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Mixed Adsorbed Film of Dodecylammonium Chloride with Decylammonium Chloride at Water/Air Interface MAKOTO ARATONO, SHOZO URYU, YOSHITERU HAYAMI, KINSI MOTOMURA, AND RYOHEI MATUURA Department of Chemistry, Faculty of Science, Kyushu University 33, Fukuoka 812, Japan Received February 25, 1982; accepted September 9, 1982 The surface tension of the aqueous solution containing dodecylammonium chloride and decylammonium chloride has been measured as a function of total concentration at 298.15°K under atmospheric pressure. It has been observed that the surface tension decreases with increasing the composition of dodecylammonium chloride at a fixed total concentration and the surface tension vs concentration curve has a distinct break point. By applying the thermodynamic relations developed, the surface densities of surfactants have been evaluated numerically. Examining the relation of the composition in the bulk phase to the one in the adsorbed film at constant surface tension, the difference in the surface activities of surfactants has been found to be pronounced at high surface tension. It has been proved that the break point corresponds to the phase transformation of the adsorbed film from a gaseous to an expanded state. It has been shown that the phase transition is expressed by a two-dimensional phase diagram. INTRODUCTION
The adsorption behavior of dodecylamm o n i u m chloride at water/air interface has been made clear thermodynamically in our previous paper (1); the thermodynamic quantities of interface formation have been evaluated and the adsorbed film has been found to transform its two-dimensional phase from a gaseous to an expanded state at a relatively low bulk concentration. Now it is interesting to see how the phase transformation is affected by mixing with other surfactant. It is also important to know how the composition of surfactants in the adsorbed film vary with the composition in the bulk phase. Measurements of the surface tension of mixed surfactant solutions have been widely made in connection with the formation of mixed micelles (2-6). Also, the thermodynamic treatments for multicomponent surfactant systems based on the Gibbs adsorption equations have been proposed and applied to the experimental results (7-13). Lucassen-Reynders considered recently the
surface interactions in mixed surfactant systems (14) in which the mixtures of dodecylammonium chloride and decylammonium chloride in the presence of 0.005 M HC1 (15) was also included. However, most of the investigations have been carried out at relatively high bulk concentrations. In this paper we treat the adsorption of the mixed systems of dodecylammonium chloride and decylammonium chloride at water/ air interface from their aqueous solutions below the critical micelle concentrations and extend our previous thermodynamic treatment (1) so as to be applied to this system. The surface tension was measured as a function of the bulk concentrations. MATERIALS AND METHOD
Decylammonium chloride was obtained by the reaction of fractionally distilled decylamine, of which purity was confirmed more than 99% by gas-liquid chromatography, with dry hydrochloride gas in ethanol followed by the recrystallization of five times
162 0021-9797/83 $3.00 Copyright© 1983by AcademicPress,Inc. All rightsof reproductionin any form reserved.
Journal of Colloidand InterfaceScience,Vol.93, No. 1, May 1983
163
M I X E D A D S O R B E D FILM
7°!
72
70
•
E
6C
68
Z
E
50
66
64 40
1098
I
0
10 15 20 m tW/mmo[ kg -1
0
25
I
I
]
1
2
3
765 I
I
4 I
3 I
4 5 6 7 mWt/rnmot kg -1
2
1
I
I
8
9
FIG. 1. (a and b) Surface tension vs total molality curves at constant bulk composition: (1) X w = 1; (2) 0.974; (3) 0.940; (4) 0.881; (5) 0.820; (6) 0.756; (7) 0.693; (8) 0.500; (9) 0.360; (10) 0.
