l e kg-1; (2) 0.316; (3) 0.524; (5) 1.11; (6) 1.34; (7) 1.61; (8) 1.95; (9) 2.17; (11) 2.73; (12) 3.14.
curves at pressure: (4) 0.811, (10) 2.49;
Journal of Colloid and Interface Science, Vol. 80, No. 1, March 1981
The surface tension of the aqueous solution of dodecylammonium chloride (DAC) was measured as a function of temperature at a given molality under atmospheric pressure. In Figs. la and b, the values of 3' are plotted against T at various concentrations. It is seen from these figures that the 3' vs T
35
T H E R M O D Y N A M I C STUDIES ON ADSORPTION, IV
0.15 0.10 ? E
"--
0.05 0
- 0.05
-0.10 i
2.0
h
i
~
4.0 6.0 8.0 rnlW/m tool kg-1
i
10.0
FIG. 2. Entropy of surface formation vs molality curves at constant temperature under atmospheric pressure: (1) 288.15°K; (2) 298.15°K; (3) 308.15°K.
curve has a distinct minimum at higher concentrations, while it is a m o n o t o n o u s l y decreasing curve, like that of pure water, at lower concentrations. This b e h a v i o r resembles that of DAC at w a t e r / h e x a n e interface (9). The o c c u r r e n c e of such a minimum indicates that the surface tension vs concentration curves at different t e m p e r a t u r e s intersect each other and the e n t r o p y of surface formation b e c o m e s zero at the minimum point. By applying Eq. [8] to the experimental data shown in Figs. l a and b, one can evaluate the entropy of surface formation of DAC numerically. The values of As obtained at the temperatures 288.15,298.15, and 308.15°K are drawn as a function of m w in Fig. 2. As expected, As decreases with increasing m w and ultimately b e c o m e s negative. Further, we note that As decreases with rising T and its decrease is p r o n o u n c e d at a higher concentration. This b e h a v i o r seems similar to that at water/hexane interface (9). Inspecting Fig. 3 in m o r e detail, h o w e v e r , we find some differences b e t w e e n the As vs m w curve at water/air interface and that at water/ hexane interface at 298.15°K. The f o r m e r has a higher value of As, and it exhibits a discontinuous change, although small, at a relatively low concentration. This is the most characteristic for water/air interface. The
adsorbed film at water/air interface appears to display a phase transition at this concentration. The phase transition is examined well by estimating the surface density o f D A C . Selecting the values of surface tension at a given t e m p e r a t u r e f r o m Figs. l a and b, we can obtain the plot of 7 against m w at constant T under atmospheric pressure, which is illustrated in Fig. 4. Figure 4 also shows how the 7 vs m w curve varies with temperature. As expected, the curves are found to intersect each other. It is of great importance to note that a b r e a k point is observed on the c u r v e and its concentration is in a g r e e m e n t with the one at which the As vs m w c u r v e changes discontinuously. Assuming the aqueous solution of DAC to be ideal and with v + = v - = 1, the surface density F H can be evaluated b y means of Eq. [III. 17]: [17]
F H = -(mW/2RT)(OT/OmW)T,p.
Application of Eq. [17] to the curves in Fig. 4 gives the F H vs m w plots at 288.15,298.15, and 308.15°K. The results are drawn in Fig. 5. It is seen that the value of F~ increases with an increase in concentration and changes discontinuously at the concentration corresponding to the b r e a k point. It is also found that the F~ vs m w c u r v e is shifted d o w n w a r d with a rise in t e m p e r a t u r e . H e r e we again note the difference of the a d s o r p -
0.15 0.10
E 0.05 (.9
0 -0.05 -0.1~
i
2.0
h
i
4.0 6.0 8.0 m~/mmol kg-1
i
10.0
FIG. 3. Entropy of surface formation vs molality curves at 298.15°K under atmospheric pressure: (1) water/air interface; (2) water/hexane interface. Journal of Colloid and Interface Science, Vol. 80, No. 1, March 1981
36
M O T O M U R A E T AL.
70
¥
1
60
Z
E
~5o 40
30
i
2.0
i
i
i
i
4.0 6.0 8.0 10.0 rr~/mmol ko-I
FIG. 4. Surface tension vs molality curves at constant temperature u n d e r atmospheric pressure: (1) 288.15°K; (2) 298.15°K; (3) 308.15°K.
