Determination of Contact Angles on Microporous Particles Using the

Aug 2, 2005 - probe liquids into a porous bed of silica (commercial TLC plates) using the thin-layer wicking technique. For all liquids, the differenc...
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Langmuir 2005, 21, 8319-8325

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Determination of Contact Angles on Microporous Particles Using the Thin-Layer Wicking Technique Zheng-Gang Cui, Bernard P. Binks, and John H. Clint* Surfactant & Colloid Group, Department of Chemistry, The University of Hull, Hull HU6 7RX, United Kingdom Received April 20, 2005. In Final Form: July 6, 2005 The properties of particle-stabilized emulsions, especially with regard to phase inversion, are very dependent on the contact angle that the particles experience at the oil-water interface. For the very small particles used for such emulsions (often a few tens of nm), it is impossible to measure this contact angle directly. Its value could be calculated if it were possible to determine the components of the solid surface free energy. To establish a method suitable for such particles, we have investigated the imbibition of five probe liquids into a porous bed of silica (commercial TLC plates) using the thin-layer wicking technique. For all liquids, the difference between wicking rate for bare plates and for those pre-contacted with the vapors is large but it is not due to an advancing angle effect on bare plates. Our analysis shows that it is due to the diversion of flowing liquid into blind pores which are already filled in the pre-contacted case. Thus a new model is proposed describing wicking in a porous medium with very small blind pores by introducing a parameter into the Washburn equation that corrects for this capillary condensation effect. The parameter needed is determined independently using gravimetric adsorption measurements. When this modified Washburn equation is used, the difference between advancing and receding contact angle is actually quite small. When the averages are used as the Young’s contact angles, values for the surface energy components of silica are obtained that are completely consistent between the five liquids and have magnitudes expected for this type of silica surface.

Introduction Small colloidal particles are able to adsorb at an oil/ water interface and can act alone (for example in the absence of surfactant) as emulsion stabilizers.1-3 The type of emulsion formed depends on the wettability of the particles at the oil/water interface.4 In selecting such particles for a given oil-water system, the contact angle made by the oil/water interface at the particle surface is a key parameter.4 The direct measurement of contact angles is straightforward only when applied to smooth flat surfaces. Our primary interest is in particles that are very efficient emulsion stabilizers and these often have diameters of only a few tens of nanometers. For powdered solids, some researchers have attempted to obtain smooth surfaces by pressing the particles into disks. However, no matter how firmly compressed, the disks still have pores between the particles, invariably resulting in unstable and unreliable contact angles.5 There are a number of studies that allow the determination of contact angles directly on particles with diameters in the micrometer range. One of these is the film trapping method6 in which a spherical particle is trapped in a film of equilibrium thickness smaller than the particle diameter. Analysis of the interference patterns for reflected monochromatic light allows the meniscus shape, and hence the contact angle, to be determined. In the gel trapping method,7 particles at an air-water or * To whom correspondence should be addressed. Tel: +44(0)1482 465456. E-mail: [email protected]. (1) Binks, B. P.; Lumsdon, S. O. Langmuir 2000, 16, 8622. (2) Ashby, N. P.; Binks, B. P. Phys. Chem. Chem. Phys. 2000, 2, 5640. (3) Binks, B. P.; Lumsdon, S. O. Langmuir 2001, 17, 4540. (4) Binks, B. P.; Clint, J. H. Langmuir 2002, 18, 1270. (5) Costanzo, P. M.; Wu, W.; Giese, R. F., Jr.; van Oss, C. J. Langmuir 1995, 11, 1827. (6) Hadjiiski, A.; Dimova, R.; Denkov, N. D.; Ivanov, I. B.; Borwanker, R. Langmuir 1996, 12, 6665. (7) Paunov, V. N. Langmuir 2003, 19, 7970.

