Langmuir 1992,8, 190-196
190
Wetting Dynamics Studies on Silica Surfaces of Varied Hydrophobicity Gayle Newcombet and John Ralston' School of Chemical Technology, University of South Australia, The Levels, South Australia 5095, Australia Received January 2, 1991. In Final Form: June 19, 1991
The kinetics of movement of the three-phaseline of contact (tplc) have been studied as nitrogen displaces water from hydrophobic, smooth silica surfaces. The silica surfaces were quantitatively hydrophobized with trimethylchlorosilane, tert-butyldimethylchlorosilaneand long-chain alcohols over a range of contact angles. Both forced and spontaneous movement were studied by high-speed photography. Neither the geometry of the experiment nor variations in electrical double-layer forces had any detectable influence on the results obtained. The difference between the cosines of the dynamic and static water receding contact angles, A cos, is related to the velocity of the tplc, V,by A cos = (2 s m-l)V + B for 20 X 10-3 m s-1 < V < 100 X 10-3 m s-l, where B may reflect molecular reorientation changes at the solid-liquid and solid-vapor interfaces.
Introduction The spreading of liquids over solid surfaces is a common phenomenon, the practical applications of which include droplet impaction on leaves during insecticide spraying, printing, painting, flotation, and adhesion. The movement and growth of cells on surfaces is a significant biological example of spreading. Despite ita importance, our understanding of the kinetics of wetting is rather incomplete. There is both a shortage of high-quality experimental evidence and some difficulty with present theories. A major problem concerns the significance of the dynamic contact angle and precisely how its measured value can be related to the velocity of wetting as well as to the material properties of the system. The problem is made more complex by our poor understanding of the exact nature of the contact angle adjacent to the threephase line of contact (tplc) even under wetting conditions. In some instances (e.g., ref 1)the local dynamic contact angle has been taken as fixed, Le., velocity independent. White2 remarks that, a t the molecular level, equilibrium contact angles are always zero (or 180'). Comfortingly the Young equation is still valid. The White observation may also be true in the dynamic case; however, for other angles it appears highly probable that the balance of forces at the wetting line would result in the angle of a moving wetting line changing with the velocity of that line. Two approaches have frequently been used to describe wetting kinetics, viz., the hydrodynamic and surface chemical approaches. It is pertinent to reflect upon these for a moment or two, for they illustrate the dilemma which confronts one who wishes to use theory as a predictor. Huh and Striven: among others (e.g., ref 4),showed that the classical hydrodynamic approach predicts, quite wrongly, that the flow of liquid near the contact line exerts an infinite stress on the substrate. This suggests that the classical "no-slip" boundary conditions may not be valid near the wetting line. This serious problem was "overcome" by relaxing the classical hydrodynamic boundary
* To whom correspondence should be addressed. t Present address: State Water Laboratory, Engineeringand Water Supply Department, PrivateMail Bag,Salisbury, S.A. 5108,Australia. (1)Hocking, L. M.;Rivers, A. D. J . Fluid Mech. 1982,121,425-442. (2)White, L. R. J. Chem. Soc., Faraday Trans. 1 1977,73,39+398. (3)Huh, C.; Scriven, L. E. J . Colloid Interface Sei. 1971,35,85-101. (4)Dussan, E. B. Annu. Reu. Fluid Mech. 1979,1 1 , 371-400.
0743-7463/92/2408-Ol90$03.00/0
conditions and allowinglimited slip between the fluid and the solid in the immediate vicinity of the tplc. The presence of a thin boundary layer is invoked. For example, Hansen and Toong5 predict that the moving meniscus shape, determined exclusively by hydrodynamic considerations, does not approach the true dynamic solid/liquid contact angle until within about 5 X lo+ m of the wall. Their work suggests that studies of the dynamic contact angle measured in close proximity to the tplc, but a t a distance considerably greater than the thickness of the boundary layer, do not yield information about the surface forces acting along the tplc, where continuum theory is likely to break down. At present, however, the physical basis for slip and the justification of a boundary layer remain a matter for debate. The surface chemical approach attempts to devise a model for the moving wetting For example, it has been proposed that, for displacement of the wetting line, irreversible work must be done in overcoming energy barriers to molecular displacement within the three-phase zone. In another case, for the spreading of viscous polymers8the energy barriers were associated with viscous flow. These attempts spring from the Eyring theory of reaction rates as applied to transport processes. These two extreme cases were merged by, for example, Hoffmang who recognized that, depending on the system and the tplc velocity, the movement could be dominated by viscous, inertial, and interfacial forces. The relative importance of these forces is best judged by the relative magnitudes of the capillary (Ca) and weber (We)numbers. Hoffman examined the forced flow of silicone and other oils as well as various industrial products in a glass capillary, for C a between lo-" and 10. Hoffman found that the apparent contact angle was a function of the capillary number together with a "shift factor" which depended on interfacial forces in some unexplained fashion. These experiments suffer from defects such as possible contaminants in the industrial fluids used; (5)Hansen, R.J.;Toong, T. Y. J. ColloidInterjace Sci. 1971,37,196207. ( 6 ) Blake, T. D.; Haynes, J. M. J . Colloid Interface Sci. 1969,30,421423. (7)Schwartz, A. M.;Tejada, S. B. J . Colloid Interface Sci. 1972,38, 359-375. (8) Cherry, B. W.; Holmes, C. M. J. Colloid Interface Sci. 1969,29, 174-176. (9)Hoffmann, R.L.J. Colloid Interface Sci. 1975,50, 228-241.
