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Articles Trisiloxane Surfactants: Surface/Interfacial Tension Dynamics and Spreading on Hydrophobic Surfaces T. Svitova,* H. Hoffmann, ² and Randal M. Hill Institute of Physical Chemistry, Russian Academy of Sciences, Leninsky Prospect 31, 117915 Moscow, Russian Federation, Bayreuth, Universitatstrasse 30, Postfach 101251, D-8580 Bayreuth, Germany, and Central Research and Development, Dow Corning Corporation, 2200 West Salzberg Road, Midland, Michigan 48686-0994 Received June 26, 1995. In Final Form: October 20, 1995 X Dynamics of surface (at the solution/air interface) and interfacial (at the solution/n-dodecane interface) tension of nonionic siloxane surfactants, some of which are known as “superwetter”, and ethoxylated isododecyl alcohols was studied by the drop volume method. The influence of surfactant concentration and hydrophilicity (length of the ethoxy chain) on surface/interfacial tension dynamics and spreading of aqueous solutions on the liquid hydrocarbon surface was investigated. Surface and interfacial tension fall rates were estimated on the basis of the Hua and Rosen approach (Hua, X. Y.; Rosen, M. J. J. Colloid Interface Sci. 1988, 124 (2), 652). It was found that concentrated solutions of surfactants with intermediate ethoxy chain length show unusually high surface/interfacial tension fall rates. These solutions spread very fast on a liquid hydrocarbon surface: a drop of aqueous solution with a volume of about 3 μL forms a thin spreading film with an area of several square centimeters in 5-10 s. The rate of spreading and the resulting film thickness were found to depend on the surfactant concentration and the hydrophilicity and hydrocarbon subphase chain length. A good correlation between surface/interfacial tension fall rate, rate of spreading, and the dynamic spreading coefficient was found. Diffusion coefficient values were calculated according to the method of Fainerman et al. (Fainerman, V.; Makievski, A.; Miller, R. Colloids Surf. A 1994, 87, 61), and it was found that for the siloxane surfactant with eight ethoxy groups the diffusion coefficient values are 1 order of magnitude higher than that of the hydrocarbon analogue with 5 ethoxy-groups. An increase of the ethoxy chain length for siloxane as well as for hydrocarbon surfactants causes a decrease of the diffusion coefficient and the surface/interfacial tension fall rate and leads to a suppression of surfactant spreading ability. Introduction In many cases, for instance, during wetting and spreading, emulsification, foaming, and dispersion forma- tion, the processes in the presence of the surfactants take place under nonequilibrium conditions, and in these cases the dynamic properties of the surfactant adsorption layer are of great importance. One of the methods to investigate amphiphile adsorption kinetics at freshly formed inter- faces is to measure the dynamic interfacial tension. Different dynamic tension techniques are available now, and the theory has reached a level where a quantitative description is possible. 1-8 A new method for measuring dynamic tensions by a growing drop technique is described in refs 4 and 5. One can find the reviews of modern dynamic tension methods in refs 6 and 7. It is worth noting that most of the dynamic tension work mentioned here was performed for dilute surfactant solutions, and it has been shown that diffusion and two- dimensional phase transitions due to surfactant molecule reorientation play an important role in such cases. 1-3,8-11 It was also found that usually at surfactant concentrations above the cmc, surface/interfacial tension only slightly depends on surface age. 12 In ref 13 a theoretical analysis of adsorption kinetics from micellar solutions was per- formed and it was shown that the presence of aggregates can influence the rate of adsorption. The authors of ref 14 have analyzed the experimental data of Triton X 100 surface tension dynamics at concentrations above the cmc, and they have proposed a way to evaluate the rate of demicellization on the basis of these data. For the processes of wetting and spreading of surfactant solutions, occurring under nonequilibrium conditions, as was mentioned above, as far as these processes obey the Young equation and Neuman inequality, surface/inter- facial tension dynamics must be one of the most important factors, determining spreading dynamics. In work ref 15 it was found that retention of nonionic surfactant solutions * Corresponding author. E-mail: [email protected]. ² Universitat Bayreuth. Dow Corning Corporation. X Abstract published in Advance ACS Abstracts, February 1, 1996. (1) Miller, R.; Kretzchmar, G. Adv. Coll. Interface Sci. 1991, 37, 97. (2) Krotov, V. V.; Rusanov, A. I. Kolloidn. Zh. 1977, 39, 58. (3) van den Tempel, M.; Lucassen-Reynder, E. Adv. Colloid Interface Sci. 1983, 18, 281. (4) MacLeod, C. A.; Radke, C. J. J. Colloid Interface Sci. 1993, 160, 435. (5) MacLeod, C. A.; Radke, C. J. J. Colloid Interface Sci. 1994, 166, 73. (6) Miller, R.; Joos P.; Fainerman, V. P. Adv. Colloid Interface Sci. 1994, 49, 249. (7) Chang, C.-H.; Franses, E. I. Colloids Surf., A: Physicochem. Eng. Aspects 1995, 100, 1. (8) Fainerman, V. B.; Makievski, A. V.; Miller, R. Colloids Surf., A: Physicochem. Eng. Aspects, 1994, 87, 61. (9) Miller, R.; Schano, K.-H.; Hofmann, A. Colloids Surf., A: Physi- cochem. Eng. Aspects 1994, 92, 189. (10) Svitova, T.; Smirnova, Yu.; Yakubov, G. Colloids Surf., A: Physicochem. Eng. Aspects, in press. (11) Svitova, T.; Smirnova, Yu.; Churaev, N.; Rusanov, A. Kolloidn. Zh. 1994, 56 (3), 441. (12) Davies, J. T.; Rideal, E. K. In Interfacial Phenomena; Academic Press: New York, 1963. (13) Miller, R. Colloid Polym. Sci. 1981, 259, 1124. (14) Rillaerts, E.; Joss, P. J. Phys. Chem. 1982, 86, 3471. (15) Anderson, N. H.; Hall, D. J. Adjuvants Agrochem. 1989, 2, 51. 1712 Langmuir 1996, 12, 1712-1721 0743-7463/96/2412-1712$12 00/0 © 1996 American Chemical Society + +

Trisiloxane Surfactants:  Surface/Interfacial Tension Dynamics and Spreading on Hydrophobic Surfaces

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Articles

Trisiloxane Surfactants: Surface/Interfacial TensionDynamics and Spreading on Hydrophobic Surfaces

T. Svitova,* H. Hoffmann,† and Randal M. Hill‡

Institute of Physical Chemistry, Russian Academy of Sciences, Leninsky Prospect 31,117915 Moscow, Russian Federation, Bayreuth, Universitatstrasse 30, Postfach 101251,D-8580 Bayreuth, Germany, and Central Research and Development, Dow Corning

