Superspreading of Trisiloxane Surfactant Mixtures on Hydrophobic

Langmuir 2002, 18, 2205-2215

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Superspreading of Trisiloxane Surfactant Mixtures on Hydrophobic Surfaces 2. Interaction and Spreading of Aqueous Trisiloxane Surfactant-N-Alkyl-Pyrrolidinone Mixtures in Contact with Polyethylene Yongfu Wu and Milton J. Rosen* Surfactant Research Institute, Brooklyn College of the City University of New York, Brooklyn, New York 11210 Received August 20, 2001. In Final Form: December 12, 2001 On the basis of the results of interfacial adsorptions of an ethoxylated trsiloxane(L77) and its mixtures with various N-alkyl-pyrrolidinones, the changes in interfacial pressure at the air/aqueous solution, polyethylene/aqueous solution, and air/polyethylene interfaces caused by the surfactant mixture solutions have been evaluated by use of the Gibbs equation. At the air/aqueous solution interface, the change in the surface tension, (∆γLA), is always positive, indicating that there is no effect that could enhance spreading at this interface upon the addition of N-alkyl-pyrrolidinones to the trisiloxane surfactant solution. At the polyethylene/aqueous solution interface, the change in interfacial pressure, (∆πSL), can be positive when N-alkyl-pyrrolidinones are mixed at a certain ratio, indicating that the mixtures can show a spreading enhancement effect at this interface. Compared with the changes at the air/aqueous solution interface and the polyethylene/aqueous solution interface, the change in interfacial pressure at the solid/air interface, (∆πSA), is insignificant. The change in the value of the spreading coefficient (SMixL/S - S L77L/S) on polyethylene film of an aqueous solution of the ethoxylated trisiloxane L77 upon the addition to it of an N-alkylpyrrolidinone has been evaluated from these changes in the interfacial pressures. It was found that the change in the spreading coefficient is in about the same order as the enhancement of its spreading factor (SF) on the polyethylene. In addition, the interaction (β) parameters of L77 with the different pyrrolidinones at the various interfaces have been calculated. βσLA for all mixtures was between 0 and -1, indicating that the interaction at the air/aqueous solution interfaces is very weak. However, the values of βσSL were between -2.7 and -6.7 for the mixtures with those N-alkyl-pyrrolidinones that produce enhancement of the superspreading of aqueous solution of L77 on polyethylene, indicating a significant attractive interaction with L77 at the polyethylene/aqueous solution interface. A comparison of values of the mole fraction of L77 at the polyethylene/aqueous solution interface, either calculated or measured from adsorption data, shows that the nonideal solution treatment of the data for calculation of interaction parameters is valid.

Introduction Trisiloxane surfactants have been applied in aqueous herbicides solution to promote spreading and uptake of the active ingredients on waxy plant leaves1-5 because of their extraordinary ability to spread on hydrophobic solid surface such as Parafilm or polyethylene to a much greater area than aqueous solutions of hydrocarbon-based surfactants. During the past decade, this spreading of aqueous trisiloxane surfactant solutions over low-energy hydrophobic surfaces, often called “superspreading”, has attracted considerable interest from chemists because of its theoretical and practical implications.6-13 To date, various * To whom correspondence should be addressed. (1) Gaskin, R. E.; Kirkwood, R. C. In Mode of Action and Physiological Activity; Chow, N. P., Grant, C. A., Hinshalwood, A. M., Simmundsson, E., Eds.; Adjuvants and Agrochemicals, Vol. 1; CRC Press: Boca Raton, FL, 1989; p 129. (2) Zabkiewicz, J. A.; Gaskin, R. E. In Mode of Action and Physiological Activity; Chow, N. P., Grant, C. A., Hinshalwood, A. M., Simmundsson, E., Eds.; Adjuvants and Agrochemicals, Vol. 1; CRC Press: Boca Raton, FL, 1989; p 141. (3) Klein, K. D.; Wilkowski, S.; Selby, J. Int. Symp. Adjuvants Agrochemicals; NZ FRI Bull, No. 193, 1995. (4) Knoche, M.; Tamura, H.; Bukovac, M. J. Agric. Food Chem. 1991, 39, 202. (5) Stevens, P. J. G. Pestic. Sci. 1993, 38, 103. (6) Ananthapadmanabhan, K. P.; Goddard, E. D.; Chandar, P. Colloids Surf. 1990, 44, 281. (7) Zhu, S.; Miller, W. G.; Scriven, L. E.; Davis, H. T. Colloids Surf., A 1994, 90, 63. (8) Rosen, M. J.; Song, L. D. Langmuir 1996, 12, 4945. (9) Lin, Z.; He, M.; Davis, H. T.; Scriven, L. E.; Snow, S. A. J. Phys. Chem. 1993, 97, 3571.