0 1992 American Chemical Society
Wetting Dynamics Studies on Silica Surfaces however, the link between hydrodynamic and interfacial forces is noteworthy. The dynamic aspects of wetting have undergone a renaissance since the mid 19808,marked by a major review on the topic of wetting by de Gennes.lo In both this work and a subsequent analysis by Teletzke, Davis, and Scriven,” the importance of fluid dynamics and interfacial forces is stressed. However, as noted by de Gennes,lo systematic data on pure liquids are still lacking. In addition, there is also an almost complete lack of evidence available for the spreading of a particular fluid (or fluids) on surfaces of variable hydrophobicity. T o a reasonable degree, the behavior of pure liquids has been explored in the case of “dry” spreading (Le., the tplc kinetics of nonvolatile liquids) in the elegant experiments of Cazabat e t al.I2-l4 In the case of the poly(dimethy1siloxane) oils investigated, the radius of spreading droplets depends on time through relatively simple power laws which do not involve the spreading parameter; i.e., they are independent of the chemical nature of the surface provided that it is completely wetted (s > 0) and smooth. Furthermore, very thin films of such simple liquids apparently spread in well-defined steps or layers of molecular thickness. It is with the second problem of spreading on surfaces of variable hydrophobicity that this present paper is concerned. In the past, such experiments have been performed in the presence of soluble surfactants. Any interpretation is plagued by attendant adsorptionldesorption phenomena a t the respective interfaces. In this present study we have investigated the kinetics of movement of the tplc on silica surfaces which have been rendered hydrophobic with trimethylchlorosilane, tert-butyldimethylchlorosilane, and long-chain alcohols. The latter are firmly attached to the surface so that there is no adsorption or desorption taking place during the experiments. The surface hydrophobicity has been quantitatively controlled using methods developed in this labor a t ~ r y . ’ ~ JAs~ far as we are aware, these are the first reported studies of this type on surfaces of controlled, but variable, hydrophobicity. The kinetics of movement of the tplc a t the nitrogenlwaterlmodified silica interface have been studied under conditions of both spontaneous and forced movement. Contact angles have been determined by a photographiclgoniometric technique. We will report a comparison with dynamic angles obtained from wetting balance studies in future papers.
Experimental Section Allreagents used were at least of analyticalgrade. Conductivity water was produced by passage through a Milli RO reverse osmosis system and then through a Milli-Q system which incorporated two stages of ion exchange, two stages of activated carbon, and a final 0.22-pm filter. The conductivity of the resulting water was 5 1X f2-l m-l, with a surface tension of 72.8 mN m-l at 25 “C. Glasswarewas cleaned according to a procedure described elsewhere.17J8 A hot nitric acid wash was followed by brief (10)deGennes, P. G. Reo. Mod. Phys. 1985,57,827-863. (11)Teletzke, G. F.; Davis, H. T.; Scriven, L. E. Chem. Eng.Commun. 1987,55,41-81. (12)Cazabat, A. M.; Cohen Stuart, M. A. J. Phys. Chem. 1986,90, 5845-5849. (13)Heslot, F.;Fraysse, H.; Cazabat, A. M. Nature 1989,338,12891290. (14)deGennes, P. G.; Cazabat, A. M. C. R . Acad. Sci., Ser. 2 1990,310, 1601-1606. (15)Blake, P.; Ralston, J. Colloids Surf. 1985,15, 101-118. ~ .K.: Ralston. J. Colloids Surf. 1987.27, (16)Crawford. R.: K O O D L. 57-64. (17)Pashlev. R. M.: Kitchener, J. A. J. ColloidInterface Sci. 1979,71 (3),491-500.
