Axisymmetric Drop Shape Analysis as a Film Balance - American

The rate dependence of collapse pressure was studied systematically by axisymmetric drop shape analysis for an octadecanol monolayer. Results suggest ...
0 downloads 0 Views 269KB Size
Download PDF
+

+

Langmuir 1996, 12, 1851-1859

1851

Axisymmetric Drop Shape Analysis as a Film Balance: Rate Dependence of the Collapse Pressure and Molecular Area at Close Packing of 1-Octadecanol Monolayers D. Y. Kwok,†,‡ B. Tadros,‡ H. Deol,‡ D. Vollhardt,§ R. Miller,§ M. A. Cabrerizo-Vı´lchez,| and A. W. Neumann*,‡ Department of Mechanical Engineering, University of Toronto, 5 King’s College Road, Toronto, Ontario, Canada M5S 3G8, Max-Planck-Institut fu¨ r Kolloid- und Grenzfla¨ chenforschung, Rudower Chaussee 5, D-12489 Berlin-Adlershof, Germany, and Departamento de Fı´sica Aplicada, Universidad de Granada, Campus de Fuentenueva, 18071 Granada, Spain Received July 10, 1995. In Final Form: January 11, 1996X The rate dependence of collapse pressure was studied systematically by axisymmetric drop shape analysis for an octadecanol monolayer. Results suggest that collapse pressure is not uniquely dependent on the compression rate; it depends on the amount of surfactant spread on the drop surface. It was also found that the shape of the surface pressure-area (π-A) isotherms changes with the rate of molecular area compression; increasing the compression rate shifts the lower part of the isotherm to the right. It was also found that the values of the molecular area at collapse are more reproducible and consistent than the conventional extrapolation of the limiting molecular area; the former was found to be 19.6 ( 0.1 Å2/ molecule, independent of both the amount of surfactant and motor speed, whereas the latter was found to be dependent on both the amount of surfactant and motor speed. All of these findings were explained by a morphological study of an octadecanol monolayer using Brewster angle microscopy.

Introduction Since Langmuir1 developed the first film balance and subsequent modifications by others,2,3 film balances have been used to determine many monolayer properties for different substances. One of these properties is the collapse point or the collapse pressure of a monolayer. Collapse occurs when the monolayer is essentially incompressible; further compression makes the film unstable and forces molecules out of the interface or into the bulk phase to form a three-dimensional entity. In the literature,4-12 the collapse pressure is often identified as the point where a “spike” occurs or a plateau of maximum surface pressure π in the π-A isotherms begins; A is the area per molecule. The collapse pressure provides information on the stability of a monolayer; the higher the collapse pressure, the more stable the monolayer. Lung surfactants are known to give stable monolayers with a surface tension as low as 1 mJ/m2. Thus, collapse pressures as high as * Author to whom correspondence should be addressed. † This paper represents, in part, the M.A.Sc. thesis of D. Y. Kwok (University of Toronto, Toronto, Canada, 1994). ‡ University of Toronto. § Max-Planck-Institut fu ¨ r Kolloid-und Grenzfla¨chenforschung. | Universidad de Granada. X Abstract published in Advance ACS Abstracts, March 1, 1996. (1) Langmuir, I. J. Chem. Soc. (London) 1917, 39, 1848. (2) Gaines, G. L., Jr. Insoluble Monolayers at Liquid-Gas Interfaces; Wiley Interscience: New York, 1966. (3) Adamson, A. W. Physical Chemistry of Surfaces, 5th ed.; John Wiley & Sons: New York, 1990. (4) Langmuir, I.; Schaefer, V. J. J. Am. Chem. Soc. 1937, 59, 2400. (5) Rabinowitch, W.; Robertson, R. R.; Mason, S. G. Can. J. Chem. 1960, 38, 1881. (6) Crisp, D. J. J. Colloid Sci. 1946, 1, 49. (7) Harkins, W. D.; Boyd, E. J. Phys. Chem. 1941, 45, 20. (8) Jeffers, P. M.; Daen, J. J. Phys. Chem. 1965, 69, 2368. (9) Dervichian, D. G. J. Chem. Phys. 1939, 7, 931. (10) Munden, J. W.; Blois, D. W.; Swarbrick, J. J. Pharm. Sci. 1969, 58, 1308. (11) Heikkila, R. E.; Kwong, C. N.; Cornwell, D. G. J. Lipid Res. 1970, 11, 190. (12) Fasman, G. D., Ed. Handbook of Biochemistry and Molecular Biology, Lipids, Carbohydrates, Steroids, 3rd ed.; CRC Press: Cleveland, OH, 1975; p 497.