theories have been proposed to explain the superspreading behavior of the trisiloxane aqueous solution on low-energy hydrophobic surfaces; there has been considerable research on spreading of trisiloxane surfactants on various hydrophobic surfaces, including mineral oil.14-25 On the other hand, most aqueous applications of trisiloxane surfactants involve their uses in combination (10) He, M.; Hill, R. M.; Lin, Z.; Scriven, L. E.; Davis, H. T. J. Phys. Chem. 1993, 97, 8820. (11) Svitova, T. F.; Hoffmann, H.; Hill, R. M. Langmuir 1996, 12, 1712. (12) Stoebe, T.; Lin, Z.; Hill, R. M.; Ward, M. D.; Davis, H. T. Langmuir 1996, 12, 337. (13) Svitova, T. F.; Smirnova, Y. P.; Yakubov, G. J. Colloid Interface Sci. 1995, 101, 251. (14) Churaev, N. V.; Esipova, N. E.; Hill, R. M.; Sobolev, V. D.; Starov, V. M.; Zorin, Z. M. Langmuir 2001, 17, 1338. (15) Churaev, N. V.; Esipova, N. E.; Hill, R. M.; Sobolev, V. D.; Starov, V. M.; Zorin, Z. M. Langmuir 2001, 17, 1349. (16) Li, X.; Washengberger, R. M.; Scriven, L. E.; Davis, H. T.; Hill, R. M. Langmuir 1999, 15, 2278. (17) Lin, Z.; Hill, R. M.; Davis, H. T.; Ward, M. D. Langmuir 1994, 10, 4060. (18) Svitova, T. F.; Hill, R. M.; Smirnova, Y.; Stuermer, A.; Yakubov, G. Lagmuir 1998, 14, 5023. (19) Perez, E.; Schaffer, E.; Steiner, U. J. Colloid Interface Sci. 2001, 234, 178. (20) Kabalnov, A. Langmuir 2000, 16, 2595. (21) Chauhan, A.; Svitova, T. F.; Radke, C. J. J. Colloid Interface Sci. 2000, 222 (2), 221. (22) Stoebe, T.; Lin, Z.; Hill, R. M.; Ward, M. D.; Davis H. T. Langmuir 1997, 13, 7282. (23) Svitova, T. F.; Hill, R. M.; Radke, C. J. Lagmuir 1999, 15, 7392. (24) Svitova, T. F.; Hill, R. M.; Radke, C. J. Lagmuir 2001, 17, 335. (25) Gentle, T. E.; Snow, S. A. Lagmuir 1995, 11, 2905.

10.1021/la0113318 CCC: $22.00 © 2002 American Chemical Society Published on Web 02/21/2002

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with organic surfactants and polymers. Since it is well known that different classes of surfactants can interact strongly,26,27 it becomes very important to understand the interactions between siloxane surfactants and organic surfactants. However, there are few papers on the interaction of trisiloxane surfactant with the other surfactants28,29 and on the mechanism of enhanced spreading of aqueous surfactant solutions.30-35 Also, the mechanism responsible for surfactant-enhanced spreading has not been established fully. The objective of this paper is to elucidate the mechanism involved in the phenomenon of synergism in superspeading shown by certain trisiloxane-N-alkyl-pyrrolidinone surfactant mixtures on hydrophobic substrates. Our previous study36 on these mixtures dealt with the adsorption onto polyethylene of the components of these mixtures at the three interfaces(air/liquid, air/solid, and solid/liquid) involved. It showed that the most significant effect of the addition of the N-alkyl pyrrolidinone to the trisiloxane is its enhancement of the adsorption of the latter at the solid/ liquid interface. A liquid may spontaneously wet a solid substrate if the spreading coefficient SL/S ) γSA - γSL - γLA, where γSA, γSL, and γLA refer to the interfacial tensions at the solid/ air, solid/liquid, and liquid/air interfaces, respectively, is positive.37a Addition of surfactant can promote spreading by reducing the interfacial tensions at the solid/liquid and liquid/air interfaces, yielding a more positive spreading coefficient. Experimental Section Materials. The trisiloxane surfactant and N-alkyl-pyrrolidinones used, which are shown in Chart 1, are the same as those reported in our previous paper.36 Since hydrolysis of the siloxane results in loss of surface activity,38the aqueous SILWET L77 solution must be made with phosphate buffer, pH ) 7.00, to prevent this hydrolysis. The polyethylene powder is also the same as that reported in the previous paper. First, the polyethylene powder was cleaned by washing at least eight times with spectranalyzed methanol and then was dried in a vacuum desiccator. Then, the polyethylene film was made by melting the polyethylene powder on a 10 cm × 10 cm clean glass square and removing it when it had cooled. The side of the polyethylene film that had contacted the glass (which was much smoother than the other side) was used for measuring the spreading factors. Methods of Measurement of Spreading Factor. Four pieces of glass (about 1 cm2) were placed at the corners of a clean polyethylene film, which is mounted on an optically flat glass plate (10 cm × 10 cm) resting upon the horizontal mouth of a (26) Scamehorn, J. F. In Phenomena in Mixed Surfactant Systems; Scamehorn, J. F., Ed.; ACS Symposium Series 311; American Chemical Society; Washington, DC, 1986; p 1. (27) Scamehorn, J. F. In Phenomena in Mixed Surfactant Systems; Scamehorn, J. F., Ed. ACS Symposium Series 311; American Chemical Society; Washington, DC, 1986; p 324. (28) Hill, R. M. In Mixed Surfactant Systems; Holland, P. M., Rubingh, D. N., Eds.; ACS Symposium Series 501;American Chemical Society; Washington, DC, 1991; p 278. (29) Ohno, M.; Esumi, K.; Meguro, K. JAOCS 1992, 69, 80. (30) Stoebe, T.; Lin, Z.; Hill, R. M.; Ward, M. D.; Davis, H. T. Langmuir 1997, 13, 7270. (31) Stoebe, T.; Lin, Z.; Hill, R. M.; Ward, M. D.; Davis, H. T. Langmuir 1997, 13, 7276. (32) Ruckenstein, E. J. Colloid Interface Sci. 1996, 179, 136. (33) Starov, V. M.; Kosvintsev, S. R.; Velarde, M. G. J. Colloid Interface Sci. 2000, 227, 185. (34) Cazabat, A. M.; Valignat, M. P.; Villette, S.; Coninck, J. D.; Louche, F. Langmuir 1997, 13, 4754. (35) Tiberg, F.; Cazabat, A. M. Langmuir 1994, 10, 2301. (36) Rosen, M. J.; Wu, Y. F. Langmuir 2001, 17, 7296. (37) Rosen, M. J. Surfactant and Interfacial Phenomena, 2nd ed.; John Wiley and Sons: New York, 1989; pp 242, 394. (38) Schlachter, I.; Feldmann-Krane, G. In Novel Surfactants: Preparation, Applications and Biodegradability Holmberg, K., Ed.; Surfactant Science Series 74; Marcel Dekker: New York, 1998; p 232.