oil-water interface are trapped by gelling the water phase and then forming on top of this a removable cast of polymerizable silicone oil. Observation of the trapped particles in this cast by scanning electron microscopy allows the contact angle to be determined from simple geometrical considerations. A method based on an atomic force microscopy probe measures the force acting on a single spherical particle attached to the microscope cantilever as the particle is pushed through the liquid interface.8,9 The contact angle can be deduced from the force-distance curve. Finally, a method has been developed10 that uses scanning confocal microscopy to observe individual particles floating at the air-water interface. The contact angle is deduced from the ratio of the diameter of the three-phase contact line to that of the particle. Except for the gel trapping technique, all of these direct methods require particle diameters of at least 1 µm. A so-called “thin-layer wicking” technique proposed by Giese et al.11 has been found to be useful for the determination of contact angles on small particles and, when used with several probe liquids, for the estimation of the components of the solid surface free energy. In this method, a thin layer of the powder is deposited as a coating on a glass slide and the rate of wicking of pure liquids along this layer is studied. With this technique, Li et al.12,13 determined the surface free energy of talc particles modified by octadecylamine and contact angles on hydrotalcite particles; Costanzo et al.5 determined contact (8) Preuss, M.; Butt, H.-J. Langmuir 1998, 14, 3164. (9) Gillies, G.; Bu¨cher, K.; Preuss, M.; Kappl, M.; Butt, H.-J.; Graf, K. J. Phys. Condens. Matter 2005, 17, S445. (10) Mohammadi, R.; Amirfazli, A. J. Dispersion Sci. Technol. 2004, 25, 567. (11) Giese, R. F.; Costanzo, P. M.; van Oss, C. J. J. Phys. Chem. Miner. 1991, 17, 611. (12) Li, Z.; Giese, R. F.; van Oss, C. J.; Yvon J.; Cases, J. J. Colloid Interface Sci. 1993, 156, 279. (13) Li, Z.; Giese, R. F.; van Oss, C. J. Langmuir 1994, 10, 330.

10.1021/la0510578 CCC: $30.25 © 2005 American Chemical Society Published on Web 08/02/2005

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angles on synthetic hematite. Chibowski et al.14-21 further developed this technique and applied it to the determination of surface free energy components of several types of particulate materials. Depending on measurement conditions, the contact angle can be distinguished as equilibrium or Young’s contact angle and nonequilibrium or dynamic contact angles. The latter can be further differentiated as advancing and receding contact angles, with the difference called “contact angle hysteresis”.22 Theoretically, the thinlayer wicking technique is based on Washburn’s equation23 describing liquid penetration through capillaries. Studies on the capillary wicking showed that even with liquids which can completely wet the capillary surface the contact angle calculated from the Washburn equation, usually described as “apparent contact angle”, is not the Young’s contact angle.24-29 In the case of drainage, the apparent contact angle corresponds to the dynamic receding angle determined on a flat surface,26,29 whereas in the case of imbibition (advancing), the apparent contact angle is always larger than Young’s angle.24-29 Similar results have been shown by studies on the dynamic spreading of drops on flat surfaces.30 The advancing contact angle in a capillary wicking process is found to be an increasing function of capillary number or penetration velocity22,24,26,29,31 and a decreasing function of capillary radius.26 On the other hand, independence of the advancing contact angle on penetration velocity25,32 and geometry25,33 was also reported. By comparing advancing contact angles measured directly on a smooth flat surface coated with hematite and that obtained indirectly by thin-layer wicking of hematite particles, Costanzo et al.5 showed that both are coincident within a few degrees. Yang et al.,28 however, showed that although the horizontal one-dimensional capillary penetration of liquid into packs of monodispersed spherical beads of various surface energy obeyed the Washburn equation, deviation was found between contact angles calculated using the cylindrical tube model of Washburn and the known values. Chibowski et al.18,19,21 concluded that the contact angle obtained by the thin(14) Chibowski, E.; Holysz, L. Langmuir 1992, 8, 710. (15) Holysz, L.; Chibowski, E. Langmuir 1992, 8, 717. (16) Chibowski, E.; Gonzalez-Caballero, F. Langmuir 1993, 9, 330. (17) Chibowski, E. Solid Surface Free Energy Component Determination by the Thin-Layer Wicking Technique. In Contact Angle, Wettability and Adhesion; Mittal K. L., Ed.; VSP: The Netherlands, 1993; pp 641-662. (18) Chibowski, E.; Holysz, L. J Adhesion Sci. Technol. 1997, 11, 1289. (19) Teixeira, P.; Azeredo, J.; Oliveria, R.; Chibowski, E. Colloids Surf., B 1998, 12, 69. (20) Chibowski, E. Thin-Layer Wicking-Methods for the Determination of Acid-Base Free Energies of Interaction. In Acid-Base Interaction: Relevance to Adhesion Science and Technology; Mittal, K. L., Ed.; VSP: The Netherlands, 2000; Vol. 2, pp 419-437. (21) Chibowski, E.; Perea-Carpio, R. Adv. Colloid Interface Sci. 2002, 98, 245. (22) Berg, J. C. ed., Surfactant Science Series; Marcel Dekker: New York, 1993; Vol. 49, Chapter 1. (23) Washburn, E. W. Phys. Rev. Ser. 2, 1921, 17, 273. (24) Hoffman, R. L. J. Colloid Interface Sci. 1975, 50, 228. (25) Fisher, L. R. J. Colloid Interface Sci. 1979, 69, 486. (26) Legait, B.; Sourieau, P. J. Colloid Interface Sci. 1985, 107, 14. (27) Yang, Y.-W.; Zografi, G.; Miller, E. E. J. Colloid Interface Sci. 1988, 122, 24. (28) Yang, Y.-W.; Zografi, G.; Miller, E. E. J. Colloid Interface Sci. 1988, 122, 35. (29) Van Remoortere, P.; Joos, P. J. Colloid Interface Sci. 1991, 141, 348. (30) Neogi, P.; Miller, C. A. J. Colloid Interface Sci. 1983, 92, 338. (31) Jiang, T.-S.; Oh, S.-G.; Slattery, J. C. J. Colloid Interface Sci. 1979, 69, 74. (32) Morrow, N. R.; Nguyen, M. D. J. Colloid Interface Sci. 1982, 89, 523. (33) Chen, J.-D. J. Colloid Interface Sci. 1988, 122, 60.

