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Effect of humidity on desorption of fatty acid monolayers at constant area
Effect of Humidity on Desorption of Fatty Acid Monolayers at Constant Area 1 ZAYN BILKADI 2 AND RONALD D. N E U M A N Department of Forest Products, University of Minnesota, St. Paul, Minnesota 55108 Received August 4, 1980; accepted January 5, 1981 It is observed that the relative humidity of the atmosphere has an important effect on the surface pressure relaxation of myristic and lauric acid monolayers at the air-water interface. The relaxation at constant area increases with decreasing relative humidity, which suggests that hydrodynamic convection in the liquid due to evaporation may be the origin of the effect. The desorption rate of the monolayer in a saturated environment has been deduced from the surface pressure relaxation behavior using an equation of state. The time course of monolayer desorption at constant area in a saturated environment for myristic and lauric acid is discussed in light of a recently proposed model based on the Brownian motion of a particle in a potential well. INTRODUCTION
When a monolayer of surface-active molecules is freshly spread at the air-water interface it often undergoes a process of depletion by evaporation or dissolution that manifests itself in an increase of surface tension with time. In many systems at room temperature, in the absence of chemical reactions and at surface pressures not exceeding the equilibrium spreading pressure (ESP), the monolayer depletes primarily by desorption into the aqueous phase. The most extensive investigation of monolayer desorption, and in fact the earliest one, was that of Ter Minassian-Saraga (1-3) using lauric and myristic acid. In a series of articles she established that the rate of desorption of fatty acids is determined by the size of the hydrophobic portion of the desorbing molecules, the surface density, temperature, and degree of ionization. In this article we report that the apparent 1 Published as Scientific Journal Series Paper No. 10,193 of the University of Minnesota Agricultural Experiment Station. 2 Present address: Central Research Laboratories, 3M Company, St. Paul, Minn. 55103.
desorption rates for monolayers of lauric and myristic acid also are determined by the relative humidity of the air above the interface (4). The observation that humidity effects are important in studies of the physicochemical properties of spread monolayers seems to have been overlooked in the past and could account for many conflicting findings on monolayer desorption (5-8). An interpretation of the humidity effect based on hydrodynamic convection encompassing the surface of the liquid is presented. A brief discussion of the time dependence of desorption at 100% RH is also given using a recently proposed model based on Brownian motion theory (9). EXPERIMENTAL
Most investigations of monolayer desorption in the past have utilized the constantpressure technique, which requires continuous compression of the film to maintain it at the desired pressure while monitoring its total area as a function of time. It can be argued that in this method the motion of the compression barrier disturbs both the monolayer and the subsolution beneath it by
480
0021-9797/81/080480-10502.00/0 Copyright © 1981 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and Interface Science, Vol. 82, No. 2, August 1981
MONOLAYER
stirring. The effect of stirring (rate of barrier motion) depends on the solubility of the film and may also vary from one worker to another. The present investigation utilizes the constant-area technique, which involves confining the film to a constant area while measuring the relaxation of surface pressure. This method eliminates virtually all of the complications inherent in the constantpressure technique since none of the components need be disturbed at any time following the adjustment of surface pressure to its desired initial value. It is recognized, however, that the meniscus curvature about the pressure-sensing device, e.g., Wilhelmy plate, does change somewhat during the desorption process. It can be shown that the change in the interfacial area, as well as the resulting film pressure change, is negligible over the pressure relaxation range examined in this study. Except for early attempts by Ter Minassian-Saraga (1,3), the method has not been exploited to its full potential as yet, probably because of the previous lack of a theoretical model. In this section we describe the apparatus used and discuss briefly the sources of error in the measurement of surface pressure relaxation.
Appa'ratus The basic units of the apparatus have been described previously (10). The system includes a Teflon trough, Cahn Model RG electrobalance, suspended platinum plate, and a Texas Instruments recorder. The trough was milled from a 1-in.-thick slab of Teflon and clamped firmly to a heavy block of aluminum tooling plate. The milled portion was 66 cm long, 5.6 cm wide, and 1.6 mm deep. The trough assembly, cleaned in H2SO4/Nochromix, was enclosed in a Lucite cabinet (94 x 50 x 34 cm) having a metal bottom and fitted with small pluggable ports. The access ports served two functions: first, to allow spreading of the monolayer from a solvent through long capillary tubes, thus
481
DESORPTION
minimizing disturbances of the physical conditions of the system, and second, to allow for adjustment of the humidity levels in the cabinet, which also contained small beakers containing moistened filter paper. This method of adjusting the humidity level inside the cabinet is preferable to passing moist air streams through the enclosed volume. The temperatures of both the liquid and gas phases were continuously monitored by three Fenwal (GB31P2) glass probe thermistors using a Keithley Model 616 digital electrometer. Each thermistor (3 mm o.d.) was calibrated to _0.02°C against a certified calorimeter thermometer in a constanttemperature bath. The thermistors were attached to an adjustable vertical Unislide assembly (Velmex Inc.) with scale and vernier, thus permitting their position to be measured to within +_0.05 mm. Typically one thermistor was placed in the liquid surface, and the remaining two were located at 13 and 22 mm above it. The relative humidity in the region between 5 and 20 mm above the surface was measured by a Hygrodynamics No. 4-4839 hygrosensor (American Instrument Co.) placed parallel to the surface and attached to a Hygrodynamics Model L15-3050 universal indicator. In addition, a second hygrosensor (No. 615-1810) was also used in the study. The factory calibration of both humidity probes was checked against the vapor pressure of saturated salt solutions, and their accuracy was at least ___2% RH. All experiments were conducted entirely in a clean environment room, where the humidity could be controlled to within +_3% RH between 30 and 95% RH and the temperature controlled to within +0.5°C.
Materials Myristic and lauric acid were obtained from Applied Science Laboratories. The chemical purity of the samples (99+%) w a s confirmed by gas chromatography. Journal of Colloid and Interface Science, Vol. 82, No. 2, August 1981
482
BILKADI
AND NEUMAN
The spreading solvent was n-hexane Phillips Pure Grade (99 mole%) and was purified further by a single percolation through a silica gel-activated charcoal adsorption column at room temperature. The pH of the subsolution was adjusted by Suprapur concentrated HCI (EM Laboratories). The water was first purified by a reverse-osmosis unit, then distilled twice in an all-glass apparatus, the first time from alkaline permanganate. Its conductivity was 0.8/xmho at 24°C. The water was stored in Pyrex containers in the controlled-environment room prior to use. One-hundred and fifty milliliters of subsolution was used for each kinetic run and resulted in a liquid height of 4.5 mm in the trough.