71 mJ/m2 will occur. Nevertheless, the collapse mechanism is not well understood:13 Langmuir and Schaeffer4 published photographs of severely overcompressed films which show visible and permanent “crumple patterns”. Long narrow ridges of C36 saturated fatty acid were observed by Ries et al.14 at high surface pressures from electron micrographs of collapsing films. Subsequent studies15-19 on other films revealed other structures as well. In fact, most of the information on monolayer collapse comes from film balance studies. Disagreement among investigators about the collapse pressure has been enormous; it has often been found that the collapse pressures of a monolayer cannot be easily reproduced, even at the same rate of molecular area compression. In general, the collapse mechanism seems to be complicated. It has long been thought to depend on the nature of the substance, temperature, pH, pressure, and the rate of molecular area compression.2,3,5,20-23 Recent electron micrographs and atomic force microscopy (AFM) images obtained by Kato et al. showed platelet-like layers on the order of a micrometer in size and small granular structures with a height of several nanometers.24,25 Considerable progress has recently been achieved in the understanding of monolayer instability. Above the (13) Smith, R. D.; Berg, J. C. J. Colloid Interface Sci. 1980, 74, 273. (14) Ries, H. E., Jr.; Walker, D. C. J. Colloid Sci. 1961, 16, 361. (15) Ries, H. E., Jr. J. Colloid Interface Sci. 1976, 57, 396. (16) Ries, H. E., Jr.; Cook, H. D. J. Colloid Sci. 1954, 9, 535. (17) Ries, H. E., Jr.; Kimball, W. A. Nature (London) 1958, 181, 901. (18) Shappard, E.; Bronson, R. P.; Tcheurekdjian, J. J. J. Colloid Sci. 1965, 20, 755. (19) Neuman, R. D. J. Colloid Interface Sci. 1976, 56, 505. (20) Nutting, G. C.; Harkins, W. D. J. Am. Chem. Soc. 1939, 61, 2040. (21) Min˜ones, J.; Iribarnegaray, E.; Varela, C.; Vila, N.; Conde, O.; Cid, L.; Casas, M. Langmuir 1992, 8, 2781. (22) Joos, P. Bull. Soc. Chim. Belge. 1972, 80, 277. (23) McFate, C.; Ward, D.; Olmsted, J., III Langmuir 1993, 9, 1036. (24) Kato, T.; Iriyama, K.; Araki, T. Thin Solid Films 1992, 210/211, 79. (25) Kato, T.; Matsumoto, N.; Kawano, M.; Suzuki, N.; Araki, T.; Iriyama, K. Thin Solid Films 1994, 242, 223.

+

1852

+

Langmuir, Vol. 12, No. 7, 1996

Kwok et al.