Cui et al. Table 1. Densities, Viscosities, and Surface Tensions of Penetrating Liquids at 25 °C

liquid

density/ g cm-3

viscosity/ mPa s

surface tension/ mN m-1

n-octane n-nonane n-decane n-dodecane water 1-bromo-naphthalene ethylene glycol di-iodomethane formamide

0.69862 0.71375 0.72635 0.74518 0.99708 1.48 1.113 3.325 1.130

0.5136 0.6676 0.8588 1.374 0.8904 4.690 16.77 2.682 3.116

21.14 22.38 23.37 24.91 71.97 44.4 48.3 50.8 58.2

layer wicking technique is quite different from Young’s contact angle, and the surface free energy components calculated based on such contact angle are not the true values. Based on whether a liquid can or cannot completely wet the solid surface and whether a duplex film (thick enough that its outermost layer resembles bulk liquid) is present or not ahead of liquid penetration, Chibowski et al.14,16-18,20,21 distinguished four distinct wicking systems: (1) completely wetting and with a duplex film; (2) completely wetting but without a duplex film, (3) incompletely wetting and with a duplex film; and (4) incompletely wetting and without a duplex film. With commercial silicagel plates for TLC analysis as model systems, Chibowski et al. obtained higher penetration velocity for system (1) than for system (2) and proposed a free energy change expression different from that derived by Good34,35 to explain their results. Good34,35 has shown theoretically and experimentally that the capillary penetration in system (2) would not be slower than that in system (1). It seems that the thin-layer wicking technique is more complicated than expected and the determination of contact angle or surface free energy components by this technique is still a subject of debate. For relevance to emulsion stabilization by colloidal particles, one should determine contact angles on powdered solids at the oil/water interface rather than a liquid/ air interface, and this adds a further complication to the experiments. Wicking methods with one liquid displacing another would be almost impossible to carry out and to interpret. An alternative approach is to use a wicking technique with a series of single probe liquids against air to determine the components of the solid surface free energy as was done by Chibowski et al. but then to use these to calculate the appropriate oil/water contact angle by the methods outlined by Binks and Clint.4 In this paper, the thin-layer wicking technique is theoretically and experimentally studied with commercial silicagel plates as model systems and some new findings are reported which we interpret in terms of the uptake of liquid into “blind” pores that do not form part of the system of through channels. Experimental Section Materials. HPLC grade n-heptane from Rathburn, n-octane of 98+% from Lancaster, n-nonane of 99% (GC) from Fluka, n-decane of 99% from Lancaster, and n-dodecane of 99+% from Avocado were purified by passing them several times through a column filled with alumina to remove polar impurities. n-Hexadecane with purity 99% (GC) from Aldrich was used as received. Their densities, viscosities and surface tensions at 25 °C are listed in Table 1. Ethylene glycol of 99+% (GC) from Aldrich, 1-bromonaphthalene of 96% from Acros, di-iodomethane (34) Good, R. J. J. Colloid Interface Sci. 1973, 42, 473. (35) Good, R. J.; Lin, N.-J. J. Colloid Interface Sci. 1976, 54, 52.