Sources of Error We describe in this section our efforts to eliminate artifacts due to monolayer leakage, contact angle hysteresis, mechanical disturbances, monolayer evaporation, and solvent effects. It should be realized, however, that while the first three sources of error could be eliminated or at least reduced to an insignificant level, the remaining two effects are much harder to assess experimentally. (a) Monolayer leakage. This source of error becomes relatively minor in the case of soluble surfactants such as lauric acid. On the other hand, for monolayers such as myristic acid, considerable effort must be expended to ensure that no defects are present, by carefully machining the edges and sides of the troughs and barriers. To establish the absence of monolayer leakage in a given trough the following experiment was repeated several times: The compression barrier was placed one-quarter of the way from a trough end, and a lens of tritolyl phosphate was spread at the other end. The surface tension of the clean surface was then monitored continuously for as long as 12 hr with the position of the compression barrier changed every 2 hr to detect any defects along the trough edges. The criterion Journal of Colloid and Interface Science, Vol. 82, No. 2, August 1981
for a leak-proof system in our experiments was that the change in surface tension of the film-free portion of the surface did not exceed 0.1 mN m -1 over a period of 2 hr. As an additional confirmation of the absence of monolayer leakage, we compared the desorption rates of myristic acid at 100% RH obtained with and without use of compression barriers, i.e., the correct amount of film material corresponding to the desired surface pressure was spread onto a trough having no barriers. The desorption rates had to be (and were) identical. (b) Contact angle effects. Before the monolayer was spread, the Wilhelmy plate was equilibrated with the subphase for at least 2 hr so that ample time was allowed for wetting of the surface and its thermal equilibration with the liquid. In order to minimize possible contact angle hysteresis the platinum plate was first sandblasted, then electroplated in chloroplatinic acid solution (11). Our decision to electroplate the sandblasted plate was based on the following observation: When the platinum plate was sandblasted only, a shift in the baseline was observed for a monolayer of stearic acid subjected to repeated compression-expansion cycles from its surface vapor pressure to 31 mN m -1. In particular, the baseline corresponding to the surface vapor pressure shifted upward by about 0.5 mN m -1 for each cycle up to the third one. This hysteresis did not appear to occur with the platinized plate. (c) Mechanical disturbances. The efforts to eliminate mechanical vibrations included anchoring the entire apparatus onto a heavy concrete base and avoiding the use of moist air streams in the cabinet for maintaining high humidity levels. The forks supporting the barriers were moved manually by means of a Unislide mechanical slide assembly chosen for its smooth motion. (d) Monolayer evaporation. Obviously, this could be a serious source of error since it constitutes a competing route for monolayer depletion. The opinions concerning the magnitude of this effect differ from one
MONOLAYER DESORPTION 7
I
i
I
~'~
i
I
100"/o RH
Z ,~
8 5 % RH
{3-
g O3 M I
I
10
20
47*/* RH
J-~ 50 TIME
40
50
60
70
(rain)
F[G. 1. Effect of relative humidity on the surface pressure relaxation of myristic acid monolayers on 0.01 N HC1 at 21.0 4- 1.0oc. worker to another (5, 12). In the case of myristic acid a direct p r o o f of the relative insignificance of monolayer evaporation will be provided (see Fig. 4). In the case oflauric acid the effect of monolayer evaporation remains unassessed. (e) Solvent effects. There are controversies regarding the effect of residual spreading solvent on the properties of lipid monolayers. In some instances it was claimed that entrapped organic solvent remained in the monolayer for periods exceeding 10 min (13, 14). Other studies imply complete evaporation of solvent within a few seconds (1, 7). In order to maximize the rate of solvent evaporation and minimize possible occlusion of solvent molecules in the monolayer, we delivered the spreading solution dropwise, at 5-sec intervals, to the largest possible surface area so that the surface pressure never e x c e e d e d 0.3 m N m - L The monolayer was then compressed fairly rapidly to the desired initial pressure. Solvent effects were not observed when this procedure was adopted.
483
as a function of time for various atmospheric humidities are given in Figs. 1 and 2. The kinetics at the saturation point (100% RH) were always reproducible to within 0.1 mN m -z, whereas at lower humidities the reproducibility was generally lower as indicated by the error bars, which represent the maximum deviation from the mean value of the film pressures. It is seen that at a given temperature, the higher the apparent " d e sorption" rate, the lower the steady-state value of atmospheric humidity. The observed relative humidities are average values from a fixed humidity probe, the center of which is located at about 13 mm above the surface. The values of the relative humidities at more remote locations in the cabinet were usually slightly lower. At the saturation point the humidity throughout the entire volume was always uniform. The temperatures noted in Figs. 1 and 2 are those given by a fixed thermistor located at 2.2 cm above the surface. The temperature profile throughout the liquid and gas phases is shown in Fig. 3 to be a function o f the relative humidity near the surface. Only under a saturated atmosphere was the temperature of the gas phase uniform and equal to that of the liquid. In all other cases the temperature of the liquid drops below that of the gas but appears uniform over its entire depth. On the other
'E Z
GO CO llJ 100% RH
ne ffl
RESULTS AND DISCUSSION
Desorption in Unsaturated Atmospheres The observed changes in the surface pressure o f myristic and lauric acid monolayers
i
~o
J
~o
~o TIME
i
~o
~'o
~'o
(rain)
FIG. 2. Effect of relative humidity on the surface pressure relaxation of lauric acid monolayers on 0.01 N HC1 at 21.0 _+ 0.5°C. Journal of Colloid and Interface Science, Vol. 82, N o . 2, A u g u s t 1981
484
BILKADI AND N E U M A N
hand, the temperature of the gas increases with distance from the surface and becomes uniform at distances slightly exceeding 2 cm. The only reasonable explanation of the lower temperature of the liquid relative to that of the gas is in terms of water evaporation from the surface. Obviously, under a saturated atmosphere the net rate of evaporation or the net mass flux across the water surface should be zero, and no net heat (energy) transfer across the surface is expected. Under these conditions the temperature throughout the liquid-gas system should be constant, as is the case for the uppermost curve in Fig. 3. At lower relative humidities, however, the net mass flux of water molecules initially causes a heat loss from the liquid and lowers its temperature relative to the gas. The finding that the temperature lowering of the liquid increases with decreasing relative humidity in the gas phase is simply an indication of enhanced evaporation rates. This result is consistent with many experimental findings in the literature, some of which reported drops in the temperature of the liquid surface exceeding 10°C (15, 16). Likewise, the existence of a temperature gradient in the gas phase is not surprising considering its rather low coefficient of thermal conductivity and the fact that at steady state the latent heat of vaporization is withdrawn from the gas layer adjacent to the liquid. The temperature profile in the gas layer could actually be estimated (17) from the coefficient of thermal conductivity of the gas and the rate of evaporation from the liquid. A rather striking observation from Fig. 3 is that the temperature of the liquid, in all cases, appears to have been uniform with depth (to within ±0.04°C) even when evaporation was taking place. This observation does not necessarily rule out the possibility that thermal gradients confined to very thin layers of liquid do in fact exist but the size of the thermistor is too large for their detection. This point of view has been discussed in the literature (18). Moreover, it is likely that at atmospheric humidities below Journal of Colloid and Interface Science, Vol. 82, No. 2, August 1981
22 0 1 0 0 % RH
21
68O/oR. ,.~.,'J':'"
,~ z0
,,2~5O, o,,
1B
I<--Liquid )1( - 0• 4I
/
Air 01.4
DISTANCE
210 I I 12 16 FROM I N T E R F A C E ( c m ) 018
I
2.4
FIG. 3. Temperature profile in the bulk phases.