Figure 2. Schematic of a π-A isotherm; extrapolation for the collapse pressure is shown.

by ADSA will be explained by considering the morphological properties of an octadecanol monolayer. Figure 1. Surface pressure (mJ/m2) versus area per molecule (Å2/molecule) of pendant drops with an octadecanol film compressed at 22.8 Å2/(molecule min), for two repeat experiments; good reproducibility is observed for both the shape of the curves and the collapse pressures.

equilibrium surface pressure, the surface pressure-area (π-A) isotherms are in a state of supersaturation which is characterized by monolayer relaxation. As demonstrated by Kato et al.,26 such relaxation processes lead to changes of the shape of the isotherms. The relaxation of supersaturated monolayers below the collapse pressure has been described by a nucleationgrowth-collision theory.27-30 The Brewster angle microscopy (BAM) recently developed31 offers an attractive possibility to visualize directly the 2D-3D transformation of supersaturated monolayers before and beyond the collapse pressure. The growth of three-dimensional structures during constant surface pressure relaxation of supersaturated fatty acid monolayers has been investigated by BAM.32 Very recently, a drop shape technique (Axisymmetric drop shape analysis, ADSA) for interfacial tensions has been operated as a film balance.33,34 Figure 1 shows a typical π-A isotherm for an insoluble surfactant, 1-octadecanol, measured by ADSA. This isotherm was established at a compression rate of 22.8 Å2/(molecule min). As can be seen, the two runs overlay each other very well. It should be noted that the collapse pressure in this figure can easily be identified as a “spike” in the π-A isotherm. However, as discussed earlier, collapse can also occur as a plateau of maximum surface pressure (see Figure 2); we shall, therefore, specify the criterion of collapse for the present study as the point where the upper part of the isotherm starts to deviate from the straight line (Figure 2). The purpose of this paper is to study the rate dependence of the collapse pressure for an octadecanol monolayer using Axisymmetric drop shape analysis. The results obtained (26) Kato, T.; Hirobe, Y.; Kato, M. Langmuir 1991, 7, 2208. (27) Vollhardt, D. Adv. Colloid Interface Sci. 1993, 47, 1. (28) Vollhardt, D.; Retter, U. J. Phys. Chem. 1991, 95, 3723. (29) Vollhardt, D.; Ziller, M.; Retter, U. Langmuir 1993, 9, 3208. (30) Retter, U.; Vollhardt, D. Langmuir 1991, 9, 3723. (31) Ho¨nig, D.; Mo¨bius, D. J. Phys. Chem. 1991, 95, 4590. (32) Siegel, S.; Ho¨nig, D.; Vollhardt, D.; Mo¨bius, D. J. Phys. Chem. 1992, 96, 8157. (33) Kwok, D. Y.; Vollhardt, D.; Miller, R.; Li, D.; Neumann, A. W. Colloids Surf., A 1994, 88, 51. (34) Kwok, D. Y. Axisymmetric Drop Shape Analysis as a Film Balance. M.A.Sc. Thesis, University of Toronto, Toronto, Canada, 1994.

Materials and Apparatus 1-Octadecanol was used as supplied by Sigma Co. in >99% purity. Water used in this experiment was doubly distilled and deionized. The surface tension of the water was found to be γlv ) 72.5 ( 0.06 mJ/m2 at room temperature (22 °C), in agreement with literature values. The spreading solvent, heptane, was supplied by Aldrich Chemical Company, with 99% purity. In all experiments, a stock solution of 64.7 µg/mL of 1-octadecanol in heptane was used. It was prepared from 6.47 mg of purified octadecanol in 100 mL of heptane inside a volumetric flask. In the actual experiment, 5 mL of the stock solution was pipetted into a 25 mL volumetric flask, resulting in a dilute solution of 12.9 µg/mL of 1-octadecanol in heptane. This solution was always freshly prepared from the stock solution and subsequently used in all experiments. Axisymmetric drop shape analysis (ADSA)35-37 was used to determine the surface tension and hence the surface pressure.33,34 ADSA is a technique to determine liquid-fluid interfacial tensions and contact angles from the shape of axisymmetric menisci, i.e., from sessile as well as pendant drops.35 The strategy employed is to fit the shape of an experimental drop to a theoretical drop profile according to the classical Laplace equation. The surface tension is then computed from the best numerical fit to the Laplacian curve using nonlinear least-squares optimization techniques. Apart from local gravity and densities of liquid and fluid phases, the only information required by ADSA is several arbitrary but accurate coordinate points selected from the drop profile. To achieve rapid and accurate data acquisition and preprocessing, an automatic digitization technique utilizing digital image acquisition and analysis has been used.36,37 Computer software has been developed to implement this method, and computational results provide the values of interfacial tension γ, drop volume V, surface area A, radius of curvature at the apex R0, and, in the case of a sessile drop, contact angle θ and the radius of the threephase contact line. In this study, a Teflon capillary with an outside diameter of 0.1 in. and an inside diameter of 0.076 in. was used to form pendant drops. The apparatus was the same as that described previously,33,34 except that the dc motor and the micropipettor to deliver the heptane/octadecanol solution were replaced by more sophisticated equipment: A Hamilton microliter syringe with 0.01% accuracy was used to replace the digital micropipettor. The preliminary setup with a dc motor used in a previous paper has recently been redesigned and automated.38 Instead of a dc (35) Rotenberg, Y.; Boruvka, L.; Neumann, A. W. J. Colloid Interface Sci. 1983, 93, 169. (36) Cheng, P.; Li, D.; Boruvka, L.; Rotenberg, Y.; Neumann, A. W. Colloids Surf. 1990, 43, 151. (37) Cheng, P. Automation of Axisymmetric Drop Shape Analysis Using Digital Image Processing. Ph.D. Thesis, University of Toronto, Toronto, Canada, 1990.