Langmuir, Vol. 8, No. 1, 1992 191 immersion in warm 30% potassium hydroxide followed by generous rinsing with conductivity water. Glassware was judged to be clean when a jet of steam directed at the surface condensed evenly, without ”beading”. Experiments were performed in a controlled-temperatureroom at 25.0 f 0.4 O C . Normally experiments were performed with conductivity water at pH 5.6. Modification of Silica Surfaces. Disks used in the investigation of the spontaneous movement of the tplc were 1X 10-2 m in diameter and 0.1 x 10-2 m thick and were made from an artificially prepared silica, Suprasil,supplied by H.A. Groiss LM. The disks were polished to a smoothness of better than X/4, measured by interferometry. When viewed under magnification of X250, the polished surfaces showed no signs of roughness.@ Suprasil tubes used for the study of forced movement of the tplc were of internal diameter 1.25 X to 4.50 X 10-3 m. Under magnification the internal tube surfaces showed no signs of roughness. The surfaces were cleaned accordingto the procedure described above. The “steam test”, described in detail by Vig et al.,1* was used to determine the cleanlinessof the surface of the silica disks. A clean, dry, cool disks was held over hot conductivity water. The appearance of uniform interferencefringes, caused by the even condensation of a wetting film of water, indicated that the surface was clean with a contact angle of 4O or less. The silicatubes were found to have a contact angle approaching zero when a gentle jet of steam condensed evenly on the internal surfaces. Surface ModificationUsing Trimethylchlorosilane and tert-Butyldimethylchlorosilane. It is generallyaccepted that the reaction between trimethylchlorosilane (tmcs) and surface silanol groups on the surface of silica is of the form SiOH + (CH,),SiCl-
SiOSi(CH,), + HCI
Evidence in support of this reaction is ~ t r o n g , ~ although ~ J * ~ ~ the nature of both the reaction products and the type of surface bond is still the subjectof debate (e.g., ref 56). Little information is availableon the reaction of tert-butyldimethylchlorosilane(tbdmcs) with the silica surface. It has been assumed in the present study, as in ref 24, that the molecule reacts with silanol groups in the same manner as tmcs. The silicatubes or disks to be modified were placed in a reaction vessel and heated at 140 O C overnight to remove any physically adsorbed water. After heating, the reaction vessel was sealed and taken immediately to a dry nitrogen filled polyethylene glovebag, where it was allowedto cool for at least 2 h. Large evaporating dishes filled with P205 ensured that the atmosphere in the glovebag remained dry. Solutionsof tmcs (or tbdmcs) in cyclohexane were prepared, in the glovebag,in 100 X 10” m3standard flasks. Concentrationsof 1drop to 10 x 10” m3of reactant in 100 x 1o-B m3of cyclohexane were used. The solution was poured into the reaction vessel, with the silica surfaces, and stirred for 30-60 min, depending on the required contact angle. After reaction, the surfaces were rinsed five times with cyclohexane, dried at 100 O C overnight, and then cooled in a vacuum desiccator and used immediately. Surfaces obtained using this procedure displayed static water receding contact angles ranging from 3 3 O to 780.15J6 For these surfaces, there is significant hysterisis between static advancing and receding water contact angles, reflectingsurface roughness and/or inhomogeneitesin the organic surface film.l6 For example, the advancing water contact angle on a surface fully methylated with tmcs is 880.16 (18)Vig, J. R.; LeBus, J. W.; Filler, R. L. Proc. Annu. Freq. Control Symp. 1975,29,220-229. (19)Laskowski, J.; Kitchener, J. A. J. Colloid Interface Sci. 1969,29 (41. .,, 67M79. - . - - .-. ~
(20)Iskra, J.; Laskowski, J. Trans.Inst. Min. Mettal. Sect. C 1969,78, 113-117. (21)Wood, S. Chemical Modification of Silica Surfaces. B. App. Sci. Final Year Project Report, South Australian Institute of Technology, 1988. (22)Hair, M. L. J. Colloid Interface Sci. 1977,60 (l),154-162. (23)Chmielowiec, J.; Morrow, B. A. J. Colloid Interface Sci. 1983,94 (2),319-327. (24)Menewat, A.; Henry, J., Jr.; Sirawadane, R. J. Colloid Interface Sci. 1984,101 (l),110-119.