Wu and Rosen Chart 1

glass bottle. Using a microsyringe, which had previously been rinsed with the solution being tested, a 20-µL drop of the solution is placed on the polyethylene film. The stop watch is started and another 10 cm × 10 cm glass square is immediately placed over the four pieces of glass so that it is parallel to the polyethylene film. After three minutes (when the solution has stopped spreading), an outline of the spread solution is traced onto the top glass. This area is then retraced onto standard white paper from which it is cut and weighed. The exact spreading area is then calculated from the mass of a piece of the same paper of known area, with the assumption that the paper has a constant mass per unit area. After each measurement, the polyethylene substrate is thoroughly rinsed with methanol, tap water ,and distilled water, and is then put into boiling distilled water for at least 30 min to remove any adsorbed surfactant. The solutions, all at 1.0 g/L total surfactant concentration, which is much above the cmc of the mixture, are made at 10%, 20%, 30%, and so forth replacements of the trisiloxane surfactant by the N-alkyl-pyrrolidinone being tested. Each spreading measurement was done three to five times until the reproducibility was satisfactory to ensure minimal relative error. The spreading area is the average of the areas obtained in each set of measurements. The spreading factor (SF) is the ratio: spreading area of the surfactant solution/ spreading area of the same volume of solvent.

Results and Discussions 1. Synergism in Superspreading. In the measurements of the spreading, a series of solutions (total concentration always 1.0 g/L) with different wt % replacement of trisiloxane L77 by pyrrolidinones were used. To make the results more convenient for comparison with other results, such as the adsorption at the solid/liquid interface, the mass percent of replacement of L77 by pyrrolidinone was converted to the mole fraction of L77 in the mixture. Plots of spreading factor (SF) versus mole fraction of L77 (RL77) for aqueous mixtures of L77 and pyrrolidinones on the polyethylene substrate are shown in Figure 1. The points at RL77 ) 0 and RL77 ) 1.00 correspond to N-alkyl-pyrrolidinone in buffer solution and L77 in buffer solution, respectively. The data in Figure 1 show that all the pyrrolidinones (C4P; CHP; C6P; C2,6P; C8P; and C10P) in buffer solutions have very small spreading factors (2 ∼ 3), meaning that

Superspreading of Trisiloxane Surfactant Mixtures

Langmuir, Vol. 18, No. 6, 2002 2207

Figure 1. Plots of spreading factor (SF) vs mole fraction of L77 (RL77) for aqueous mixtures of L77 and pyrrolidinones on the polyethylene substrate. Mixture with C4P, 4; CHP, 2; C6P, ]; C2,6P, [; C8P, O; C10P, b.

the spreading abilities of all the pyrrolidinones by themselves are very poor on polyethylene film. On the hand, the trisiloxane L77 in buffer solution has a very large spreading factor, around 150, indicating its superspreading ability. There is a small difference among measured spreading factors for L77 because they were measured on different days with different humidity and temperature. Most significant in Figure 1 is the finding of a “synergistic effect”, defined as existing when the spreading factor of the L77-N-alkyl pyrrolidinone mixture, at the same weight concentrations as that of the L77 solution, is greater than that of the latter, for mixtures of trisiloxane L77 and certain pyrrolidinones. From the plots of spreading factor (SF) versus RL77, one can see that the mixtures of L77 with C4P; CHP; C6P; C2,6P; or C8P show a nonideal spreading on the polyethylene substrate. When the mole fraction of L77 is larger than about 0.25, the spreading factors of the mixed solutions are larger than that of the L77 solution itself. The effectiveness of superspreading enhancement by the pyrrolidinone (the maximum SF value of the mixture) is different for the different pyrrolidinones. SFmax ) 162 for the mixture with C4P; 180 with CHP; 212 with C6P; 208 with C8P; and 234 with C2,6P. Therefore, the effectiveness of the pyrrolidinones in enhancing the spreading of trisiloxane L77 on the polyethylene substrate decreases in the order: C2,6P > C6P, C8P > CHP > C4P. The mixtures of L77 with C10P show no synegistic effect at all; the plot of spreading factor versus RL77 for the mixtures of L77 with C10P is almost linear over the whole range of mole fractions of L77. Apparently, spreading of

the mixture of L77 and C10P on the polyethylene film is an ideal one. 2. The Spreading Coefficient. The spreading coefficient of the liquid over the solid substrate, SL/S, is the surface free energy decrease per unit area as a result of the spreading:

SL/S ) - ∆G/a ) γSA - γSL - γLA

(1)

When SL/S g 0, the spreading occurs spontaneously; when SL/S < 0, spontaneous spreading does not occur and the liquid produces a contact angle, θ, with the substrate. For L77 only:

SL77L/S ) γL77SA - γL77SL - γL77LA

(2)

When mixed with pyrrolidinone (or other surfactants):

SMixL/S ) γMixSA - γMixSL - γMixLA

(3)

Therefore, the change of the spreading coefficient upon the addition of the pyrrolidinone is equal to

SMixL/S - SL77L/S ) (γMixSA - γL77SA) - (γMixSL γL77SL) - (γMixLA - γL77LA) (4) In eq 4, only the value of (γMixLA - γL77LA) can be obtained directly (from the plots of γMixLA vs lnC and γL77LA vs LnC). The values of (γMixSA - γL77SA) and (γMixSL - γL77SL) cannot be obtained directly because direct interfacial tension measurements at the solid/air and solid/liquid interfaces are not available. However, they can be obtained indirectly.