from ethanol. D o d e c y l a m m o n i u m chloride was synthesized and purified by the m e t h o d described previously (16). The purities of respective surfactants were guaranteed by the absence of m i n i m u m near the critical micelle concentration on the surface tension vs concentration curves at 298.15°K. Water distilled triply from alkaline permanganate was used to prepare all solutions. Surface tension was measured by means of the drop volume technique, using a glass dropping tip. The detailed procedure of the m e a s u r e m e n t p e r f o r m a n c e was described previously (1). All the surface tensions were reproducible to _+0.05 m N m -1, and the measurement was carried out under atmospheric pressure at 298.150K by immersing the glass cell in a thermostat. RESULTS
The present system is composed of four components, i.e., two surfactants, water, and air which is assumed to be one component, and two bulk phases. T h e n we can adopt temperature T, pressure p, total molality of the surfactants m w defined by rn w = m w + m w
[1]
and composition of the second surfactant X TM defined by
X~: = mW/(mwl + m w)
[2]
as t h e r m o d y n a m i c variables. Subscripts 1 and 2 refer to d o d e c y l a m m o n i u m chloride (DAC) and d e c y l a m m o n i u m chloride (DeAC), respectively. The surface tension "r was measured as a function of m TM and X w at constant T under atmospheric pressure. Figure l a shows the variation of surface tension with m w at fixed X w. It is of great importance to note that the "r vs m w curve varies gradually with X w from that of D A C to DeAC and each curve has a break point. It m a y be said that the phase transition o f the adsorbed films of DeAC and the mixed system take place at the break point as is seen for DAC (1), which will be m a d e clear in the later discussion. Also magnified in Fig. lb are the curves in the vicinity of the break point in Fig. l a to examine the precise behavior. The value of m w at the break point increases, while that of 3' decreases, with increasing X~v. In Fig. 2 the selected values o f 3' at some fixed m w from Fig. 1 are plotted against X w. It is seen that the surface tension increases with increasing X TM and some y vs Journal of Colloid and Interface Science, VoL 93, No. 1, May 1983
164
A R A T O N O ET AL.
X2w curves have the break point designated by an arrow.
1
70 -
!
2 _
DISCUSSION
The surfactants used in the present study are uni-univalent strong electrolytes which have c o m m o n anion and dissociate completely. Taking notice of these situations, surface tension can be expressed as a function of chemical potential of ions at constant temperature and pressure (1, 17, 18): d7 = --Fill+ dg,+
-
~
FH+ dt~2+ -re"-due-,
40~)
= (O#i/Omw)T,p,mwdm
w
+ (Ol~i/OmW)r,p,mwdm w.
,/
0.2
04
[3]
where P lu+, F 2H+,and F cH_ are the surface excess numbers of moles o f dodecylammonium, d e c y l a m m o n i u m , and chloride ions per unit area, respectively. The surface excess quantities are defined with respect to the two dividing planes which m a k e the surface excess numbers of moles of water and air to be zero. The chemical potential of ion i in the aqueous solution can be expressed as a function of the molality o f DAC m w and that o f DeAC m~v at constant T and p as d#i
I
[4]
Though it is necessary to m a k e allowance for the nonideality in the aqueous solution at high concentrations, it seems that the assumption of the ideality does not cause the essential errors, as the first-order approximation, on the adsorption over the concentration range in the present study. Taking into consideration that there exist the relations r ~ = Fi+, H i = 1,2, [5]
x~
0.6
0.8
FIG. 2. Surface tension vs bulk composition curves at constant total molality: (1) m w = 1 m m o l kg-~; (2) 2 m m o l kg-~; (3) 3 m m o l kg-1; (4) 4 m m o l kg-~; (5) 6 m m o l kg-I; (6) 8 m m o l kg i; (7) 10 m m o l kg-1; (8) 15 m m o l kg -I.
d3, = - R T [ F ~ I m w
+ (rP + r~)/(m w + m~V)]dm w -
RT[(P7 + r~)/(m w + m w) + r~lm w] dmw.
[8]
An equation formally similar to Eq. [8] was derived by Ikeda (12) for the aqueous solution of anionic surfactant with an added electrolyte. In the present study, as the total molality m w and the composition of DeAC X w are chosen instead of m w and m~v as the therm o d y n a m i c variables, Eq. [8] can be convetted into
d3' = - 2 R T ( P t H / r n w) d m w - R T x [(xwr~ " -
xwr",)/xwx w] dXg,
[91
[61
and
where Ftn is t h e total surface excess n u m b e r of moles of surfactants per unit area defined by FtH = Flu + FT. [10]
PcH_ = Flu+ + F~+ = Flu + F ~ , [71 substitution of Eq. [4] into Eq. [3] leads us to
This equation is the fundamental one to obtain important information in understanding of properties and structures of adsorbed film.
m w = m w + m w,
Journal of Colloid and Interface Science, Vol. 93, No. 1, May 1983
M I X E D ADSORBED FILM
~
165
5,0'
the mixed adsorbed film, it is useful to plot the surface pressure defined by
40
II = 3,0 - "r
3.0
against the mean area per adsorbed molecule defined by A = 1~NArd, [13]
2.0
10
00
Y i
5
i
ll0 15 210 mtw/rumor kg -1
FIG. 3. Total surface density vs total molality curves at constant bulk composition; (1)X TM = 1; (2) 0.974; (3) 0.940; (4) 0.881; (5) 0.820; (6) 0.756; (7) 0.693; (8) 0.500; (9) 0.360; (10) 0.