Corporation, 2200 West Salzberg Road, Midland, Michigan 48686-0994

Received June 26, 1995. In Final Form: October 20, 1995X

Dynamics of surface (at the solution/air interface) and interfacial (at the solution/n-dodecane interface)tension of nonionic siloxane surfactants, some of which are known as “superwetter”, and ethoxylatedisododecyl alcohols was studied by the drop volume method. The influence of surfactant concentrationand hydrophilicity (length of the ethoxy chain) on surface/interfacial tension dynamics and spreading ofaqueous solutions on the liquid hydrocarbon surface was investigated. Surface and interfacial tension fallrates were estimated on the basis of the Hua and Rosen approach (Hua, X. Y.; Rosen, M. J. J. ColloidInterfaceSci.1988,124 (2), 652). Itwas found that concentrated solutions of surfactantswith intermediateethoxy chain length show unusually high surface/interfacial tension fall rates. These solutions spreadvery fast on a liquid hydrocarbon surface: a drop of aqueous solution with a volume of about 3 µL formsa thin spreading film with an area of several square centimeters in 5-10 s. The rate of spreading andthe resulting film thickness were found to depend on the surfactant concentration and the hydrophilicityand hydrocarbon subphase chain length. A good correlation between surface/interfacial tension fall rate,rate of spreading, and the dynamic spreading coefficient was found. Diffusion coefficient values werecalculated according to the method of Fainerman et al. (Fainerman, V.; Makievski, A.; Miller, R. ColloidsSurf. A 1994, 87, 61), and it was found that for the siloxane surfactant with eight ethoxy groups thediffusion coefficient values are 1 order of magnitude higher than that of the hydrocarbon analogue with5 ethoxy-groups. An increase of the ethoxy chain length for siloxane aswell as for hydrocarbon surfactantscauses a decrease of the diffusion coefficient and the surface/interfacial tension fall rate and leads to asuppression of surfactant spreading ability.

Introduction

In many cases, for instance, during wetting andspreading, emulsification, foaming, and dispersion forma-tion, the processes in the presence of the surfactants takeplaceundernonequilibriumconditions, and in these casesthe dynamic properties of the surfactant adsorption layerare of great importance. Oneof themethods to investigateamphiphile adsorption kinetics at freshly formed inter-faces is to measure the dynamic interfacial tension.Different dynamic tension techniques are available now,and the theory has reached a level where a quantitativedescription is possible.1-8 A new method for measuringdynamic tensionsbyagrowingdrop technique isdescribedin refs 4 and 5. One can find the reviews of moderndynamic tension methods in refs 6 and 7.

It is worth noting that most of the dynamic tensionworkmentioned herewas performed for dilute surfactantsolutions, and it has been shown that diffusion and two-dimensional phase transitions due to surfactantmoleculereorientation play an important role in such cases.1-3,8-11

Itwasalso found thatusuallyat surfactant concentrationsabove the cmc, surface/interfacial tension only slightlydepends on surface age.12 In ref 13 a theoretical analysisof adsorption kinetics from micellar solutions was per-formed and it was shown that the presence of aggregatescan influence the rate of adsorption. The authors of ref14 have analyzed the experimental data of Triton X 100surface tensiondynamicsat concentrationsabove the cmc,and they have proposed a way to evaluate the rate ofdemicellization on the basis of these data.For theprocesses ofwettingand spreading of surfactant

solutions, occurring under nonequilibrium conditions, aswas mentioned above, as far as these processes obey theYoung equation and Neuman inequality, surface/inter-facial tensiondynamicsmust be one of themost importantfactors, determining spreading dynamics. In work ref 15itwas found that retentionofnonionic surfactant solutions

* Correspondingauthor.E-mail: [email protected].† Universitat Bayreuth.‡ Dow Corning Corporation.X Abstract published in Advance ACS Abstracts, February 1,

1996.(1) Miller, R.; Kretzchmar, G. Adv. Coll. Interface Sci. 1991, 37, 97.(2) Krotov, V. V.; Rusanov, A. I. Kolloidn. Zh. 1977, 39, 58.(3) vandenTempel,M.; Lucassen-Reynder, E.Adv.Colloid Interface

Sci. 1983, 18, 281.(4) MacLeod, C. A.; Radke, C. J. J. Colloid Interface Sci. 1993, 160,

435.(5) MacLeod, C. A.; Radke, C. J. J. Colloid Interface Sci. 1994, 166,

73.(6) Miller, R.; Joos P.; Fainerman, V. P. Adv. Colloid Interface Sci.

1994, 49, 249.(7) Chang, C.-H.; Franses, E. I.Colloids Surf., A: Physicochem.Eng.

Aspects 1995, 100, 1.(8) Fainerman, V. B.; Makievski, A. V.; Miller, R. Colloids Surf., A:

Physicochem. Eng. Aspects, 1994, 87, 61.

(9) Miller, R.; Schano, K.-H.; Hofmann, A. Colloids Surf., A: Physi-cochem. Eng. Aspects 1994, 92, 189.

(10) Svitova, T.; Smirnova, Yu.; Yakubov, G. Colloids Surf., A:Physicochem. Eng. Aspects, in press.

(11) Svitova, T.; Smirnova, Yu.; Churaev, N.; Rusanov, A. Kolloidn.Zh. 1994, 56 (3), 441.

(12) Davies, J. T.; Rideal, E. K. In Interfacial Phenomena; AcademicPress: New York, 1963.

(13) Miller, R. Colloid Polym. Sci. 1981, 259, 1124.(14) Rillaerts, E.; Joss, P. J. Phys. Chem. 1982, 86, 3471.(15) Anderson, N. H.; Hall, D. J. Adjuvants Agrochem. 1989, 2, 51.

1712 Langmuir 1996, 12, 1712-1721

0743-7463/96/2412-1712$12 00/0 © 1996 American Chemical Society

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wasrelated todynamic, not to equilibrium, surface tensionvalues anddependedmore on solution concentration thanon the chemical structure of the surfactants. A numberof siloxane surfactants exhibit “superwetting” or“superspreading”;16-19 according to ref 18 a surfactant isa superspreader if the addition of a small amount, sayless than 0.1%, to a small droplet of water enables it,when placed on a hydrophobic surface (they mean a solidsurface), to spread into a thin, wetting film within tensof seconds. The interesting work was done to study thespreading behavior of the pure siloxane surfactants onhigh- and low-energy surfaces.20,21 These investigationsshowed the importance of the aggregate organization andatmospheric humidity for spreading of amphiphilic mol-ecules on a low-energy surface. Some authors attributedthe special properties of the trisiloxane surfactants to theunique “T”, hammer-like or “umbrella” shape of thesesurfactants.16,17 Recently the results of systematic studiesof siloxane surfactant aqueous solutions spreading onParafilm (a paraffin wax) surface were published.18 Inref 18 it has been shown that for linear as well as“hammer”-shaped siloxane surfactants, spreading abilityis related to dispersed particle size and to the transportrate of surfactant fromdispersedparticles to the interfacesat the spreading front. The authors concluded that thesilicone hydrophobicmoiety, the presence of water vapor,and a dispersed surfactant-rich phase are necessary forsuperspreading, but themolecular geometry of surfactantis not a critical factor. The spreading mechanism is,however, still largely unexplained. The authors18 haveproposed that a thin pre-existing high-tension film isformed at the leading edge of the spreading drop, and sospreading is driven by a Marangoni effect, but themechanism of this precursor film formation is unclear.They also studied a series of aqueous dispersions of bothhammer-like and linear hydrocarbon polyoxyethylenesurfactants and found that none were superspreaders.The explanations of superspreading, proposed in refs 16-19, apparently should be applied to each surfactant, andthus themainquestion,namely,whatare thepeculiaritiesof siloxane surfactants determining their unusual spread-ing behavior, is still open.In thepresentworkdynamics of surface (at the solution/

air interface) and interfacial (at the solution/n-dodecaneinterface) tension was studied for nonionic trisiloxanesurfactants with different ethoxy chain length, EO ) 8,12,and16,andethoxylated isododecylalcoholswithethoxygroup numbers 4.9, 9.8, and 14.6. The influence of thesurfactant concentration and chemical structure on the

surface/interfacial tension dynamics was studied. Theseresults were compared with the spreading behavior ofthese solutions on a liquid hydrocarbon surface. Thusweintended to clarify the relationbetween interfacial tensiondynamics of surfactant solutions and their spreading ona uniform hydrophobic fluid surface and to make a newshort step toward understanding the mechanism of thesuperspreading phenomenon.