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The interfacial pressure, π, of a system is the difference between the interfacial tension of the solvent, γ0, and the interfacial tension of the surfactant solution, γ. Therefore,

π ) γ0 - γ

(5)

According to eq 5, for the L77 solution, the interfacial pressure at solid/aqueous solution interface equals

πL77SL) γ SolvSL- γL77SL

(6)

Similarly, for the mixed surfactant solution, the interfacial pressure at the solid/aqueous solution interface equals

πMixSL ) γ SolvSL- γMixSL

(7)

Equations 6 and 7 can be rearranged as below

γL77SL ) γSolvSL- πL77SL

(8)

γMixSL ) γSolvSL- πMixSL

(9)

and

Subtraction of eq 8 from eq 9 yields

γMixSL - γL77SL ) πL77SL- πMixSL

(10)

In the same fashion, we obtain the equation at the solid/ air interface:

γMixSA - γL77SA ) πL77SA - πMixSA

Figure 2. Surface tension (γLA) vs LogC curves for L77; C2,6P; and their mixtures at 25 °C (pH ) 7.00 in phosphate buffer): L77, 9; RL77: 0.381, [; 0.005, 2; C2,6P, b.

(11)

Substitution of eqs 10 and 11 into eq 4 yields the following:

SMixL/S - SL77L/S ) (πL77SA - πMixSA) (πL77SL - πMixSL) - (γMixLA - γL77LA) ) - ∆γLA + ∆πSL - ∆πSA (12) where

∆γLA ) γMixLA - γL77LA

(13)

∆πSL ) πMixSL - πL77SL

(14)

∆πSA ) πMixSA - πL77SA

(15)

Thus, the effect of the addition of the N-alkyl-pyrrolidinone on the superspreading of the L77 solution (the difference between the spreading coefficients of the mixture and the L77 solution by itself) can be evaluated from the changes in surface tension at the liquid/air and the changes in the interfacial pressures at the liquid/solid and solid/air interfaces. 3. Evaluation of ∆γLA. According to eq 13 and the previous discussion, the value of (γMixLA - γL77LA) can be obtained from the plots of γMixLA versus lnC and γL77LA versus LnC. Figure 2 shows plots of γLA versus LnC for L77 itself and the mixed surfactant solution containing C2,6P at mole fraction of RL77 ) 0.381. Since both solutions are above their cmc’s at the used concentrations (1.0 g/L), both γL77LA and γMixLA are constant, 20.7 mN/m and 22.6 mN/m, respectively, and consequently, the value of (γMixLA - γL77LA) is a constant, which equals 1.9 mN/m. Figure 3 shows plots of γLA versus LnC for L77 itself and the mixed

Figure 3. Surface tension (γLA) vs LogC curves for L77, C8P, and their mixtures at 25 °C (pH ) 7.00 in phosphate buffer): L77, 9; RL77: 0.375, [; 0.010, 2; C8P, b.

surfactant solution containing C8P at mole fraction of RL77 ) 0.375. The value of (γMixLA - γL77LA) can be found to be 1.8 mN/m. Similarly, the value of (γMixLA - γL77LA) for mixed solution of L77 and C10P with mole fraction of L77, RL77 ) 0.307, which is 2.2 mN/m, can be found in Figure 4. The results of ∆γLA ) (γMixLA - γL77LA) for L77 and the mixtures with C4P; CHP; C6P; C2,6P; C8P; and


Langmuir, Vol. 18, No. 6, 2002 2209 Table 4. Results for L77 and Its Mixtures with C2,6P RL77 (eq)

∆γLA (mN/m)

∆πSL (mN/m)

L77 (SMix. S/L - SS/L ) (mN/m)

1.000 0.823 0.651 0.503 0.381 0.200 0.097 0.015

0 0.2 0.3 1.0 1.9 1.8 2.6 4.8

0 2.5 5.3 7.5 9.0 4.5 -0.9 -6.1

0 2.3 5.0 6.5 7.1 2.7 -3.5 -10.9

Table 5. Results for L77 and Its Mixtures with C8P RL77 (eq)

∆γLA (mN/m)

∆πSL (mN/m)


1.000 0.905 0.791 0.660 0.535 0.375 0.222 0.085

0 0.1 0.2 0.3 0.6 1.8 2.3 2.8

0 0.4 1.1 2.5 4.9 10.1 1.3 -4.0

0 0.3 0.9 2.2 4.3 8.3 -1.0 -6.8

Table 6. Results for L77 and Its Mixtures with C10P

Figure 4. Surface tension (γLA) vs LogC curves for L77, C10P, and their mixtures at 25 °C (pH ) 7.00 in phosphate buffer): L77, 9; RL77: 0.078, 2; C10P, b. Table 1. Results for L77 and Its Mixtures with C4P RL77 (eq)

∆γLA (mN/m)

∆πSL (mN/m)

(SMix.S/L - SL77S/L) (mN/m)

1.000 0.805 0.611 0.473 0.313 0.209 0.115 0.024

0 0.3 0.6 1.4 2.1 2.4 2.9 4.0

0 1.1 2.1 3.6 4.0 1.9 -2.3 -6.6

0 0.8 1.5 2.2 1.9 -0.5 -5.2 -10.6

RL77 (eq)

∆γLA (mN/m)

∆πSL (mN/m)

1.000 0.838 0.694 0.581 0.406 0.263 0.155 0.058

0 0.2 0.4 1.0 1.4 2.1 2.5 3.8

0 0.9 1.7 3.0 4.8 3.0 -2.1 -4.3

∆γLA (mN/m)

∆πSL (mN/m)


1.000 0.865 0.707 0.572 0.435 0.307 0.185 0.077

0 0.4 0.9 1.4 1.8 2.2 3.1 4.5

0 -1.6 -2.3 -4.7 -5.8 -6.5 -8.3 -9.5

0 -2.0 -3.2 -6.1 -7.6 -8.7 -11.4 -14.0

solution over all the concentrations used in the measurements. There is no synergistic effect at the air/aqueous solution interface. 4. Evaluation of ∆πSL. According to the Gibbs adsorption equation, at the solid/liquid interface

dγSL ) - nRT ΓSL‚dlnC

Table 2. Results for L77 and Its Mixtures with CHP (SMix. S/L

RL77 (eq)