Now let us consider to evaluate the surface densities of surfactant by applying Eq. [9] to the experimental results. At first the total surface density FtH, which is of course equal to the surface density of chloride ion, can be calculated by means of the equation derived from Eq. [9]: r t H = -mtW(o'y/OmtW)r,p,xw/2RT.
NA being Avogadro number. The typical 17 vs A curves, which are obtained by making use of Figs. 1 and 3, are drawn in Fig. 4. It is seen clearly that each II vs A curve shows a flat portion and alters its shape gradually with X w. Such a two-dimensional behavior is explicable in terms of the difference in the lateral attractive force of molecules between DAC and DeAC. Therefore we may conclude that the phase transition of the mixed adsorbed films as well as of the adsorbed films o f pure DAC and DeAC takes place from a gaseous to an expanded state. Next we shall estimate the respective surface densities o f DAC and DeAC. For this purpose it is necessary to solve two simultaneous equations, i.e., Eq. [10] and the equation
(a1'/aXW2 )T,p,m~ =_RT[XWr~
[11]
The results are expressed in the form of Ftn vs mtw plot at some fixed values o f X w in Fig. 3. The values of Ftn increase with an increase in mtw and decrease with an increase in X w. It should be noted that the values of Ptn change discontinuously at the value of mtw corresponding to the break point in Fig. 1. This behavior assures that the phase transformation between two phases takes place in the adsorbed film. It has been observed that the adsorbed films of octadecanol (19, 20) and dioctadecyl ether (2 l) at oil/water interface are transformed between expanded and condensed states and the adsorbed film of DAC at water/air interface is transformed between gaseous and expanded states (1). To learn what kind o f two-dimensional phases participate in the phase transition of
[12]
- X z FwI ] / H X,
wX2,
[14]
which is derived from Eq. [9]. Thus we have PHI = x W p t H + x W x W ( o 3 , / O x w ) / R T
[15]
10
8 z E6 \
:::::::::::::::::::::
4
05
1.0
1.5 210 A/rim ~
25
310
FIG. 4. Surface pressure vs area curves at constant bulk composition: (1) X w = 1; (2) 0.881; (3) 0.500;
(4) O. Journal of Colloid and Interface Science, Vol. 93, No. 1, May 1983
166
A R A T O N O ET AL.
and V~ = X W F ~ - s W x W ( o ' y / o x W ) / R T . [16]
The numerical values of O"//OX w are obtained from Fig. 2. In Figs. 5 and 6 the values of F H and F2H are illustrated against X w at fixed mtW; the F H vs X~v curves obtained from Fig. 3 are also included. The typical curves in the region of rntw where the phase transition does not take place are given in Fig. 5, where the curves 1 and 2 correspond to the expanded and gaseous states, respectively. In Fig. 6, on the other hand, the curves in the region of rntw where the phase transition takes place are given. It can be seen that the phase transition from the gaseous to the expanded state is attended by the discontinuous increase in surface densities. Below and above the transition point, the variation of surface densities at constant mtw is ascribed to the change of the composition in the bulk phase; the values of I'~ increase, while those of r p decrease, with increasing X~v. It is worthwhile to note that the surface density of DeAC decreases remarkably with decrease in X w. Taking into account of the observation that DeAC adsorbs appreciably at water/air interface from its aqueous solution as seen in Fig. 3, it may be said that
~
.,! 1.0
~ !;
0
0.2
0.4
x~
0.6
0.8
1
FIG. 6. Surface density vs bulk composition curves at constant total molality: (l) m TM = 6 mmol kg-~; (2) 4 mmol k g - ~ ; - - , PtH; - - -, r ~ ; ---, F p .
a slight difference in surface activity between DeAC and DAC has a great influence on the adsorption when they are mixed. The examination of the relation between the composition of DeAC in the bulk aqueous solution X w and that in the interfacial layer X~ defined by
X~ = F~/(FP + F H)
[17]
will provide an important information. Figure 7 shows the variation of X2H with X w at constant surface tension. It is seen from Fig. 7 that the deviation of the value of X~ from that ofX~v becomes small as the surface ten-
4.0 T
E '6
1 3.0
\
>,
,20
0.8
\
0.6
0.4 0.2S 0 0 C)
0.2
0A
x~
0.6
0.8
1
FIG. 5. Surface density vs bulk composition curves at constant total molality: (1) m w = 10 m m o l kg-t; (2) 1 m m o l kg-l; - - , FtH; - - - , P~; "", F~. Journal of Colloid and InterfaceScience, VoL 93, No. 1. May 1983
0
I 0.2
0.4
x7
0.6
0.8
1
FIG. 7. Surface composition vs bulk composition curves at constant surface tension: (1) 3' = 55 m N m l; (2) 60 m N m-]; (3) 65 m N m - L
MIXED ADSORBED FILM
167
say that Fig. 8 is a two-dimensional phase diagram of the transition between the gaseous and expanded states o f D A C - D e A C mixed adsorbed film at 298.15°K under atmospheric pressure. On the other hand, there exists the equation
67
0
02
0.4
0.6
0
d,~eq = - 2 R T ( F ~ ' ~ / m w) d m w - R T
x7 × [(xwr
FIG. 8. Equilibrium surface tension vs surface composition curves: (1) 3,eq vs X~X; (2) ~/eqvs X~"g.