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192 Langmuir, Vol. 8, No. 1, 1992
Surface Modification Using Long-chain Alcohols. The grafting of alcohols onto a silica surface is usually termed surface esterification, viz. -SiOH
+ ROH
-
SiOR + H,O
Alcohols of various chain lengths, from 1 to 22 carbon atoms, have been reacted with surface s i l a n 0 1 s . ~It~ ~is~ generally a ~ c e p t e dthat ~ ,complete ~ ~ ~ esterification of the silica surface (Le., conversion of all silanol groups) will take place only under autoclave conditions or under high-temperature reflux. Under milder conditions, esterification will take place but to a lesser degree.30~3~ Freshly cleaned disks or tubes were heated overnight at 140 "C to remove physically adsorbed water. The alcohol was simply heated to 120 OC in a beaker on a hotplate. The silica tubes or disks were transferred quickly from the oven to the heated alcohol,the temperature of which was kept constant. The reaction time varied from 5 to 24 h depending on the degree of reaction (and therefore the contact angle) required. After reaction the surfaceswere rinsed many times with asuitable solvent.Warm cyclohexane was used for the lower molecular weight alcohols whereas for C16-22alcohols,which are less soluble in cyclohexane, warm acetone was used. After rinsing, the surfaces were dried at 110 'C overnight, cooled in a vacuum desiccator, and then used immediately. Silica surfaces modified using this esterification procedure exhibited static water receding contact angles between 55' and 93'. Movement of the Three-phase Contact Line (Tplc). Forced Movement. Silica capillaries of internal radius (1.25m were treated, as described above, to obtain surfaces 4.5) X of various degrees of hydrophobicity. A dynamic,water recedingthree-phasecontact line was formed by simply applying nitrogen, at various pressures, to a conductivity water meniscus in a treated capillary. All experiments were recorded photographicallyusing an NAC rotating prism high-speed camera and 500 asa Ilford HP5 16mm film. The camera, supported on a heavy tripod, was completelyisolated from the capillary. The camera could record up to 10 OOO framesh; however, for the present experimentsspeeds ranging from 500 to 1200 frames/s were found to be sufficient to record the tplc dynamics. A small light source in the camera marked the film, as it was running, at a frequency of 1OOO 9-1 so that the time lapse between frames could be accurately determined. Enlarged prints were made of the relevant frames of the film, and contact angles and distances moved by the tplc were measured directly from the print. A tangent was drawn to the meniscus at the tplc, and the angle formed was measured with a protractor. The reproducibility of these dynamic, water receding contact angles, considering both angles formed by the meniscus and measured over at least eight frames, was found to be h1.5'. A cos was calculated from the difference between the cosines of the dynamic and static water receding contact angles. The error in A cos involved depended on the value of the angles but was, on average, h0.04. The (25) Hair, M. L. Infrared Spectroscopy in Surface Chemistry;Edward Arnold Ltd.: London, 1967. (26) Iler, R. The Chemistry of Silica; Wiley-Interscience: New York,
.".
1979 *"
(27) Broge, E. C. (Du Pont) U S . Patent 2736668, 1956. (28) Akabayashi, H.; Yoshida, A.; Otsubo, Y . Kogyo Kagaku Zasshi 1965,68 (3), 429. (29) Folman, M.; Yaks, D. J. C. Proc. R . SOC.London 1958, A246, 32-48. (30) Iler, R. K. (Du Pont) U.S. Patent 2657149, 1953. (31) Edwards, J.; Everett, D. H.; O'Sullivan,T.;Pangalou, I.; Vincent, B. J . Chem. SOC.,Faraday Trans. 1 1984,80, 2599-2607. (32) Kessaisa, Z.; Papirer, E.; Donnet, J. B. J. Colloid Interface Sci. 1981, 79 (I), 257-263. (33) Kessaisa, Z.; Papirer, E.; Donnet, J. B. J . Colloid Interface Sci. 1981,82 (2), 526-532. (34) Ballard,C. C.;Broge,E. C.;Iler,R. K.; St. John, D. S.; McWhorter, J. R. J . Phys. Chem. 1961,65,20-25. (35) Utsugi, H.; Nishimura, S.; Shimazaki,M. Nippon Kagaku Kaishi 1972, 11, 2007-2020. (36) Stober, W. Kolloid-2. 1956,145, 17-23. (37) Belyakova, L. D.; Kiselev, A. V. Zh. Fiz. Khim. 1959, 33, 15341545. (38) Stober, W.; Bauer, G . Die Staublungenerkrankungen 1957, 3, 31-39.