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Figure 1. Schematic diagram of the wicking apparatus. The whole apparatus is housed in a transparent plastic (Perspex) box in which the temperature is controlled by an “Air Therm” air thermostat (World Precision Instruments) to 25 ( 0.1 °C. of 99+% from Acros, and formamide of 99% from Aldrich were used as received. Their viscosities at 25 ( 0.1 °C were determined with an Ostwald-type viscometer using as reference water from a Milli-Q water purification apparatus. The surface tensions are from various literature sources. Milli-Q water is also used as a wicking liquid. Silica gel 60 F254 thin-layer chromatography plates were from Merck and had a coating thickness of 250 µm and dimensions 200 × 200 mm. The particles in the coating have diameters in the range 5-20 µm and contain pores with average diameter 60 Å. For use in the wicking apparatus, they were cut into smaller plates of dimensions 25 × 75 mm, dried at 150 °C for 1 h, and stored in a desiccator containing dried silica gel particles as desiccant. Methods. The apparatus used for wicking measurements is shown schematically in Figure 1. A sheet of glass 300 × 200 mm is used as the base-plate, leveled with three adjustable screws to eliminate possible effects of gravity. The liquid reservoir comprises a small glass box 60 × 40 × 6 mm filled with cotton wool which has been washed three times with the wicking liquid. At one end the wall height is only 3 mm to form a slit-shaped opening of 40 × 3 mm into which is fitted the coated chromatography plate. At least 5 cm3 of liquid can be held in the reservoir of which less than 0.3 cm3 is used in a single wicking experiment. Most of the box is covered by a glass plate held to the base-plate by two screws (not shown). To prevent evaporation during wicking experiments, the rest of the box is covered by a tight fitting glass plate that can be removed easily for adding the wicking liquid. The thin-layer plate rests on a support 3 mm thick so that it can fit into the slit and be horizontal and is enclosed in a glass cover to minimize evaporation. The glass cover, in the form of a shallow box, has markings at 10 mm intervals along two edges to allow measurement of the time required for the liquid frontier to penetrate a given distance during the wicking process. It is important for the thin-layer plate not to be in contact with the cover glass to avoid preferential wicking pathways. Similarly the support for the plate must not contact the aluminum box as this allows liquid to leak out of the reservoir by capillary flow. The amount of preadsorbed liquid on the plates ()Vmax for equilibration with saturated vapor) was determined by weight difference of the plate before and after contact with the liquid vapor in a closed container. The total void volume of the porous plate Vb is calculated from the weight difference before and after complete wicking. Mass changes after pre-contact with vapor, or after the wicking experiment, ranged between 0.1 and 0.3 g and were measured on a balance with a precision of 0.1 mg (i.e., 0.2 mg for any difference). The precision of these liquid contents per slide is thus around 1%. For highly volatile liquids such as octane, the plate was covered with a weighed glass slide of the same size to prevent any evaporation during weighing. Evaporation of absorbed vapor (mass loss) was not noticed during the time on the balance. The plate was then immediately placed in the wicking apparatus. The wicking apparatus was housed in a transparent plastic cabinet in which the air temperature was controlled to 25 ( 0.1 °C using an “Air Therm” (World Precision Instruments). To start a wicking experiment the weighed plate is put on the glass support and a timer is started at the moment that the plate is moved toward the reservoir opening to make contact with the penetrating liquid in the reservoir. Then the plate is covered immediately

Figure 2. Plots according to the Washburn equation for wicking of n-octane (squares), n-nonane (circles), and n-decane (triangles) through thin layer silica gel chromatography plates preconditioned with the corresponding saturated vapor for 24 h (octane and nonane) or 48 h (decane). Table 2. Effective Radius Reff Calculated for Precontacted Silica Gel Plates from Eq 1 Based on Wicking with Different Alkanes at 25 °Ca alkane

(dx2/dt)/cm2 s-1

Reff/µm

n-octane n-nonane n-decane n-dodecane

0.0985 ( 0.0049 0.0798 ( 0.0040 0.0659 ( 0.0033 0.0304 ( 0.0015

0.493 ( 0.025 0.501 ( 0.025 0.506 ( 0.025 0.336 ( 0.017

a Errors are shown as standard deviations based on a separate study of 21 repeat experiments (results not reported in the present paper).

with the marker cover to avoid evaporation of the wicking liquid. Readings of time are taken when the liquid front reaches the calibrated distance marks.

