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Dynamic surface tension of aqueous surfactant solutions
Dynamic Surface Tension of Aqueous Surfactant Solutions I. Basic Parameters
XI Y U A N H U A AND M I L T O N J. R O S E N Surfactant Research Institute, Brooklyn College, City University of New York, Brooklyn, New York 11210 Received July 14, 1987; accepted September 9, 1987 A treatment to deal with dynamic surfacetension data of surfactant solutions is suggested.The typical dynamic surface tension versus log time curve is divided into four stages: induction region, fast fall region, meso-equilibriumregion, and equilibrium region. An empirical equation is suggested to fit the dynamic surfacetension data and used to obtain the parameters: induction time, meso-equilibriumhalftime, meso-equilibriumtime, and fallrate of dynamic surfacetension. The effectof electrolyte, surfactant concentration, and temperature change on these parameters is described and discussed. © 1988Academic Press, Inc.
In m a n y interfacial processes, such as high speed wetting or foaming, equilibrium conditions are not attained and dynamic processes play a major role. Unfortunately, such data as dynamic surface tension values have been difficult to obtain in the past and only a few workers have attempted such studies (1-5). There is no agreement on the mechanisms involved or on the treatment of data. The present study suggests a method of treatment that elucidates the factors that determine the rate at which surface tension is rapidly reduced. APPARATUS, PROCEDURE, AND MATERIALS The m a x i m u m bubble pressure apparatus (Fig. l a) consists of a gas-feeding system and a pressure and bubble rate measuring system. The gas-feeding system consists of a pressure regulator, a capillary, and a flow control meter with a filter to further purify the gas. The gas used in the work is N2. The pressure variation in the capillary during bubble formation is monitored by a pressure transducer. The output from the pressure transducer is fed into an IBM personal computer. With "Notebook" software, we measure both the bubble frequency and the m a x i m u m bubble pressure. 0021-9797/88 $3.00 Copyright © 1988 by Academic Press, Inc. All rights of reproduction in any form reserved.
We can also estimate the bubble break time (so called "dead t i m e " ) . Figure lb shows a graph of the computer output, with the x-axis being time in seconds and the y-axis the voltage, V. The digital output of the computer also shows the time and voltage from which the m a x i m u m voltage, bubble frequency, and dead time (6) are obtained. As gas flows through a capillary tube immersed at a depth, h, under the surface of a liquid, the radius of the liquid/gas interface formed at the tip of the capillary is related to the gas pressure, P, by the Laplace equation. P reaches a m a x i m u m , Pmax, when the radius of the bubble reaches the radius of the capillary. Prnax = P -
23' Po =---~ + p gh,
[1]
where P0 is the atmospheric pressure, 3+ the surface tension, R the radius of the capillary, p the density of the liquid, and g the acceleration of gravity. The capillary was made by pulling out a glass tube. To obtain the calibration factor, voltage to surface tension, we used several pure compounds of known surface tension; calibration
652 Journal of Colloid and Interface Science, Vol. 124, No. 2, August 1988
DYNAMIC SURFACE TENSION
653
a
6
I 4
--'
1.04
k02
Z ~.o2 ® 1.0
1.01 I
I
o
6
I
8
I
I0
Time ( sec.}
FIG. 1. (a) Block diagram of maximum bubble pressure apparatus. 1. N2 gas cylinder regulator. 2. Capillary for stabilizing gas flow. 3. Flow control meter. 4. Sample beaker and capillary. 5. Gas pressure transducer. 6. Personal computer. 7. Printer. (b). Computer printout of signal from transducer. 0
curves for capillaries o f different radius are shown in Fig. 2. The slope o f the voltage versus surface tension curve depends on the capillary radius. All o f the curves have a c o m m o n intercept o f - 0 . 0 2 1 ___ 0.003 V, which we call the instrumental zero correction factor. Table I shows the data for line 2 (capillary 2). T h e calibration equation for capillary 2 is 3' = 49.94V + 0.87, where 3" is in m N m-1 and V is in volts. The calibration is checked each day by measuring the response o f pure water. The reproducibility o f the d y n a m i c surface tension values o f the surfactant solutions is about 1%.
Materials Sodium di(2-ethylhexyl) sulfosuccinate (DESS). Aerosol OT-100 ( A m e r i c a n Cya n a m i d ) was dissolved in water (previously deionized and then distilled twice, the last time from alkaline p e r m a n g a n a t e solution t h r o u g h a 3-ft-high Vigreaux c o l u m n with quartz condenser and receiver), and passed four times t h r o u g h a m i n i c o l u m n o f octadecylsilanized
20 40 Surface tension, ) t m N m -I
60
80
FIG. 2. Calibration curves, voltage to surface tension, for capillaries of radius (1) 0.0088 cm, (2) 0.0135 cm, (3) 0.0238 cm, (4) 0.0318 cm.
silica gel ( 7 ) until the surface t e n s i o n - c o n c e n tration curve was identical to that o f the highly purified material reported by Williams et al. (8).