sion decreases. Since the lowering of surface tension is attended by the increment of surface density, the difference in the surface activity between two surfactants under study is found to be more pronounced at the low surface density. G6ralczyk (10) observed a similar result for the adsorption of anioniccationic surfactant at water/air interface from the solution of 1/1 molar ratio. Finally, we shall discuss the change in the composition of surfactants at the transition point between gaseous and expanded phases. With the aid of the curves in Fig. 6 and the analogous ones at other values of rn w, the mole fractions of DeAC in the gaseous phase X~ 'g and in the expanded phase X~ x are estimated at the transition point. They are plotted against the equilibrium surface tension ~,eq in Fig. 8. From Fig. 1, we can also draw the ,~eq VS X ~ 'V plot, which is shown in Fig. 9. As expected from Fig. 7, when we compare the curves in Fig. 8 with the one in Fig. 9, both the curves deviate downward from the 3,eq vs X w curve. It is also seen that the value o f X ~ 'e is smaller than that o f X ~ 'g. It is important to note that the gaseous phase is realized for the adsorbed film in the area above the 3,~q vs X~ "g curve, the expanded phase is realized in the area below the 3,eq vs X H'~ curve, and these two phases coexist in equilibrium in the area between two curves. A similar behavior was observed for the mixed insoluble monolayers composed of two filmforming substances (22). Therefore, we may
,o - xwr"
,
)/xwxwl d X w , [18]
for a phase and the same equation for /3 phase. These two equations must hold simultaneously at the transition point. Eliminating d m tw at constant T and p and rearranging the resulting equation, we can obtain the expression = -xwxw(1/r
,e-
",e - 1 / r
× (03,/oxW)~p/RT.
[19]
This equation indicates that the value of X2n'e - X2H'g in Fig. 8 is closely related to the slope of 3,eq vs X~v curve. The right side of Eq. [19] can be calculated numerically by making use of Figs. 3 and 9. The calculated value of X2H'~- X2H'g was found to be approximately equal to the corresponding one in Fig. 8. This fact substantiates that the phase transition takes place in the mixed adsorbed film.
67
0
I
I
I
I
0.2
0.4
0.6
0.8
x~ FIG. 9. Equilibrium surface tension vs bulk composition curve. Journal of Colloid and Interface Science, Vol. 93, No. 1, May 1983
168
ARATONO ET AL. REFERENCES
1. Motomura, K., Iwanaga, S., Hayami, Y., Uryu, S., and Matuura, R., J. Colloid Interface Sci. 80, 32 (1981). 2. Clint, J. H., J. Chem. Soc. Faraday Trans 1 71, 1327 (1975). 3. Lange, H., and Beck, K.-H., Kolloid Z. Z. Polym. 251, 424 (1973). 4. Schwuger, H. J., Kolloid Z. Z. Polym. 243, 129 (1971). 5. Funasaki, N., and Hada, S., Bull. Chem. Soc. Jpn. 49, 2899 (1976). 6. Ingrain, B. T., and Luckhurst, A. H. W., Surface Act. Agents, SCI Symp. (Nottingham), 89 (1979). 7. Lucassen-Reynders, E. H., Lucaseen, J., and Giles, D., J. Colloid Interface Sci. 81, 150 (1981). 8. Huchinson, E., Z Colloid Sci. 3, 413 (1948). 9. Nakamura, A., and Muramatsu, M., J. Colloid Interface Sci. 62, 165 (1977). 10. G6ralczyk, D., J. Colloid Interface Sci. 77, 68 (1980). 11. Tajima, K., Nakamura, A., and Tsutsui, T., Bull. Chem. Soc. Jpn. 52, 2060 (1979).