+

+

1-Octadecanol Monolayers

Langmuir, Vol. 12, No. 7, 1996 1853

Figure 4. Surface pressure (mJ/m2) versus area per molecule (Å2/molecule) of pendant drops with an octadecanol film compressed at 5.71, 11.6, and 22.8 Å2/(molecule min). These isotherms were established with the same amount of surfactant (1.3 × 1014 octadecanol molecules) but were compressed at different motor speed settings: 4, 5, and 6. Collapse pressures of 53.0 ( 0.5 mJ/m2 were obtained, independent of the motor speed. Extrapolations for the limiting molecular areas and the molecular area at collapse are shown. Figure 3. (a) Surface tension (mJ/m2), (b) drop volume (cm3), (c) surface area (cm2), and (d) radius of curvature at the apex (cm) versus time (s) of a pendant drop with an octadecanol film. The pendant drop was controlled by means of an automated motor driven syringe. motor, a stepper motor incorporated into a new syringe mechanism was used in all experiments. Image acquisition and motor speed were controlled through a SUN SPARCstation 10 computer. The stepper motor in this experiment has nine different speed settings, from 1 to 9; 1 is the slowest and 9 is the fastest speed. With the automation of the new motor driven syringe, repeat experiments at specific speeds can easily be performed. The capability of this automated motor driven syringe with repeated cycles is shown in Figure 3, where the motor was set as specified starting and ending points of the drop volumes, providing definitive drop surface areas and surface tensions. As shown in Figure 3b, the pendant drop with the insoluble octadecanol monolayer was subjected to a constant rate of drop volume change from about 30 to 150 s. Varying the drop volume in this manner changes the surface area linearly until a plateau of the surface area at about 120 s is observed (see Figure 3c). In the plateau region, the film is essentially incompressible and the surface tension is reduced from about 50 to 32 mJ/m2 (cf. Figure 3a). After 150 s, the motor was operated at a faster rate of drop volume change; by expanding and compressing the drop volume at specified drop volumes, three and a half cycles of the surface tensions, drop volumes, drop surface areas, and radius of curvature at the apex were obtained. Detailed descriptions of the experimental apparatus can be found elsewhere.34,38

Brewster Angle Microscopy (BAM) Brewster angle microscopy (BAM) is a new and powerful method to obtain morphological information on insoluble mono(38) Susnar, S. S. Development of Facility for Axisymmetric Drop Shape Analysis (ADSA). Ph.D. Thesis, University of Toronto, Toronto, Canada (in preparation).

layers. BAM results will be used to interpret the results of the ADSA experiments (see later). In the BAM experiment, a zero reflectance of the p-polarized light with the Brewster angle at the pure air/water interface is used. A monolayer at the airwater interface leads to a measurable change in the reflectivity which is observable through a microscope. This principle allows a direct visualization of monolayer morphology with a spacial resolution of 4 µm. Details of the Brewster angle microscope and the description of the setup were given elsewhere.39 Images of the texture of condensed monolayer phases are stored using a video system including a video recorder, a monitor, and a video printer.