tion b e h a v i o r with that at water/hexane interface (9). Evidently the discontinuous change of F~ p r o v e s that a transformation occurs b e t w e e n phases of the a d s o r b e d film. When the 7 vs m w curves in Fig. 4 are c o m p a r e d with the corresponding curves of octadecanol at hexane/water interface (7), the variation in the concentration of b r e a k point with t e m p e r a t u r e is o b s e r v e d to be rem a r k a b l y small. Such a b e h a v i o r m a y be accounted for b y Eq. [ 14], which in the present case is written as
with temperature. By substituting the a b o v e numerical values into Eq. [13], on the other hand, we can evaluate the slope of the surface tension of b r e a k point vs t e m p e r a t u r e curve. Thus we obtain (O3"/OT)~ q = - 0 . 1 6 m N m -1 K - L It is now explicable by this result that a b r e a k point has not been o b s e r v e d on any y vs T curve in Figs. la and b. These findings support the view that the a d s o r b e d film of D A C at water/air interface displays the phase transition. It is v e r y important to k n o w what kinds of phases participate in the transformation. F o r this purpose, the surface pressure vs area curve of adsorbed film seems m o s t useful. By use of Figs. 4 and 5, we can plot the surface pressure defined b y 7r = 3 , ° -
%
[19]
3'0 being the surface tension of pure water, against the area per DAC molecule given b y A = 1/NAF~,
[20]
NA being A v o g a d r o ' s number. The plot of ~r vs A at 298.15°K is shown b y curve 1 in Fig. 6. This curve is found to be quite similar in shape to a typical curve of insoluble film attended by a phase transition. Taking into
5.0 f l f 2
i
( a m W l OT)~ q = -(mW/2RT)(As
~' "3
4.0
~ -
As~)/
(F n,~ - r~,~).
% [18]
The right side of Eq. [18] can be calculated by making use of the a b o v e results. On substituting the n u m e r i c a l v a l u e s m w = 1.40 m m o l e kg -1, As ~ = 0.156 mJ K -~ m -2, As s = 0.150 mJ K -I m -2, F~ "~ = 0.74 tzmole m -2, and F H'o = 1.40 /zmole m -2 estimated from Figs. 2 and 5 at 298.15°K, we now obtain (OmW/OT)~ q = 2.6 tzmole kg -1 K - L It is easily understood that this small value explains the observation that the b r e a k point does not shift appreciably
"6 3.0 E :::L
2.0
1.0
/ i
0
0
2,0
i
i
i
i
4.0 6.0 8.0 I0,0 rnW/rnmol kg-I
FIG. 5. Surface density vs molality c u r v e s at c o n s t a n t temperature u n d e r a t m o s p h e r i c pressure: (1) 288.15°K; (2) 298.15°K; (3) 308.15°K.
37
T H E R M O D Y N A M I C S T U D I E S ON A D S O R P T I O N , IV
40
3O
¥ z
20
10
i
0
1.0
0
i
i
2.0 3,0 A /nrn 2
i
4.0
FIG. 6. Surface pressure vs area curves at 298.15°K under atmospheric pressure: (1) water/air interface: (2) water/hexane interface.
account that the transition area is fairly large compared with that of the expanded s t a t e condensed state transformation, we may conclude that the phase transition of the adsorbed film of DAC takes place from a gaseous state to an expanded state. This is in accord with the fact that the value of (0y/ OT)~ q is appreciably different from that of octadecanol at hexane/water interface (7). It is also important to consider the temperature dependence of As. As we have seen previously, the value of A s decreases with increasing T. It also decreases with increasing m w and, consequently, with increasing FIH. Using a method similar to that in Part I (3), we can correlate As to F~n by the relation
observation. Thus we may say that the difference between g~ and s w is magnified by a rise in temperature, which might be accounted for by a change in the properties of water with temperature. Such a result has been obtained in the case of the adsorption of DAC (9) and also of sodium dodecylsulfate (5) at water/hexane interface. L e t us now evaluate the energy of surface formation Au. In terms of Eq. [10], Au is related to other thermodynamic quantities. Since the values of 7 and As are known already, the value of Av is required for the evaluation of Au. Thermodynamically, Av is given by the derivative of surface tension with respect to the pressure of air phase in equilibrium with the surfactant solution: [22]
Av = (Oy/Op)r, ml w',
which is derived in a similar way as Eq. [8]. It seems reasonable to assume that the value of Av is of the order of the value at nitrogen/water interface. The latter one can be estimated by using the data of Massoudi and King (16). Thus, we obtain Av = - 0 . 8 2 0 mm 3 m -2, which y i e l d s p h v = -0.0831 mN m -1. Therefore, we may conclude that the value o f p S v is negligibly small as compared with the values of 7 and T A s and accord-
120 ~
...........