Results and Discussion Effective Wicking Radius for Silica Gel Plates. Figure 2 shows the plots of x2 against t for octane, nonane and decane wicking into pre-contacted plates, where x is the distance from the liquid reservoir travelled in time t by the advancing liquid front. Pre-contact with the saturated vapor was for 24 h for octane and nonane, and 48 h for decane. The graphs are accurate straight lines showing that the wicking process obeys the Washburn equation (see later). The wicking rate decreases with increasing alkane chain length because the increase in liquid viscosity outweighs the increase in liquid surface tension. From the gradients in Figure 2 and assuming that the contact angle is zero, it is possible to calculate the effective pore radius (Reff) using eq 1 (see later). The results for these three alkanes and also for n-dodecane are shown in Table 2. For octane, nonane and decane, the values of Reff agree to within about 1% giving an average of 0.500 ( 0.006 µm, where the error has been expressed as a standard deviation. This indicates that the assumptions of zero contact angle and identical flow channels apply to these experiments. In contrast, the result for n-dodecane (marked in italics) is completely out of line (Reff ) 0.336 µm) despite a contact time with saturated vapor of 48 h. It is our opinion that this discrepancy is due to an incomplete equilibration with vapor and this is confirmed by the more detailed study that follows, starting with a comparison of wicking through bare and preconditioned plates. Wicking Velocity Difference between Bare and Precontacted Plates. Figure 3 shows wicking plots for n-octane in silica gel plates that are bare or precontacted with saturated vapor for 24 h. This very significant

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Figure 4. Schematic drawing of the proposed model for the pore space in thin-layer plates. Through channels of effective radius Rp account for a pore volume Vp. The total pore volume including the blind pores is Vb.

Figure 3. Wicking of n-octane into silica gel chromatography plates. Diamonds, bare plates; squares, plates preconditioned by exposure to n-octane vapor for 24 h.

difference as a result of preconditioning was also seen with other alkanes. If the slower penetration rate for bare plates is attributed to the operation of an advancing contact angle (θa) during this process, then a value of θa > 50° is calculated from eq 1 (see later) assuming the flow channels and effective capillary radius is the same as for the precontacted plate. This is felt to be a totally unacceptable advancing contact angle for octane on silica gel particles. Octane is a low surface tension (21 mN/m) liquid which wets most surfaces except for fluorinated ones. Alkanes including octane are known to spread on silica,36 i.e., the equilibrium contact angle is zero. Therefore for octane wicking into silica gel plates, the maximum advancing angle, calculated by the method of Van Remoortere and Joos,29 based on the average penetration velocity, liquid viscosity and surface tension, is approximately 3°. Because of this we feel that an advancing angle >50° is unacceptable. In our opinion the large difference is due to the existence of “blind pores” that contribute to the liquid uptake but which do not form part of the matrix of through channels, and an analysis of this situation is presented below. This model is chosen because the morphology of the silica gel thin-layer chromatography plates is wellknown. They consist of particles with diameters in the range 5-20 µm which contain micropores with diameter around 6 nm. Because of this, it is felt that the through pores will be the spaces between the particles and the blind pores will be the micropores within the particles. With the vapor saturation levels used in this work for preconditioning the plates, only the micropores will be expected to fill. Adsorption will be expected to take place on the walls of the through pores but this will cause an insignificant change in the diameter of these large pores. Strong evidence for the validity of this model is provided by comparing the volume of liquid condensed from almost saturated vapor with that taken up by the plates at the end of the wicking experiment, when the liquid front has traversed the whole plate. The manufacturers specify a pore volume (for the 6 nm pores) of 0.65 mL/g and a bulk density of the coating of 0.4 g/mL. These values correspond to a volume fraction of micropores equal to 0.26. In our experiments, the volume of solvent taken up at the end of the wicking process corresponds to a total volume fraction (micropores plus large pores between particles) equal to 0.70. The ratio of these two volume fractions is 0.26/0.74 ) 0.35. From the results of 21 separate runs using octane (not reported in the present paper), the average volume per plate of liquid taken up from almost saturated vapor (Vmax) is 0.131 mL and the average total (36) Gee, M. L.; Healy, T. W.; White, L. R. J. Colloid Interface Sci. 1989, 131, 18.

volume after wicking (Vb) is 0.332 mL. The ratio of these volumes is 0.39, in reasonable agreement with the estimated value of 0.35 based on the model. Theoretical Model For a pure liquid wicking into the porous bed, we first treat the flow as if in a system of parallel capillaries obeying the Washburn equation. For pre-contacted plates equilibrated with saturated vapor23

(dx2/dt)p ) Rpγ/2η

(1)

and for bare plates

(dx2/dt)b ) Rbγ/2η

(2)

where Rp and Rb are the effective radii of the pores in the two cases and γ is the surface tension of the liquid of viscosity η. Therefore

(dx2/dt)p (dx2/dt)b

)

Rp Rb

(3)

