Langmuir 1991, 7, 2748-2755
2748
Physical Principles of Marangoni Drying J. Marra' and J. A. M. Huethorst Philips Research Laboratories, P.O. Box 80 000, 5600 J A Eindhoven, The Netherlands Received March 4, 1991. I n Final Form: June 3, 1991 An account is given about the relevant physical phenomena that govern Marangoni drying of hydrophilic surfaces. Marangoni drying is possible when vapor of a water-soluble organic liquid absorbs into the water meniscus against a partially immersed solid substrate. Because of the meniscus curvature, vapor absorption induces a surface tension gradient along the meniscus. The gradient causes the meniscus to partially contract via a Marangoniflow and assumean apparent finite contact angle. Experimentalevidence is presented which shows that the magnitude of the observed contact angle reflects the magnitude of the induced surfacetension gradient. The surfacetension gradient enablesa hydrophilicsurfacetobe withdrawn from water with a visibly dry surface. After Marangoni drying, only a very thin water film remains on the surface. Ita thickness depends on the nature of the organic vapor, the surface roughness, and the substrate withdrawal speed. Under suitably chosen conditions, this thickness is more than 1 order of magnitude smaller than the remaining film thickness after conventional spin drying. This ensures Marangoni dryingto be an intrinsically much cleaner dryingprocess with important technological applications.
Introduction A proper handling on thin liquid films on solid substrates is an issue of considerable technological importance. On the one hand, the spinning of a liquid film that contains dissolved or suspended materials is widely applied to enable a homogeneous coating of the substrate. Meyerhofer' gave a quantitative description of such coating processes, involving both the hydrodynamics of the spinning and the simultaneous solvent evaporation. According to his theory, the deposition from solution is primarily due to solvent evaporation during spinning. On the other hand, industry often faces the challenge of removing liquid films from hydrophilic substrates for the purpose of drying them without simultaneously inducing contamination. A well-known example comes from the IC industry, where water has to be removed from ultraclean silicon wafers after a wet processing sequence.2 When wafers are withdrawn from the final rinse bath, a water film remains on the surface. The thickness ho of this film is a function of the substrate withdrawal speed UO, the liquid viscosity 9, the liquid density p, and the surface tension y according to3
h, = 0.944[(aU,)2/3/y'/s(pg)'/2] (1) Thus, for uo = 10 mm/s, ho will be close to 7 pm. The IC industry usually removes this water film with spin drying. However, according to Meyerhofer' some degree of surface contamination will inevitably occur if the water is not scrupulously purified. Obviously, the latter requirement has its practical limitations. Evaporation could be avoided by humidifying the air inside the spin dryer to nearly 100%. Water is then removed from substrates only by centrifugation, and no evaporation-induced substrate contamination should occur. In that case, the water film thickness h ( t ) after a spinning time t depends on the spinning speed w according to' h(t) = h,[l + (4~~ph,-,%/31)]-'/~ (2) Thus for w = 1500 rpm and ho = 7 pm, h(t) is reduced to 0.7 pm after 1 min and to 0.2 pm after 10 min of ~~
(1) Meyerhofer, D. J. Appl. Phys. 1978,49, 3993. (2) Semiconductor Znt. 1989, 12, 80. (3) Levich, V. G.PhysicochemicalHydrodynomics,Prentice-Hall, Inc.: Englewood Cliffs, NJ, 1962; Chapter 12.
0743-7463/91/2407-2748$02.50/0
centrifugation. In the latter case, the substrate will visually appear dry because the film thickness is less than half the wavelength of visible light. For w = 5000 rpm and ho = 7 pm, the remaining film thicknesses amount to 0.2 pm and slightly less than 0.1 pm, respectively, after 1and 10 min of spinning. From a practical point of view, these calculations demonstrate the near impossibility of reducing the film thickness to less than 0.2-0.1 pm. After spinning, the remaining film eventually evaporates, leaving the suspended contaminanta behind on the substrate. Clearly, the latter amount will be less than in the case where evaporation occurred during spin drying and may therefore be considered to lead to a minimum but also inevitable amount of spin-drying-induced contamination. A challenge still lies in removing the final 0.2pm of water without resorting to evaporation. Water removal from hydrophobic substrates, on which water assumes a finite contact angle, can be accomplished by withdrawing them vertically from a water bath or by allowing the water to slide from the surface by tilting the substrate. The drying efficiency depends on the magnitude of the dynamic receding contact angle &,Re The dynamic contact angle concerns the macroscopic contact angle of the liquid when the liquid perimeter moves across the substrate. Quantitative removal of a liquid is possible only when &,R remains nonzero.4 The present paper describes how absorption of a watersoluble organic vapor can also induce a nonzero contact angle of water on a hydrophilic surface. As with hydrophobic surfaces, it is the existence of a contact angle that can subsequently be used for substrate drying (here, Marangoni drying). This paper extends on ref 5, which gives a preliminary account of Marangoni drying. Reference 5 mentions the probably important role of surface tension gradients in a water meniscus against a hydrophilic substrate that accompany organic vapor absorption. The present study attempts to elaborate on this idea in order to obtain a better physical insight into the underlying surface chemistry. An account will be given of experimental observations that relate to organic vapor absorption in water. Together with surface tension measurements, macroscopically visible contact angles of water on several hydro(4) Blake, T. D.; Ruschak, K. J. Nature 1979,282, 489.