SL77 S/L )

(mN/m) 0 0.7 1.3 2.0 3.4 0.9 -4.6 -8.1

Table 3. Results for L77 and Its Mixtures with C6P RL77 (eq)

∆γLA (mN/m)

∆πSL (mN/m)


1.000 0.868 0.735 0.574 0.416 0.243 0.152 0.018

0 0.2 0.3 1.1 1.3 2.0 2.3 4.2

0 0.8 1.7 4.3 5.5 8.5 5.9 -9.9

0 0.6 1.4 3.2 4.2 6.5 3.6 -14.1

C10P at different mole fractions of L77 are listed in Tables 1-6. From the tables, it can be seen that all ∆γLA values are positive, which means that the surface tension of the mixed solution is always greater than that of the L77

(16)

where γSL is the surface tension at the solid/liquid interface in mN/m, ΓSL is the adsorption at the solid/liquid interface in mol/ cm2, C is the concentration of surfactant in bulk solution below cmc in mol/L, T is the temperature of the system in K, n is 1 for nonionic surfactants, and R is 8.3143 Joules‚mol-1‚K-1. If we integrate both sides of eq 16, we have

∫γγ

SL

0

SL

∫0C ΓSL‚dlnC

dγSL ) γSL - γ0SL ) - πSL ) - RT

(17)

Therefore, we obtain

∫0C ΓSL‚dlnC

πSL ) RT

(18)

Applying eq 18 to the L77 aqueous solution and its mixed aqueous solution with pyrrolidinones, we obtain the following equations:

∫0C

πL77SL ) RT

∫0C

πMixSL ) RT

ΓL77SL‚dln CL77

(19)

ΓTotalSL‚dlnCTotal

(20)

L77

Total

2210


Figure 5. Adsorption isotherms of L77; C2,6P; and their mixtures (total adsorption) onto the powdered polyethylene at 25 °C (pH ) 7.00 in phosphate buffer): L77 by itself, 0; C2,6P by itself, O; L77 from the mixture, 9; C2,6P from the mixture, b; Mixture with a fixed initial RL77: 0.381, 2.

where πL77 SL is the surface pressure at the solid/aqueous solution interface caused by the L77 aqueous solution; CL77 is the concentration of L77 in the bulk solution by itself; ΓL77 SL is the adsorption of L77 at the solid/aqueous solution interface. Similarly, πMix SL is the surface pressure at the solid/aqueous solution interface caused by the mixed aqueous solution of L77 and pyrrolidinone; CTotal is the total concentration of L77 and pyrrolidinone in the bulk is the total adsorption of L77 and pyrrosolution; ΓTotal SL lidinone at the solid/aqueous solution interface. L77 From their adsorption isotherms, ΓTotal SL and ΓSL can be found as a function of lnCTotal and lnCL77, respectively. L77 Therefore, πMix SL and πSL can be calculated from the plots Total of ΓSL versus LnCTotal and ΓL77 SL versus lnCL77, respectively. The definite integrals in eqs 19 and 20 are just the areas under the plots of Γ versus lnC from C equals 0 to πL77 C. In this fashion, the values of (πMix SL SL ) at the concentrations of CTotal and CL77 can be calculated. Figure 5 shows the adsorption isotherms of L77 and C2,6P by themselves and from their mixture with a fixed initial mole fraction of L77 RL77 ) 0.381 on the powdered polyethylene surface. From Figure 5, it can be seen that the adsorption of L77 from the mixture at the solid/aqueous solution interface is larger than that of L77 by itself. This enhancement of adsorption of L77, caused by the addition of C2,6P, has been discussed in our previous publication.1 On the other hand, the adsorption of C2,6P from the mixture is smaller than that by itself. The total adsorption of their mixture is also shown in Figure 5. Figure 6 shows the adsorption isotherms of L77 and C8P by themselves and from their mixture with a fixed initial mole fraction of L77 RL77 ) 0.375 on the powdered polyethylene surface. As found in Figure 5, the adsorption of L77 from the mixture is enhanced by the addition of C8P to their

Wu and Rosen

Figure 6. Adsorption isotherms of L77, C8P, and their mixtures (total adsorption) onto the powdered polyethylene at 25 °C (pH ) 7.00 in phosphate buffer): L77 by itself, 0; C8P by itself, O; L77 from the mixture, 9; C8P from the mixture, b; Mixture with a fixed initial RL77: 0.375, 2.

mixture, but the adsorption of C8P decreases. The total adsorption of their mixture is also shown in Figure 6. In the same fashion, the adsorption isotherms of L77 and C10P by themselves and from their mixture with a fixed initial mole fraction of L77 RL77 ) 0.307 are shown in Figure 7. In Figure 7, it can be seen that, quite different from the adsorptions of the previous mixtures, both adsorptions of L77 and C10P from their mixture are smaller than that by themselves. The total adsorption of their mixture is also shown in Figure 7. Surprisingly, even their total adsorption is less than the adsorption of C10P by itself. There is a negative synergistic (antagonistic) effect on the adsorption of the mixture. Figure 8 shows the plots of adsorption of L77 and C2,6P and their mixed solution with a fixed initial mole fraction, RL77 ) 0.381 versus logarithm concentration. The curves are fitted by use of the software of Origin6.0, and the fitted functions are shown in the figures. The area enclosed by the curves and the X axis is then calculated through the fitted function of the curves. Although adsorption of surfactants at the solid/liquid interface cannot be zero if the equilibrium concentration of surfactants at bulk solution phase is not zero, the resultant error in the calculated areas is insignificant. The relevant plots of adsorption at the solid/aqueous solution interface (ΓSL) versus lnC for the L77-C8P and L77-C10P mixtures are shown in Figure 9 and Figure 10, respectively. Plots of πL77SL, πC26PSL, and πMixSL, calculated by use of eqs 19 and 20, versus lnC for the L77-C2,6P system are shown in Figure 11. From Figure 11, at the cmc of L77 (ln cmc ) -8.94), πMixSL and πL77SL equal 31.5 mN/m and 22.5 mN/m, respectively. Thus, the change in interfacial pressure (πMixSL - πL77SL) for L77 and its mixture with C2,6P at a fixed initial mole fraction of RL77 ) 0.381 at the cmc of L77 equals 9.0 mN/m. Similar plots for L77, C8P, and their mixture at a fixed initial mole fraction of


Figure 7. Adsorption isotherms of L77, C10P, and their mixtures (total adsorption) onto the powdered polyethylene at 25 °C (pH ) 7.00 in phosphate buffer): L77 by itself, 0; C10P by itself, O; L77 from the mixture, 9; C10P from the mixture, b; Mixture with a fixed initial RL77: 0.307, 2.