Experimental Section

Materials. Four trisiloxane surfactants were studied (seeTable 1). These products were of 90% purity. The ethoxylatedisododecyl alcohols with ethoxy chain length n ) 4.9, 9.8, and14.6, narrow ethoxy chain length distribution, of 98% purity,were kindly supplied by Hoechst Company, Germany. All thesurfactants were used without special purification.Distilled anddeionizedwaterwasused for surfactant solution

preparation. n-hydrocarbons (Fluka) and paraffin oil (Fluka),of spectroscopic grade purity, were used for interfacial tensionmeasurements and spreading behavior studies.The reason why we chose these substances as subphases for

spreading behavior investigations was to permit us to measureinterfacial tension on the surfaces of solution/subphase andsubphase/air and therefore be able to calculate both the dynamicand the equilibrium spreading coefficients. At the same time,the liquid hydrocarbon surface is always horizontal,molecularlysmooth, and homogeneous, and its surface properties areindependent of surface prehistory and treatments. Theseproperties are often difficult to reproduce for solid hydrophobicsurfaces, alwayshavingsomeroughnessandheterogeneitywhichproduces a significant influence on the character and rate ofspreading.18

Methods. Dynamicsurface/interfacial tensionmeasurementswere performed by using the drop volume technique; a TVT-1drop volume tensiometer, Lauda, Germany, was used for thesemeasurements. The detailed description of this apparatus canbe found in refs 9, and 22. Drop volume measurements weremainly made in the dynamic regime, using Dyn Mode of theapparatus, 9-15measurements of drop volumewere performedfor eachdrop formation time, and theaveragedropvolumevalueswereused for the calculationof surface/interfacial tensionvalues.The mean reproducibility of the drop formation time was (0.2s, and drop volume deviations did not exceed (0.3 µL from oneset of measurements to another; this provided the meanreproducibility of the interfacial tension as(0.5mN/m. We alsoused thequasi-static regime formeasurementsofdynamicsurfacetension of dilute D-8 solutions. This method was developed byAddison andTornberg23 and consists of growing a drop of a givenvolume Vo at the tip of a capillary in the shortest possibleformation time. In this case, the drop volume Vo and droppingtime t do not have to be corrected. The mean reproducibility ofthe drop formation time for dilute surfactant solutions was(0.5s at short dropping times, but it became worse (the deviationswascomparablewith thedropping time)with increasingdroppingtimes. For concentrated solutions, the dynamic drop volume isquite close to the equilibrium one; the quasi-static regime givesinadmissibly large deviations in dropping time, exceeding this

(16) Ananthapadmanabham, K. P.; Goddard, E. E.; Chandar, P.Colloids Surf. 1990, 44, 281.

(17) Roggenbuck, F. C.; Rowe, L.; Penner, D.; Petroff, L.; Burow, R.Weed Technol. 1990, 4, 576.

(18) Zhu, S.; Miller,W. G.; Scriven, L. E.; Davis, H. T.Colloids Surf.,A: Physicochem. Eng. Aspects 1994, 90, 63.

(19) Lin, Z.; Hill R. M.; Davis H. T.; Ward M. D. Langmuir 1994, 10,4060.

(20) Tiberg, F.; Cazabat, A.-M. Europhys. Lett. 1994, 25 (3), 205.(21) Tiberg, F.; Cazabat, A.-M. Langmuir 1994, 10, 2301.

(22) Miller, R.; Hofmann, A.; Hartman, R.; Shano, K.-H.; Halbig, A.Adv. Mater. 1992, 5 (4), 370.

(23) Addison, C. C. J. Chem. Soc., 1946, 579. Tornberg, E. J. ColloidInterface Sci. 1978, 64, 391.

Table 1. Objects of Investigation

abbrev source chemical structure

Trisiloxane SurfactantsM(D′E8OH)M D-8 Dow Corning (Me3SiO)2Si(Me)(CH2)3(OCH2CH2)8OHM(D′E12OH)M D-12 Corporation (Me3SiO)2Si(Me)(CH2)3(OCH2CH2)12OHM(D′E7OH)M PR-7 Goldschmidt (Me3SiO)2Si(Me)(CH2)3(OCH2CH2)7OHM(D′E16OH)M PR-28 Goldschmidt (Me3SiO)2Si(Me)(CH2)3(OCH2CH2)16OH

Hydrocarbon Surfactantsethoxylated i-C12 alcohol, EO n ) 4.9 i-C12 EO4.9 Hoechst (CH3)2C10H19O(CH2CH2O)4.9OHethoxylated i-C12 alcohol, EO n ) 9.8 i-C12 EO9.8 Hoechst (CH3)2C10H19O(CH2CH2O)9.8OHethoxylated i-C12 alcohol, EO n ) 14.6 i-C12 EO14.6 Hoechst (CH3)2C10H19O(CH2CH2O)14.6OH

Trisiloxane Surfactants Langmuir, Vol. 12, No. 7, 1996 1713

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time, we were forced to use the dynamic regime for theinvestigation of the solution dynamic tension.To choose the right way of accounting for hydrodynamic drop

volumeperturbationunderdynamic conditions,wehaveanalyzedthe different modes of hydrodynamic correction, developed atpresent for pure liquids and surfactant solutions,9,24-26 and wehave selected the hydrodynamic correction equation, proposedbyMiller etal.9,22 Thishydrodynamic correctionmodewaschosenbecause (i) itwasdevelopedespecially for thedropvolumemethod,using a TVT apparatus; (ii) it seems to be based on quite simpleand physically proven assumptions; (iii) it provides a goodcorrelationbetween the results, obtainedusingdifferent capillarytip radii, for pure solvents as well as for surfactant solutions(Figure 1a); (iv) in the cases when it was possible, we havecompared the results of quasi-static and thus corrected dynamicmeasurements, and very good agreementwas found (Figure 1b).