But dx2/dt ) 2x(dx/dt) so that, for a liquid front at the same position x

(dx2/dt)p 2

(dx /dt)b

)

(dx/dt)p (dx/dt)b

)

Rp Rb

(4)

To proceed further we introduce a model of the porous bed illustrated in Figure 4. The void space consists of ‘through channels’ in which liquid will flow for all conditions, and small “blind pores” which fill, possibly by capillary condensation, and then play no further part in the overall liquid flow. If Vb is the total volume available to wicking liquid in a plate of length l, and Vp is the void volume remaining after filling of blind capillaries with condensed liquid, then the cross-sectional areas of void space available for wicking liquid are Vb/l for bare plates and Vp/l for pre-contacted plates. However, the flow rate in the through channels (i.e., not involving the blind pores) is the same in the two cases since, according to our model, the radius of these channels is the same and the capillary driving force is the same. Therefore, at the same distance x

Vp(dx/dt)p ) Vb(dx/dt)b

(5)

Therefore from eqs 2, 4, and 5, we have

(dx2/dt)b ) RpKpγ/2η

(6)

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Table 3. Wicking of n-Dodecane into Silica Gel Plates Partly Preconditioned with n-Dodecane Vapor Vads/cm3

Vmax/cm3

Vb/cm3

K

(dx2/dt)/cm2 s-1

Rp/µm

0.0000 0.0383 0.0539 0.0969 0.1275

0.1294 0.1309 0.1373 0.1292 0.1327

0.3282 0.3320 0.3483 0.3277 0.3366

0.606 0.685 0.717 0.860 0.975

0.02535 0.02814 0.02982 0.03530 0.04083

0.474 0.477 0.480 0.474 0.479

where

Kp ) Rb/Rp ) Vp/Vb

(7)

More generally, for a volume Vads of liquid adsorbed from the vapor at conditions less than saturation

(Vb - Vads)(dx/dt) ) Vp(dx/dt)p

(8)

so that from eqs 6-8 we can write a general equation for wicking in a bed of microporous particles where the liquid wets the solid surface

dx2/dt ) RpKγ/2η

(9)

K ) Vp/(Vb - Vads)

(10)

where

When the liquid cannot completely wet the surface, a contact angle θ will be present. The driving force is still proportional to the Laplace capillary pressure and thus the following general wicking equation can be derived

dx2 RpK ) γ cos θ dt 2η

(11)

In summary, for wicking in a porous plate of the type used in thin-layer chromatography, with a liquid that forms a finite contact angle, deviations from the Washburn equation could result from both capillary condensation (different values of K) and the existence of a finite contact angle, θ. To determine contact angle from wicking experiments, it is thus necessary to know K in eq 11. A major advantage of the approach outlined above is that K, as defined by eq 10, can be measured independently using the gravimetric adsorption technique described earlier. To test this approach, silica gel plates were prepared with different amounts of preadsorbed n-dodecane by placing in a desiccator containing a dish of liquid ndodecane to allow transfer via the vapor for different lengths of time. For each plate, the volume of liquid adsorbed Vads is calculated from the difference in weight before and after this pre-contact. By weighing the plates at the end of the wicking experiment, it is possible to calculate the total volume of pore space Vb. Because of the low volatility of n-dodecane and hence the difficulty of reaching saturation, the maximum volume of capillary condensed liquid Vmax was assumed to be the same as that for n-octane determined gravimetrically in the same way by leaving the plates in the desiccator for sufficient time for complete equilibration with the saturated vapor. The volume of the through channels Vp () Vb - Vmax) can then be calculated and hence K determined from eq 10. The results for n-dodecane are shown in Table 3. For all extents of preadsorption, the wicking plots of x2 against t were accurately linear. The preadsorbed liquid covered the range from zero (bare plates) to almost complete saturation. Over this range, K increases from 0.6 to almost 1, and as a result, the wicking rates vary considerably.