N-dodecyl-N-benzyl-N-methylglycine ( C l eBMG). This was synthesized in our laboratory TABLE I Data for Calibration Curve (Capillary 2) V Compound
-r ° ( m N m - t )
(volts)
Water Nitrobenzene
72.0 43.9
Acetonitrile Benzene
29.3 28.85
1-Octanol
27.53 23.70 22.61
1.425 0.855 0.867 0.563 0.573 0.560 0.530 0.452 0.442 0.433
Acetone Methyl alcohol
a Literature values at 20°C, except for water (25°C). Journal of Colloid and Interface Science, Vol. 124, N o . 2, A u g u s t 1988
654
H U A AND ROSEN I
"tr
>,.~
In Ym '~
50
)'co 40 -2.0
I
-I.0
I 0
I 1.0
rv
a ~ - -
Log t
FIG. 3. Generalized dynamic surface tension, %, versus log time, t, curve--region I: induction; region II: rapid fall; region III: meso-equilibrium; region IV: equilibrium.
and purified by methods previously described (9). Before being used for dynamic surface tension measurements, solutions of this material in the water described above were passed several times through a minicolumn of octadecylsilanized silica gel.
3`0 - - ~ m 3`t - - 3 ` m =
1 + (t/t*)"
,
[2]
where 3`m is the meso-equilibrium surface tension and t* and n are constants, with t* having the dimensions of time in the same units as t, and n being dimensionless.
ANALYSIS OF A GENERALIZED SURFACE TENSION-LOG TIME CURVE
Figure 3 shows a typical curve of the change in dynamic surface tension with time. We divide this curve into four regions--region I: induction region; region II: rapid fall region; region III: meso-equilibrium region; region IV: equilibrium region. The first three regions are important in highspeed dynamic processes. As a result, in this paper we discuss only regions I-III. We also define ti as the time at the end of the induction region, tm as the time at the beginning of mesoequilibrium, and tl/2 as the time for the surface pressure, II ( =3'0 - 3`/, where 3`0 is the surface tension of the pure solvent and 3`t the surface tension at time, t), to reach one-half its value at meso-equilibrium. The dynamic surface tension data for the first three regions fit the equation Journal of Colloid and Interface Science, Vol. 124, No. 2, August 1988
7t -)'m
FIG. 4. Diagram illustrating relationship of (3'0 - %) to (3't - 7m).
655
DYNAMIC SURFACE TENSION a
70
b
70 I~ ,7°5O Z - -
E
.
50
"trr
>"60 6O
-~0
~
I0
7
t
I0
20
40
.7
25 - 2,5 50 -2.0
t -tO
I 0 Log t
2.0
FIG. 5. Model curves of Eq. [2]. (a) For n = 2, t* = 0.67 (s), "to - 7m equals (I) 10.0 mN m-l; (II) 19.4 mN m-l; (III) 38.8 mN m -t. (b) For n = 2, 70 - 3'm = 19.4 mN m -l, t* equals (I) 0.67 s; (II) 0.33 s; (III) 0.23 s. (c) For 3"0 - 7m = 19.4 mN m -~, (I) t* = 0.67 s, n = 2;(II) t* = 0.33 s, n = 1; (III) t* = 0.23 s, n = 0.5. E q u a t i o n [2] is in a f o r m s i m i l a r to t h e Fourier transform of a correlation function, o f t e n u s e d in r e l a x a t i o n t h e o r y ( 1 0 ) . T h i s e q u a t i o n c a n also b e p u t in t h e f o r m 70
-
-
-
%
] I 1.0
~)
.1,10
Log
I I0.
FIG. 6. Effect of electrolyte on dynamic surface tension, %, vs log t curve for DESS, 5.84 × 10 -3 mole dm -3 at 25°C in (I) water; (II) 0.1 M NaCI (aqueous). Solid lines calculated by Eq. [2] using constants in Table II.
1
log tm = log t* + n
[5] [6]
tl/2 = t *
n =
-- 7 t ) / ( 7 , -
log[(70
7m)]
[7]
log(t/t*)
W e d e f i n e t h e s u r f a c e t e n s i o n fall rate at h / 2 , R l / 2 , as
[3]
= (t/t*)L
rim
7t -- 7m R~/2
S i n c e 70 - 7m is t h e d e p r e s s i o n o f t h e surface t e n s i o n ( o r t h e surface pressure, IIm) at m e s o e q u i l i b r i u m , (70 - % ) / ( % - 7m) is t h e r a t i o o f t h e d e p r e s s i o n o f t h e s u r f a c e t e n s i o n at t i m e t ( o r s u r f a c e p r e s s u r e at t i m e t, 1-It) t o t h a t r e m a i n i n g b e f o r e m e s o - e q u i l i b r i u m is r e a c h e d (Fig. 4 ) . W e c o n s i d e r r e g i o n I ( t h e i n d u c t i o n r e g i o n ) to e n d w h e n t h e r a t i o (70 - % ) / ( % - 7m) e q u a l s 1 / 1 0 a n d t h e r a p i d fall r e g i o n to e n d w h e n t h a t ratio e q u a l s 10. T h e m i d p o i n t b e t w e e n 3'o a n d 7m is w h e n t h e r a t i o e q u a l s 1. F r o m Eq. [ 3 ], 1
l o g ti = log t* - n
[4]
-
-
-
(70 -- 7m)
[8]
-
2tl/z
2t*
TABLE II Dynamic Surface Tension Parameters for DESS (5.84 × 10-4 mole dm -3) in Water and in 0.1 MNaC1 (25°C) Parameter