On the basis of the approach of Miller et al.,9,22 taking intoaccount the dependence of the drop volume on the flow rate

we have calculated R and â coefficients from our experimentaldata as the slope and intercept with the Y axis of the ∆V(F)dependence for pure water/air and water/n-dodecane systems.Thecorrecteddropvolume for surfactant solutionswas calculatedusing eq 1 with the thus obtained R and â coefficients.The surface/interfacial tension was then calculated using the

following well-known equation:27

in which ∆F is the density difference between the studied liquidand air or oil, g is the acceleration of gravity, R is the capillarytip radius, and F is the correction factor, tabulated in ref 27 .Figure 1a illustrates the surface tension vs flow rate depend-

encies, obtained for 0.25%D-8aqueous solutionusing capillariesof different radii. As it is seen the dependence of the surfacetension on the flow rate is normal and there is a good correlationfor the results, corresponding to the different capillary sizes.The comparisonof thedynamic surface tensionmeasurements,

performed using dynamic (curve 1) and quasi-static (curve 2)regimes, for 0.025% D-8 solution is presented in Figure 1b. It isseen that there is very good coincidence between these two setsof measurements. Note that for the dynamic regime the timescale corresponds to the surface age or diffusion time,8,9,22 equalto 3/7 of the drop formation time for a continuously growingdrop; for the quasi-static regime, the time scale corresponds toa dropping time. The same coincidence of dynamic and quasi-static results was obtained for the 0.1% D-8 solution (Figure 2,curves 2 and 3) for short dropping times; this fact proves thatthehydrodynamic correctionmodeusedhere gives accurate dropvolume values that correspond to reality.Equilibrium interfacial tension measurements at the D-8

aqueous solution/n-hydrocarbon interface were performed byusing a spinning drop tensiometer, Kruss, Germany.Spreading of surfactant solutions on hydrocarbon subphases

was studied by visual observations without humidity control atroom temperature. A drop of surfactant solution was put on thesubphase surface, and the maximum radius of the spread drop(24) Jho, C.; Burke, R. J. Colloid Interface Sci. 1983, 95 (1), 9.

(25) vanHunsel, J.; Joss, P.Colloid Polym. Sci. 1989, 267 (11), 1026.(26) Kloubek, J.; Friml, K.; Krejci, F. Czech. Chem. Commun. 1976,

41, 1845.(27) Padday, J. In Surface and Colloid Science; Matijevic, E., Ed.;

Wiley-Interscience: New York, 1969.

Figure 1. Dependence of the dynamic surface tension on (a)the flow rate at the 0.25% (wt/wt) D-8 aqueous solution/airinterface, 25 °C. 1, rcap ) 1.055 mm; 2, rcap ) 1.71 mm; (b) timedependence at the 0.025% (wt/wt) D-8 aqueous solution/airinterface, rcap ) 1.38 mm, 25 °C. 1, dynamic mode; 2, quasi-static mode.

Figure2. Dynamic surface tensionat theD-8aqueoussolution/air interface, 25 °C. 1, 0.05% (wt/wt); 2,3, 0.1% (wt/wt) (2, quasi-static mode; 3, dynamic mode); 4, 0. 25% (wt/wt); 5, 0.5% (wt/wt) D-8.

Ve ) V(t) - (R + âF), F ) V(t)/t (1)

γ ) Vdyn cor ∆ρ g F/R (2)

1714 Langmuir, Vol. 12, No. 7, 1996 Svitova et al.

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and the time of spreading to maximum radius were estimated.Mean values for 5-7 measurements were calculated for eachsolution. Spreading coefficients were calculated according to28

where γΒ is the hydrocarbon surface tension, γΑ is the solutionsurface tension, and γ ΑΒ is the solution/hydrocarbon interfacialtension.

ResultsSurface/Interfacial Tension Dynamics. Figures

2-5 show the plots of the dynamic surface tension forD-8, D-12, PR-7, PR-28, and i-C12EO4.9 aqueous solutionsat 25 °C, which the capillary radius was 1.055mm. Data

are shown for several surfactant concentrations. In allcases, the surfactant concentrationwas near or above thecritical micelle concentration (cmc), which for nonionicsurfactants is usually about 0.01% (wt/wt)29 and is equal30to 0.007% (wt/wt) (1.24 × 10-4 mol/kg30) for D-8 andincreases from 7 × 10-5 M to 5 × 10-4 M for ethoxylatedisododecyl alcohols with an increase in the ethoxy chainlength from 5 to 15. In these plots the X-axis time scaleasmentioned above corresponds to the diffusion time8,9,22(except curve 2 of Figure 2, where it corresponds to thedropping time, measured in the quasi-static regime). Atlow surfactant concentration, 0.01-0.025% (wt/wt) onecan see the usual surface tension dependencies on time,namely, the surface tension decreases slowly with in-creasing surface age. The higher the solution concentra-tion, the less pronounced the dependence of the surfacetension on time, for example, the dynamic surface tensionof 0.5%D-8 (curve 5 of Figure 2) andPR-7 (curve 3, Figure3) aqueous solutions decreases about 0.25-1.0 mN/mduring all the time of the observations. For D-12 (Figure4), having an ethoxy chain longer than that of D-8 andPR-7, the decrease of the surface tensionwith time is stillwell pronounced at a solution concentration of 0.5% (wt/wt). For PR-28, the most hydrophilic trisiloxane surfac-tant studied here, having 16 ethoxy groups, the surfacetensiondynamicsat the0.5% (wt/wt) solution/air interfacehas its usual character and the surface tension slowlydecreases with surface age, according to curve 1 of Figure3. As is seen fromFigure5, thesameregularity is observedfor ethoxylated isododecyl alcohol i-C12EO4.9, the increaseof the surfactant concentration from 0.01% to 0.5% (wt/wt) leads to the suppression of the surface tension vs timedependence.Next, Figure 6 shows the results of dynamic surface

tension measurements of 0.5% (wt/wt) aqueous solutionsof the ethoxylated isododecyl alcohols with differentnumbers of ethoxy groups. It is seen from this figure thatfor these surfactantsunder certain conditions thedynamic

(28) Thorpeis Dictionary of Applied Chemistry, 4th ed.; Longmans,Green and Co.: London, New York, Toronto, 1954; X1, p 348.

(29) Shinoda, K.; Nakagawa, T.; Tamamushi, B.-I.; Isemura, T.Colloidal Surfactants; Academic Press: New York, 1963; Schonfeldt,N. Grenzflachenaktive Athylenoxid-Addukte; Wissenschaftliche Ver-lagsgesellschaft MBH: Stuttgart, 1976.

(30) Hill, R.; He, M.; Davis, H. T.; Sciven, L. E. Langmuir 1994 10(6), 1724.

Figure 3. Dynamic surface tension at the PR-28 and PR-7aqueous solution/air interfaces, 25 °C. 1, 0.25% (wt/wt) PR-28;2, 0.05% (wt/wt); 3, 0.25% (wt/wt) PR-7.

Figure 4. Dynamic surface tension at the D-12 aqueoussolution/air interface, 25 °C. 1, 0.25% (wt/wt); 2, 0.5% (wt/wt)D-12.

K ) γB - γA - γAB (3)

Figure 5. Dynamic surface tension at the i-C12EO4.9 aqueoussolution/air interface, 25 °C. 1, 0.01% (wt/wt); 2, 0.1% (wt/wt);3, 0.25% (wt/wt); 4, 0.5% (wt/wt) i-C12EO4.9.