saturation the aqueous layer is the site of hydrodynamic convective movement as a result of water evaporation. The existence of convective motion in liquids due to evaporation was demonstrated experimentally by B6nard (19) at the turn of the century; and his work, as well as more recent results, has been exhaustively reviewed (20). The main conclusion relevant to this discussion is that while the origin of evaporative convection in pure liquids is surface cooling, its driving force is a complex function of the surface tension fluctuations (Marangoni effect) and the density gradient along the depth of the liquid (buoyancy effect). It is very difficult in many cases to decouple the surface tension instability from the instability due to the density gradient. However, it is claimed, mainly on theoretical grounds (21, 22), that the relative importance of the Marangoni and buoyancy effects in triggering and sustaining convection appears to be governed by the depth of the liquid layer. Theoretical calculations (22) have suggested that for a water layer with a free surface the surface tension mechanism, rather than the buoyancy mechanism, predominated whenever the depth was less than about 1 ram. The effect of spread monolayers on evaporative convection has been studied by Jarvis (23), who has shown by measuring the temperature fluctuations that even a highly compressed monolayer of oleic acid did not significantly inhibit convection at a depth of approximately 4 mm in the aqueous
MONOLAYER DESORPTION
47
57
RELATIVE HUMIDITY (percent) 67 77 s7
97
Z o
!I
~op
J o_
o_ 1~
i
i i TIME {min)
i
/
720
FIG. 4. M o n o m o l e c u l a r film behavior of myristic acid on 0.01 N HCI at c o n s t a n t area with continually increasing a t m o s p h e r i c humidity for two initial surface p r e s s u r e s . (a) 170 = 6.5 and (b) Yl0 = 0.3, where H0 is the initial surface p r e s s u r e in m N m -1 at t = 0. C u r v e (c) c o r r e s p o n d s to the subsolution t e m p e r a t u r e given by a thermistor located in the liquid surface.
subsolution. Similarly, Berg et al. (24) have shown qualitatively by schlieren optics that the presence of surface-active molecules on evaporating water layers suppressed cellular convective movement when the depth was 1 mm or less, but convection in the form of "cold streamers" was visible when the depth was about 1 cm. It is concluded on the basis of the experimental evidence in the literature that for water layers of thicknesses comparable to that in the present investigation (4.5 mm) the presence of surface-active molecules quite likely retards convective motion but does not eliminate it altogether. This motion could serve as a competing route for monolayer depletion from the surface whereby the surface-active species are carried or "forced" into the interior by the downward motion of the cold liquid. The fact that the intensity of convection increases with the rate of evaporation has been established (22) and could then be at the origin of the observed dependence of surface pressure relaxation on atmospheric humidity. In view of these considerations it can be statedthat true desorption, driven solely by the excess chemical potential of the lipid molecules at the surface, is represented only by the curves in Figs. 1 and 2 obtained under saturated atmospheres. An interesting behavior of the monolayer is observed when the humidity of the atmos-
485
phere is not held constant throughout the experiment. This is illustrated in Fig. 4 in the case of myristic acid. Figure 4 depicts the apparent temperature and surface pressure dependence on relative humidity. In practice, this condition is achieved by closing all ports of the cabinet immediately following spreading of the monolayer, thereby causing a gradual increase in the water content of the atmosphere by evaporation. This procedure closely corresponds to that commonly practiced today in film balance studies performed in ambient laboratory environments. Curve 4a illustrates the behavior when the initial surface pressure is 6.5 mN m -1. The film appears to deplete at a very fast rate initially, perhaps as a consequence of convection in the liquid. As the relative humidity rises, the convective movement presumably subsides somewhat, allowing the excess surface-active molecules in the interior of the liquid to readsorb gradually to the surface. The net effect would then be an increase in the surface pressure following the rapid initial decrease. It seems that readsorption persists even when the monolayer pressure is originally very small, as is the case in Curve 4b. Here, in some extreme cases, the surface pressure increased from 0.3 mN m -1 and leveled off for 12 hr at values as high as 2.91 mN m -1 when the humidity reached the saturation limit. The final value of film pressure depended on the volume of spreading solution used. The fact that the final surface pressure remained constant for periods of several hours not only rules out evaporation of myristic acid as a significant depletion mechanism, but also confirms the absence of monolayer leakage in our system. It is to be noted that the rise in atmospheric humidity is accompanied by a rise in the temperature of the liquid subsolution as shown in Curve 4c and predicted by the findings in Fig. 3. One could speculate that the difference in the relaxation rates shown in Figs. 1, 2, and 4 might arise solely from differences in the subsolution temperature. Journal of Colloid and Interface Science, Vol. 82, No. 2, August 1981
486
BILKADI AND NEUMAN
However, an experiment conducted at 100% RH revealed that the desorption kinetics at 18.5 and 21.5°C are almost indistinguishable. Thus, other factors besides the difference in subsolution temperatures should be at play. The behavior depicted in Fig. 4 could not be observed in the case of lauric acid, probably because of its higher solubility. Figure 5 shows the results of the control experiment where the surface of the aqueous subsolution was not covered with a fatty acid film. The change of the baseline registered by the Cahn electrobalance corresponds to the total decrease in the surface tension of the aqueous phase due to the increased temperature of the subsolution. The quantity -Ay/AT is very nearly 0.15 mN m -~ ° C - l , which is the accepted literature value for water (25). An important consideration relative to the results in Fig. 4 is that the environment is not at equilibrium or even at steady state. In particular, the rate of increase in humidity, and consequently the rate of surface pressure increase, depends on the volume of the enclosed atmosphere, i.e., the size of the cabinet. Therefore, no significance should be given to the time scale of these phenomena. On the other hand, the effects illustrated in the other figures were undertaken in environments at equilibrium or at steady state; they are therefore independent of the apparatus. The kinetics of desorption at 100% RH have been reproduced using troughs of varying shapes and construction material. In a concluding note, convective motion certainly exists in the liquid, not only in the bulk but also in the surface region, when the atmosphere above the monolayer-covered surface is unsaturated. The increase in the apparent desorption rate at lower relative humidities is due to this convective motion which causes a more rapid depletion of film molecules from the surface. No stagnant or calm liquid layer exists, as assumed by other investigators (26, 27), and this interpretation Journal of Colloid and Interface Science, Vol. 82, No. 2, A~lgust 1981
RELATIVE HUMIDITY
,,
2;
7;
0;
(percent)
7
T
22
TE OS
°"
, ~o
,~o
TIME (min)
F[o. 5. Changes in surface tension ( ) and ternperature (- - -) of 0.01 N HC1 subsolution as a function of time and relative humidity. is in agreement with other recent studies (28). Rarely does anyone measure the relative humidity in film balance studies and when it has been measured, values of only 70% (29, 30) or somewhat higher (31) have been reported. Most, if not all, investigations of desorption, as well as those of other film properties, e.g., typical rI-A isotherms and surface diffusion measurements, very likely have had convective currents present in the surface because of the general unawareness of the need to control the humidity and its relationship to the onset of the development of convective cells in thin liquid layers.