"bubble ' holder solid brass block
ootical rail
Figure 1. Schematic diagram of apparatus used for tplc kinetics experiments. distances traveled by the moving tplc were measured simplyfrom the top or bottom of each frame using an accurate ruler. The maximum error involved in this measurement was f0.2 X 10-3 m which,after scaling,produced a maximum error in the velocities calculated from these measurements of h7 X m 5-1. Magnifications were determined using the internal diameters of the capillaries which were measured, to within fO.O1 X 10" m, with vernier calipers. Vibration was minimized by the use of an optical bench consisting of a marble top and a heavy wooden base. Spontaneous Movement. These experiments were carried out in a fused silica cell (cube of internal dimension 10 X 10-3 m) secured to a solid brass block mounted on an optical rail. A glass bubble holder could be maneuvred up and down in the cell with a micrometer. The apparatus is shown in Figure 1. The hydrophobilized silica disk was placed in the cell which was then filled with conductivity water. A long glass capillary, connected to a nitrogen source, was used to blow a bubble into the bubble holder. The radius of the bubble could be varied between 0.40 and 2.5 X 10-3 m by using different sized bubble holders and different quantities of nitrogen. The bubble was lowered gently on to the modified silica surface until a slight deformation of the bubble was observed. The aqueous film between the bubble and the solid subsequently drained and ruptured, and the resultant nitrogen gas/solid contact expanded until equilibrium was established. The movement of the tplc was recorded using high-speed photography as described above. A glass capillary, of known external diameter, was photographed in the cell to determine the correct magnification. The radius of the gadsolid contact and the dynamic water receding contact angles obtained were measured directly from enlarged prints of the film, as described above. Velocities were determined, in this case, by finding the tangent to the radius versus time curve at a particular time. Errors involvedin these measurements are as described above.
Results Examples of forced and spontaneous movement are shown in Figures 2 and 3. The results are shown as graphs of A cos versus velocity, where A COS = A COS 8 = COS 8d - COS es
(1)
where 8 is the receding water contact angle and 8d and 8, refer to the dynamic and static cases, respectively. A cos is linked to the driving force, y ~ Av cos 8, at the tplc6.43 where ~ L is V the liquid-vapor surface tension. A plot of A cos versus velocity (V)was made for each static, water receding contact angle for each type of surface. The relationship between A cos and V was found to be identical for the tmcs and tbdmcs surfaces so that no distinction is henceforth made and the surfaces are therefore described as trimethylsilyl (tms) surfaces. Similarly, no difference in kinetics behavior was found between
Langmuir, Vol. 8, No. 1, 1992 183
Wetting Dynamics Studies on Silica Surfaces
ff,
f
Figure 2. Example of forced spreading. Three-phase line of contact moves as nitrogen is forced through a capillary under
pressure. Stages of movement viewed from top to bottom.
the hydrocarbon chains of length C12 to C22, so that all surfacesare classified as hydrocarbon chain (hcc)surfaces. The results of forced movement of the tplc were plotted along with those of spontaneous movement, for no differences were detected between the two types of movement, within experimental error. Thus, under the experimental conditions, any relationship between A cos and V is determined by the forces acting a t the tplc and not by the geometry of the apparatus, a feature also noted by Furthermore, there were no detectable differences in the relationship between A cos and V when the pH was varied between 2 and 11and when the concentration of KN03, a known inert electrolyte,45was varied between 0 and 10-LM. Care was taken to ensure that the static, water receding contact angle and its dynamic equivalent were measured under the same pH and ionic strength conditions, for it is well known that variations in surface charge have a substantial influence on wettability (e.g., ref 46). Once it had been established that the A cos versus V relationship was independent of pH and ionic strength, all experiments were performed in conductivity water at pH 5.6 f 0.2. (39)Hopf, W.;Geidel, T. H. Colloid Polym. Sci. 1987,265,1075-1084. (40)Jiang, T.S.;Oh, S. G.; Slattery, J. C. J. Colloid Interface Sci. 1979,69 (l),74-83. (41)Schwartz,A. M.; Tejada, S. B. NASA Contract Report CR 72728, 1970. (42)Hoffman, R. L. J. Colloid Interface Sci. 1983,94 (21,470-479. (43)Schulze, H.J. Physicochemical Elementary Processes in Flotation; Elsevier: Amsterdam, 1984; pp 169-181. (44)Mumley, T.E.;Radke, C. J.; Williams, M. C. J. Colloid Interface Sci. 1986, 109, 398-411. (45)Hunter, R.J. Zeta Potential in Colloid Science; AcademicPress: London, 1981;Chapter 7,pp 258-302. (46)Fokkink, L. G. J.; Ralston, J. Colloids Surf. 1989,36,69-76.
Figure 3. Example of spontaneous spreading. Bubble contacts hydrophobicdisk and spreads to form a stable wetting perimeter.