Journalof Colloidand_InterfaceScience,Vol.93, No. 1, May 1983
12. Ikeda, S., Bull. Chem. Soc. Jpn. 50, 1403 (1977). 13. Tajima, K., Bull. Chem. Soc. Jpn. 44, 1767 (1971). 14. Lucassen-Reynders, E. H., Z Colloid Interface Sci. 85, 178 (1982). 15. Lucassen-Reynders, E. H., Z Colloid Interface Sci. 41, 156 (1972). 16. Aratono, M., Yamanaka, M., MatUbayasi, N., Motomura, K., and Matuura, R., J. Colloidlnterface Sci. 74, 489 (1980). 17. Motomura, K., ,L Colloid Interface Sci. 64, 348 (1978). 18. Motomura, K., Aratono, M., Matubayasi, N., and Matuura, R., J. Colloid Interface Sci. 67, 247 (1978). 19. Matubayasi, N., Motomura, K., Aratono, M., and Matuura, R., Bull. Chem. Soe. Jpn. 51, 2800 (1978). 20. Ikenaga, T,, Matubayasi, N., Aratono, M., Motomura, K., and Matuura, R., Bull. Chem. Soc. Jpn. 53, 653 (1980). 21. Matubayasi, N., Dohzono, M., Aratono, M., Motomura, K., and Matuura, R., Bull. Chem. Soc. Jpn. 52, 1597 (1979). 22. Motomura, K., Advan. Colloid Interface Sci. 12, 1 (1980).
The adsorption behavior of dodecylamm o n i u m chloride at water/air interface has been made clear thermodynamically in our previous paper (1); the thermodynamic quantities of interface formation have been evaluated and the adsorbed film has been found to transform its two-dimensional phase from a gaseous to an expanded state at a relatively low bulk concentration. Now it is interesting to see how the phase transformation is affected by mixing with other surfactant. It is also important to know how the composition of surfactants in the adsorbed film vary with the composition in the bulk phase. Measurements of the surface tension of mixed surfactant solutions have been widely made in connection with the formation of mixed micelles (2-6). Also, the thermodynamic treatments for multicomponent surfactant systems based on the Gibbs adsorption equations have been proposed and applied to the experimental results (7-13). Lucassen-Reynders considered recently the
surface interactions in mixed surfactant systems (14) in which the mixtures of dodecylammonium chloride and decylammonium chloride in the presence of 0.005 M HC1 (15) was also included. However, most of the investigations have been carried out at relatively high bulk concentrations. In this paper we treat the adsorption of the mixed systems of dodecylammonium chloride and decylammonium chloride at water/ air interface from their aqueous solutions below the critical micelle concentrations and extend our previous thermodynamic treatment (1) so as to be applied to this system. The surface tension was measured as a function of the bulk concentrations. MATERIALS AND METHOD
Decylammonium chloride was obtained by the reaction of fractionally distilled decylamine, of which purity was confirmed more than 99% by gas-liquid chromatography, with dry hydrochloride gas in ethanol followed by the recrystallization of five times
162 0021-9797/83 $3.00 Copyright© 1983by AcademicPress,Inc. All rightsof reproductionin any form reserved.
Journal of Colloidand InterfaceScience,Vol.93, No. 1, May 1983
163
M I X E D A D S O R B E D FILM
7°!
72
70
•
E
6C
68
Z
E
50
66
64 40
1098
I
0
10 15 20 m tW/mmo[ kg -1
0
25
I
I
]
1
2
3
765 I
I
4 I
3 I
4 5 6 7 mWt/rnmot kg -1
2
1
I
I
8
9
FIG. 1. (a and b) Surface tension vs total molality curves at constant bulk composition: (1) X w = 1; (2) 0.974; (3) 0.940; (4) 0.881; (5) 0.820; (6) 0.756; (7) 0.693; (8) 0.500; (9) 0.360; (10) 0.