Langmuir, Vol. 18, No. 6, 2002 2211

Figure 9. Plots of adsorption on the powdered polyethylene (ΓSL) vs lnC for aqueous solutions of L77, C8P, and their mixture (pH ) 7.00 in phosphate buffer): L77, 9; Mixture with a fixed initial RL77: 0.375, 2; C8P, b.

Figure 8. Plots of adsorption on the powdered polyethylene (ΓSL) vs lnC for aqueous solutions of L77; C2,6P; and their mixture (pH ) 7.00 in phosphate buffer): L77, 9; Mixture with a fixed initial RL77: 0.381, 2; C2,6P, b.

Figure 10. Plots of adsorption on the powdered polyethylene (ΓSL) vs lnC for aqueous solutions of L77, C10P, and their mixture (pH ) 7.00 in phosphate buffer): L77, 9; Mixture with a fixed initial RL77: 0.307, 2; C10P, b.

RL77 ) 0.375 are shown in Figure 12. The change in the solid/liquid interfacial pressure at the cmc of L77 is 10.1 mN/m. Plots for L77, C10P, and their mixture at a fixed

initial mole fraction of RL77 ) 0.307 are shown in Figure 13. Here, the value of the surface pressure for the mixture at the cmc of L77 is found to be 18.5 mN/m, which is

2212


Figure 11. Plots of surface pressure at the solid/aqueous solution interface (πSL) vs lnC for aqueous solutions of L77; C2,6P; and their mixture (pH ) 7.00 in phosphate buffer): L77, 9; Mixture with a fixed initial RL77: 0.381, 2; C2,6P, b.

Wu and Rosen

Figure 13. Plots of surface pressure at the solid/aqueous solution interface (πSL) vs lnC for aqueous solutions of L77, C8P, and their mixture (pH ) 7.00 in phosphate buffer): L77, 9; Mixture with a fixed initial RL77: 0.307, 2; C10P, b.

of C10P, is -3.8 mN/m. This means that the addition of C10P to the aqueous solution of L77 results in a decrease in the interfacial pressure at the solid/liquid interface. The results of ∆πSL for L77 and its mixtures with C4P; CHP; C6P; C2,6P; C8P; and C10P at different mole fractions of L77 are listed in Tables 1-6. Except for initial RL77 values of 0.115 or less, the ∆πSL values for the L77 mixtures with C4P; CHP; C6P; C2,6P; and C8P are all positive, indicating an increase in the solid/liquid interfacial pressure resulting from the addition of the pyrrolidinones and consequently, a lower interfacial tension caused by the mixture aqueous solution at the interface. By contrast, all the L77 mixtures with C10P (Table 6) show negative values of ∆πSL, indicating a decrease in the solid/liquid interfacial pressure resulting from the addition of C10P. 5. Evaluation of ∆πSA. In the same fashion, we obtain

∫0C ΓSA‚dlnC

πSA ) RT

Figure 12. Plots of surface pressure at the solid/aqueous solution interface (πSL) vs lnC for aqueous solutions of L77, C8P, and their mixture (pH ) 7.00 in phosphate buffer): L77, 9; Mixture with a fixed initial RL77: 0.375, 2; C8P, b.

smaller than that of L77 by itself (πL77SL ) 22.3 mN/m) at the same concentration. Consequently, the change in the interfacial pressure (πMixSL - πL77SL), caused by the addition

(21)

where ΓLA is the adsorption at the air/solid interface and C is the equilibrium concentration of the surfactant in the solution phase below the cmc. In our previous paper,36 we found that the adsorption of L77 and its mixtures with pyrrolidinones at the solid/air interface (ΓSA) on the polyethylene surface is smaller by 1 order of magnitude than that at the air/aqueous solution interface (ΓLA) or at the solid/aqueous solution interface (ΓSL) at all surfactant concentrations. Since, from eq 21, πSA is directly proportional to ΓSA, it can be concluded that πSA will be smaller by 1 order of magnitude than πLA and πSL and consequently that ∆πSA must be smaller by 1 order of magnitude than ∆πLA and ∆πSL. Therefore, compared with ∆πLA and ∆πSL, the effect of ∆πSA on change in the spreading coefficient (SMixL/S- SL77L/S) is negligible.


Langmuir, Vol. 18, No. 6, 2002 2213

Figure 14. Plots of mole fraction of L77 in bulk solution phase (RL77) vs lnC and mole fraction of L77 at the solid/aqueous solution interface (X1) vs lnC at adsorption equilibrium for mixed solution of L77 and C2,6P with a fixed initial RL77: 0.381. RL77, 0; X1, O.