(5) Leenaars, A. F. M.; Huethorst, J. A. M.; Van Oekel, J. J. LQngmUir 1990, 6, 1701.
0 1991 American Chemical Society
Physical Principles of Marangoni Drying
Langmuir, Vol. 7, No. 11, 1991 2749
Table I. Some Physical Constants of Investigated Organic Liauids at 20 'C saturated density,
vapor
pressure, mbar 1.6
Lift
Platform
surface
tension, mN/m
Henry liquid MW g/cmS coeffm' diacetone alcohol 116.2 0.94 30.8 8.2 X 1o-B 5 2-ethoxyethanol 90.1 0.93 28.0 2.0 X 10-5 0.92 11 l-methoxy-290.1 27.8 4.5 X 10-6 propanol 0.78 2-propanol 60.1 43 21.0 1.4 X lo-' acetone 58.1 0.79 233 23.7 7.0 X 10-4 n-butyl acetateb 116.2 0.88 13 24.8 6.9 X I, The Henry coefficient m denotes the ratio between the molar vapor concentration in air at saturated vapor pressure (2' = 20 "C) and the molar concentration in the pure liquids. * n-Butyl acetate is only soluble in water up to a concentration of 0.08 M.
Vapour/N stream
Vapour/N,
stream
Vapour
fi-l! outlet
w ....... \... h lq
Lid
Vapour inlet
Vapour -inlet
Figure 1. Cross section of the cell used for contact angle measurments. The arrows indicate the direction of the vapor flow.
philic substrates in various organic vapors will be reported as a function of absorption time. The accompanying papers deals with dynamic contact angles that determine the movement of small water drops across hydrophilic substrates in an organic vapor atmosphere.
Materials and Methods Silicon wafers were obtained from Wacker Chemitronic Co. NHdOH 30% HgO*/H20 solution (Merck, Mos-Selectipur) in a 1:1:5 volume ratio at 60 O C , rinsed with filtered, deionized (DI) water, and dried in a Semitool spin dryer. Just before being used, they were additionally treated in a UV/ozone reactor (UVP Inc.; PR100) for 10 min to remove remaining traces of hydrocarbons. Optically polished glass substrates were cleaned similarlyto silicon wafers. Platinum sheets were made hydrophilic by rinsings in acetone and heating in a flame. Mica sheets were purchased from Dumico Agencies (Rotterdam) and cleaved just prior to use. Diacetone alcohol, 2-ethoxyethanol, 1-methoxy-2-propanol, 2-propanol (IPA), acetone, and n-butyl acetate were purchased from Merck, PA grade or Mos-Selectipur grade. A few relevant physical properties of these liquids are listed in Table I. Organic vapors were produced by bubbling charcoal-purified Nn gas through an aspirator bottle thermostated at 20 "C. The N2 flow was regulated with a precision bore flowmeter. Vapor pressures in the outcoming NZ gas were determined as a function of the flow rate by weighing the amount of liquid evaporated from the aspirator bottle after a specified bubbling time. Up until a flow rateof 12 L/min, the diacetonealcoholvapor pressure remained unchanged at 1.6 mbar, which is identical with the saturated vapor pressure. Vapor pressures of 1-methoxy-2-propanol and n-butyl acetate decreased linearly to 10% at a flow rate of 12 L/min. With IPA and acetone, this decrease amounted to approximately 20 70. Such pressure decreasesmust be ascribed to local cooling effects in a solvent subjected to a high evaporation rate. Macroscopically visible contact angles of sessile droplets exposed to an organic vapor were measured from video prints with a protractor. The video printer was connected to a U-matic videorecorder,a TVmonitor, and a CCD camera. Liquid droplets were deposited onto the surface with a syringethrough an opening in the lid of the measuring cell (see Figure 1) after the vapor pressure had reached its desired level. Vapors could be introduced (Burghausen, Germany). They were cleaned in a 25 %
-
(6) Huethorst, J. A. M.; Marra, J. Langmuir, following paper in this issue.