Desorption in Saturated Atmospheres The surface pressure relaxation at 100% RH was measured for myristic acid at initial pressures of 6.49 and 8.76 mN m -1. In addition, it was measured for lauric acid at initial pressures of 6.49 and 13.3 mN m-L The desorption kinetics can be interpreted in terms of a recently proposed model derived from diffusion theory (9). The model assumes that the fatty acid molecule at the surface is in a potential energy well which is the result of its hydrophobic character. The molecule desorbs into the bulk liquid by virtue of its thermal motion, but to do so it must escape the potential well. In this formulation the desorption process is basically one-dimensional diffusion in the presence of a short-range force field Q(z), and the rate of particle escape is controlled by
487
MONOLAYER DESORPTION
•
•
•
molecules are ignored, the general solution of the Smoluchowski equation with appropriate boundary and initial conditions is given by F p(t) - e azt erfc (ottZ/2), [|] F0
$M= - Lfl7 x IO-t
09 l t-.* 0.8
SL = " 3 " 6 6 t 10-2
0.7
~
I 4
; ,/V
I
I S
I
rain ~z
F10. 6. The variation of F/F0 with t 1~2 for the desorption of myfistic and lauric acid from the airwater interface at 21.0°C. Myristic acid: (A) II o = 6.49, (&) 1Io = 8.76. Lauric acid: (©) 17o = 6.49, ( 0 ) II o = 13.3.
the depth and range of the potential well. This requires the use of the Smoluchowski equation rather than Fick's equation to derive the evolution of probability P ( z , t ) that a surfactant molecule will have position z at time t given it had position z = 0 at t = 0. It is important to recognize that if desorption were caused by diffusion alone from a concentration gradient near the surface, the film would desorb much too quickly with a time constant r-=-z2/D, where D is the diffusion coefficient3 of the surfactant molecule and z0 is the thickness of the surface zone. Thus, for D -= 10-6 cmVsec and z0 "=- 20 A, z is a microscopic time of the order of 10-8 sec. The mathematical details of the model have been thoroughly discussed (9). A simple analytic solution has been found only for a square-well potential. When the lateral interactions between neighboring surfactant The diffusion coefficient employed in t h e s e calculations is that for diffusion in bulk water. This a s s u m p tion that the diffusion coefficient in the surface zone a n d bulk liquid are equal m a y be questioned on the g r o u n d s that the stochastic forces in the surface zone are likely to be anisotropic. It is to be noted that at the p r e s e n t time m e a s u r e m e n t s of surface diffusion in fluids are inconclusive, and w h e r e a s s o m e studies indicate differences in the motions at the surface and in the bulk, other investigations do not. The conclusions p r e s e n t e d herein, h o w e v e r , are not affected by this question.
where F is the surface density at time t, and 1 / a 2 is the time constant for desorption given by 1 z2 e 20 = "re zQ, [2] a 2
D
where Q and z0 are the two adjustable parameters corresponding to the height (in k T ) and width of the potential well. For t small compared to the relaxation constant, Eq. [1] reduces to the simple expression p(t)
-
F F 0
~
1 -
2a
~ t 1/2. "/71/2
[3]
Since the measured quantity in the present experiments is the surface pressure, one needs an equation of state to compute p ( t ) . As a first approximation we assume that the empirical equation of state H ~ (F) ~'8~ proposed by Ter MinassianSaraga (3) is valid for lauric acid. For myristic acid, .experimental H-A data (Tompkins and Neuman, unpublished) obtained at 100% RH were used. The results shown in Fig. 6 lead to two important conclusions: First, the kinetics predicted by Eq. [3] are valid, indeed, over a time period of almost 30 min for lauric acid and 1 hr for myristic acid. At longer times the kinetics are more appropriately described by Eq. [1]. Second, the observed desorption rate is independent of the initial surface density F0 and, therefore, independent of the initial surface pressure 170 as predicted by Eqs. [1] and [3]. This finding seems to validate the assumption made in the model that the lateral interactions in the monolayer are relatively unimportant, at least in the liquid-expanded phase. The monolayer desorption experiment is a particularly elegant method for extracting Journal of Colloid and Interface Science, Vol. 82, No. 2, August 1981
488
BILKADI AND NEUMAN
rich information on h y d r o p h o b i c interactions. In particular, in the present model the difference in the desorption kinetics of lauric and myristic acid is due to the repulsive forces b e t w e e n the a q u e o u s subsolution and the two additional methylene ( - C H ~ - ) groups in the myristic acid h y d r o c a r b o n chain. The ratio of the slopes SM and SL in Fig. 6 for myristic and lauric acid, respectively, is given by SL a M
---
O~.L
[4]
o/M
ACKNOWLEDGMENTS
Combining Eqs. [2] and [4] one obtains In SL = ( Q M - Q L ) SM
pear to be in good a g r e e m e n t with our theoretical model for desorption at constant area. Further tests of our model, h o w e v e r , require equations o f state or experimental H - A data m o r e accurate than those presently available. Future studies will delineate the d e p e n d e n c e of the depth and range of the potential well on the molecular structure of the surfactant molecule and shed further insight into the nature of the intermolecular forces in m o n o m o l e c u l a r films.
+--lln--rM , 2 ~-L
[5]
where the last term in Eq. [5] is v e r y small and can be neglected. Since f r o m Fig. 6, S L / S M = 21.9, it can be shown that the activation energy for the transfer of a single methylene group f r o m the m o n o l a y e r to the aqueous subsolution amounts to 901 cal/ mole. This value of 901 cal/mole is to be c o m p a r e d with the 884 cal/mole reported for the increment in free energy per added methylene group for the transfer of hydrocarbons from a pure h y d r o c a r b o n liquid to an aqueous phase at 25°C under equilibrium conditions (32). CONCLUSION The dynamics of m o n o l a y e r depletion f r o m the a i r - w a t e r interface are shown to depend, at least in the case of two fatty acids, on an environmental factor thought to be of relatively little importance in the past, namely, the partial pressure of w a t e r near the interface, e x p r e s s e d as p e r c e n t a g e relative humidity. It is argued that at atmospheric humidities below the saturation point an additional depletion m e c h a n i s m involving c o m p l e x h y d r o d y n a m i c convection in the surface region needs to be considered. It is v e r y likely that earlier disagreements concerning the o b s e r v e d desorption rates of fatty acids h a v e b e e n the result of i m p r o p e r humidity control. The experimental desorption results apJournal of Colloid and Interface Science, Vol. 82, No. 2, August 1981
Financial support from the National Science Foundation (PCM76-81363 and ENG77-25130) and the University of Minnesota Agricultural Experiment Station is gratefully acknowledged. REFERENCES 1. Ter Minassian-Saraga, L., J. Chim. Phys. 52, 80 (1955). 2. Ter Minassian-Saraga, L., J. Chim. Phys. 52, 99 (1955). 3. Ter Minassian-Saraga, L., J. Chim. Phys. 52, 181 (1955). 4. Bilkadi, Z., and Neuman, R. D., Nature (London) 278, 842 (1979). 5. Matuura, R., Sekita, K., and Motomura, K., in "Chimie, physique et applications pratiques des agents de surface," Vol. 2, p. 375. Ediciones Unidas, Barcelona, 1969. 6. Patil, G. S., Matthews, R. H., and Cornwell, D. G., J. Lipid Res. 14, 26 (1973). 7. Baret, J. F., Bois, A. G., Casalta, L., Dupin, J. J., Firpo, J. L., GoneUa, J., and Melinon, J. P., J. Colloid Interface Sci. 53, 50 (1975). 8. Gershfeld, N. L., Ann. Rev. Phys. Chem. 27, 349 (1976). 9. Bilkadi, Z., Parsons, J. D., Mann, J. A., Jr., and Neuman, R. D. , J. Chem. Phys. 72, 960 (1980). 10. Wirz, J. H., and Neuman, R. D., J. Colloid Interface Sci. 63, 583 (1978). 1l. Berg, J. C., presented at the 64th Annual AIChE Meeting, San Francisco, Calif., 1971. 12. Good, P. A., and Schechter, R. S., J. Colloid Interface Sci. 40, 99 (1972). 13. Archer, R. J., and La Mer, V. K., J. Phys. Chem. 59, 200 (1955). 14. Robbins, M. L., and La Mer, V. K., J. Colloid Sci. 15, 123 (1960). 15. Alty, T., Canad. J. Res. 4, 547 (1931). 16. Morikawa, A., Keii, T., Aonuma, T., J. Colloid Interface Sci. 40, 349 (1972). 17. Bird, R. B., Stewart, W. E., and Lightfoot, E. N.,
MONOLAYER DESORPTION
18. 19. 20.