Consequently, from eq 12, we have Mix SL/S - SL77 L/S ≈ ∆πSL - ∆γLA

(22)

L77 The results of (SMix L/S - SL/S ) for L77 and the mixtures with C4P; CHP; C6P; C2,6P; C8P; and C10P at different mole ratios of L77 are also listed in Tables 1-6. From the data in those tables, it can be found that the increase in the value of the interfacial pressure at polyethylene/ aqueous solution interface (∆πSL) upon the addition of the N-alkylpyrrolidinone is the dominant factor in increasing the value of the spreading coefficient. 6. Relationship between Spreading Coefficient and Spreading Factor. From Tables 1-5, it is seen that the spreading coefficients of the mixed solutions are greater than that of the solution of L77 by itself for the mixtures with C4P; CHP; C6P; C2,6P; and C8P when the mole fraction of L77 is larger than a certain value, for example, 0.209 for C4P. That means that if the pyrrolidinone, except for C10P, is mixed with L77 at a proper mole ratio, it can make the spreading coefficient of the mixture more positive than that of the L77 by itself. That is, the free energy decrease per unit area of the mixed solution upon spreading (eq 1) becomes larger than that for the solution of L77 by itself. It has been shown that the spreading coefficient is proportional to the spreading rate of pure liquids on homogeneous smooth solids.39 If we can assume that this applies also to solutions, and since there was a constant amount of spreading time (3 min) used in this study, the larger the (positive) spreading coefficient, the larger will be the area spreaded. From the values of (SMixL/S - SL77L/S) in Tables 1-5, the order of increase in the spreading coefficient by the pyrrolidinones is C8P > C2,6P > C6P > CHP > C4P. This is almost the same as the order of their enhancement of the spreading factor (Figure 1) mentioned above. In view of the very different experimental techniques involved in the calculation of the values of (SMixL/S - SL77L/S) and the measurement of the spreading factors, the data correlate well with each other.

(39) Hill, R. M. In Silicone Surfactants; Hill, R. M., Ed.; Surfactant Science Series 86; Marcel Dekker: New York, 1999; p 20.

7. Interactions between L77 and Pyrrolidinones at the Aqueous Solution/Air and the Aqueous Solution/Solid Interfaces. The molecular interaction parameter between two surfactants at an interface can be evaluated by the following equation:37b

X12ln(RC12/X1C10) (1 - X1)2 ln[(1 - R)C12/(1 - X1)C20] β ) σ

ln(RC12/X1C10) (1 - X1)2

)1

(23)

(24)

where R is the mole fraction of surfactant 1 in the total surfactant in the solution phase (i.e., the mole fraction of surfactant 2 equals 1-R); X1 is the mole fraction of surfactant 1 in the total surfactant on the adsorbed monolayer; C10, C20, and C12 are the solution phase molar concentrations of surfactant 1, 2, and their mixture, respectively, required to produce a given π value at an interface; and βσ is the molecular interaction parameter for mixed monolayer formation at the same interface. βσLA is the interaction parameter at the aqueous solution/air interface using constant γLA; βσSL is the parameter at the aqueous solution/solid interface using constant πSL. Equation 23 can be solved numerically for X1 when R, C10, C20, and C12 are obtained from experimental data. The more negative the value of βσ, the stonger the attractive interaction between the two different surfactant molecules in the mixed monolayer at the interface. A value of zero indicates ideal mixing. In the following part of this paper, the surfactant 1 always refers to surfactant L77. (a) Interaction Parameters at the Air/Liquid Interface. Molecular interactions between L77 and pyrrolidinones C4P; C6P; CHP; C2,6P; C8P; and C10P at the air/aqueous solution interface at pH ) 7.00 in phosphate buffer have been evaluated by using eqs 23 and 24. Data of C10, C20, and C12 for L77; C2,6P; and their mixture at a given surface tension of γLA ) 35.0 mN/m are shown in Figure 2. Using C12 of the mixture with mole fraction of L77, R1 ) 0.005, the molecular interaction parameter between L77 and C2,6P at the air/aqueous

2214


Wu and Rosen

Figure 15. Plots of mole fraction of L77 in bulk solution phase (RL77) vs lnC and mole fraction of L77 at the solid/aqueous solution interface (X1) vs lnC at adsorption equilibrium for mixed solution of L77 and C8P with a fixed initial RL77: 0.375. RL77, 0; X1, O.

Figure 16. Plots of mole fraction of L77 in bulk solution phase (RL77) vs lnC and mole fraction of L77 at the solid/aqueous solution interface (X1) vs lnC at adsorption equilibrium for mixed solution of L77 and C10P with a fixed initial RL77: 0.375. RL77, 0; X1, O. Table 7. Molecular Interaction Parameters (βσLA) for Mixtures of L77 with Pyrrolidinones at 25 ( 0.2 °C mixtures

X1LA

βσLA

L77-C4P L77-CHP L77-C6P L77-C2,6P L77-C8P L77-C10P

0.78 0.76 0.76 0.75 0.67 0.62

-0.43 -0.57 -0.82 -0.67 -0.40 +0.14

solution interface (βσLA) is calculated to be -0.76. Values of C10, C20, and C12 for L77, C8P, and their mixture at a given surface tension of γLA ) 30.0 mN/m are shown in Figure 3. The molecular interaction parameter between L77 and C8P at the air/aqueous solution interface (βσLA) is calculated to be -0.40. Data of C10, C20, and C12 for L77, C10P, and their mixture at a given surface tension of γLA ) 30.0 mN/m are shown in Figure 4. The molecular interaction parameter between L77 and C10P at the air/

aqueous solution interface (βσLA) is calculated to be 0.14. The molecular interaction at air/liquid interface, βσLA, between L77 and pyrrolidinones are listed in Table 7. From the results, it appears that the mixtures all exhibit very weak interactions at the air/aqueous solution interface. The L77-C10P mixture shows a very weak repulsion between the two surfactant molecules. This is consistent with the ∆γLA results described above, which indicate no synergism at the air/aqueous solution interface. (b) Interaction Parameters at the Solid/Liquid Interface. Interaction parameters at the aqueous solution/polyethylene interface (βσSL) are calculated from the adsorption isotherms of the two individual surfactants and their mixture (L77; C2,6P; and their mixture in Figure 5; L77, C8P, and their mixture in Figure 6; L77, C10P, and their mixture in Figure 7.) in the following manner: (1) the values of ΓSL are plotted versus lnC (L77; C2,6P; and their mixture in Figure 8; L77, C8P, and their mixture