Figure 2. Setup for the surface tension measurements on water layers that absorb organic vapors inside a closed chamber. The surfacetension is measured with a vertical cylindricalrod attached to a bottom-loading balance. via inlets in the bottom of this cell underneath the substrate. Because the cell is sealed except for a 8-mm outlet, organic vapor can only escape the cell as indicated in Figure 1. This setup ensured an optimal and immediate contact between vapor and droplet. The total cell volume was 6 L and the vapor flow was set at 4 L/min. Time-dependent surface tensions of water layers with thicknesses down to 1 mm were measured with the setup shown in Figure 2. Water layers were made by pouring an appropriate volume of water into a leveled Petri dish via an inlet in the measuring chamber (volume of 120 L) as soon as the desired vapor pressure inside the chamber was reached. The relative amount of vapor turbulence inside the chamber was controlled with the vapor inlet. No turbulence (i.e., quiescent) existed when the vapor flow was switched off. A minor degree of turbulence (i.e., semiquiescent) was attained by placing the vapor inlets at the top of the chamber. The total flow rate was then chosen to be 10 L/min from two inlets. Much higher levels of turbulence were reached by blowing a stream of the vapor directly onto the water. Surfacetensionscan accurately be measured with the Wilhelmy plate method' provided that the static receding contact angle 0, is known. As will be shown, however, 8.3 is usually nonzero and becomes time dependent when vapor absorps into water. Therefore, use was made of the maximum pull on a vertical rod method." With this method, no knowledge is required about contact angles. A stainless steel cylindrical rod with a diameter of 5 mm was used. By measuring the maximum weight of the water column underneath this rod with a bottom-loading balance of 1-mg sensitivity, surface tensions could be determined to an accuracy of 0.5 mN/m. To induce Marangoni drying on solid substrates, either the organic vapor was blown directly from a series of nozzles onto the substrates during withdrawal from a water bath or it was present as a quiescent or semiquiescent vapor environment. In the latter two cases, the complete drying process was carried out inside a sealed chamber with a volume of -200 L. Vapor turbulence was then controlled in a manner similar to that used in the surface tension measurement chamber. The water bath inside the chamber was connected to a DI water supply and, if desired, could be left to overflow continuously to keep the water surface free from organics as much as possible. When smooth reflective silicon wafers are chosen as hydrophilic substrates, the extent of vapor-induced drying can easily be visualized. Remaining water films thicker than 0.2 pm become visible through their interference colors. For a more quantitative (7) Hiemenz,P. C. Principles of Colloid and Sur/ace Chemistry;Marcel Dekker, Inc.: New York, 1977. (8)Paddar, J. F.; Pitt, A. R.; Pashley, R. M. J. Chem. SOC., Faraday Trans. 1 1975, 71, 1919.
Marra and Huethorst
2750 Langmuir, Vol. 7, No.11, 1991 Table 11. Maximum Drying Speeds ,,v ("/a) of Smooth Silicon Surfacer in Quiercent and Semiquiercent Vapor Environments. vamr
diacetone alcohol
2-ethoxyethanol
1-methoxy-2-propanol 2-propanol acetone n-butyl acetate 4
vapor turbulence none slight 1.0 2.2 2.5 =12 0 0.6
2.2 2.3 2.5
4 3 0 0
Measured immediately after an overflow of the water bath.
analysis, the DI water was replaced by a 0.01 M CoC12 solution. Thin films withdrawn from this solution will betray themselves by CoClz deposition on the surface after evaporation. When physical adsorption of CoCll to the surface is ignored,the surface density of CoClz becomes proportional to the evaporated film thickness. Measurements of Co concentrationswere performed with total reflection X-ray fluorescence spectroscopy (TRXFS). TRXFS has a sensitivity of -5 X 10" Co atoms/cm2. Hence, with a 0.01 M CoC12 solution, film thicknesses of 100 A can still be detected.