H20
0.1 M NaCI (aqu.)
n t* (s) 7o - 3'm (mN m -l) 3% (mN m -t) 3
1.28 0.173 24.9 47.1 40.7 0.028 1.05 71.6
1.64 0.125 45.6 26.7 26.7 0.031 0.51 180.9
Journal of Colloid and Interface Science, Vol. 124, No. 2, August 1988
656
HUA AND ROSEN
70 Eg
l 2.0
60 'E z E LO
o
0
4O
i
_o.~
~
o.~5
~
115
i
2.5
Log t
-"o4.0
?.o
-ii.o
2.0
Log t
FIG. 7. Effect of surfactant concentration on dynamic surface tension of C~2BMG, pH 9.0, 25°C. (a) % vs log t, log Cin water equals [] -2.992; ® -3.224; ~ -3.410; •, -3.525; • -3.701; J2~-3.826; • -4.108. Solid lines calculated by Eq. [2] using constants from Table III. (b) log[(3,0 - 3"t)/(% - 3'm)] vs log t, log Cin water equals [] -2.992; ® -3.224; ~ -3.410; • -3.525; A -3.701; (D -3.826; • -4.108. Solid lines are drawn using least-squares constants from Table III.
By putting Eq. [3] in logarithmic form, it can be converted to linear form: log[(3"0 - 3"t)/(3"t- 3"m)] = n log t - n log t*.
[9]
This provides a convenient m e t h o d o f evaluating the constants n and t*, by plotting log(3"o - 3"t)/(3"t - 3"m) versus log t. However, when the ratio (3"0 - 3"t)/(3"t - 3"m) is close to 0 or ~ , the values o f n and t* calculated in this m a n n e r show large errors and fitting values o f these constants by c o m p u t e r 1 to Eq. [ 2 ] gives m o r e accurate values. Figures 5a, 5b, and 5c show three sets o f model curves for Eq. [2]. In Fig. 5a, n a n d t* are constant, and (3"0 - 3"m) is changed. We observe that (i) changing (3"0 - 3"m) does not change the induction time and other charac-
1Curve fitting is done by "Notebook" (Data Translation, Inc., Marlborough, MA). Journal of Colloid and Interface Science, Vol. 124, No. 2, August 1988
teristic times, (ii) the slope o f the curve becomes larger with an increase in the value o f (3"0 - 3"m). In Fig. 5b, n and (3'0 - 3"m) are constant, and t* is changed. We observe that (i) changing t* does not change the slope o f the curve at q/2 (in the rapid fall region), (ii) the induction time and other characteristic times b e c o m e longer with increase in t*. In Fig. 5c, (3"0 - 3"m) is constant and t* a n d n are changed. Since change in t* does n o t change the slope o f the curve, we observe that the slope at tl/2 (in the rapid fall z o n e ) becomes larger with an increase in n.
RESULTS AND DISCUSSION
Electrolyte Effect: Sodium Di ( 2-ethylhexyl) Sulfosuccinate (DESS) in Water and in 0.1 M NaCI at 25°C Figure 6 shows the relationship between 3't and log t for this c o m p o u n d in water a n d in 0.1 M N a C I at the same concentration (5.84
657
DYNAMIC SURFACE TENSION TABLE 1II Dynamic Surface Tension Parameters for C12 BMG at Various Concentrations in Water (25°C) Fit to Eq. [2] 3'm
3'o
From plot of Eq. [3]
-- Tm
log C
(mN m -~)
(mN m -t)
n
t* (s)
n
t* (s)
-2.992 -3.224 -3.410 -3.525 -3.701 -3.826 -4.108
34.6 34.8 37.3 39.9 41.9 44.8 48.4
37.4 37.2 34.7 32.1 30.1 27.2 23.6
1.19 1.31 1.37 1.49 1.53 1.56 2.24
0.082 0.153 0.340 0.509 1.19 1.86 3.61
1.17 1.18 1.13 1.39 1.32 1.39 2.17
0.085 0.155 0.345 0.526 1.24 1.89 3.73
X 10 -4 mole d m - 3 ) . 2 The curves look like those in Fig. 5a. The constants that fit Eq. [ 2 ], and other characteristic parameters, are listed in Table II. The surfactant shows more than twice the surface tension fall rate, R1/2, in 0.1 M NaC1 than in distilled water, with the difference between them being mainly due to the m u c h larger value of 3'0 - 3"m in 0.1 M NaC1, the result of the m u c h lower equilibrium surface tension (3"oo) value of an ionic surfactant in the presence of electrolyte. In this case, dynamic surface tension behavior appears to be determined mainly by equilibrium surface tension. It is also noteworthy here that in 0.1 MNaC1, 3"m = 3'00.
the surfactant concentration. There appears to be, in all cases, a linear decrease of the log of the characteristic times with an increase in log C and a linear increase in the log of the surface tension fall rate, R1/2, with increase in log C. It is noteworthy that there is no change in the linearity of these relationships when the surfactant concentration in the bulk phase exceeds the critical micelle concentration, log CMC = - 3 . 2 (8).