Langmuir, Vol. 18, No. 6, 2002 2215

Table 8. Molecular Interaction Parameters (βσSL) for Mixtures of L77 with Pyrrolidinones at 25 ( 0.2 °C mixtures

πMax SL (mN/m)

R1 (eq)

βσSL (calcd)

βσSL (expt)

X1SL (calcd)

X1SL (expt)

L77-C4P L77-CHP L77-C6P L77-C2,6P L77-C8P L77-C10P

2.5 5.0 7.5 8.0 16.5 17.5

0.046 0.105 0.145 0.182 0.269 0.295

-2.7 -3.6 -5.3 -6.7 -5.1 +0.7

-3.5 -4.2 -5.9 -6.7 -5.4 +1.2

0.74 0.68 0.62 0.55 0.49 0.51

0.77 0.71 0.64 0.55 0.55 0.40

in Figure 9; L77, C10P, and their mixture in Figure 10.), and the areas under the curves (ΓSL vs lnC) are substituted into eqs 19 and 20 to calculate πSL as a function of lnC. This is plotted for the individual surfactants and the mixture in Figure 11 for L77; C2,6P; and their mixture; in Figure 12 for L77, C8P, and their mixture; in Figure 13 for L77, C10P, and their mixture. (2) The values of C10, C20, and C12 at the largest common value of πSL are shown in Figures 11-13. They are 8.0 mN/m (lnC12 ) -11.50) for L77; C2,6P; and their mixture; 16.5 mN/m (lnC12 ) -10.52) for L77, C8P, and their mixture; 17.5 mN/m (lnC12 ) -9.05) for L77, C10P, and their mixture. (3) For use in eqs 23 and 24, the value of R1, which is the equilibrium value in the bulk solution phase, is generally not equal to the initial value. It can be calculated as a function of lnC by using the data on the adsorption of the individual surfactant in their mixture in Figures 5-7. A plot of the calculated equilibrium R1 versus lnC for the mixture of L77 and C2,6P with a fixed initial R1 ) 0.381 is shown in Figure 14. Similarly, a plot of the calculated value of equilibrium R1 versus lnC for the mixture of L77 and C8P with a fixed initial R1 ) 0.375 is shown in Figure 15; a plot of the calculated equilibrium R1 versus lnC for mixture of L77 and C10P with a fixed initial R1 ) 0.307 is shown in Figure 16. Using the C10, C20, and C12 values in Figures 11-13 and the equilibrium R1 values for the relevant lnC12 values from Figures 14-16, respectively, these are substituted in eqs 23 and 24 to calculate the respective βσ SL values. These are listed in Table 8. Table 8 shows that the mixtures of L77 with C4P; CHP; C6P; C2,6P; and C8P have negative interaction parameters, which means attractive interactions between L77 and pyrrolidinones C4P; CHP; C6P;, C2,6P; and C8P; while the mixture of L77 and C10P has a small positive interaction parameter, indicating weak repulsive interaction. The more negative the interaction parameters, the stronger the attraction. The order of negative βσSL values is C2,6P > C6P > C8P > CHP > C4P. This is exactly the same order of decrease in the enhancement of the spreading factor observed above (Figure 1). (c) Comparison of Measured and Calculated Mole Fraction of L77 at the Solid/Liquid Interface. Equa-

tion 23 was used above to calculate the values of X1, the mole fraction of surfactant 1 (L77, in this case) in the total surfactant at the solid/liquid interface. Since this value can also be obtained from the adsorbed amount of the two surfactants from their mixture (Figures 5-7), this permits evaluation of the validity and accuracy of eq 23, which is based upon the assumptions of nonideal solution theory.40,41 Table 8 also lists the experimental values of X1 (exp) and the interaction parameter, βσSL (exp), calculated from it at the same lnC12 values at which X1 and βσSL were calculated, using eqs 23 and 24. Considering the complexity of the calculation of X1 (calcd) by using eq 23, the agreement between these values and those (X1 (calcd)) obtained directly from the data in Figures 5-7 is considered good validation of the nonideal solution treatment of the adsorption data. The values of βσSL (exp) are also in the same order as those of βσSL (calcd). Conclusions 1. The change in the values of the spreading coefficient on polyethylene of an aqueous solution of the ethoxylated trisiloxane L77 upon the addition to it of an N-alkyl pyrrolidinone can be approximated from the difference between the change in interfacial pressure at the polyethylene/aqueous solution interface and the change in the surface tension of the aqueous solution. The increase in the value of the former is the dominant factor in increasing the value of the spreading coefficient. 2. The change in the spreading coefficient on the polyethylene of an aqueous solution of L77 upon the addition to it of different N-alkyl pyrrolidinones is in about the same order as their enhancement of its spreading factor on polyethylene. 3. Interaction of L77 with the different N-alkyl pyrrolidinones investigated at the aqueous solution/air and polyethylene/air interface is very weak. However, those N-alkyl pyrrolidinones that produce enhancement of the superspreading of aqueous solutions of L77 on polyethylene show significant attractive interaction with L77 at the polyethylene/aqueous solution interface, and the order of increasing attractive interaction is in the same order as that of enhancement of the spreading factor. 4. Comparison of values of the mole fraction of L77 at the polyethylene/aqueous solution interface, either calculated by use of the nonideal solution treatment or measured directly from adsorption data, shows that the nonideal solution treatment of the data for calculation of interaction parameter is valid. LA0113318 (40) Hua, X. Y.; Rosen, M. J. J. Colloid Interface Sci. 1982, 87, 469. (41) Hua, X. Y.; Rosen, M. J. J. Colloid Interface Sci. 1982, 90, 212.

Superspreading of Trisiloxane Surfactant Mixtures on Hydrophobic

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