Results A. Observations on Vapor-Induced Drying of Silicon. After a hydrophilic substrate is withdrawn from water, a water film remains on its surface. However, apparently dry hydrophilic silicon substrates emerge from water when an IPA/N2 stream is directed onto them during withdrawal. Of course, at IPA vapor pressures below saturation, no IPA condensation can occur. Therefore, surface drying cannot be a consequence of water displacement by condensing IPA. With IPA vapor, withdrawal speeds could be increased to at least 15 mm/s before visible traces of water remained on the surfaces. Similar observations were made with vapors from the other liquids listed in Table I, but their effectivity for substrate drying varied considerably. Optimal drying was generally found when the vapor stream was directed down a vertically positioned substrate surface onto the meniscus region. No drying could be induced with pure N2 gas or with, for example, alkane vapors. In order to more accurately observe differences in the drying process as a function of several parameters, silicon wafers were withdrawn from water in semiquiescent atmospheres of organic vapors at a controlled vapor pressure inside a nearly sealed chamber. The maximum withdrawal speed v- was measured below which no visible water film remained on the wafers. Investigated parameters were as follows: (a) the relative vapor pressure PIP0 (POis the saturated vapor pressure at 20 "C),(b) the vapor turbulence near the substrates, and (c) whether the water bath had overflown prior to substrate withdrawal. Some results are compiled in Table 11. Table I1 shows that, with the exception of acetone, vincreases with the vapor pressure P at PIP0 H 0.9 for all vapors that are fully water soluble. But these listed vvalues were always well below U m u values when a vapor stream was deliberately directed onto the silicon. A slight increase in vapor tubulence near the substrates did not generally affect Vmm except for diacetone alcohol vapor (vm= increased) and IPA vapor (vdecreased). In fact, minor amounts of water on silicon were always observed with IPA vapor, even at very slow withdrawal speeds, in spite of the fact that IPA vapor is overall very effective in removing most of the water. With regard to the magnitude of P/Po,vonly decreased significantly at PIP0 < 0.5. Similarly, vmar decreased with increasing surface roughness.
Table 111. Effectively Evaporated Water Film Thicknearer (A20 A) during Marangoni Drying at Variour Withdrawal Speeds v in a Semiquiercent Vapor Environment or in a Vapor Stream Directed onto the Menircur Redon. film thickness. A
semiquiescentvapor u = 0.7 u = 1.5 vapor mm/s mm/s diacetone alcohol 500 760 1-methoxy-2420 520 propanol 2-propanol 1100 1600 a
Relative vapor pressure PIP0
directed vapor stream u = 0.7
u = 1.5
mm/s 160 100
mm/s 230 110
140
140
0.9.
For maximum drying efficiency in quiescent IPA vapor, it was found necessary to overflow the water bath prior to substrate withdrawal. For the other vapors in Table 11, an initial overflow hardly affected.,v Apparently it becomes more important at higher vapor pressures and thus higher absorption rates to remove absorbed organics from the bulk water surface. Perhaps unexpectedly, substrate drying was impossible in (semi) quiescent acetone vapor. An overflow of the water bath prior to substrate withdrawal gave no improvement. Observation of the water /organic vapor interface during vapor absorption showed that randomly directed Marangoni flows were only visible with acetone vapor and (to a lesser extent) with IPA vapor. Such flows may well affect substrate drying. Note that IPA and acetone have the highest vapor pressures (at PIP0 N 0.9) of the vapors listed in Table 11. Obviously, the absorption rate will increase with the vapor pressure. Along this line, our observations agree with the predictions of Sternling and Scriveng that Marangoni convections become more pronounced at higher rates of mass transport through an interface. Some TRXFS results after silicon drying from a 0.01 M CoClz solution under various conditions are given in Table 111. Note that the listed film thicknesses are upper limits because no adsorption of Co to silicon has been accounted for. Film thicknesses are found to increase with the withdrawal speed. B. Surface Tension Measurements on Aqueous Solutions. To investigate the relative surface acitivities of the organic liquids in Table I, surface tension measurements were performed on aqueous solutions of diacetone alcohol, 1-methoxy-2-propanol, n-butyl acetate, acetone, 2-ethoxyethanol, and 2-propanol. The data in Figure 3 show that apart from n-butyl acetate, which has only a limited solubility in water, the relative degrees of surface activity are similar. In concentrated solutions, IPA has the highest degree of surface activity. C. Response of Horizontal Water Films to Organic Vapors. When an IPA droplet was held at the tip of a syringe a few millimeters above the center of a horizontal water-wetted silicon wafer, a dry patch appeared and expanded readily on the silicon just underneath the IPA droplet (see Figure 4). The thinning process could be followed by observing the motion of circular interference colors around the thinnest part of the wetting film. Similar observations were made with the other polar liquids listed in Table I. However, the precise response of the water film on the various vapors strongly depended on the kind of vapor. For example, a (visiblyjudged) dry spot appeared within a few seconds and expanded rapidly when a l-methoxy-2-propanol droplet was brought above a wetted wafer. (9) Scriven, L. E.; Sternling, C. V. Nature 1960,187,186. Stemling,
C.V.; Scriven, L. E. AIChE J . 1959,5, 514.