100 80
AS
I -I =ra(Sa
-
-
I -I Sa~)+ rw(Sw
Sw)
+ Fa(S~ n - H - sW),
[21]
where gi represents the mean partial molar entropy of c o m p o n e n t i and the superscript I denotes the quantity to be inherent in the interface. Accordingly, a decrease in As implies that the mean partial molar entropy change gln - s w has a negative value. On the other hand, the value of FIa decreases as T rises. Therefore, the value of As should increase with rising T, if g~ - s w is independent of T. This is in conflict with the
~ 60 E \
.~ 4o
-
20
'
0
1.0
'
'
2.0 3.0 r ~ / ~ m o t m-~
'
4.0
FIG. 7. Energy of surface formation vs surface density curves at 298.15°K under atmospheric pressure: (1) water/air interface; (2) water/hexane interface. Journal of Colloid and Interface Science, Vol. 80, No. 1, March 1981
38
MOTOMURA ET AL.
ingly Eq. [10] reduces to A u = 3, + T A s .
[23]
N o w Au is calculated numerically b y use of Figs. 3 and 4. The Au vs F~ c u r v e obtained is drawn as curve 1 in Fig. 7. It appears that the value of Au decreases with increasing F~. This fact indicates that the adsorption process is an energetically favorable one in the case of the adsorption of DAC at water/air interface. Comparing the results at water/air interface with those at water/hexane interface, invaluable information m a y be e x p e c t e d regarding properties of the adsorbed film. Let us first consider the energy of surface formation. The 2~u vs F~ curves are compared in Fig. 7. It is found that the a d s o r b e d film at water/air interface has a higher value when c o m p a r e d at the same F~. H o w e v e r , the shapes of curves are similar as a whole except for the phase transition. It is obvious from Fig. 3 that this is the case for the entropy of surface formation. These facts m a y indicate that the D A C molecules b e h a v e similarly in both the adsorbed films at water/ air and water/hexane interfaces. L e t us next c o m p a r e the 7r vs A curves which are shown in Fig. 6. It is seen that the curves are rem a r k a b l y different. Thus we m a y say that the difference in the state of adsorbed film is best revealed b y the 7r vs A curve. On examining Fig. 6, the curve at water/hexane interface is supposed to c o r r e s p o n d to that which is o b s e r v e d at a t e m p e r a t u r e a b o v e the critical temperature. Therefore, it is inferred from analogy with the insoluble film that the DAC molecules in the adsorbed film at water/hexane interface m a y b e h a v e as though their mutual interaction could be w e a k e n e d by the p r e s e n c e of hexane. A similar explanation was 0ffele~ b y Scho= field and Rideal (17) for the difference in the adsorption of butylic acid between
Journal of Colloid and Interface Science, Vol. 80, No. 1, March 1981
water/air and water/benzene interfaces. H o w e v e r , it must be kept in mind that the adsorbed film is a two-dimensional solution c o m p o s e d of three c o m p o n e n t s , of which the surface densities are not determined experimentally except the surfactant. REFERENCES 1. Gibbs, J. W., "Collected Works," Vol. 1, p. 219. Dover, New York, 1961. 2. Defay, R., Prigogine, I., and Bellemans, A., "Surface Tension and Adsorption" (D. H. Everett, Transl,), p. 89. Longmans, London, 1966. 3. Motomura, K., J. Colloid Interface Sci. 64, 348 (1978). 4. Motomura, K., Matubayasi, N., Aratono, M., and Matuura, R., J. Colloid Interface Sci. 64, 356 (1978). 5. Motomura, K., Aratono, M., Matubayasi, N., and Matuura, R., J. Colloid Interface Sci. 67, 247 (1978). 6. Motomura, K., Advan. Colloid Interface Sci. 12, 1 (1980). 7. Matubayasi, N., Motomura, K., Aratono, M., and Matuura, R., Bull. Chem. Soc. Japan 51, 2800 (1978). 8. Matubayasi, N., Dohzono, M., Aratono, M., Motomura, K., and Matuura, R., Bull. Chem. Soc. Japan 52, 1597 (1979). 9. Aratono, M., Yamanaka, M., Matubayasi, N., Motomura, K., and Matuura, R., J. Colloid Interface Sci. 74, 489 (1980). 10. Ikenaga, T., Matubayasi, N., Aratono, M., Motomura, K., and Matuura, R., Bull. Chem. Soc. Japan 53, 653 (1980). 11. Hansen, R. S., J. Phys. Chem. 66, 410 (1962). 12. Harkins, W. D., and Brown, F. E., J. Amer. Chem. Soc. 4i, 499 (1919). 13. Wilkinson, M. C., J. Colloid Interface Sci. 40, 14 (1972). 14. Lando, J. L., and Oakley, H. T., J. Colloid Interface Sci, 25, 526 (1967). 15. Chemical Society of Japan, Ed., "Kagaku Benran," Part II, p. 667. Maruzen, Tokyo, 1975. 16. Massoudi, R., and King, A. D., Jr.,J. Phys. Chem. 78, 2262 (1974). 17. Schofield, R. K., and Rideal, E. K., Proc. Roy. Soc. London A 109, 57 (1925).