Experimental Procedures Deposition of the spreading solution onto the pendant drop was performed as described in a previous paper.33 All pendant drop experiments were conducted at room temperature, 22 °C. The rate of image acquisition was between 1 and 2 images per second, depending on the speed setting of the motor. In all experiments, a pendent drop with the insoluble monolayer was compressed until the drop fell off (due to necking) or became very small. It should be noted that changes in the rate of molecular area compression

area 1 area ) molecule min molecule min

(

)( )

(1)

can be brought about in two different ways: (1) by varying the motor speed settings or (2) by varying the amount of surfactant on the drop surface. To investigate systematically the dependence of the molecular compression rate with respect to the collapse pressure, the following procedures were used. 1. Varying the Motor Speed Settings. Experiments were first performed by changing the rate of molecular area compres(39) Vollhardt, D.; Gehlert, U.; Siegel, S. Colloids Surf., A 1993, 76, 187.

+

1854

+

Langmuir, Vol. 12, No. 7, 1996

Figure 5. Drop surface area (cm2) versus time (s) for the data in Figure 4. By linear regression, the motor speed settings 4, 5, and 6 correspond to the rate of change in drop surface area of 0.0741, 0.151, and 0.296 cm2/min, respectively. sion, by varying the speed of the motor, using settings 4, 5, and 6, while the amount of octadecanol on the drop surface was constant at 1.3 × 1014 molecules. 2. Varying the Amount of Surfactant on the Drop Surface. For the second type of experiment, the rate of compression was changed by varying the amount of octadecanol on the drop surface while keeping the motor setting constant. Always using the stock solution of 12.9 µg/mL of octadecanol in heptane, the amount of solution deposited in the water drop ranged from 2 to 5.5 µL in increments of 0.5 µL. These experiments were performed for three motor settings, i.e. settings 4, 5, and 6. The rate of change in drop surface area for the three motor settings can be calculated subsequently from the surface area-time plot by linear regression (see later).

Results and Discussion 1. Varying the Motor Speed Settings. In the experiment described in section 1 above, keeping the amount of surfactant unchanged and varying the motor speed setting changes the rate of molecular area compression (see eq 1). The results of this experiment for the three motor speed settings, 4, 5, and 6, are shown in Figure 4; a collapse pressure of 53.0 ( 0.5 mJ/m2 was found in all cases. These π-A isotherms were established with the same amount of surfactant (4.5 µL of 1-octadecanol/ heptane solution or 1.3 × 1014 octadecanol molecules). The actual rate of change in drop surface area by these motor speed settings was calculated using linear regression in the linear region of the drop surface area-time curves for each case (see Figure 5). In all cases, linear regression coefficients of >0.992 were obtained. As indicated in this figure, all curves show similar behavior; a linear region is followed by a region of essentially constant surface area. As discussed in a previous paper,33 this region indicates that the monolayer is essentially closely packed and incompressible. Thus, by linear regression in Figure 5, it was found that motor speed

Kwok et al.