from ethanol. D o d e c y l a m m o n i u m chloride was synthesized and purified by the m e t h o d described previously (16). The purities of respective surfactants were guaranteed by the absence of m i n i m u m near the critical micelle concentration on the surface tension vs concentration curves at 298.15°K. Water distilled triply from alkaline permanganate was used to prepare all solutions. Surface tension was measured by means of the drop volume technique, using a glass dropping tip. The detailed procedure of the m e a s u r e m e n t p e r f o r m a n c e was described previously (1). All the surface tensions were reproducible to _+0.05 m N m -1, and the measurement was carried out under atmospheric pressure at 298.150K by immersing the glass cell in a thermostat. RESULTS
The present system is composed of four components, i.e., two surfactants, water, and air which is assumed to be one component, and two bulk phases. T h e n we can adopt temperature T, pressure p, total molality of the surfactants m w defined by rn w = m w + m w
[1]
and composition of the second surfactant X TM defined by
X~: = mW/(mwl + m w)
[2]
as t h e r m o d y n a m i c variables. Subscripts 1 and 2 refer to d o d e c y l a m m o n i u m chloride (DAC) and d e c y l a m m o n i u m chloride (DeAC), respectively. The surface tension "r was measured as a function of m TM and X w at constant T under atmospheric pressure. Figure l a shows the variation of surface tension with m w at fixed X w. It is of great importance to note that the "r vs m w curve varies gradually with X w from that of D A C to DeAC and each curve has a break point. It m a y be said that the phase transition o f the adsorbed films of DeAC and the mixed system take place at the break point as is seen for DAC (1), which will be m a d e clear in the later discussion. Also magnified in Fig. lb are the curves in the vicinity of the break point in Fig. l a to examine the precise behavior. The value of m w at the break point increases, while that of 3' decreases, with increasing X~v. In Fig. 2 the selected values o f 3' at some fixed m w from Fig. 1 are plotted against X w. It is seen that the surface tension increases with increasing X TM and some y vs Journal of Colloid and Interface Science, VoL 93, No. 1, May 1983
164
A R A T O N O ET AL.
X2w curves have the break point designated by an arrow.
1
70 -
!
2 _
DISCUSSION
The surfactants used in the present study are uni-univalent strong electrolytes which have c o m m o n anion and dissociate completely. Taking notice of these situations, surface tension can be expressed as a function of chemical potential of ions at constant temperature and pressure (1, 17, 18): d7 = --Fill+ dg,+
-
~
FH+ dt~2+ -re"-due-,
40~)
= (O#i/Omw)T,p,mwdm
w
+ (Ol~i/OmW)r,p,mwdm w.
,/
0.2
04
[3]
where P lu+, F 2H+,and F cH_ are the surface excess numbers of moles o f dodecylammonium, d e c y l a m m o n i u m , and chloride ions per unit area, respectively. The surface excess quantities are defined with respect to the two dividing planes which m a k e the surface excess numbers of moles of water and air to be zero. The chemical potential of ion i in the aqueous solution can be expressed as a function of the molality o f DAC m w and that o f DeAC m~v at constant T and p as d#i
I
[4]
Though it is necessary to m a k e allowance for the nonideality in the aqueous solution at high concentrations, it seems that the assumption of the ideality does not cause the essential errors, as the first-order approximation, on the adsorption over the concentration range in the present study. Taking into consideration that there exist the relations r ~ = Fi+, H i = 1,2, [5]
x~
0.6
0.8
FIG. 2. Surface tension vs bulk composition curves at constant total molality: (1) m w = 1 m m o l kg-~; (2) 2 m m o l kg-~; (3) 3 m m o l kg-1; (4) 4 m m o l kg-~; (5) 6 m m o l kg-I; (6) 8 m m o l kg i; (7) 10 m m o l kg-1; (8) 15 m m o l kg -I.
d3, = - R T [ F ~ I m w
+ (rP + r~)/(m w + m~V)]dm w -
RT[(P7 + r~)/(m w + m w) + r~lm w] dmw.
[8]
An equation formally similar to Eq. [8] was derived by Ikeda (12) for the aqueous solution of anionic surfactant with an added electrolyte. In the present study, as the total molality m w and the composition of DeAC X w are chosen instead of m w and m~v as the therm o d y n a m i c variables, Eq. [8] can be convetted into
d3' = - 2 R T ( P t H / r n w) d m w - R T x [(xwr~ " -
xwr",)/xwx w] dXg,
[91
[61
and
where Ftn is t h e total surface excess n u m b e r of moles of surfactants per unit area defined by FtH = Flu + FT. [10]
PcH_ = Flu+ + F~+ = Flu + F ~ , [71 substitution of Eq. [4] into Eq. [3] leads us to
This equation is the fundamental one to obtain important information in understanding of properties and structures of adsorbed film.
m w = m w + m w,
Journal of Colloid and Interface Science, Vol. 93, No. 1, May 1983
M I X E D ADSORBED FILM
~
165
5,0'
the mixed adsorbed film, it is useful to plot the surface pressure defined by
40
II = 3,0 - "r
3.0
against the mean area per adsorbed molecule defined by A = 1~NArd, [13]
2.0
10
00
Y i
5
i
ll0 15 210 mtw/rumor kg -1
FIG. 3. Total surface density vs total molality curves at constant bulk composition; (1)X TM = 1; (2) 0.974; (3) 0.940; (4) 0.881; (5) 0.820; (6) 0.756; (7) 0.693; (8) 0.500; (9) 0.360; (10) 0.