2.0
Concentration Effect: N-Dodecyl-N-benzyl-Nmethylglycine (C:2BMG) in Water Figure 7 shows the relationship between dynamic surface tension and log t for ClzBMG at different bulk concentrations (C, mole dm -3) in water at 25°C. In Fig. 7a the solid curves were calculated from Eq. [ 2 ] with constants n and t* fit to the data by computer; in Fig. 7b Eq. [3] is plotted, with solid lines drawn using least-squares constants obtained by computer. The values of the parameters used are listed in Table III. Figure 8 shows the relationship between the parameters tl/2 ( = t * ) , ti, tin, and RI/2, and 2 Time t is obtained by subtracting the dead time from the bubble interval.
_J
O
,o
-,o
-2,C
_4r.5
~3,5
-4,0
-3.0
Log C
FIG. 8. Relationshipsbetween dynamic surfacetension parameters and surfactant concentration for C12BMGin water at 25°C: ® ti; • t~/2;~/m; -0- RI/2. Journal of Colloid and Interface Science, VoL 124, No. 2, August 1988
658
HUA AND ROSEN
70
\ 60 iE z E 5¢
4o
~ -
, .0
I 0
f -I.0 Log t
-2.0
II0
FIG. 9. Effect of temperature on 7t vs log t curve for DESS, 8.84 × 10 -4 mole d m -3 in water. • 10°C; 0 25°C; ~ 45°C. Solid lines were calculated by Eq. [2] using constants in Table IV.
in R1/2 here appears to be the large decrease in t*, rather than the change in 3'0 - 3"m.
Temperature Effect: Sodium Di(2ethylhexyl) Sulfosuccinate in Water at Various Temperatures
CONCLUSIONS Figure 9 shows the effect of temperature on the 3"t - log t curve of DESS at a fixed concentration (8.85 × 10 -4 mole dm-3). The solid lines are based upon constants fitted to Eq. [2]. The values of these constants are listed in Table IV. Figure 10 shows the relationships of the characteristic times and surface tension fall rate, R1/2, to the absolute temperature, T. There is an apparent linear relationship between the log of each of these parameters and T, at least over the range investigated, with the characteristic times decreasing with an increase in T a n d the falling rate increasing. The major factor causing the very rapid increase
For the systems investigated, the following conclusions can be drawn: (i) The fall rate of dynamic surface tension,
R1/2, increases with an increase in the concentration of the surfactant, with an increase in temperature at a fixed surfactant concentration, and, for an ionic surfactant, with an increase in the electrolyte concentration of the solution. (ii) The induction time, the meso-equilibrium half-time, and the meso-equilibrium time all decrease with increases in temperature and in surfactant concentration, while the ad-
TABLE IV Dynamic Surface Tension Parameters for DESS (8.85 ×
10 -4
mole dm-3) in Water at Various Temperatures
T (K)
n
t* (s)
To - "Ym (mN m -1)
~'m (mN m -1)
'Y~ (mN m -I)
Ruz (mN m -1 s -I)
283.1 298.1 318.1
1.68 1.32 0.703
0.131 0.0513 0.00676
29.9 29.3 27,3
44.4 42.7 41.5
40.0 38.0 37.2
113.4 285.6 2019.0
Journal of ColloM and Interface Science, Vol. 124, No. 2, August 1988
659
DYNAMIC SURFACE TENSION ACKNOWLEDGMENTS 35 d-
o
This material is based upon work supported by the National Science Foundation (Grants CBT-8413162 and INT-8603193 ) and by Exxon Research and Engineering, GAF Chemical, Shell Development, and Shulton Re: search. REFERENCES
-2.0
-5.0
-4.0
250
300 TOK
350
FIG. 10. Relationship between dynamic surface tension parameters and absolute temperature for DESS, 8.84 × 10 -4 mole dm -3 in water. ~ ti; • tl/2; <~ tin; z~RI/2.
dition of electrolyte to anionic surfactant (DESS) has little effect on these characteristic times. (iii) The meso-equilibrium surface pressure (3'0 - 3'm) decreases with a decrease in the bulk phase concentration of the surfactant and increases with an increase in the electrolyte concentration of a solution of an ionic surfactant, but shows only a slight decrease with increase in the temperature.
1. Addison, C. C., J. Chem. Soc. 535 (1943); 252, 477 (1944); 98, 354 (1945). 2. Ward, A. F. H., and Tordai, L., J. Chem. Phys. 14, 453 (1946). 3. Burcik, E. J., J. Colloid Sci. 5, 421 (1950); Burcik, E. J., and Vaughn, C. R., J. Colloid Sci. 6, 522 (1951); Burcik, E. J., J. ColloidSci. 8, 520 (1953); Burcik, E. J., and Newman, R. C., J. Colloid Sci. 9, 498 (1954). 4. Lange, H., J. ColloidSci. 20, 50 (1965). 5. Thomas, W. D. E., and Hall, D. J., in "Surface Active Agents," pp. 107-116. Soc. Chem. Ind., London, 1979. 6. Kloubek, J., J. Colloidlnterface Sci. 41, 1 (1972). 7. Rosen, M. J., J. Colloid Interface Sci. 79, 587 (1981). 8. Williams, E. F., Woodberry, N. T., and Dixon, J. K., J. Colloid Sci. 12, 452 (1957). 9. Dahanayake, M., and Rosen, M. J., in "Structure/ Performance Relationships in Surfactants" ACS Syrnp. Ser. 253, p. 49. Amer. Chem. Soc., Washington, DC. 1984. 10. Atherton, N. M., "Electron Spin Resonance Theory and Applications," p. 260. Halsted Press, New York, 1973.