21. 22. 23. 24. 25.
"Transport Phenomena," pp. 554-591. Wiley, New York, 1960. Jarvis, N. L., and Kagaris, R. E., J. Colloid Sci. 17, 501 (1962). B6nard, H., Rev. Gen. Sci. Pure Appl. Bull. Assoc. Franc. Avan. Sci. 11, 1309 (1900). Berg, J. C., Acrivos, A., and Boudart, M., in "Advances in Chemical Engineering" (T. B. Drew, and J. W. Hoopes, Jr., Eds.), Vol. 6, p. 61. Academic Press, New York, 1966. Pearson, J. R. A., J. Fluid Mech. 4, 489 (1958). Berg, J. C., and Acrivos, A., Chem. Eng. Sci. 20,737 (1%5). Jarvis, N. L., J. Colloid Sci. 17, 512 (1962). Berg, J. C., Boudart, M., and Acrivos, A., J. Fluid Mech. 24, 721 (1966). Cini, R., Loglio, G., and Ficalbi, A., J. Colloid Interface Sci. 41, 287 (1972).
489
26. Ter Minassian-Saraga, L., J. Colloid Sci. 11, 398 (1956). 27. Gershfeld, N. L., in "Techniques of Surface and Colloid Chemistry and Physics" (R. J. Good, R. R. Stromberg, and R. L. Patrick, Eds.), Voh 1, p. 1. Dekker, New York, 1972. 28. Cammenga, H. K., and Rudolph, B. E., in "Proceedings, 5tb InternationalSymposium on Fresh Water from the Sea." Alghero, Vol. 1, p. 231, 1976. 29. Honig, E. P., Hengst, J. H. Th., and den Engelsen, D., J. Colloid Interface Sci. 45, 92 (1973). 30. Smith, R. D., Ph.D. thesis, University of Washington, Seattle, 1977. 31. Tabak, S. A., Ph.D. thesis, The Pennsylvania State University, University Park, 1977. 32. Tanford, C., "The Hydrophobic Effect: Formation of Micelles and Biological Membranes," pp. 4-8. Wiley, New York, 1973.
Journal o f Colloid and Interface Science, Vol. 82, No. 2, August 1981
When a monolayer of surface-active molecules is freshly spread at the air-water interface it often undergoes a process of depletion by evaporation or dissolution that manifests itself in an increase of surface tension with time. In many systems at room temperature, in the absence of chemical reactions and at surface pressures not exceeding the equilibrium spreading pressure (ESP), the monolayer depletes primarily by desorption into the aqueous phase. The most extensive investigation of monolayer desorption, and in fact the earliest one, was that of Ter Minassian-Saraga (1-3) using lauric and myristic acid. In a series of articles she established that the rate of desorption of fatty acids is determined by the size of the hydrophobic portion of the desorbing molecules, the surface density, temperature, and degree of ionization. In this article we report that the apparent 1 Published as Scientific Journal Series Paper No. 10,193 of the University of Minnesota Agricultural Experiment Station. 2 Present address: Central Research Laboratories, 3M Company, St. Paul, Minn. 55103.
desorption rates for monolayers of lauric and myristic acid also are determined by the relative humidity of the air above the interface (4). The observation that humidity effects are important in studies of the physicochemical properties of spread monolayers seems to have been overlooked in the past and could account for many conflicting findings on monolayer desorption (5-8). An interpretation of the humidity effect based on hydrodynamic convection encompassing the surface of the liquid is presented. A brief discussion of the time dependence of desorption at 100% RH is also given using a recently proposed model based on Brownian motion theory (9). EXPERIMENTAL
Most investigations of monolayer desorption in the past have utilized the constantpressure technique, which requires continuous compression of the film to maintain it at the desired pressure while monitoring its total area as a function of time. It can be argued that in this method the motion of the compression barrier disturbs both the monolayer and the subsolution beneath it by
480
0021-9797/81/080480-10502.00/0 Copyright © 1981 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and Interface Science, Vol. 82, No. 2, August 1981
MONOLAYER
stirring. The effect of stirring (rate of barrier motion) depends on the solubility of the film and may also vary from one worker to another. The present investigation utilizes the constant-area technique, which involves confining the film to a constant area while measuring the relaxation of surface pressure. This method eliminates virtually all of the complications inherent in the constantpressure technique since none of the components need be disturbed at any time following the adjustment of surface pressure to its desired initial value. It is recognized, however, that the meniscus curvature about the pressure-sensing device, e.g., Wilhelmy plate, does change somewhat during the desorption process. It can be shown that the change in the interfacial area, as well as the resulting film pressure change, is negligible over the pressure relaxation range examined in this study. Except for early attempts by Ter Minassian-Saraga (1,3), the method has not been exploited to its full potential as yet, probably because of the previous lack of a theoretical model. In this section we describe the apparatus used and discuss briefly the sources of error in the measurement of surface pressure relaxation.
Appa'ratus The basic units of the apparatus have been described previously (10). The system includes a Teflon trough, Cahn Model RG electrobalance, suspended platinum plate, and a Texas Instruments recorder. The trough was milled from a 1-in.-thick slab of Teflon and clamped firmly to a heavy block of aluminum tooling plate. The milled portion was 66 cm long, 5.6 cm wide, and 1.6 mm deep. The trough assembly, cleaned in H2SO4/Nochromix, was enclosed in a Lucite cabinet (94 x 50 x 34 cm) having a metal bottom and fitted with small pluggable ports. The access ports served two functions: first, to allow spreading of the monolayer from a solvent through long capillary tubes, thus
481
DESORPTION
minimizing disturbances of the physical conditions of the system, and second, to allow for adjustment of the humidity levels in the cabinet, which also contained small beakers containing moistened filter paper. This method of adjusting the humidity level inside the cabinet is preferable to passing moist air streams through the enclosed volume. The temperatures of both the liquid and gas phases were continuously monitored by three Fenwal (GB31P2) glass probe thermistors using a Keithley Model 616 digital electrometer. Each thermistor (3 mm o.d.) was calibrated to _0.02°C against a certified calorimeter thermometer in a constanttemperature bath. The thermistors were attached to an adjustable vertical Unislide assembly (Velmex Inc.) with scale and vernier, thus permitting their position to be measured to within +_0.05 mm. Typically one thermistor was placed in the liquid surface, and the remaining two were located at 13 and 22 mm above it. The relative humidity in the region between 5 and 20 mm above the surface was measured by a Hygrodynamics No. 4-4839 hygrosensor (American Instrument Co.) placed parallel to the surface and attached to a Hygrodynamics Model L15-3050 universal indicator. In addition, a second hygrosensor (No. 615-1810) was also used in the study. The factory calibration of both humidity probes was checked against the vapor pressure of saturated salt solutions, and their accuracy was at least ___2% RH. All experiments were conducted entirely in a clean environment room, where the humidity could be controlled to within +_3% RH between 30 and 95% RH and the temperature controlled to within +0.5°C.