The notable feature of the results is the near constancy of the radius of through channels (Rp), calculated using eq 11 and assuming θ ) 0. The correct interpretation of the blind pore effect appears to overcome the difficulty that was found with n-dodecane in Table 2 where the filling of the blind pores was not complete for this alkane because of its low vapor pressure and long equilibration time through the vapor phase. Determination of Contact Angles with Probe Liquids. For the determination of solid surface free energy components, it is necessary to measure contact angles made with the solid by probe liquids such as water, glycerol, ethylene glycol, and formamide and nonpolar liquids such as 1-bromonaphthalene and di-iodomethane. Except for glycerol, whose viscosity is too high, all of the other liquids were found to be useful for such measurements by wicking in the silica gel plates. For each plate, the radius of the through channels, Rp, was determined first using n-octane with presaturated plates. The plates were then thoroughly dried out in an oven at 150 °C and stored in a desiccator until used. Wicking experiments were then carried out with the various probe liquids on both bare and pre-contacted plates. The results are summarized in Table 4 in which eq 11 has been used to calculate contact angle. It was assumed that bare plates give advancing angles and pre-contacted ones give receding angles, regardless of the extent of the preadsorption by capillary condensation. This is seen to be acceptable except in the case of one run (marked in italics) using 1-bromonaphthalene for which Vads ) 0.0259 cm3. The value of θ obtained in this case is more in line with the advancing angles, presumably because of the quite small preadsorbed amount. Accordingly, this value has been omitted from the average. A notable feature of the contact angle results for the five probe liquids, listed in Table 4, is the very small difference between advancing and receding angles, except for ethylene glycol. This gives confidence in the calculation of an “equilibrium” contact angle θ0 using the equation37

cos θ0 ) (cos θa + cos θr)/2

(12)

Solid Surface Free Energy Components for Chromatographic Silica Gel. We shall illustrate the use of contact angle data for the determination of the components of solid surface free energy by using the approach of Owens and Wendt.38 In this approach, the total surface tension of a liquid or a solid γi can be divided into a dispersion force component γdi and a polar component γpi

γi ) γdi + γpi

(13)

Expressing interfacial tensions by means of geometric mean combining rules, and introducing Young’s equation, enables the following equation to be derived38 for the contact angle θ that a probe liquid (l) makes with a solid (s) surface

γl(1 + cos θ)/2 ) xγds γdl + xγps γpl

(14)

Values for contact angle for two different probe liquids thus enable values for the two components of the solid surface free energy, γds and γps to be determined by simultaneous solution of the two versions of eq 14. Only one of these two probe liquids may be apolar. (37) Everett, D. H. Pure Appl. Chem. 1980, 52, 1279. (38) Owens, D. K.; Wendt, R. C. J. Appl. Polym. Sci. 1969, 13, 1741.

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Table 4. Wicking of Probe Liquids into Both Bare and Partially Precontacted Silica Gel Plates Vads/cm3

Vmax/cm3

Vb/cm3

K

0.0856 0.1309 0.1324 0.1298 0.1147 0 0 0 0

0.1254 0.1287 0.1346 0.1300 0.1279 0.1340 0.1281 0.1413 0.1454

0.3181 0.3265 0.3415 0.3296 0.3244 0.3399 0.3249 0.3584 0.3688

0.829 1.011 0.989 0.999 0.937 0.606 0.606 0.606 0.606

0.0784 0.1143 0.1224 0 0 0

0.1231 0.1202 0.1212 0.1287 0.1264 0.1201

0.3123 0.3048 0.3074 0.3263 0.3205 0.3046

0.1327 0.1285 0.0259 0 0

0.1294 0.1286 0.1267 0.1284 0.1326

0.0965 0.1129 0.0298 0 0 0.1291 0.1010 0.0898 0.0901 0.1111 0 0 0

(dx2/dt)/ cm2 s-1

Rp/µm

θ/deg

Ethylene Glycol 0.00505 0.00615 0.00575 0.00598 0.00579 0.00350 0.00339 0.00347 0.00328