Journal of Colloid and Interface Science, Vol. 124, No. 2, August 1988
XI Y U A N H U A AND M I L T O N J. R O S E N Surfactant Research Institute, Brooklyn College, City University of New York, Brooklyn, New York 11210 Received July 14, 1987; accepted September 9, 1987 A treatment to deal with dynamic surfacetension data of surfactant solutions is suggested.The typical dynamic surface tension versus log time curve is divided into four stages: induction region, fast fall region, meso-equilibriumregion, and equilibrium region. An empirical equation is suggested to fit the dynamic surfacetension data and used to obtain the parameters: induction time, meso-equilibriumhalftime, meso-equilibriumtime, and fallrate of dynamic surfacetension. The effectof electrolyte, surfactant concentration, and temperature change on these parameters is described and discussed. © 1988Academic Press, Inc.
In m a n y interfacial processes, such as high speed wetting or foaming, equilibrium conditions are not attained and dynamic processes play a major role. Unfortunately, such data as dynamic surface tension values have been difficult to obtain in the past and only a few workers have attempted such studies (1-5). There is no agreement on the mechanisms involved or on the treatment of data. The present study suggests a method of treatment that elucidates the factors that determine the rate at which surface tension is rapidly reduced. APPARATUS, PROCEDURE, AND MATERIALS The m a x i m u m bubble pressure apparatus (Fig. l a) consists of a gas-feeding system and a pressure and bubble rate measuring system. The gas-feeding system consists of a pressure regulator, a capillary, and a flow control meter with a filter to further purify the gas. The gas used in the work is N2. The pressure variation in the capillary during bubble formation is monitored by a pressure transducer. The output from the pressure transducer is fed into an IBM personal computer. With "Notebook" software, we measure both the bubble frequency and the m a x i m u m bubble pressure. 0021-9797/88 $3.00 Copyright © 1988 by Academic Press, Inc. All rights of reproduction in any form reserved.
We can also estimate the bubble break time (so called "dead t i m e " ) . Figure lb shows a graph of the computer output, with the x-axis being time in seconds and the y-axis the voltage, V. The digital output of the computer also shows the time and voltage from which the m a x i m u m voltage, bubble frequency, and dead time (6) are obtained. As gas flows through a capillary tube immersed at a depth, h, under the surface of a liquid, the radius of the liquid/gas interface formed at the tip of the capillary is related to the gas pressure, P, by the Laplace equation. P reaches a m a x i m u m , Pmax, when the radius of the bubble reaches the radius of the capillary. Prnax = P -
23' Po =---~ + p gh,
[1]
where P0 is the atmospheric pressure, 3+ the surface tension, R the radius of the capillary, p the density of the liquid, and g the acceleration of gravity. The capillary was made by pulling out a glass tube. To obtain the calibration factor, voltage to surface tension, we used several pure compounds of known surface tension; calibration
652 Journal of Colloid and Interface Science, Vol. 124, No. 2, August 1988
DYNAMIC SURFACE TENSION
653
a
6
I 4
--'
1.04
k02
Z ~.o2 ® 1.0
1.01 I
I
o
6
I
8
I
I0
Time ( sec.}
FIG. 1. (a) Block diagram of maximum bubble pressure apparatus. 1. N2 gas cylinder regulator. 2. Capillary for stabilizing gas flow. 3. Flow control meter. 4. Sample beaker and capillary. 5. Gas pressure transducer. 6. Personal computer. 7. Printer. (b). Computer printout of signal from transducer. 0
curves for capillaries o f different radius are shown in Fig. 2. The slope o f the voltage versus surface tension curve depends on the capillary radius. All o f the curves have a c o m m o n intercept o f - 0 . 0 2 1 ___ 0.003 V, which we call the instrumental zero correction factor. Table I shows the data for line 2 (capillary 2). T h e calibration equation for capillary 2 is 3' = 49.94V + 0.87, where 3" is in m N m-1 and V is in volts. The calibration is checked each day by measuring the response o f pure water. The reproducibility o f the d y n a m i c surface tension values o f the surfactant solutions is about 1%.
Materials Sodium di(2-ethylhexyl) sulfosuccinate (DESS). Aerosol OT-100 ( A m e r i c a n Cya n a m i d ) was dissolved in water (previously deionized and then distilled twice, the last time from alkaline p e r m a n g a n a t e solution t h r o u g h a 3-ft-high Vigreaux c o l u m n with quartz condenser and receiver), and passed four times t h r o u g h a m i n i c o l u m n o f octadecylsilanized
20 40 Surface tension, ) t m N m -I
60
80
FIG. 2. Calibration curves, voltage to surface tension, for capillaries of radius (1) 0.0088 cm, (2) 0.0135 cm, (3) 0.0238 cm, (4) 0.0318 cm.
silica gel ( 7 ) until the surface t e n s i o n - c o n c e n tration curve was identical to that o f the highly purified material reported by Williams et al. (8).