Langmuir, Vol. 7, No. 11, 1991 2751
Physical Principles of Marangoni Drying
' " 0
IO-'
IO-'
to-*
10
bulk
Figure 3. Surface tensions y m as a function of the organic concentrationin water givingthe surface tensions of (- -) n-butyl acetate, (-) diacetone alcohol, (- -) IPA, (- - -) l-methoxy2-propanol, and (...) acetone solutions. The surface tensions of 2-ethoxyethanolsolutions virtuallycoincidewith those of l-methoxy-2-propanol solutions. Experimental points are omitted for clarity.
Figure 4. Response of a thin water film on a local high concentrationof IPA vapor. Circularinterferenceringsare clearly visible around the dry patch.
On the other hand, virtually no response was obtained with diacetone alcohol vapor, even though diacetone alcohol vapor is quite effectivefor silicon drying (seeTable 11). For a n-butyl acetate droplet just above a wetted wafer, most (but not all) of the water from the wetting film was virtually immediately drawn away from underneath the droplet. Nevertheless, the subsequent further film thinning underneath the droplet proceeded extremely slowly and no visible dry patch appeared. A similar observation was made with acetone. A response of a water film to an organic vapor implies that a tangential stress is exerted onto the film. This can be brought about by local differencesin the surfacetension. Position-dependent variations in the vapor pressure just above the water will induce analogous differences in the local vapor absorption rate. For water-soluble organics, the surfacetension decreaseswith increasingconcentration in water. According to Defay and Petre,lo the surface tension is determined by the solute concentration just
Figure 5. Contraction of a thin water film into droplets and puddles while being exposed to a stream of IPA vapor.
below the surface,provided that an equilibrium exists with adsorbed solutes on the surface. In this way, surface tension gradients can indeed arise. These gradients induce Marangoni flows of water from positions with a low surface tension to positions with a high surface tension. Thus, when a 1-methoxy-2-propanol droplet is positioned above a water film, the readily emerging dry patch indicates that a surface tension gradient is created that persists down to film thicknesses less than 0.2 pm. With acetone or n-butyl acetate, the more rapid initial response of the water film indicates a steep initial gradient. However, the much weaker response of the thinned remaining film points out that the surfacetension gradient decreases rapidly to almost zero for submicron water films. When 1-methoxy-2-propanol, IPA, diacetone alcohol, 2-ethoxyethanol, or acetone vapor was directed onto a water-wetted silicon wafer, the water film was observed to contract and often break up into droplets or puddles of water (see Figure 5). They expanded again after the organic vapor was removed. The relative effectiveness with which film contraction took place decreased along the following order: 1-methoxy-2-propanol,2-ethoxyethanol, diacetone alcohol, IPA, acetone, n-butyl acetate. Obviously, when droplet formation occurs, the presence of organic vapor must induce a macroscopic contact angle of water. D. Surface Tension Measurements during Vapor Absorption. Figures 6-1 1give surface tension measurements on stagnant water layers as a function of absorption time in several semiquiescent vapor environments. A t time t = 0 the water was brought into contact with the vapors (at PIP0 0.95) and the first measurements were recorded after about 1-2 min. The data show that in all cases, in particular for the thinner layers and at high vapor pressures, the surface tension decreaseswith increasingabsorptiontime. Clearly, the solute concentration just underneath the surface increases with time. With semiquiescent IPA and acetone vapors, it was found that, above water layer thicknesses of 6 f 1mm, the surface tension changes became independent of the depth of the water. At the same time, for a much thicker water layer, it could be visually observed that a concentrated layer of IPA (or acetone) of about 5-7-mm thickness accumulated underneath the surface after some 20 min of absorption. This observation parallelsthe aforementioned surface tension results. No such distinct surface accu(10) Defay, R.; Petre, G. In Surface and Colloid Science; Matijevic, E., Ed.;Plenum Press, Inc.: New York, 1971; Vol. 3, p 27.
Marra and Huethorst
2752 Langmuir, Vol. 7, No. 11, I991
9
*
3020
2ot
-
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I 0;
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lo 0
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0
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20
Figure 6. Dependence of YLG on the absorption time in semiquiescent diacetone alcohol vapor. Water layer thicknesses are indicated.
60
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Figure 9. Same as Figure 7 but for IPA vapor.
60
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Absorption time (min)
Absorption time (min)
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lot
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ob
I 20
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J 20
60
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Absorption lime (min)
Figure 7. Dependence of 7% on the absorption time in 2-ethoxyethanol vapor. Initial water layer thicknesses are indicated. Vapor was either present in a semiquiescent atmosphere or directed streamwise from a tube from a distance of 10 cm with a flow of 10 L/min onto the water surface (diameter of the water surface is 20 cm) under an angle of 45" with respect to the water surface.