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surface tension is nearly constant with an increase in thesurface age, although some temporary oscillations, re-producible fromone set ofmeasurements to another,wereobserved. Similardropvolumebifurcationswereobservedin ref 31, and the authors have proposed that this may becaused by capillary waves, arising at the drop surfaceunder specific conditions. Note that with increasingethoxy chain lengthbothdynamicandequilibriumsurfacetension values increase. The same regularity is ob-served for trisiloxane surfactants, as is seen fromFigures2-4.The results of equilibrium interfacial tension measure-

ments at the 0.5% (wt/wt) D-8 aqueous solution/n-hydrocarbon interface are presented in Figure 7. Onecan see that the equilibrium interfacial tension risesalmost linearlywith an increase in thehydrocarbon chainlength. For 0.5% (wt/wt) D-8/n-hexane system the in-terfacial tension reaches a very low value, 0.03 mN/m,and the formation of a thin layer of an intermediate phase,probably a microemulsion, surrounding the hexane dropin the surfactant solutionwas observedduring interfacialtensionmeasurements on the spinning drop tensiometer.In the systems with long-chain hydrocarbons this phe-nomenon was not observed and the interfacial tensionvalue for 0.5% (wt/wt) D-8/tetradecane system is an orderof magnitude higher than that with hexane.Thedynamic interfacial tensionwasmeasuredbyusing

the drop volume method for 0.25% (wt/wt) D-8 and 0.5%(wt/wt)D-12 solutionsagainstn-dodecane, and the resultsof these measurements are presented in Figure 8. It isseen that for both solutions the interfacial tensiondecreases with a time increase. The dependence of theinterfacial tension on time ismore significant for the 0.5%D-12 solution; for theD-8 solution, the interfacial tensiononly slightly decreaseswith time, and the same regularitywasobservedat the solution/air interface. Unfortunately,we could not measure the interfacial tension for the 0.5%(wt/wt) D-8 solution because it was very low (the equi-librium value is 0.23 mN/m, as is seen from Figure 7),below theTVT1apparatus limits; in this caseweobservednonstop flow of the D-8 solution. On the other hand, for

the spinningdropmethod there is aminimumtime, about1 min, below which measurements cannot be performed,and it is impossible to compare the measurementsperformed on the TVT and spinning drop apparatusesdue to the differences in time scale of these methods.The results of the interfacial tension measurements in

i-C12EOn/n-dodecane systems, presented inFigure9, showthat the interfacial tension decreases with time in thei-C12EO4.9 /n-docecane system; in the i-C12EO14.6/n-doce-cane system the dynamic interfacial tension is more orless constant, and in the i-C12EO9.8/n-docecane system theinterfacial tension even slightly increaseswith time.Notethat indistinctionwith the i-C12EOn solution/air interface,wherewehave observedan increase of the surface tensionwith an ethoxy chain length increase, at the i-C12EOn/n-dodecane interface thedynamic aswell as the equilibriuminterfacial tensionwas found tobeminimumin i-C12EO9.8/n-docecane system. The same dependence of the inter-

(31) Fainerman, V. B.; Miller, R. Colloids Surf., A: Physicochem.Eng. Aspects 1995, 97, 255.

Figure 6. Dynamic surface tension at the i-C12EOn aqueoussolution/air interface, 25 °C. Surfactant concentration, 0.5%(wt/wt). 1, i-C12EO14.6; 2, i-C12EO9.8; 3, i-C12 EO4.9.

Figure 7. The dependence of the interfacial tension at the0.5% (wt/wt) D-8 aqueous solution/hydocarbon interface on thehydrocarbon chain length, 25 °C.

Figure 8. Dynamic interfacial tension at the D-n aqueoussolution/dodecane interface, 25 °C. 1, 0.25% (wt/wt)D-8; 2, 0.5%(wt/wt) D-12.

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facial tension on ethoxy chain length with a minimumwas observed in ref 32 for the ethoxylated isononylphenolsolution/octane systems.Spreading Behavior. The spreading behavior of

surfactant solutions on the hydrocarbon surface wasstudied in the open air at room temperature. First of allwe studied thebehavior of apurewaterdropon the surfaceof different hydrocarbons. It was observed that a smalldrop of water, about 5 µL, being put on an octane and adecane surface, drowned nearly immediately. At thesurfaceofdodecaneand longer-chainhydrocarbonsasmalldrop ofwater can float a long time, held by surface tensionlike a thin steel needle at the surface of purewater duringthe well-known demonstration of surface tension action.The same behavior was observed for dilute (0.01-0.025%(wt/wt)) trisiloxaneand i-C12EOn surfactant solutionsand0.5% (wt/wt) PR-28 and i-C12EO14.6 solutions. Moreconcentrated D-8, D-12, PR-7, i-C12EO4.9, and i-C12EO9.8solutions spread at the dodecane and longer-chain hy-drocarbon surface, the rate of spreading depends on thesolution concentration, thehydrocarbon chain length, andthe surfactant ethoxy chain length. Note that a dropletof the pure “dry” siloxane surfactants D-8 and D-12 didnot spread significantly on the liquidhydrocarbon surfaceand it could float on the surface for a few minutes, butafter contact with the humid atmosphere it started tospread. This observation is in accordance with thespreading behavior of pure D-8 on solid low-energysurfaces,20,21 andwe can say that in our case the presenceofwater isnecessary for fast spreading on the fluid surfaceand likewise on solid ones. As for solid surfaces,18-21 forour case the main driving term for spreading is thedifference in chemical potential between the edge of thefilm and the main drop. Taking that into account,according to Figures 1-6, 8, and 9, at freshly-createdinterfaces the tension is higher than at aged ones, we cansay that this spreading is caused by a Marangoni effect.The results are summarized in Table 2.Analysis of Table 2 data shows that the spreading of

surfactant solutions on the hydrocarbon surface occursonly in the cases when the equilibrium spreading coef-

ficient value is positive; this is in good agreement withthe theory of spreading.24 On the other hand, Kspr ispositive for a D-8 solutionwith decane and undecane, butaqueous surfactant solution drops, weighing 3-5 mg,drownuponbeingputonthesurfaceof thesehydrocarbons,and spreading cannot be observed. The smaller drop of0.5% (wt/wt) D-8 solution, about 1 mg, spreads on theundecane surface, and the rate of spreading is 5.2 mm2/s.In all cases we saw that in the open air a spreading filmwas unstable and tended to contract or to break into tinydroplets of surfactant-rich phase, perhaps this occurreddue to water evaporation. At 100% humidity the filmswere stable and the spreading rate was even greater insupersaturated air; the same trends were observed in ref18whenthesesolutionswerespreadonasolidhydrophobicsurface.It is seen fromTable2 that there isnotagood correlation

between the equilibrium spreading coefficient value andthe rate of spreading; for instance, the equilibriumspreading coefficient for i-C12EO4.9/paraffin oil is 4 timessmaller than that for D-8/paraffin oil, but the rates ofspreading are comparable. The maximum rate of spread-ing of a 0.5% (wt/wt) D-8 solution and the minimumresulting film thicknesswere observedon tetradecaneandparaffin oil surfaces. Thesehydrocarbonshave very closesurface tension values, 30.6 and 31.5mN/m, respectively.Themaximumdependence of the radial spreadingvelocityon the surface energy was found for a D-8 solutionspreading onvariousmonolayers immobilized onquartz-Au resonator surfaces.19 The influence of the subphasecritical surface tension on the spreading behavior of pureD-8 on solid low-energy surfaces was also observed in ref21. The authors have remarked that in this case thedecreaseof the solid surface critical tensionof∼1-3mN/mled to a total depression of the D-8 spreading. It appearsthat spreading on a low-energy surface is governed by thevery delicate balance of the surface energy excesses onthe three-phase contact line and thus the surface/interfacial tension dynamics may play an important rolein this process. To clarify the relationship between thesurface/interfacial tension dynamics and the spreadingbehavior of the surfactant solutions on the hydrophobicsurfaceswehave analyzed the results of dynamic surface/interfacial tension measurements on the basis of theapproach of Hua and Rosen,33 as is described further inthe Discussion.