Materials Myristic and lauric acid were obtained from Applied Science Laboratories. The chemical purity of the samples (99+%) w a s confirmed by gas chromatography. Journal of Colloid and Interface Science, Vol. 82, No. 2, August 1981
482
BILKADI
AND NEUMAN
The spreading solvent was n-hexane Phillips Pure Grade (99 mole%) and was purified further by a single percolation through a silica gel-activated charcoal adsorption column at room temperature. The pH of the subsolution was adjusted by Suprapur concentrated HCI (EM Laboratories). The water was first purified by a reverse-osmosis unit, then distilled twice in an all-glass apparatus, the first time from alkaline permanganate. Its conductivity was 0.8/xmho at 24°C. The water was stored in Pyrex containers in the controlled-environment room prior to use. One-hundred and fifty milliliters of subsolution was used for each kinetic run and resulted in a liquid height of 4.5 mm in the trough.
Sources of Error We describe in this section our efforts to eliminate artifacts due to monolayer leakage, contact angle hysteresis, mechanical disturbances, monolayer evaporation, and solvent effects. It should be realized, however, that while the first three sources of error could be eliminated or at least reduced to an insignificant level, the remaining two effects are much harder to assess experimentally. (a) Monolayer leakage. This source of error becomes relatively minor in the case of soluble surfactants such as lauric acid. On the other hand, for monolayers such as myristic acid, considerable effort must be expended to ensure that no defects are present, by carefully machining the edges and sides of the troughs and barriers. To establish the absence of monolayer leakage in a given trough the following experiment was repeated several times: The compression barrier was placed one-quarter of the way from a trough end, and a lens of tritolyl phosphate was spread at the other end. The surface tension of the clean surface was then monitored continuously for as long as 12 hr with the position of the compression barrier changed every 2 hr to detect any defects along the trough edges. The criterion Journal of Colloid and Interface Science, Vol. 82, No. 2, August 1981
for a leak-proof system in our experiments was that the change in surface tension of the film-free portion of the surface did not exceed 0.1 mN m -1 over a period of 2 hr. As an additional confirmation of the absence of monolayer leakage, we compared the desorption rates of myristic acid at 100% RH obtained with and without use of compression barriers, i.e., the correct amount of film material corresponding to the desired surface pressure was spread onto a trough having no barriers. The desorption rates had to be (and were) identical. (b) Contact angle effects. Before the monolayer was spread, the Wilhelmy plate was equilibrated with the subphase for at least 2 hr so that ample time was allowed for wetting of the surface and its thermal equilibration with the liquid. In order to minimize possible contact angle hysteresis the platinum plate was first sandblasted, then electroplated in chloroplatinic acid solution (11). Our decision to electroplate the sandblasted plate was based on the following observation: When the platinum plate was sandblasted only, a shift in the baseline was observed for a monolayer of stearic acid subjected to repeated compression-expansion cycles from its surface vapor pressure to 31 mN m -1. In particular, the baseline corresponding to the surface vapor pressure shifted upward by about 0.5 mN m -1 for each cycle up to the third one. This hysteresis did not appear to occur with the platinized plate. (c) Mechanical disturbances. The efforts to eliminate mechanical vibrations included anchoring the entire apparatus onto a heavy concrete base and avoiding the use of moist air streams in the cabinet for maintaining high humidity levels. The forks supporting the barriers were moved manually by means of a Unislide mechanical slide assembly chosen for its smooth motion. (d) Monolayer evaporation. Obviously, this could be a serious source of error since it constitutes a competing route for monolayer depletion. The opinions concerning the magnitude of this effect differ from one
MONOLAYER DESORPTION 7
I
i
I
~'~
i
I
100"/o RH
Z ,~
8 5 % RH
{3-
g O3 M I
I
10
20
47*/* RH
J-~ 50 TIME
40
50
60
70
(rain)
F[G. 1. Effect of relative humidity on the surface pressure relaxation of myristic acid monolayers on 0.01 N HC1 at 21.0 4- 1.0oc. worker to another (5, 12). In the case of myristic acid a direct p r o o f of the relative insignificance of monolayer evaporation will be provided (see Fig. 4). In the case oflauric acid the effect of monolayer evaporation remains unassessed. (e) Solvent effects. There are controversies regarding the effect of residual spreading solvent on the properties of lipid monolayers. In some instances it was claimed that entrapped organic solvent remained in the monolayer for periods exceeding 10 min (13, 14). Other studies imply complete evaporation of solvent within a few seconds (1, 7). In order to maximize the rate of solvent evaporation and minimize possible occlusion of solvent molecules in the monolayer, we delivered the spreading solution dropwise, at 5-sec intervals, to the largest possible surface area so that the surface pressure never e x c e e d e d 0.3 m N m - L The monolayer was then compressed fairly rapidly to the desired initial pressure. Solvent effects were not observed when this procedure was adopted.
483
as a function of time for various atmospheric humidities are given in Figs. 1 and 2. The kinetics at the saturation point (100% RH) were always reproducible to within 0.1 mN m -z, whereas at lower humidities the reproducibility was generally lower as indicated by the error bars, which represent the maximum deviation from the mean value of the film pressures. It is seen that at a given temperature, the higher the apparent " d e sorption" rate, the lower the steady-state value of atmospheric humidity. The observed relative humidities are average values from a fixed humidity probe, the center of which is located at about 13 mm above the surface. The values of the relative humidities at more remote locations in the cabinet were usually slightly lower. At the saturation point the humidity throughout the entire volume was always uniform. The temperatures noted in Figs. 1 and 2 are those given by a fixed thermistor located at 2.2 cm above the surface. The temperature profile throughout the liquid and gas phases is shown in Fig. 3 to be a function o f the relative humidity near the surface. Only under a saturated atmosphere was the temperature of the gas phase uniform and equal to that of the liquid. In all other cases the temperature of the liquid drops below that of the gas but appears uniform over its entire depth. On the other
'E Z
GO CO llJ 100% RH
ne ffl
RESULTS AND DISCUSSION
Desorption in Unsaturated Atmospheres The observed changes in the surface pressure o f myristic and lauric acid monolayers
i
~o
J
~o
~o TIME
i
~o
~'o
~'o
(rain)
FIG. 2. Effect of relative humidity on the surface pressure relaxation of lauric acid monolayers on 0.01 N HC1 at 21.0 _+ 0.5°C. Journal of Colloid and Interface Science, Vol. 82, N o . 2, A u g u s t 1981
484
BILKADI AND N E U M A N
hand, the temperature of the gas increases with distance from the surface and becomes uniform at distances slightly exceeding 2 cm. The only reasonable explanation of the lower temperature of the liquid relative to that of the gas is in terms of water evaporation from the surface. Obviously, under a saturated atmosphere the net rate of evaporation or the net mass flux across the water surface should be zero, and no net heat (energy) transfer across the surface is expected. Under these conditions the temperature throughout the liquid-gas system should be constant, as is the case for the uppermost curve in Fig. 3. At lower relative humidities, however, the net mass flux of water molecules initially causes a heat loss from the liquid and lowers its temperature relative to the gas. The finding that the temperature lowering of the liquid increases with decreasing relative humidity in the gas phase is simply an indication of enhanced evaporation rates. This result is consistent with many experimental findings in the literature, some of which reported drops in the temperature of the liquid surface exceeding 10°C (15, 16). Likewise, the existence of a temperature gradient in the gas phase is not surprising considering its rather low coefficient of thermal conductivity and the fact that at steady state the latent heat of vaporization is withdrawn from the gas layer adjacent to the liquid. The temperature profile in the gas layer could actually be estimated (17) from the coefficient of thermal conductivity of the gas and the rate of evaporation from the liquid. A rather striking observation from Fig. 3 is that the temperature of the liquid, in all cases, appears to have been uniform with depth (to within ±0.04°C) even when evaporation was taking place. This observation does not necessarily rule out the possibility that thermal gradients confined to very thin layers of liquid do in fact exist but the size of the thermistor is too large for their detection. This point of view has been discussed in the literature (18). Moreover, it is likely that at atmospheric humidities below Journal of Colloid and Interface Science, Vol. 82, No. 2, August 1981
22 0 1 0 0 % RH
21
68O/oR. ,.~.,'J':'"
,~ z0
,,2~5O, o,,
1B
I<--Liquid )1( - 0• 4I
/
Air 01.4
DISTANCE
210 I I 12 16 FROM I N T E R F A C E ( c m ) 018
I
2.4
FIG. 3. Temperature profile in the bulk phases.