Stages of contact are shown from top to bottom. .6 .5 -
.4
.I
I
v)
8 Q
3.2
-
1-
, 10
20
30
40
50
60
70
I
80
90
100
V x 10'3 ms-'
Figure 4. A cos as a function of V for tms surface (&tic = 67').
Examples of A cos versus velocity plots are shown in Figures 4 and 5 for tms and hcc surfaces respectively at specific 8, values. Each A cos versus V plot represents the results of ut least four e ~ p e r i m e n t s .The ~ ~ scatter of points around each average curve falls within the anticipated experimental error. In an attempt to define a relationship between the dynamic contact angle and the velocity of movement of the tplc, a smooth, average curve was drawn through the experimental points plotted on each graph of A cos versus V . From these average curves A cos, cos 8d, and 8d were found, for each 6, a t velocities of 10, 20,30, 40, 50,60, 70,80,90,and 100 X m s-l. Plots of cos 6d versus cos 8, were then made for each surface, a t each of these velocities. An example is shown in Figure 6. A (47)Newcombe, G. M. App.Sci. Thesis, South Australian Institute of Technology, Ingle Farm, South Australia, 1989.
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194 Langmuir, Vol. 8, No. 1, 1992
A cos = 2V + B (4) 6 where B is a constant which depends only on the type of
I
/
i 1
10
30
20
50
40
€0
70
80
90
100
V~l0+3ms-~
Figure 5.
A
cos as a function of Vfor hcc surface (Ostatic = 65').
surface (i.e., tms or hcc). Furthermore, further forced tplc movement experiments a t velocities up to 200 X m s-l indicated that eq 4 still persists. The low-velocity region, below 20 X m s-l is also clearly of interest. Here there is a sharp change in A cos for a small change in V. Unfortunately the measurements in this region are too imprecise to engender confidence in any interpretation a t present. For example, a measured velocity of 7 X m s-l has an error of f100%. We are presently obtaining precise and accurate data on this region using a dynamic Wilhelmy plate technique and will report the results of this work in a future publication.
Discussion It is pertinent to consider previous work which relates to the present study. Blake and Haynes6 developed a useful theoretical treatment of dynamic contact angles. They considered the essential motion to be the sliding of molecules along the solid surface from the liquid to the vapor site of the LSV tplc. The work consumed in causing this flow is
w = YLV(coseeq- COS ed)
1
0
1
2
3
4
5
6
7
8
9
er Figure 6. cos @d as a function of cos Os for hcc (0) and tms (W) m 5-l. surfaces at V = 30 X
(5) and is used to increase or reduce the activation energy for forward or reverse molecular migration along the solid surface. O,, is the equilibrium contact angle. The master equation developed by Blake and Haynes is
COS
linear regression analysis was performed for each set of data, the results of which are shown in Table I. For each surface of known Os, a t all velocities studied between 10 and 100 X m s-l, when cos 6d is plotted against cos Os, a straight line with a gradient of 1is obtained. The relationship between cos Os and cos 6d for each surface is simply cos 6, = cos Os + C (at constant velocity)
(2)
where C is a constant or A cos = C (at constant velocity) (3) One original aim of this study was to determine the relationship between A cos and Vas a function of varying hydrophobicity of the silica surface. The results clearly indicate that A cos is a constant, regardless of Os, a t constant velocity. Above V = 20 X m s-l, the relationship between A cos and V is linear. Recalling, for example, Figure 6, the y intercept of the cos 6d versus cos Os plots, obtained from linear regression analysis a t each velocity, represents the average value of A cos. These values, for each velocity, are given in Table I and are plotted in Figure 7. m s-l, a plot of A m s-l I V I 100 X For 20 X cos versus Vfor a tms surface is a direct linear relationship with a correlation coefficient of 0.95. The line has a gradient of 2 f 0.4 s m-l. The relationship between A cos and V for the hcc surface is also linear, with a correlation coefficient of 0.99 and a d o p e of 2 f 0.4 s m-1. Within experimental error, both lines possess the same gradients; however, their positions relative to the A cos axis differ. m Therefore, for velocities between 20 and 100 x s-l, the A cos as a function of tplc velocity obeys the simple relationship
v = 2Ky sinh [mYLV T ( c o S Be, - COS Od)] where Vis the fluid velocity, K is the number of molecular displacements occurring per unit time per unit length of the LSV line, X is the average distance between sites on the solid surface, An is the surface concentration of sites, k is the Boltzmann constant, and T i s the absolute temperature. When the argument of sinh is small (7) and when it is large
V = KX exp
aT
[
A cos]
Thus, a plot of A cos versus V will be linear where eq 7 is valid and A cos versus In V linear where eq 8 holds. Simple calculation shows that for eq 7 to be used at, say, a A cos of 0.3 and An 2 5 X 10l8 sites m-2 and with a symmetric, square distribution of sites, X C 0.5 nm. This value is substantially less than that estimated by Blake and Haynes for a similar system.6 Furthermore, given a circular cross sectional area of 27.5 Az for the trimethylsilyl groups,48a An of 5 X 10l8sites m-2 corresponds to more than monolayer site coverage. Recall that in this study we have shown that the dependence of A cos on V is unaffected by the number of hydrophobic groups attached to the surface (i.e., is independent of 0,) and that the chemical nature of the group (Le., tms or hcc) does affect the A cos (V) dependence. From the Blake and Haynes theory, a dependence of A cos (V) on An, A, and K is expected. One cannot therefore reconcile their theory with the results observed here; i.e., the type of group affects the ACOS(V) relationship whereas An and X do not. It seems that the linear relationship (48)Herzberg, W. J.;Marian, J.E.;Vermeulen, T.J . Colloid Interface S C ~1970, . 33, 164-170.