Discussion

HuaandRosen have studied dynamic surface tension33and adsorption dynamic behavior for 15 highly purifiedsurfactants34 by use of the maximum bubble pressuremethod. They have proposed the division of the dynamicsurface tension vs log time curves into four stages: aninduction region, a fast fall region, a mesoequilibriumregion, andanequilibriumregion. All fourof these regionscanbeobservedwhendilute surfactant solutionsareunderstudy.10,11,33 As we deal with surfactant solutions near orabove the cmc, the regions of fast fall, mesoequilibrium,and equilibrium can be observed in Figures 1-6, 8, and9. In the cases when our curves could be satisfactorilyfitted by single-exponential decay we had defined themesoequilibriumsurface/interfacial tensionas the limitingsurface/interfacial tension value of the fitting curves. Thefitting curves have been used to estimate the surface/

(32) Svitova, T.; Smirnova, Yu.; Pisarev, S. Kolloidn. Zh. 1994, 56(3), 436.

(33) Hua, X. Y.; Rosen, M. J. J. Colloid Interface Sci. 1988, 124 (2),652.

(34) Rosen, M. J.; Hua, X. Y. J. Colloid Interface Sci. 1990, 139 (2),397.

Figure9. Dynamic interfacial tensionat the i-C12EOnaqueoussolution/dodecane interface, 25 °C. 1, 0.5% (wt/wt) i-C12EO14.6;2, 0.25% (wt/wt) i-C12EO4.9; 3, 0.5% (wt/wt) i-C12 EO9.8.

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interfacial tension values at t f 0 and γtf0 and thus tocalculate the dynamic spreading coefficients,K0

spr, at tf0.According to ref 33, the surface tension fall rate R1/2 at

t1/2 ) t* is determined as

where γm is the mesoequilibrium tension, γ0 is the puresolvent tension, t* is constant, having the meaning of thetime at which the dynamic surface pressure Π ) γ0 - γtreaches 1/2 of the mesoequilibrium value. The constantt* can be evaluated by plotting log[(γ0 - γt)/(γt - γm)] vslog t, where γt is the dynamic surface tension.We perceived that Hua and Rosen’s analysis has quite

an empirical character and other parameters they haveproposed to define33,34 do not have deep physical sense.Neverthelesswe thought that the surface tension fall ratethus calculatedmay be used as ameasure of the dynamicsurface activity and thus will be useful for comparison ofsurface/interfacial tensiondynamicsofdifferentsurfactantsolutions. In Table 3 the surface/interfacial tension fallrate, calculated according to eq 4, is compared with therate of spreading and spreading coefficients of studiedsurfactant solutions on a dodecane surface.It is seen fromTable 3 that an increase of the surfactant

concentration leads to a significant rise of the surfacetension fall rate. The highest value ofR1/2 is observed for

a 0.5%D-8 solution at the boundary with air and a 0.25%solution with dodecane. It is noticeable that an increaseof the ethoxy chain length causes a decrease of R1/2 fortrisiloxane as well as for hydrocarbon surfactants. Notealso that in all cases R1/2 at the boundary with air issignificantly higher than that in the solution/dodecanesystems. In so far as we studied nonionic surfactants,which are not individual substances but a mixture ofhomologues with different ethoxy chain length, this maybe explained by partial dissolution and distribution ofsurfactant homologues with short ethoxy chains betweenan oil and an aqueous phase, occurring in the solution/dodecane systemsand thus retarding interfacial adsorbedlayer equilibration.It is seen that D-8 solutions at a concentration of 0.05%

(wt/wt) and above have a positive spreading coefficient asat equilibrium so as at t f 0 and for these solutions thereis a good correlation between the surface tension fall rateand the rate of spreading. Knowing the area of thespreading film and assuming that the area per moleculein the spreading film cannot be smaller than that in thesaturated adsorbed layer, equal to 59 Å2 for D-8 and 47Å2 for C12EO4.6,17,35 we could estimate a ratio betweenamount of surfactant molecules adsorbed on a totallyspread film surface and the total amount of surfactantmolecules in the drop. This value is almost constant forD-8 solutions of different concentrationsandequal to 0.4-

(35) He, M.; Hill, R. M.; Lin, Z.; Sciven, L. E.; Davis, H. T. J. Phys.Chem. 1993, 97 (34), 8820.

Table 2. Spreading of Surfactant Solutions on Fluid Hydrocarbons

surfactant conc, % wt subphase rate of spreading, mm2/s Keqsp, mN/m

resulting filmthickness, µm

D-8 0.5 C10H22 drown 7.7D-8 0.5 C11H24 drown 8.2D-8 0.5 C12H26 70 8.7 3.5D-8 0.5 C14H30 240 9.3 1.2D-8 0.5 C16H34 160 9.4 1.8D-8 0.5 paraffin oil 230 9.5 1.8D-8 0.5 C10H21OH 1.4 340D-8 0.5 C12H25OH 40 8D-12 0.5 C12H26 50 4.5 3.5PR-7 0.5 C12H26 68 8.5 4.0PR-7 0.5 paraffin oil 220 9.2 1.4PR-28 0.5 paraffin oil no spreading -4.5i-C12EO4.9 0.5 paraffin oil 80 2.1 5.0i-C12EO9.8 0.5 paraffin oil 46 0.2 8.1i-C12EO14.6 0.5 paraffin oil no spreading -8.6

Table 3. Parameters of Spreading and Surface Tension Dynamics

system surfactant conc, % R1/2, mN/(m s) rate of spreading, mm2/s K0spr, mN/m Keq

spr, mN/m

D-8/air 0.025 224 no spreading -6.55 3.50.05 484 15 1.1 7.60.05a 90 no spreading -2.5 6.40.1 1.9 × 103 28 3.2 7.80.25 3.4 × 107 40 3.4 8.60.5 5.9 × 107 70 4.2 9.1

D-12/air 0.25 7.8 × 103 26 1.6 3.50.5 1.1 × 104 50 2.1 5.1

PR-7/air 0.05 430 14 1.0 7.30.25 8.6 × 103 68 5.0 8.2

PR-28/air 0.5 3.4 no spreading -18.1 -12.3C12EO4.9/air 0.01 25.3 no spreading -26.4 -12.6

0.1 161 2 0.03 0.050.25 2.9 × 103 17.6 0.08 0.80.5 5.6 × 105 80 0.12 1.031.0 7.8 × 105 280

C12EO14.6/air 0.5 4.6 × 104 no spreading -9.0 -6.8C12EO14.6/C12H26 0.5 70C12EO4.9/C12H26 0.25 1.2 × 103D-8/C12H26 0.25 1.1 × 106D12/C12H26 0.5 270a Two weeks after preparation.