N-dodecyl-N-benzyl-N-methylglycine ( C l eBMG). This was synthesized in our laboratory TABLE I Data for Calibration Curve (Capillary 2) V Compound
-r ° ( m N m - t )
(volts)
Water Nitrobenzene
72.0 43.9
Acetonitrile Benzene
29.3 28.85
1-Octanol
27.53 23.70 22.61
1.425 0.855 0.867 0.563 0.573 0.560 0.530 0.452 0.442 0.433
Acetone Methyl alcohol
a Literature values at 20°C, except for water (25°C). Journal of Colloid and Interface Science, Vol. 124, N o . 2, A u g u s t 1988
654
H U A AND ROSEN I
"tr
>,.~
In Ym '~
50
)'co 40 -2.0
I
-I.0
I 0
I 1.0
rv
a ~ - -
Log t
FIG. 3. Generalized dynamic surface tension, %, versus log time, t, curve--region I: induction; region II: rapid fall; region III: meso-equilibrium; region IV: equilibrium.
and purified by methods previously described (9). Before being used for dynamic surface tension measurements, solutions of this material in the water described above were passed several times through a minicolumn of octadecylsilanized silica gel.
3`0 - - ~ m 3`t - - 3 ` m =
1 + (t/t*)"
,
[2]
where 3`m is the meso-equilibrium surface tension and t* and n are constants, with t* having the dimensions of time in the same units as t, and n being dimensionless.
ANALYSIS OF A GENERALIZED SURFACE TENSION-LOG TIME CURVE
Figure 3 shows a typical curve of the change in dynamic surface tension with time. We divide this curve into four regions--region I: induction region; region II: rapid fall region; region III: meso-equilibrium region; region IV: equilibrium region. The first three regions are important in highspeed dynamic processes. As a result, in this paper we discuss only regions I-III. We also define ti as the time at the end of the induction region, tm as the time at the beginning of mesoequilibrium, and tl/2 as the time for the surface pressure, II ( =3'0 - 3`/, where 3`0 is the surface tension of the pure solvent and 3`t the surface tension at time, t), to reach one-half its value at meso-equilibrium. The dynamic surface tension data for the first three regions fit the equation Journal of Colloid and Interface Science, Vol. 124, No. 2, August 1988
7t -)'m
FIG. 4. Diagram illustrating relationship of (3'0 - %) to (3't - 7m).
655
DYNAMIC SURFACE TENSION a
70
b
70 I~ ,7°5O Z - -
E
.
50
"trr
>"60 6O
-~0
~
I0
7
t
I0
20
40
.7
25 - 2,5 50 -2.0
t -tO
I 0 Log t
2.0
FIG. 5. Model curves of Eq. [2]. (a) For n = 2, t* = 0.67 (s), "to - 7m equals (I) 10.0 mN m-l; (II) 19.4 mN m-l; (III) 38.8 mN m -t. (b) For n = 2, 70 - 3'm = 19.4 mN m -l, t* equals (I) 0.67 s; (II) 0.33 s; (III) 0.23 s. (c) For 3"0 - 7m = 19.4 mN m -~, (I) t* = 0.67 s, n = 2;(II) t* = 0.33 s, n = 1; (III) t* = 0.23 s, n = 0.5. E q u a t i o n [2] is in a f o r m s i m i l a r to t h e Fourier transform of a correlation function, o f t e n u s e d in r e l a x a t i o n t h e o r y ( 1 0 ) . T h i s e q u a t i o n c a n also b e p u t in t h e f o r m 70
-
-
-
%
] I 1.0
~)
.1,10
Log
I I0.
FIG. 6. Effect of electrolyte on dynamic surface tension, %, vs log t curve for DESS, 5.84 × 10 -3 mole dm -3 at 25°C in (I) water; (II) 0.1 M NaCI (aqueous). Solid lines calculated by Eq. [2] using constants in Table II.
1
log tm = log t* + n
[5] [6]
tl/2 = t *
n =
-- 7 t ) / ( 7 , -
log[(70
7m)]
[7]
log(t/t*)
W e d e f i n e t h e s u r f a c e t e n s i o n fall rate at h / 2 , R l / 2 , as
[3]
= (t/t*)L
rim
7t -- 7m R~/2
S i n c e 70 - 7m is t h e d e p r e s s i o n o f t h e surface t e n s i o n ( o r t h e surface pressure, IIm) at m e s o e q u i l i b r i u m , (70 - % ) / ( % - 7m) is t h e r a t i o o f t h e d e p r e s s i o n o f t h e s u r f a c e t e n s i o n at t i m e t ( o r s u r f a c e p r e s s u r e at t i m e t, 1-It) t o t h a t r e m a i n i n g b e f o r e m e s o - e q u i l i b r i u m is r e a c h e d (Fig. 4 ) . W e c o n s i d e r r e g i o n I ( t h e i n d u c t i o n r e g i o n ) to e n d w h e n t h e r a t i o (70 - % ) / ( % - 7m) e q u a l s 1 / 1 0 a n d t h e r a p i d fall r e g i o n to e n d w h e n t h a t ratio e q u a l s 10. T h e m i d p o i n t b e t w e e n 3'o a n d 7m is w h e n t h e r a t i o e q u a l s 1. F r o m Eq. [ 3 ], 1
l o g ti = log t* - n
[4]
-
-
-
(70 -- 7m)
[8]
-
2tl/z
2t*
TABLE II Dynamic Surface Tension Parameters for DESS (5.84 × 10-4 mole dm -3) in Water and in 0.1 MNaC1 (25°C) Parameter