Langmuir, Vol. 8, No. 1, 1992 195
Wetting Dynamics Studies on Silica S u r f a c e s
Table I. Gradient, Average A cos, and Correlation Coefficients Obtained from cos ed versus cos 8, Plots at Various Velocities, V ~~
tms surface
v x 103, m ~~~
intercept average (A cos) 0.07 0.11 0.14 0.20 0.18
gradient 1.05 1.03 1.02 0.96 1.04 1.06 1.04 1.05 0.99 0.99
s-l ~
10 20 30 40
50 60 70 80 90 100
hcc surface correlation coefficient 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99
0.19 0.21 0.22 0.28 0.28
I
I
10
XI
30
40
50
EO
i 70
80
90
100
VxIO+3ms-'
Figure 7. Average A cos (obtained from Table I) as a function surfaces. 33' IOs I78' for t h e tms of Vfor tms (w) and hcc (0) surface, and 55' IOs I93' for t h e hcc surface.
between A cos and V observed here occurs for reasons other than those inherent in the work of Blake and Haynes. It is worth noting, however, that although the experimental system to which they applied their analysis, Le., either benzene or water displacing the alternate liquid from cylindrical, glass capillaries treated with trimethylchlorosilane, the actual tplc velocities examined were generally lower ((0-10) X m s-*) than those studied here. Certainly eq 8 is not obeyed in this present study, for the observed A cos versus V dependence is linear rather than l~garithmic.~' Schwartz and Tejada7 probed the behavior of a variety of liquids spreading on metal and polymer surfaces. In no case was a linear dependence of A cos on V observed, in contrast to the pioneering, forced spreading studies of Rose and he in^.^^ These and other studies (e.g., ref 10) emphasize the surface chemical approach to wetting dynamics. In contrast, H ~ f f m a nconcentrated ~,~~ on the variation of dynamic contact angle with the capillary number of the l i q ~ i d When .~ the solid surface was clean glass, the liquids used by Hoffmang (four silicone fluids with varying viscosities) displayed equilibrium contact angles of Oo and the observed relationships between f3d and C, were identical for all fluids. In order to obtain a nonzero contact angle Hoffmann treated the surface of the glass with an industrial grade, hydrophobizing silicone agent. The curves of 8d versus C, obtained here were the same shape as previously found but were shifted along the abscissa. Hoffman did not interpret this as a surface phenomenon but simply added a shift factor to move the curves to the required position. The work of Mumley et al.44 among others provides further evidencefor the importance of the capillary number in tplc dynamics. These researchers concluded, however, (49)Rose, W.; Heins, R. W. J.Colloid Interface Sci. 1962,17,39-48.