R1/2 )Πm

2t1/2)(γ0 - γm)

2t*(4)

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0.45; that means that under the conditions studied aspreading film does not reach the full possible coverageof interfaces and that more than half of the surfactantstill remains in the bulk of the film. This value is about1 order of magnitude lower for C12EO4.6 than for D-8 andis 0.03-0.07 in its dependence on the surfactant concen-tration. Thus, C12EO4.6 is not as effective a spreadingagent asD-8, is less than1/10 of the totalC12EO4.6 amount,present in solution, and participates in adsorption layerformationat solution/air and solution/dodecane interfacesin a maximally spread film.The solutions, having a negative dynamic spreading

coefficient, as is seen from Table 3, do not spread on thedodecane surface. In Table 3 are presented the resultsfor a dilute (0.05% (wt/wt)) solution 1 day (row 2) and 2weeks (row 3) after preparation. The change, occurringafter aging the 0.05% D-8 solution (0.05a) is caused by adecomposition of the trisiloxane surfactant due tomixingin distilledwater, as it was noticed in ref 35; the lower thesurfactant concentration, the fasterdecomposition occurs.The surfactant decomposition leads to a significantdecreaseof thesurface tension fall rateandsimultaneouslyto a loss of superspreading properties. We should like toemphasize that more concentrated D-8 solutions weresignificantly more stable and no noticeable changes indynamic surface/interfacial tensionwere observedwithinat least 2 weeks after preparation. The deviations ofdynamic tension values of freshly prepared and twoweekold 0.25% D-8 solutions fell into measurement accuracylimits.For a 0.25% (wt/wt) PR-7 aqueous solution we have

observed a total loss of spreading ability 1 week afterpreparation. It was senseless to measure the surface/interfacial tension for this aged solution because theseparation of decomposition productswas observed in thebottom of a test tube. Unfortunately, we did not checkthe pH of D-8 and PR-7 solutions, but we can propose,according to ref 35, that the pH of PR-7 solutions wasshifted from its optimal value of around 7, where tri-siloxane surfactants are more stable in aqueous solutionand that this was the reason of very fast decompositionof this product.In Table 3 the analogous results of spreading behavior

and dynamic surface tension analysis for ethoxylatedalcohol aqueous solutions are also listed.As is seen from Table 3, for these surfactants a good

correlation between the rate of spreading, the surfacetension fall rate, and the dynamic spreading coefficientis also observed. The comparison of the data for D-8 andi-C12EO4.9 shows that at the same concentration D-8exhibits better superspreading properties, and this cor-responds to the higher values of the dynamic spreadingcoefficient and surface/interfacial tension fall rate.Wepropose that in the casesunder study theadsorption

barrier is not a leading factor in adsorption dynamics. Toestimate the role of diffusive mass transport in theadsorption process it is necessary to know the aggregatesize of the studied surfactants, taking into account thatwe dealt with rather concentrated solutions above thecmc. Wehaveused freeze-fracture transmissionelectronmicroscopy to estimate the aggregate size in 0.025% and0.25% (wt/wt) D-8 aqueous solutions. The micrographsof carbon-platinum replicas, obtained from these solu-tions, are presented in Figure 10 a,b. It is seen that inboth solutions small aggregates exist with a mean size ofca. 40nmandtherearenot strongdifferences in individualaggregate size in dilute andmore concentrated solutions,but in the concentrated solution some clusters of ag-gregates can be observed. The size of D-8 aggregates islarger than that of normal micelles and is comparable to

the size of double-tailed surfactant unilamellar vesicles,36and so we can propose, in accordance with refs 30 and 35that D-8 forms unilamellar vesicles in aqueous solutionat the concentrations of 0.01-0.25% (wt/wt). Regardingthese aggregates as solid spheres, fulfilled by water, thediffusion coefficientD of these particles can be calculatedfrom the Einstein formula:

and for D-8 individual aggregates with a mean diameterof 40 nm the diffusion coefficient in water is 1.3 × 10-11

m2/s.Recently8 a new approach, based on the asymptotic

solutions of the Ward and Torday equation extended forthe case of a continuously growing drop (or bubble), wasdeveloped, and it permits one to estimate the diffusioncoefficient values at tf ∞byuse of the following equation:

where C0 is the surfactant bulk concentration. Γ is thedynamic surface concentration, which was estimated byusing the Frumkin equation:

According to ref 35 Γmax ) 2.8× 10-6 mol/m2 for D-8, 1.95× 10-6 mol/m2 for D-12, and 3.5 × 10-6 mol/m2 for

(36) Svitova, T.; Smirnova, Yu.; Pisarev, S.; Berezina, N. ColloidsSurf., A: Physicochem. Eng. Aspects 1995, 98, 107.

Figure 10. Electron micrographs of D-8 aqueous solutions:(a), 0.025% and (b), 0.25 % (wt/wt); bar ) 200 nm.

D ) kT/6πηr (5)

( dγdt-1/2)tf∞

) RTΓ2

c0 ( π4D)1/2 (6)

γ0 - γ ) -ΓmaxRT ln(1 - Γ/Γmax) (7)

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i-C12EO4.9. Thediffusion coefficientswere calculated fromthe slope of the γ (t-1/2) dependencies extrapolated to t f∞, and they are listed in Table 4.In this table the values of the D-8 self-diffusion

coefficientDself-diffusion fromref17andtheapparentdiffusioncoefficient Dapparent, obtained in ref 20 for this surfactantspreading on a low-energy solid surface, are presented. Itis seen from this table that the diffusion coefficients thuscalculated decrease with surfactant concentration in-crease. Keeping inmind that theWard-Tordayapproachwas developed for monomer solutions, we can say thatthe thus calculated diffusion coefficient does not cor-respond to the diffusion coefficient of the surfactantmonomer,which is independentof concentration,but theseare effective or average values, characterizing joint masstransfer in a mixture of monomers and aggregates. Thedecrease of these valueswithan increase of concentration,here observed, is caused, according to ref 13, by theincrease in aggregate concentration at constantmonomerconcentration equal to the cmc. Unfortunately, it wasimpossible to separate the terms corresponding to mono-mers and aggregates using the approach proposed byMiller13because toomanyparameters included in themassbalance equation were unknown.Note that in all cases thediffusion coefficients, obtained