0.424 0.417 0.417 0.424 0.417 0.417 0.424 0.428 0.427

2.4 0 14.9 11.6 0 15.9 23.5 21.7 28.3

0.809 0.969 1.006 0.606 0.606 0.606

Di-iodomethane 0.0256 0.0301 0.0323 0.0212 0.0190 0.0191

0.417 0.415 0.415 0.455 0.419 0.431

36.8 37.9 36.1 35.8 37.7 39.6

0.3283 0.3261 0.3214 0.3256 0.3362

1.017 0.999 0.659 0.606 0.606

1-Bromonaphthalene 0.0187 0.0183 0.0116 0.0115 0.0112

0.409 0.408 0.411 0.435 0.422

18.4 18.4 23.4 22.4 22.4

0.1347 0.1251 0.1304 0.1299 0.1323

0.3417 0.3173 0.3308 0.3294 0.3356

0.844 0.940 0.666 0.606 0.606

Formamide 0.0275 0.0312 0.0212 0.0193 0.0191

0.425 0.428 0.444 0.448 0.440

34.8 34.0 39.9 40.6 39.9

0.1424 0.1322 0.1384 0.1354 0.1201 0.1416 0.1283 0.1319

0.3612 0.3354 0.3510 0.3433 0.3046 0.3592 0.3254 0.3345

0.943 0.867 0.814 0.821 0.953 0.606 0.606 0.606

Water 0.0568 0.0612 0.0488 0.0497 0.0617 0.0364 0.0405 0.0403

0.440 0.436 0.425 0.425 0.428 0.440 0.453 0.425

68.8 66.4 69.6 69.4 67.9 68.6 68.6 67.2

Table 5. Components of Surface Tension of Probe Liquids (Taken from Reference 40) and Their Corresponding Equilibrium Contact Angles θ0 Calculated from Eq 11 Using Data from Table 4 from Wicking into Chromatographic Silica Gel probe liquid

γdl /mJ m-2

γpl /mJ m-2

θ0/ deg

1-bromonaphthalene di-iodomethane ethylene glycol formamide water

44.4 50.8 29.0 39.0 21.8

0 0 19.0 19.0 51.0

20.4 37.3 16.3 37.4 68.3

θa/deg

θr/deg 6(6

22 ( 4

36.9 ( 0.7 37.7 ( 1.6

18.4 22.4

34.4 ( 0.4 40.3 ( 0.4

68.4 ( 1.2

68.1 ( 0.7

by Gonza´lez-Martı´n et al.41 using a similar wicking technique and the same chromatographic plates. Their solid surface energy calculations were based on advancing angles for probe liquids into bare plates. In both cases, the polar term appears low for such a hydrophilic solid as silica gel. One factor may be the presence of the polymeric binder used in the manufacture of the thin-layer chromatography plates which is known to influence the speed of uptake of water by the plates. Correct allowance for the effect of blind pores produces a consistent set of data for the probe liquids. An attempt

We prefer a method that simultaneously maximizes the fit of eq 14 to the contact angles for all five probe liquids.39 The data for the surface tension components of these liquids were taken from the compilation by van Oss40 and are listed in Table 5 together with our values for the contact angles. The result of this fitting is illustrated in Figure 5 which shows the best fit to γds and γps . The “goodness of fit” is the reciprocal of the root-mean-square difference between experimental contact angles and those calculated for each combination of the solid surface free energy components (x and y axes) for all five probe liquids. The final values obtained by this method for chromatographic silica gel are γds ) 41.5 and γps ) 8.0 mJ m-2. These values and γAB agree well with values for γLW s s (42.9 and 6.5 mJ -2 m calculated by the method of van Oss et al.39) obtained (39) Clint, J. H.; Wicks, A. C. Int. J. Adhesion Adhesives 2001, 21, 267. (40) van Oss, C. J., Interfacial Forces in Aqueous Media; Marcel Dekker: New York, 1994; Chapter 13.

Figure 5. Least-squares method for determination of dispersion and polar components of the surface free energy of chromatographic silica gel by simultaneously fitting the contact angle data for all five probe liquids.

Contact Angles on Microporous Particles

has been made by Lockington and Parlange42 to allow for the neglect of dynamic saturation gradients in the analysis of wicking data. Our much simpler analysis assumes that the saturation of pores ahead of the liquid front is at all points the same as that which results from preequilibration with the vapor. Although this is unlikely to be strictly true, especially for the more volatile liquids, it does not appear to be seriously in error judging by the consistency of data for a wide range of presaturation levels and the consistency within the set of liquids. Conclusions For thin-layer wicking in porous plates with blind pores, the liquid penetration velocity is lower for bare plates (41) Gonza´lez-Martı´n, M. L.; Jan˜czuk, B.; Labajos-Broncano, L.; Bruque, J. M.; Gonza´lez-Garcı´a, C. M. J. Colloid Interface Sci. 2001, 240, 467. (42) Lockington, D. A.; Parlange, J.-Y. J. Colloid Interface Sci. 2004, 278, 404.

Langmuir, Vol. 21, No. 18, 2005 8325

than for plates pre-contacted with vapor. The difference is due to filling of the blind pores with liquid (probably by capillary condensation) and not due to a higher advancing contact angle. For contact angle determination, a correction must be applied for this effect, but it can be determined independently using gravimetric adsorption measurements. Using this analysis, the difference between advancing and receding contact angles turns out to be small. Using five probe liquids, the dispersion and polar components of the solid surface free energy for chromatographic silica are determined to be γds ) 41.5 and γps ) 8.0 mJ m-2. Acknowledgment. The authors thank the China Scholarship Council for the award to Zheng-Gang Cui of a fellowship under the Distinguished Visiting Scholar Program of the Chinese Government. LA0510578