H20
0.1 M NaCI (aqu.)
n t* (s) 7o - 3'm (mN m -l) 3% (mN m -t) 3
1.28 0.173 24.9 47.1 40.7 0.028 1.05 71.6
1.64 0.125 45.6 26.7 26.7 0.031 0.51 180.9
Journal of Colloid and Interface Science, Vol. 124, No. 2, August 1988
656
HUA AND ROSEN
70 Eg
l 2.0
60 'E z E LO
o
0
4O
i
_o.~
~
o.~5
~
115
i
2.5
Log t
-"o4.0
?.o
-ii.o
2.0
Log t
FIG. 7. Effect of surfactant concentration on dynamic surface tension of C~2BMG, pH 9.0, 25°C. (a) % vs log t, log Cin water equals [] -2.992; ® -3.224; ~ -3.410; •, -3.525; • -3.701; J2~-3.826; • -4.108. Solid lines calculated by Eq. [2] using constants from Table III. (b) log[(3,0 - 3"t)/(% - 3'm)] vs log t, log Cin water equals [] -2.992; ® -3.224; ~ -3.410; • -3.525; A -3.701; (D -3.826; • -4.108. Solid lines are drawn using least-squares constants from Table III.
By putting Eq. [3] in logarithmic form, it can be converted to linear form: log[(3"0 - 3"t)/(3"t- 3"m)] = n log t - n log t*.
[9]
This provides a convenient m e t h o d o f evaluating the constants n and t*, by plotting log(3"o - 3"t)/(3"t - 3"m) versus log t. However, when the ratio (3"0 - 3"t)/(3"t - 3"m) is close to 0 or ~ , the values o f n and t* calculated in this m a n n e r show large errors and fitting values o f these constants by c o m p u t e r 1 to Eq. [ 2 ] gives m o r e accurate values. Figures 5a, 5b, and 5c show three sets o f model curves for Eq. [2]. In Fig. 5a, n a n d t* are constant, and (3"0 - 3"m) is changed. We observe that (i) changing (3"0 - 3"m) does not change the induction time and other charac-
1Curve fitting is done by "Notebook" (Data Translation, Inc., Marlborough, MA). Journal of Colloid and Interface Science, Vol. 124, No. 2, August 1988
teristic times, (ii) the slope o f the curve becomes larger with an increase in the value o f (3"0 - 3"m). In Fig. 5b, n and (3'0 - 3"m) are constant, and t* is changed. We observe that (i) changing t* does not change the slope o f the curve at q/2 (in the rapid fall region), (ii) the induction time and other characteristic times b e c o m e longer with increase in t*. In Fig. 5c, (3"0 - 3"m) is constant and t* a n d n are changed. Since change in t* does n o t change the slope o f the curve, we observe that the slope at tl/2 (in the rapid fall z o n e ) becomes larger with an increase in n.
RESULTS AND DISCUSSION
Electrolyte Effect: Sodium Di ( 2-ethylhexyl) Sulfosuccinate (DESS) in Water and in 0.1 M NaCI at 25°C Figure 6 shows the relationship between 3't and log t for this c o m p o u n d in water a n d in 0.1 M N a C I at the same concentration (5.84
657
DYNAMIC SURFACE TENSION TABLE 1II Dynamic Surface Tension Parameters for C12 BMG at Various Concentrations in Water (25°C) Fit to Eq. [2] 3'm
3'o
From plot of Eq. [3]
-- Tm
log C
(mN m -~)
(mN m -t)
n
t* (s)
n
t* (s)
-2.992 -3.224 -3.410 -3.525 -3.701 -3.826 -4.108
34.6 34.8 37.3 39.9 41.9 44.8 48.4
37.4 37.2 34.7 32.1 30.1 27.2 23.6
1.19 1.31 1.37 1.49 1.53 1.56 2.24
0.082 0.153 0.340 0.509 1.19 1.86 3.61
1.17 1.18 1.13 1.39 1.32 1.39 2.17
0.085 0.155 0.345 0.526 1.24 1.89 3.73
X 10 -4 mole d m - 3 ) . 2 The curves look like those in Fig. 5a. The constants that fit Eq. [ 2 ], and other characteristic parameters, are listed in Table II. The surfactant shows more than twice the surface tension fall rate, R1/2, in 0.1 M NaC1 than in distilled water, with the difference between them being mainly due to the m u c h larger value of 3'0 - 3"m in 0.1 M NaC1, the result of the m u c h lower equilibrium surface tension (3"oo) value of an ionic surfactant in the presence of electrolyte. In this case, dynamic surface tension behavior appears to be determined mainly by equilibrium surface tension. It is also noteworthy here that in 0.1 MNaC1, 3"m = 3'00.
the surfactant concentration. There appears to be, in all cases, a linear decrease of the log of the characteristic times with an increase in log C and a linear increase in the log of the surface tension fall rate, R1/2, with increase in log C. It is noteworthy that there is no change in the linearity of these relationships when the surfactant concentration in the bulk phase exceeds the critical micelle concentration, log CMC = - 3 . 2 (8).
2.0
Concentration Effect: N-Dodecyl-N-benzyl-Nmethylglycine (C:2BMG) in Water Figure 7 shows the relationship between dynamic surface tension and log t for ClzBMG at different bulk concentrations (C, mole dm -3) in water at 25°C. In Fig. 7a the solid curves were calculated from Eq. [ 2 ] with constants n and t* fit to the data by computer; in Fig. 7b Eq. [3] is plotted, with solid lines drawn using least-squares constants obtained by computer. The values of the parameters used are listed in Table III. Figure 8 shows the relationship between the parameters tl/2 ( = t * ) , ti, tin, and RI/2, and 2 Time t is obtained by subtracting the dead time from the bubble interval.