for aboundary solution/air, areabout1order ofmagnitudehigher than that in the solution/dodecane systems. As itwas mentioned above when we regarded the interfacialtension fall rate, this may be caused by surfactantdistribution between aqueous and oil phases. The agingof the 0.05%D-8 solution (row 3, 0.05a) leads to a decreaseof the diffusion coefficient and as was mentioned aboveto a loss of super spreading properties inspite of the factthat theD-8diffusion coefficient in theaged0.05%solutionwas still higher than that in the 0.25% solution. It ispossible to say that there is not a visible correlationbetween the diffusivity and spreading ability for the samesurfactant solutions, having different concentration. Onthe other hand, comparing the diffusion coefficients andthe spreading velocity of different surfactants at the sameconcentration, one can see that the higher the diffusioncoefficient the faster spreading occurs. Moreover,D-8hasdiffusion coefficient values about 1 order of magnitudehigher than that of its hydrocarbon analogue i-C12EO4.9in all surfactant concentration ranges studied. Thediffusion coefficient ofD-8 is also significantlyhigher thanthat of D-12 inspite of the fact that D-12 forms normalmicelles in aqueous solution with a mean size of ∼10 nmand has to be more diffusive than D-8, forming vesicleswith a diameter of 40 nm. Note that D-8 diffusioncoefficients, derived from surface tension dynamic data,are higher thanEinstein diffusion coefficients for spheres

with a diameter of 40 nm and than the D-8 self-diffusioncoefficient, mentioned in ref 17, and that these values areof the same order of magnitude as was found in ref 20from spreading experiment data.To check the diffusion in the bulk of these surfactant

solutions dynamic light scattering measurements werecarried out using aBrookhavenBI-9000 correlator at 90°.The apparatus is equipped with a 623.8 nm He/Ne laser,and the size distribution of the particles was calculatedby an inverse Laplace transformation. Wehave obtainedthe mean values of the particle diameter to be 196 nm for0.1% D-8, 302 nm for 1.0% D-8, 10 nm for 1.0% D-12, and330 nm for 1.0% i-C12EO4.9 aqueous solutions. Thus thediffusion coefficients of spherical aggregates in the bulkof D-8 aqueous solutions are 20-30 times lower than thatin solutions ofD-12and comparablewith that in i-C12EO4.9solutions, while from dynamic surface tension measure-ments we have gotten an opposite picture.An increase of surfactant hydrophilicity (ethoxy chain

length) suppresses diffusion coefficient values as well asthe spreading ability of trisiloxane and hydrocarbonsurfactants. As itwasmentioned inref20 theeffectmayberelated to the increasingdifficulty in formingadense zero-curvature bilayer structurewhen the length of the ethoxychain increases.Ananthapadmanabham et al.16 studied the kinetics of

the adsorption of some silicone surfactants on liquid/airand solid/liquid interfaces. They found the superspreaderSS1, having the same chemical structure as D-8 and ameannumber of ethoxy groups of 7.5,whendepleted fromthe liquid/air interface, is replenished more rapidly thanother silicone surfactants studied. They also concludedthat the SS1 dispersions have a higher mobility and ahigher solid-liquid adsorption rate than other siliconesurfactant solutionsat comparable concentrations. Theseresults are in good agreement with our observations.At the present stage it is difficult to explain this

unusually high mobility of D-8 in aqueous solutions,manifesting itself as ahigh rate of adsorptionat interfaceswith air and oil. We can only speculate that this may beconnectedwitha lowcohesive energyandahigh flexibilityof trisiloxane surfactant molecules,18,20 and thus wepropose that for these reasons the lifetime of siliconesurfactant molecules, entrapped in bilayer aggregates, islower than that in a hydrocarbon surfactant aggregate.According to ref 13, in the case when the aggregationnumber is very high (forD-8 it corresponds to about 8000)and thus the diffusion coefficient of the aggregates has tobe hundreds of times lower than that of the monomers,the terms, connected with the aggregate formation-dissolution processes, strongly influence the adsorptionrate. In such cases the rate constants of aggregateformation and dissolution are very important factors foradsorption dynamics. In ref 14 it was shown that it ispossible to estimate the rate of demicellization from thedynamic surface tension when the data for the solutionat the cmcareavailable. So, thismaybecome thedirectionof our further investigations.We perceive that all the questions, arising with regard

to superspreading processes on fluid surfaces, cannot betotally resolved in the framework of the presentwork andthat further detailed investigation is necessary.

ConclusionStudies of surface/interfacial tension dynamics and

spreading behavior of aqueous siloxane and hydrocarbonsurfactant solutions on fluid hydrocarbon surfaces wereperformed.Analysis of surface/interfacial tension dynamics has

shown that surfactants exhibit an unusually fast surface/

Table 4. Diffusion Coefficients of the Surfactants at t f∞

system surfactant conc, % Dtf∞, m2/s

D-8/air 0.025 2.5 × 10-10

0.05 1.3 × 10-10

0.05b 8.0 × 10-11

0.25 6.8 × 10-11

D-12/air 0.25 1.3 × 10 -12

PR-28/air 0.5 7.1 × 10 -13

C12EO4.9/air 0.01 7.0 × 10-11

0.1 2.1 × 10-11

0.25 6.5 × 10-12

D-8/C12H26 0.25 2.7 × 10-12

D-12/C12H26 0.5 1 × 10-13

C12EO4.9/C12H26 0.25 8.3 × 10-13

a Dapparent ) 1 × 10-10, from ref 20; Dself-diffusion ) 3.2 × 10-11,from ref 17; DEinstein ) 1.3 × 10-11, calculated using eq 9. b Twoweeks after preparation.

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interfacial tension fall rate at the concentrations corre-sponding to superspreading on hydrophobic surfaces.The diffusion coefficient values were calculated from

surface/interfacial tensiondynamicsdata,and itwas foundthat for the superspreading surfactant D-8 the diffusioncoefficient values thus obtained are 1 order of magnitudehigher than the diffusion coefficients of the hydrocarbonanalogue. A decrease of diffusion coefficients with asurfactant concentration increase was observed.For the first time liquid hydrophobic subphases were

used to study spreading of aqueous surfactant solutions,which permitted us to evaluate directly dynamic andequilibrium spreading coefficient values from dynamictension measurements.It was found that fast spreading of surfactant solutions

on a hydrocarbon surface occurred in the caseswhen bothequilibrium spreading coefficient and dynamic spreadingcoefficient valueswere positive. Thepositive equilibriumspreading coefficient is necessary but not sufficient toensure that fast spreading would take place.In distinction with solid low-energy subphases, where

as it was found in refs 15 and 18 a superspreading ofhydrocarbon surfactants does not occur, on fluid hydro-

carbon surfaces superspreading of nonionic hydrocarbonsurfactant solutions was observed.The rate of spreadingdepends on the surfactantnature,

structure (hydrophobicity), and concentration and thesubphase nature. The increase of the surfactant hydro-philicity (ethoxy chain length) suppresses the super-spreadingability of siloxaneandhydrocarbonsurfactants.Agood correlationbetween the surface/interfacial tensionfall rate and the rate of spreading was found.

Acknowledgment. The authors thank Dow CorningCorporation for financial support of this work and kindlysupplied samples of the trisiloxane surfactants. Thisworkwas partially supported by Russian Fundamental Re-search Foundation, Grant 93-03 4467. T.S. thanks Dr.Andre Stuermer (BayreuthUniversity, Germany) for thehelp with the spreading behavior observations and lightscattering measurements and Sergey Pisarev (Instituteof Physical Chemistry, RAS, Moscow) for electron micro-graph preparation.

LA9505172

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