saturation the aqueous layer is the site of hydrodynamic convective movement as a result of water evaporation. The existence of convective motion in liquids due to evaporation was demonstrated experimentally by B6nard (19) at the turn of the century; and his work, as well as more recent results, has been exhaustively reviewed (20). The main conclusion relevant to this discussion is that while the origin of evaporative convection in pure liquids is surface cooling, its driving force is a complex function of the surface tension fluctuations (Marangoni effect) and the density gradient along the depth of the liquid (buoyancy effect). It is very difficult in many cases to decouple the surface tension instability from the instability due to the density gradient. However, it is claimed, mainly on theoretical grounds (21, 22), that the relative importance of the Marangoni and buoyancy effects in triggering and sustaining convection appears to be governed by the depth of the liquid layer. Theoretical calculations (22) have suggested that for a water layer with a free surface the surface tension mechanism, rather than the buoyancy mechanism, predominated whenever the depth was less than about 1 ram. The effect of spread monolayers on evaporative convection has been studied by Jarvis (23), who has shown by measuring the temperature fluctuations that even a highly compressed monolayer of oleic acid did not significantly inhibit convection at a depth of approximately 4 mm in the aqueous
MONOLAYER DESORPTION
47
57
RELATIVE HUMIDITY (percent) 67 77 s7
97
Z o
!I
~op
J o_
o_ 1~
i
i i TIME {min)
i
/
720
FIG. 4. M o n o m o l e c u l a r film behavior of myristic acid on 0.01 N HCI at c o n s t a n t area with continually increasing a t m o s p h e r i c humidity for two initial surface p r e s s u r e s . (a) 170 = 6.5 and (b) Yl0 = 0.3, where H0 is the initial surface p r e s s u r e in m N m -1 at t = 0. C u r v e (c) c o r r e s p o n d s to the subsolution t e m p e r a t u r e given by a thermistor located in the liquid surface.
subsolution. Similarly, Berg et al. (24) have shown qualitatively by schlieren optics that the presence of surface-active molecules on evaporating water layers suppressed cellular convective movement when the depth was 1 mm or less, but convection in the form of "cold streamers" was visible when the depth was about 1 cm. It is concluded on the basis of the experimental evidence in the literature that for water layers of thicknesses comparable to that in the present investigation (4.5 mm) the presence of surface-active molecules quite likely retards convective motion but does not eliminate it altogether. This motion could serve as a competing route for monolayer depletion from the surface whereby the surface-active species are carried or "forced" into the interior by the downward motion of the cold liquid. The fact that the intensity of convection increases with the rate of evaporation has been established (22) and could then be at the origin of the observed dependence of surface pressure relaxation on atmospheric humidity. In view of these considerations it can be statedthat true desorption, driven solely by the excess chemical potential of the lipid molecules at the surface, is represented only by the curves in Figs. 1 and 2 obtained under saturated atmospheres. An interesting behavior of the monolayer is observed when the humidity of the atmos-
485
phere is not held constant throughout the experiment. This is illustrated in Fig. 4 in the case of myristic acid. Figure 4 depicts the apparent temperature and surface pressure dependence on relative humidity. In practice, this condition is achieved by closing all ports of the cabinet immediately following spreading of the monolayer, thereby causing a gradual increase in the water content of the atmosphere by evaporation. This procedure closely corresponds to that commonly practiced today in film balance studies performed in ambient laboratory environments. Curve 4a illustrates the behavior when the initial surface pressure is 6.5 mN m -1. The film appears to deplete at a very fast rate initially, perhaps as a consequence of convection in the liquid. As the relative humidity rises, the convective movement presumably subsides somewhat, allowing the excess surface-active molecules in the interior of the liquid to readsorb gradually to the surface. The net effect would then be an increase in the surface pressure following the rapid initial decrease. It seems that readsorption persists even when the monolayer pressure is originally very small, as is the case in Curve 4b. Here, in some extreme cases, the surface pressure increased from 0.3 mN m -1 and leveled off for 12 hr at values as high as 2.91 mN m -1 when the humidity reached the saturation limit. The final value of film pressure depended on the volume of spreading solution used. The fact that the final surface pressure remained constant for periods of several hours not only rules out evaporation of myristic acid as a significant depletion mechanism, but also confirms the absence of monolayer leakage in our system. It is to be noted that the rise in atmospheric humidity is accompanied by a rise in the temperature of the liquid subsolution as shown in Curve 4c and predicted by the findings in Fig. 3. One could speculate that the difference in the relaxation rates shown in Figs. 1, 2, and 4 might arise solely from differences in the subsolution temperature. Journal of Colloid and Interface Science, Vol. 82, No. 2, August 1981
486
BILKADI AND NEUMAN
However, an experiment conducted at 100% RH revealed that the desorption kinetics at 18.5 and 21.5°C are almost indistinguishable. Thus, other factors besides the difference in subsolution temperatures should be at play. The behavior depicted in Fig. 4 could not be observed in the case of lauric acid, probably because of its higher solubility. Figure 5 shows the results of the control experiment where the surface of the aqueous subsolution was not covered with a fatty acid film. The change of the baseline registered by the Cahn electrobalance corresponds to the total decrease in the surface tension of the aqueous phase due to the increased temperature of the subsolution. The quantity -Ay/AT is very nearly 0.15 mN m -~ ° C - l , which is the accepted literature value for water (25). An important consideration relative to the results in Fig. 4 is that the environment is not at equilibrium or even at steady state. In particular, the rate of increase in humidity, and consequently the rate of surface pressure increase, depends on the volume of the enclosed atmosphere, i.e., the size of the cabinet. Therefore, no significance should be given to the time scale of these phenomena. On the other hand, the effects illustrated in the other figures were undertaken in environments at equilibrium or at steady state; they are therefore independent of the apparatus. The kinetics of desorption at 100% RH have been reproduced using troughs of varying shapes and construction material. In a concluding note, convective motion certainly exists in the liquid, not only in the bulk but also in the surface region, when the atmosphere above the monolayer-covered surface is unsaturated. The increase in the apparent desorption rate at lower relative humidities is due to this convective motion which causes a more rapid depletion of film molecules from the surface. No stagnant or calm liquid layer exists, as assumed by other investigators (26, 27), and this interpretation Journal of Colloid and Interface Science, Vol. 82, No. 2, A~lgust 1981
RELATIVE HUMIDITY
,,
2;
7;
0;
(percent)
7
T
22
TE OS
°"
, ~o
,~o
TIME (min)
F[o. 5. Changes in surface tension ( ) and ternperature (- - -) of 0.01 N HC1 subsolution as a function of time and relative humidity. is in agreement with other recent studies (28). Rarely does anyone measure the relative humidity in film balance studies and when it has been measured, values of only 70% (29, 30) or somewhat higher (31) have been reported. Most, if not all, investigations of desorption, as well as those of other film properties, e.g., typical rI-A isotherms and surface diffusion measurements, very likely have had convective currents present in the surface because of the general unawareness of the need to control the humidity and its relationship to the onset of the development of convective cells in thin liquid layers.