-
-
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40-
1
s
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-
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30i
lo 00
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Absorption time (min)
30
20 10
a
1.4 mm
1 i
9
*
-
E
20
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120
Figure 10. (a, top) Dependence of yu; on the absorption time in acetone vapor. If not indicated otherwise, vapor was present as a semiquiescent atmosphere. When a vapor stream was deliberately directed onto the water, the same conditions applied as in Figure 7. (b, bottom) Dependence of TU;on the absorption time in a semiquiescent acetone vapor environment at relative vapor pressures PIP0 0.4 (curve 1) and P/Po 0.2 (curve 2). Water layer thicknesses are indicated.
Absorption time (min)
Figure 8. Same as Figure 6 but for I-methoxy-2-propanolvapor.
mulation of the other vapors listed in Table I1 could be observed. During IPA and acetone vapor absorption (Figures 9 and loa), the surface tension soon assumed a fairly constant value of 27 and 35 mN/m, respectively. According to Figure 3, these values correspond to an interfacial concentration of 5.5 f 0.5 M for both vapors. It should be recognized that IPA and acetone solutions have rather low albeit nearly identical densities. Therefore, the above observations are believed to demonstrate
a hindered diffusion of organics from the surface region (with a reduced density) into the bulk of water (with a higher density). Figure 10b gives surface tension measurements in diluted semiquiescent acetone vapors. Evidently, a lowering of PIP0 reduces the range of surface tension variation during absorption, both for thick and for thin water layers. Another feature of Figures 6-11 is that, for thick water layers, the surface tensions extrapolated to zero absorption time (in semiquiescent atmospheres) are below the surface tension of pure water YLG = 72.8 mN/m. This finding
Langmuir, Vol. 7, No. 11, 1991 2753
Physical Principles of Marangoni Drying
t
70
t
.Ot
3
30tt
i""o
0
--"
0 X
I
20
0 ~
"0 -0
20
40
60
80
100
120
Absorption time (min)
Figure 11. Dependence of YLG on the absorption time in a semi-
quiescent n-butyl acetate vapor environment. Water layer thicknesses are indicated. Table IV. Predicted Surface Tensions According to the Fick Diffusion Theory Compared with Experimentally Determined Surface Tensions at Short Absorption Times. surface tension YE, mN/m predicted C , i (from eq 4), mol/L predicted exptl vapor diacetone alcohol 6.1 x 71.5 f 0.5 70.0 0.5 2.0 x 10-2 71.0 f 0.5 68.0 f 0.5 2-ethoxy-ethanol l-methoxy-24.4 x 10-2 68.5 f 0.5 65.0 f 0.5 prop ano1 2-propanol 1.7 X 10-' 61.5 f 0.5 61.0 f 0.5 8.8 X 10-l 56.0 f 0.5 55.5 f 0.5 acetone 5.2 X 10-2 44.0 f 1.0 44.0 f 0.5 n-butyl acetate a See Figures 6-11.
may be compared with the diffusion theory based on Fick's second law." Regarding the unhindered diffusion of a quiescent vapor from an infinite domain through an interface into an infinite stagnant liquid medium, this theory predicts a constant interfacial concentration Cw,i according to (3)
Cg,b is the vapor concentration, which may be calculated from the vapor pressure via the ideal gas law. D, and D , are diffusion constants of vapor molecules in air and water, respectively. m is the Henry partitioning coefficient according to C , i = mC,,i, with C , i the interfacial concentration in the gas phase just above the interface. An impression about the magnitude of m may be obtained by considering the equilibrium between the pure organic liquid and its saturated vapor pressure (see Table I). The ratio D,/Dw should be of the order 104.12From the listed values of m in Table I, it becomes clear that the terms m(D,/D,)1/2are far smaller than unity and can be ignored in eq 3. Thus (4)
is an excellent approximation. Table IVlists the calculated concentrations Cw,i for various vapors at P/Po = 1. The corresponding surface tensions are inferred from Figure 3 and compared with extrapolated surface tensions to t = 0 (see Figures 6-11). The agreement is fair and could (11) Cranck, J. The Mathematics of Diffusion; Oxford University Press: Oxford, En land, 1956. (12)Bird,R.B.;&w&, W. E.;Lightfoot,E.N. Tramport Phenomena; John Wiley and Sons Inc.: New York, 1960.