_J
O
,o
-,o
-2,C
_4r.5
~3,5
-4,0
-3.0
Log C
FIG. 8. Relationshipsbetween dynamic surfacetension parameters and surfactant concentration for C12BMGin water at 25°C: ® ti; • t~/2;~/m; -0- RI/2. Journal of Colloid and Interface Science, VoL 124, No. 2, August 1988
658
HUA AND ROSEN
70
\ 60 iE z E 5¢
4o
~ -
, .0
I 0
f -I.0 Log t
-2.0
II0
FIG. 9. Effect of temperature on 7t vs log t curve for DESS, 8.84 × 10 -4 mole d m -3 in water. • 10°C; 0 25°C; ~ 45°C. Solid lines were calculated by Eq. [2] using constants in Table IV.
in R1/2 here appears to be the large decrease in t*, rather than the change in 3'0 - 3"m.
Temperature Effect: Sodium Di(2ethylhexyl) Sulfosuccinate in Water at Various Temperatures
CONCLUSIONS Figure 9 shows the effect of temperature on the 3"t - log t curve of DESS at a fixed concentration (8.85 × 10 -4 mole dm-3). The solid lines are based upon constants fitted to Eq. [2]. The values of these constants are listed in Table IV. Figure 10 shows the relationships of the characteristic times and surface tension fall rate, R1/2, to the absolute temperature, T. There is an apparent linear relationship between the log of each of these parameters and T, at least over the range investigated, with the characteristic times decreasing with an increase in T a n d the falling rate increasing. The major factor causing the very rapid increase
For the systems investigated, the following conclusions can be drawn: (i) The fall rate of dynamic surface tension,
R1/2, increases with an increase in the concentration of the surfactant, with an increase in temperature at a fixed surfactant concentration, and, for an ionic surfactant, with an increase in the electrolyte concentration of the solution. (ii) The induction time, the meso-equilibrium half-time, and the meso-equilibrium time all decrease with increases in temperature and in surfactant concentration, while the ad-
TABLE IV Dynamic Surface Tension Parameters for DESS (8.85 ×
10 -4
mole dm-3) in Water at Various Temperatures
T (K)
n
t* (s)
To - "Ym (mN m -1)
~'m (mN m -1)
'Y~ (mN m -I)
Ruz (mN m -1 s -I)
283.1 298.1 318.1
1.68 1.32 0.703
0.131 0.0513 0.00676
29.9 29.3 27,3
44.4 42.7 41.5
40.0 38.0 37.2
113.4 285.6 2019.0
Journal of ColloM and Interface Science, Vol. 124, No. 2, August 1988
659
DYNAMIC SURFACE TENSION ACKNOWLEDGMENTS 35 d-
o
This material is based upon work supported by the National Science Foundation (Grants CBT-8413162 and INT-8603193 ) and by Exxon Research and Engineering, GAF Chemical, Shell Development, and Shulton Re: search. REFERENCES
-2.0
-5.0
-4.0
250
300 TOK
350
FIG. 10. Relationship between dynamic surface tension parameters and absolute temperature for DESS, 8.84 × 10 -4 mole dm -3 in water. ~ ti; • tl/2; <~ tin; z~RI/2.
dition of electrolyte to anionic surfactant (DESS) has little effect on these characteristic times. (iii) The meso-equilibrium surface pressure (3'0 - 3'm) decreases with a decrease in the bulk phase concentration of the surfactant and increases with an increase in the electrolyte concentration of a solution of an ionic surfactant, but shows only a slight decrease with increase in the temperature.
1. Addison, C. C., J. Chem. Soc. 535 (1943); 252, 477 (1944); 98, 354 (1945). 2. Ward, A. F. H., and Tordai, L., J. Chem. Phys. 14, 453 (1946). 3. Burcik, E. J., J. Colloid Sci. 5, 421 (1950); Burcik, E. J., and Vaughn, C. R., J. Colloid Sci. 6, 522 (1951); Burcik, E. J., J. ColloidSci. 8, 520 (1953); Burcik, E. J., and Newman, R. C., J. Colloid Sci. 9, 498 (1954). 4. Lange, H., J. ColloidSci. 20, 50 (1965). 5. Thomas, W. D. E., and Hall, D. J., in "Surface Active Agents," pp. 107-116. Soc. Chem. Ind., London, 1979. 6. Kloubek, J., J. Colloidlnterface Sci. 41, 1 (1972). 7. Rosen, M. J., J. Colloid Interface Sci. 79, 587 (1981). 8. Williams, E. F., Woodberry, N. T., and Dixon, J. K., J. Colloid Sci. 12, 452 (1957). 9. Dahanayake, M., and Rosen, M. J., in "Structure/ Performance Relationships in Surfactants" ACS Syrnp. Ser. 253, p. 49. Amer. Chem. Soc., Washington, DC. 1984. 10. Atherton, N. M., "Electron Spin Resonance Theory and Applications," p. 260. Halsted Press, New York, 1973.
Journal of Colloid and Interface Science, Vol. 124, No. 2, August 1988