Desorption in Saturated Atmospheres The surface pressure relaxation at 100% RH was measured for myristic acid at initial pressures of 6.49 and 8.76 mN m -1. In addition, it was measured for lauric acid at initial pressures of 6.49 and 13.3 mN m-L The desorption kinetics can be interpreted in terms of a recently proposed model derived from diffusion theory (9). The model assumes that the fatty acid molecule at the surface is in a potential energy well which is the result of its hydrophobic character. The molecule desorbs into the bulk liquid by virtue of its thermal motion, but to do so it must escape the potential well. In this formulation the desorption process is basically one-dimensional diffusion in the presence of a short-range force field Q(z), and the rate of particle escape is controlled by
487
MONOLAYER DESORPTION
•
•
•
molecules are ignored, the general solution of the Smoluchowski equation with appropriate boundary and initial conditions is given by F p(t) - e azt erfc (ottZ/2), [|] F0
$M= - Lfl7 x IO-t
09 l t-.* 0.8
SL = " 3 " 6 6 t 10-2
0.7
~
I 4
; ,/V
I
I S
I
rain ~z
F10. 6. The variation of F/F0 with t 1~2 for the desorption of myfistic and lauric acid from the airwater interface at 21.0°C. Myristic acid: (A) II o = 6.49, (&) 1Io = 8.76. Lauric acid: (©) 17o = 6.49, ( 0 ) II o = 13.3.
the depth and range of the potential well. This requires the use of the Smoluchowski equation rather than Fick's equation to derive the evolution of probability P ( z , t ) that a surfactant molecule will have position z at time t given it had position z = 0 at t = 0. It is important to recognize that if desorption were caused by diffusion alone from a concentration gradient near the surface, the film would desorb much too quickly with a time constant r-=-z2/D, where D is the diffusion coefficient3 of the surfactant molecule and z0 is the thickness of the surface zone. Thus, for D -= 10-6 cmVsec and z0 "=- 20 A, z is a microscopic time of the order of 10-8 sec. The mathematical details of the model have been thoroughly discussed (9). A simple analytic solution has been found only for a square-well potential. When the lateral interactions between neighboring surfactant The diffusion coefficient employed in t h e s e calculations is that for diffusion in bulk water. This a s s u m p tion that the diffusion coefficient in the surface zone a n d bulk liquid are equal m a y be questioned on the g r o u n d s that the stochastic forces in the surface zone are likely to be anisotropic. It is to be noted that at the p r e s e n t time m e a s u r e m e n t s of surface diffusion in fluids are inconclusive, and w h e r e a s s o m e studies indicate differences in the motions at the surface and in the bulk, other investigations do not. The conclusions p r e s e n t e d herein, h o w e v e r , are not affected by this question.
where F is the surface density at time t, and 1 / a 2 is the time constant for desorption given by 1 z2 e 20 = "re zQ, [2] a 2
D
where Q and z0 are the two adjustable parameters corresponding to the height (in k T ) and width of the potential well. For t small compared to the relaxation constant, Eq. [1] reduces to the simple expression p(t)
-
F F 0
~
1 -
2a
~ t 1/2. "/71/2
[3]
Since the measured quantity in the present experiments is the surface pressure, one needs an equation of state to compute p ( t ) . As a first approximation we assume that the empirical equation of state H ~ (F) ~'8~ proposed by Ter MinassianSaraga (3) is valid for lauric acid. For myristic acid, .experimental H-A data (Tompkins and Neuman, unpublished) obtained at 100% RH were used. The results shown in Fig. 6 lead to two important conclusions: First, the kinetics predicted by Eq. [3] are valid, indeed, over a time period of almost 30 min for lauric acid and 1 hr for myristic acid. At longer times the kinetics are more appropriately described by Eq. [1]. Second, the observed desorption rate is independent of the initial surface density F0 and, therefore, independent of the initial surface pressure 170 as predicted by Eqs. [1] and [3]. This finding seems to validate the assumption made in the model that the lateral interactions in the monolayer are relatively unimportant, at least in the liquid-expanded phase. The monolayer desorption experiment is a particularly elegant method for extracting Journal of Colloid and Interface Science, Vol. 82, No. 2, August 1981
488
BILKADI AND NEUMAN
rich information on h y d r o p h o b i c interactions. In particular, in the present model the difference in the desorption kinetics of lauric and myristic acid is due to the repulsive forces b e t w e e n the a q u e o u s subsolution and the two additional methylene ( - C H ~ - ) groups in the myristic acid h y d r o c a r b o n chain. The ratio of the slopes SM and SL in Fig. 6 for myristic and lauric acid, respectively, is given by SL a M
---
O~.L
[4]
o/M
ACKNOWLEDGMENTS
Combining Eqs. [2] and [4] one obtains In SL = ( Q M - Q L ) SM
pear to be in good a g r e e m e n t with our theoretical model for desorption at constant area. Further tests of our model, h o w e v e r , require equations o f state or experimental H - A data m o r e accurate than those presently available. Future studies will delineate the d e p e n d e n c e of the depth and range of the potential well on the molecular structure of the surfactant molecule and shed further insight into the nature of the intermolecular forces in m o n o m o l e c u l a r films.
+--lln--rM , 2 ~-L
[5]
where the last term in Eq. [5] is v e r y small and can be neglected. Since f r o m Fig. 6, S L / S M = 21.9, it can be shown that the activation energy for the transfer of a single methylene group f r o m the m o n o l a y e r to the aqueous subsolution amounts to 901 cal/ mole. This value of 901 cal/mole is to be c o m p a r e d with the 884 cal/mole reported for the increment in free energy per added methylene group for the transfer of hydrocarbons from a pure h y d r o c a r b o n liquid to an aqueous phase at 25°C under equilibrium conditions (32). CONCLUSION The dynamics of m o n o l a y e r depletion f r o m the a i r - w a t e r interface are shown to depend, at least in the case of two fatty acids, on an environmental factor thought to be of relatively little importance in the past, namely, the partial pressure of w a t e r near the interface, e x p r e s s e d as p e r c e n t a g e relative humidity. It is argued that at atmospheric humidities below the saturation point an additional depletion m e c h a n i s m involving c o m p l e x h y d r o d y n a m i c convection in the surface region needs to be considered. It is v e r y likely that earlier disagreements concerning the o b s e r v e d desorption rates of fatty acids h a v e b e e n the result of i m p r o p e r humidity control. The experimental desorption results apJournal of Colloid and Interface Science, Vol. 82, No. 2, August 1981
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