400
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(s) Figure 12. Measured contact angle of a 10-pL water droplet on silicon as a function of the absorption time in diacetate alcohol vapor. The data on smooth silicon (0) virtually coincide with those on very rough silicon (X). Absorption time
possibly be improved if the ratios D,/D, were better known. Apparently, Fick's theory correctly predicts Cw,i at short absorption times, even though the effects of Marangoni convection are not accounted for. For n-butyl acetate, the calculated C , i is close to the maximum solubility in water. Experimentally, it is indeed found that the surface tension remains nearly unchanged once absorption is initiated (Figure 11). For longer absorption times, Fick's idealized diffusion model becomes inappropriate because Cw,i increases with time. Unfortunately, a mass transport analysis incorporating all nonideal aspects is forbiddingly complex and beyond the scope of this paper. Surface tension changes were also measured as a function of the water layer thickness with acetone, IPA, and 2-ethoxyethanol vapors when the vapor was directed streamwise onto the water surface (seeFigures 7,9,and loa). Although these experiments are not well-defined, it appears that the surface tension decreases less rapidly on thick water layers, but decreases more rapidly on very thin water layers as compared to the changes in a semiquiescent vapor. Here, both the forced higher absorption rate and the enhanced degree of mixing due to the vapor momentum on the surface region need to be considered. In thin films, the effect of the enhanced vapor absorption clearly dominates. In thicker layers, absorbed vapor apparently becomes better able to disperse itself rather than remain accumulated near the surface region. E. Contact Angles. When a water drop is placed on hydrophilic substrates such as platinum, silicon, glass, or mica, it spreads with a zero contact angle. However, as soon as an organic vapor is passed across the surface in the setup in Figure 1,the water droplet contracts and assumes a macroscopic nonzero contact angle. Its typical initial magnitude is between 5 and 15O (see Figures 12-16), depending on the organic vapor. Droplet contraction is a Marangoni effect. A relatively more rapid vapor concentration increase in the thinnest part of the droplet perimeter will induce a surface tension gradient and thus an inward Marangoni flow from the perimeter toward the droplet center. The same will apply for a water meniscus against a partially immersed substrate. The existence of a surface tension gradient near the perimeter of a water meniscus is consistent with the measured dependence of surface tension changes on the water layer thickness in Figures 6-11. A rapid expansion of a Marangoni-contracted droplet was observed when the organic vapor was suddenly removed. This can analogously be explained from a more rapid concentration decrease in the droplet perimeter. In
Marra and Huethorst
0 X
0 X
0
0
x
o 00
0' 0
I
1
1
I
I
400
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Absorption time (s)
Figure 13. Same as Figure 12 but for l-methoxy-2-propanol
vapor.
0'
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I
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J 1200
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Absorption time (s)
Figure 16. Measured contact angle of a 1 0 - ~ L water droplet on a smooth silicon surface in n-butyl acetate vapor.
20
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O co
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Figure 14. Same as Figure 12 but for IPA vapor.
X
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xx
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I
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(s)
Figure 15. Same as Figure 12 but for acetone vapor.
that case, the resulting surface tension gradient becomes reversed, leading to an outward Marangoni flow (wellknown from the tears-of-wine phenomenon). Figures 12-16 give macroscopic contact angles as a function of the vapor absorption time on hydrophilic surfaces such as mica, glass, silicon, and platinum. Within experimentalerror (f2O),contact angles were independent of the surface roughness or the nature of the surface (although independent contact angle measurements with a-bromonaphthalene in air clearly indicated differences between the surface energies of the dry surfaces). Therefore, only the data recorded on silicon surfaces are given. The magnitude and time dependence of the contact angles were found to strongly depend on the nature of the vapors. The sharp decrease in the contact angles in Figures 12-15 after almost 30 min of absorption occurred just before the droplets were completely evaporated. As found in the previous section, vapor absorption gradually lowers the surface tension. Surface chemical
equilibrium considerations predict that this should coincide with a decrease in the contact angle. Such a decrease was indeed always found for water droplets exposed to organic vapors on hydrophobicsurfaces (&A N 90°, results not shown) but, at least in Figures 12 and 13, not generally on hydrophilic surfaces. Together with data in Table 11, the results show that those organic vapors that induce the largest contact angles (l-methoxy-2-propanol, IPA) also induce the highest drying speeds umax. Thus, any circumstancethat increases Therefore, the contact angle appears to increase u-. the contact angle decrease in Figure 14 with a longer IPA absorption time, due to more IPA uptake into the droplet, suggests that substrate drying with IPA vapor will improve when the water bath overflows prior to the drying process. This inference agrees with experimental findings. Furthermore, contact angles could easily be increased by -5" when a vapor stream was deliberately directed onto the droplets. This observation parallels the finding that u, increases when substrates are exposed to a vapor stream during drying. To investigate the surface tension at the perimeter of a contracted meniscus, surface tensions were measured with a Wilhelmy plate, thereby accounting for the finite contact angle. In doing so, the results in Figures 6-11, measured with the vertical rod method, could be reproduced exactly. One concludes that no difference exists between the surface tension at the position where the macroscopic contact angle is measured and the surface tension above bulk water.