Now let us consider to evaluate the surface densities of surfactant by applying Eq. [9] to the experimental results. At first the total surface density FtH, which is of course equal to the surface density of chloride ion, can be calculated by means of the equation derived from Eq. [9]: r t H = -mtW(o'y/OmtW)r,p,xw/2RT.
NA being Avogadro number. The typical 17 vs A curves, which are obtained by making use of Figs. 1 and 3, are drawn in Fig. 4. It is seen clearly that each II vs A curve shows a flat portion and alters its shape gradually with X w. Such a two-dimensional behavior is explicable in terms of the difference in the lateral attractive force of molecules between DAC and DeAC. Therefore we may conclude that the phase transition of the mixed adsorbed films as well as of the adsorbed films o f pure DAC and DeAC takes place from a gaseous to an expanded state. Next we shall estimate the respective surface densities o f DAC and DeAC. For this purpose it is necessary to solve two simultaneous equations, i.e., Eq. [10] and the equation
(a1'/aXW2 )T,p,m~ =_RT[XWr~
[11]
The results are expressed in the form of Ftn vs mtw plot at some fixed values o f X w in Fig. 3. The values of Ftn increase with an increase in mtw and decrease with an increase in X w. It should be noted that the values of Ptn change discontinuously at the value of mtw corresponding to the break point in Fig. 1. This behavior assures that the phase transformation between two phases takes place in the adsorbed film. It has been observed that the adsorbed films of octadecanol (19, 20) and dioctadecyl ether (2 l) at oil/water interface are transformed between expanded and condensed states and the adsorbed film of DAC at water/air interface is transformed between gaseous and expanded states (1). To learn what kind o f two-dimensional phases participate in the phase transition of
[12]
- X z FwI ] / H X,
wX2,
[14]
which is derived from Eq. [9]. Thus we have PHI = x W p t H + x W x W ( o 3 , / O x w ) / R T
[15]
10
8 z E6 \
:::::::::::::::::::::
4
05
1.0
1.5 210 A/rim ~
25
310
FIG. 4. Surface pressure vs area curves at constant bulk composition: (1) X w = 1; (2) 0.881; (3) 0.500;
(4) O. Journal of Colloid and Interface Science, Vol. 93, No. 1, May 1983
166
A R A T O N O ET AL.
and V~ = X W F ~ - s W x W ( o ' y / o x W ) / R T . [16]
The numerical values of O"//OX w are obtained from Fig. 2. In Figs. 5 and 6 the values of F H and F2H are illustrated against X w at fixed mtW; the F H vs X~v curves obtained from Fig. 3 are also included. The typical curves in the region of rntw where the phase transition does not take place are given in Fig. 5, where the curves 1 and 2 correspond to the expanded and gaseous states, respectively. In Fig. 6, on the other hand, the curves in the region of rntw where the phase transition takes place are given. It can be seen that the phase transition from the gaseous to the expanded state is attended by the discontinuous increase in surface densities. Below and above the transition point, the variation of surface densities at constant mtw is ascribed to the change of the composition in the bulk phase; the values of I'~ increase, while those of r p decrease, with increasing X~v. It is worthwhile to note that the surface density of DeAC decreases remarkably with decrease in X w. Taking into account of the observation that DeAC adsorbs appreciably at water/air interface from its aqueous solution as seen in Fig. 3, it may be said that
~
.,! 1.0
~ !;
0
0.2
0.4
x~
0.6
0.8
1
FIG. 6. Surface density vs bulk composition curves at constant total molality: (l) m TM = 6 mmol kg-~; (2) 4 mmol k g - ~ ; - - , PtH; - - -, r ~ ; ---, F p .
a slight difference in surface activity between DeAC and DAC has a great influence on the adsorption when they are mixed. The examination of the relation between the composition of DeAC in the bulk aqueous solution X w and that in the interfacial layer X~ defined by
X~ = F~/(FP + F H)
[17]
will provide an important information. Figure 7 shows the variation of X2H with X w at constant surface tension. It is seen from Fig. 7 that the deviation of the value of X~ from that ofX~v becomes small as the surface ten-
4.0 T
E '6
1 3.0
\
>,
,20
0.8
\
0.6
0.4 0.2S 0 0 C)
0.2
0A
x~
0.6
0.8
1
FIG. 5. Surface density vs bulk composition curves at constant total molality: (1) m w = 10 m m o l kg-t; (2) 1 m m o l kg-l; - - , FtH; - - - , P~; "", F~. Journal of Colloid and InterfaceScience, VoL 93, No. 1. May 1983
0
I 0.2
0.4
x7
0.6
0.8
1
FIG. 7. Surface composition vs bulk composition curves at constant surface tension: (1) 3' = 55 m N m l; (2) 60 m N m-]; (3) 65 m N m - L
MIXED ADSORBED FILM
167
say that Fig. 8 is a two-dimensional phase diagram of the transition between the gaseous and expanded states o f D A C - D e A C mixed adsorbed film at 298.15°K under atmospheric pressure. On the other hand, there exists the equation
67
0
02
0.4
0.6
0
d,~eq = - 2 R T ( F ~ ' ~ / m w) d m w - R T
x7 × [(xwr
FIG. 8. Equilibrium surface tension vs surface composition curves: (1) 3,eq vs X~X; (2) ~/eqvs X~"g.