v x 103, m 5-1 10 20 30 40 50 60 70 80 90 100
gradient 1.00 1.01 1.03 1.03 1.00 1.05 1.06 1.06 1.04 1.04
intercept average (A cos)
correlation coefficient
0.21 0.24 0.25 0.28 0.32 0.32 0.34 0.36
0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.98 0.98
0.39 0.42
that hydrodynamic effects were solely responsible for the observed dynamic contact angles. The results of this present study demonstrate this to be incorrect, a t least for experimental system examined here. Apparently both the capillary number and the chemistry of the surface are important in determining the kinetics of movement of the tplc. One should also recall that tplc kinetics data have previously been interpreted in terms of a surface friction, e.g., S c h e l ~ d k o ' smobility ~~ coefficient, Petrov and Radoev's drag term,5l Ishimi et al.'s frictional drag,52and the resistance force of Blake and Haynes? which may be regarded as a solid-liquid interfacial viscosity. The frictional force experienced by a body moving in a liquid is given by53p ~ q V *where p~ is the coefficient of friction, rl is the viscosity of the liquid, and V* is the velocity of the body moving through the fluid. If this is applied directly to the case of the friction, or opposing force, F, experienced by a moving tplc YLV
where
ps
A cos = PS9V
(9)
is the "surface friction coefficient". Thus
where C, is the capillary number. Although this disarmingly simple view of surface friction does not predict the exact relationship between A cos and V observed here, it does predict a dependence of A cos on capillary number as well as a linear relationship between A cos and V. The difference in the "surface frictional forces" between a water/air meniscus moving over a tms and a hcc surface is shown by the value of B in the equation A cos = (2 s m-')V+ B
(11) B is greater for the hcc surface than for the tms surface, possibly due to some molecular reorientation occurring as the tplc moves. Orientation changes a t the solid-liquid and solid-vapor interfaces are certainly expected on both experimental and theoretical We cannot rule rule out, however, that the B value may be influenced by (50) Scheludko,A.; Tschaljowska, S. L.; Fabrikant, A. Spec. Discuss. Faraday SOC.1970,1,112-117. (51)Petrov, J. G.; Radoev, B. P. Colloid Polym. Sci. 1981,259,753760. (52)Ishimi, K.;Hikita, H.; Esmail, M. H. AIChE J.1986,32(3),486492. (53)Alonso, M.; Finn, E. J. Physics; Addison-Wesley: Reading, MA, 1972;Chapter 7,pp 114-116. (54)McGuiggan, P. M.; Pashley, R. M. Colloids Surf. 1987,27,227287..
(55)Cohen-Stuart, M. A.; Cosgrove, T.; Vincent, B. Adu. Colloid Interface Sci. 1986,24,143-150. (56)Trau, M.; Murray, B.; Grant, K.; Grieser, F. J. Colloid Interface Sci. 1991,in press.
Newcombe and Ralston
196 Langmuir, Vol. 8, No. 1, 1992 the surface disposition of the organic film, i.e., whether or not it is i n h o m o g e n e ~ u s . ~ ~ Any consideration of molecular reorientation a t the solid surface should also include a possible change in the interfacial tensions used to define the driving force of tplc movement. The driving force, F, for movement of the tplc may be expressed as
F = YL,(c0s
ed- COS 8,) + [Y(swd
-
-Y(sL)~
[Y(SV), - YW,,]
(12)
In the absence of soluble surfactants, YLV should remain constant for both the static and dynamic cases. YSL and ysv may well vary. For short-chain, tms surfaces, any change is probably minimal but might be anticipated to be more sip'ificant for long-chain hcc surfaces. Certainly, to achieve a specific velocity requires a greater A cos on hcc surfaces compared to tms. Thus, while the surface friction coefficient, pa,is the same for each surface, the B term could well reflect changes in molecular orientation a t the SL and SV interfaces as the tplc moves; i.e. from eqs 11and 12, B is related to the second and third terms on the right-hand side of eq 12. To resolve these issues requires further work, probably involving a spectroscopic examination of both interfaces.
Summary Astudy of the kinetics of movement of the tplc over hcc and tms silica surfaces has shown the following.
1. There was no detectable difference between the results of forced and spontaneous movement; thus, the geometry of the experiment was immaterial. m s-l < V < 100 X loF3m s-l 2. For 20 X ACOS=
(2Sm-')V+B
where Bhcc> Btm,. B may be related to a change in molecular orientation occurring a t the SL and SV interfaces in the dynamic and static cases. Inhomogeneity in the organic film may influence the B value. For velocities less t h a i 20 X m s-l, no analysis could be attempted due to imprecise data. 3. Variations in Os and, therefore, the surface concentration of hydrophobic groups had no influence on the linear A cos (V)relationship. 4. Variations in pH (2-11) and ionic strength (0-lo-' M KN03 had no detectable influences on the A cos (V) relationship. The influenceof electrical double layer forces was negligible in this present study. 5. The results of this present study indicate that the kinetics of tplc movement are dependent on both hydrodynamic and surface chemical contributions. In the latter case these appear to be related to the molecular structure of the hydrophobizing agent. Acknowledgment. Financial support from the Austrialian Research Council is gratefully acknowledged. Fruitful discussions were held with Dr. Robert Hayes. Registry No. Silica, 60676-86-0.