Discussion and Conclusions The present study has considered several phenomena relevant for Marangoni drying by organic vapors. To effectively induce Marangoni drying in a quiescent vapor atmosphere, the organic vapor should be water soluble. Vapor absorption in water lowers the surface tension to an extent that is determined by the vapor pressure, the surface activity, the absorption time, and the thickness of the absorbing water layer. Since the water within a meniscus curve has a position-dependent thickness with respect to the supporting substrate, a surface tension gradient can be induced along the meniscus through vapor absorption. The gradient causes the meniscus to partially contract through a Marangoni flow and assume a finite apparent contact angle. Experimentally, it does not seem easy to infer the magnitude or the domain of the surface tension gradient. From surface tension measurements with the Wilhelmy plate, evidence exists that the gradient only occurs within
Physical Principles of Marangoni Drying
a microscopicregion at the perimeter unaccessible to direct observation. Measured contact angles refer to macroscopic observations but do not shed light on the microscopic situation at the perimeter region. Based on our experimental results, the most logical picture of this region seems that of a horizontal microscopically thin wetting film on the substrate whose thickness gradually increases in a transition region and eventually attains a curvature consistent with the measured contact angle. The surface tension gradient exists in the transition region. The magnitude of the contact angle must reflect the significance of the surface tension gradien but, because the contact angle lies on a microscopic wetting film, not the surface energy of the dry substrate. The thin wetting film masks the surface energy and surface roughness of the underlying substrate as long as it is hydrophilic. In fact, the mere existence of an apparent contact angle expresses the nonequilibrium state of the absorbing system. In the equilibrium state of a homogeneous organic solution, the surface tension is uniform everywhere with a zero contact angle on a hydrophilic surface. Consistent with a steeper gradient, larger contact angles allow a higher speed with which a hydrophilic substrate can be withdrawn from water in a (visually judged) dry state. Conditions that increase the contact angle, such as forced higher absorption rates, higher vapor pressures, or higher bulk surface tensions, are found to indeed improve the drying performance. Moreover, the high drying speed attainable with IPA vapor (Table 11)probably reflects its better ability to reduce the surface tension of a concentrated solution (i.e., in the thinnest part of a water meniscus). However, even after a water bath overflow, which maximizes the surface tension of bulk water, Marangoni drying appeared not possible at the high pressure of nearly saturated acetone vapor in a (semi) quiescent atmosphere. Because this failure is not apparent from the surface tension results in Figure loa, its reason is likely to be associated with the observed high incidence of randomly directed Marangoni flows across the water surface. These random flows may well perturb the unidirectional Marangoni flow along the water meniscus required for Ma-
Langmuir, Vol. 7, No. l l , 1991 2755
rangoni drying. Such adverse effects only occur to a lesser extent in a quiescent IPA environment, but even then adversily affect the quality of Marangoni drying (see left column in Table 111). Although a reduction of PIP0 diminishes these random convections, this does not improve the drying performance because the absorptioninduced surface tension changes diminish in magnitude (Figure lob). Random surface tension gradients can largely be avoided by directing a focused vapor stream from a manifold only onto the meniscus region. This precaution will ensure that the direction of the surface tension gradient in the meniscus remains optimal for Marangoni drying. The foregoing suggests that, for effective drying, PIP0 should exceed 0.5 irrespective of the absolute value of P while the surface tension of bulk water should remain as high as possible. This latter requirement can be satisfied by overflowing the water bath but even better by ensuring that the total surface area of the water in the bath is much larger than the surface area directly exposed to the focused vapor stream. As such, Marangoni drying is also possible with acetone vapor or partly soluble vapors.s In the latter case, however, drying will not be possible when adsorbed vapor is able to rapidly saturate the water surface. In that case, no surface tension gradient can develop or sustain. The practical significance of Marangoni drying lies in the fact that it is a cleaner drying method than conventionally applied methods because of the much reduced amount of evaporation. Ultraclean drying is possible for regular hydrophilic surfaces if the withdrawal speed from the water bath does not exceed a few millimeters per second and if the vapor stream is focused onto the meniscus region during withdrawal. If high drying speeds are required, one must resort to IPA vapor while the water bath should overflow continuously.
Acknowledgment. We thank Miss E. Muller for carrying out most of the contact angle measurements. Registry No. IPA, 107-98-2;Si, 7440-21-3; diacetonealcohol, 123-42-2;2-ethoxyethanol,110-80-5;2-propanol,67-63-0;acetone, 67-64-1; N-butyl acetate, 123-86-4.