sion decreases. Since the lowering of surface tension is attended by the increment of surface density, the difference in the surface activity between two surfactants under study is found to be more pronounced at the low surface density. G6ralczyk (10) observed a similar result for the adsorption of anioniccationic surfactant at water/air interface from the solution of 1/1 molar ratio. Finally, we shall discuss the change in the composition of surfactants at the transition point between gaseous and expanded phases. With the aid of the curves in Fig. 6 and the analogous ones at other values of rn w, the mole fractions of DeAC in the gaseous phase X~ 'g and in the expanded phase X~ x are estimated at the transition point. They are plotted against the equilibrium surface tension ~,eq in Fig. 8. From Fig. 1, we can also draw the ,~eq VS X ~ 'V plot, which is shown in Fig. 9. As expected from Fig. 7, when we compare the curves in Fig. 8 with the one in Fig. 9, both the curves deviate downward from the 3,eq vs X w curve. It is also seen that the value o f X ~ 'e is smaller than that o f X ~ 'g. It is important to note that the gaseous phase is realized for the adsorbed film in the area above the 3,~q vs X~ "g curve, the expanded phase is realized in the area below the 3,eq vs X H'~ curve, and these two phases coexist in equilibrium in the area between two curves. A similar behavior was observed for the mixed insoluble monolayers composed of two filmforming substances (22). Therefore, we may
,o - xwr"
,
)/xwxwl d X w , [18]
for a phase and the same equation for /3 phase. These two equations must hold simultaneously at the transition point. Eliminating d m tw at constant T and p and rearranging the resulting equation, we can obtain the expression = -xwxw(1/r
,e-
",e - 1 / r
× (03,/oxW)~p/RT.
[19]
This equation indicates that the value of X2n'e - X2H'g in Fig. 8 is closely related to the slope of 3,eq vs X~v curve. The right side of Eq. [19] can be calculated numerically by making use of Figs. 3 and 9. The calculated value of X2H'~- X2H'g was found to be approximately equal to the corresponding one in Fig. 8. This fact substantiates that the phase transition takes place in the mixed adsorbed film.
67
0
I
I
I
I
0.2
0.4
0.6
0.8
x~ FIG. 9. Equilibrium surface tension vs bulk composition curve. Journal of Colloid and Interface Science, Vol. 93, No. 1, May 1983
168
ARATONO ET AL. REFERENCES
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Journalof Colloidand_InterfaceScience,Vol.93, No. 1, May 1983
12. Ikeda, S., Bull. Chem. Soc. Jpn. 50, 1403 (1977). 13. Tajima, K., Bull. Chem. Soc. Jpn. 44, 1767 (1971). 14. Lucassen-Reynders, E. H., Z Colloid Interface Sci. 85, 178 (1982). 15. Lucassen-Reynders, E. H., Z Colloid Interface Sci. 41, 156 (1972). 16. Aratono, M., Yamanaka, M., MatUbayasi, N., Motomura, K., and Matuura, R., J. Colloidlnterface Sci. 74, 489 (1980). 17. Motomura, K., ,L Colloid Interface Sci. 64, 348 (1978). 18. Motomura, K., Aratono, M., Matubayasi, N., and Matuura, R., J. Colloid Interface Sci. 67, 247 (1978). 19. Matubayasi, N., Motomura, K., Aratono, M., and Matuura, R., Bull. Chem. Soe. Jpn. 51, 2800 (1978). 20. Ikenaga, T,, Matubayasi, N., Aratono, M., Motomura, K., and Matuura, R., Bull. Chem. Soc. Jpn. 53, 653 (1980). 21. Matubayasi, N., Dohzono, M., Aratono, M., Motomura, K., and Matuura, R., Bull. Chem. Soc. Jpn. 52, 1597 (1979). 22. Motomura, K., Advan. Colloid Interface Sci. 12, 1 (1980).