Figure 6. Surface pressure (mJ/m2) versus area per molecule (Å2/molecule) of pendant drops with octadecanol film. These isotherms were compressed at 0.296 cm2/min (motor setting 6), but different amounts of surfactant, from 5 to 2 µL of octadecanol/heptane solution (12.9 µg/mL), in 1 µL increments were used. The resulting compression rates are 20.5, 25.7, 34.1, and 51.3 Å2/(molecule min), respectively. Extrapolations, for the limiting molecular areas and the molecular area at collapse are shown.

settings of 4, 5, and 6 correspond to rates of change in drop surface area of 0.0741, 0.151, and 0.296 cm2/min, respectively. Knowing the initial amount of surfactant on the drop surface, i.e., 1.3 × 1014 molecules, enables one to calculate the rate of molecular area compression from eq 1. The rates of molecular area compression for the three curves in Figure 4 were found to be 5.71, 11.6, and 22.8 Å2/(molecule min), respectively. The good reproducibility of the π-A curves was documented elsewhere.34 It should be noted that even though no dependence of the collapse pressures on the compression rate was found in Figure 4, the shapes of π-A isotherms vary significantly with the compression rate; increasing the compression rate shifts the lower part of the isotherms to the right. 2. Varying the Amount of Surfactant on the Drop Surface. In the first part of the second type of experiment, the motor speed setting was kept at setting 6 and the amount of surfactant was varied from 2 to 5.5 µL of 1-octadecanol/heptane solution, in 0.5 µL increments. Figure 6 shows every second of the π-A isotherms, i.e. those at 20.5, 25.7, 34.1, and 51.3 Å2/(molecule min), respectively, for 5, 4, 3, and 2 µL of octadecanol/heptane solution; decreasing the amount of octadecanol increases the rate of molecular area compression (cf. eq 1). It can be seen in this figure that the collapse pressure decreases from about 61.0 to 47.5 mJ/m2 as the amount of monolayer material increases. These experiments were then repeated at motor settings 5 and 4. The result in Figure 6 is different from that of the first experiment, i.e. Figure 4, where the collapse pressure did not change while the rate of compression was changed. Since changing either the amount of surfactant on the drop surface or the motor speed setting (area/minute) changes the rate of molecular

+

1-Octadecanol Monolayers

+

Langmuir, Vol. 12, No. 7, 1996 1855

Figure 7. Morphology of octadecanol monolayers at different spreading areas after evaporation of the spreading solvent visualized by Brewster angle microscopy (BAM): (a) 120 Å2/molecule; (b) 100 Å2/molecule; (c) 60 Å2/molecule; (d) 30 Å2/molecule; and (e) 20 Å2/molecule.

area compression, it is peculiar to observe change in the collapse pressure only in the second experiment. This question will be discussed below. As can be seen in both Figures 4 and 6, the shapes of the π-A isotherms change with the rate of molecular area compression in a very regular fashion: Increasing the rate of molecular area compression shifts the lower part of the π-A isotherms to the right. But one type of experiment gives a rate dependence of the collapse pressure, and the other does not. To elucidate this peculiarity, the BAM experiments were performed. The results show that at the spreading

conditions the octadecanol monolayer already consists of two monolayer phases; irregularly shaped islands of 2D condensed phase are distributed in a continuous 2D gaseous phase. It is then expected that increasing the speed of compression would reduce the available time for the irregular condensed phase domains to coalesce and to rearrange. With increasing surface pressure, the condensed phase should become a continuous 2D phase with irregular “gaps” of the residual 2D gaseous phase. At slower speed, the irregular condensed phase domains are being pushed together slowly. Hence, more time is allowed for coalescence and rearrangement. These ex-

+

1856

+

Langmuir, Vol. 12, No. 7, 1996

pectations are in agreement with the observed patterns in Figure 4. Let us now consider the second experiment, shown in Figure 6. Here, the change in the shapes of the π-A isotherms is caused only by the variation of the amount of surfactant on the drop surface. Thus, decreasing the amount of octadecanol at constant motor speed has an effect similar to increasing the motor speed at constant amount of octadecanol (see Figure 4). Nevertheless, there are significantly different patterns in the two types of procedures, manifesting themselves most immediately in the differences in the collapse pressures. To elucidate the differences in the two procedures, a morphological study of octadecanol monolayers spread in a Langmuir film balance under similar initial spreading conditions as for the droplet surface was performed. In all cases, these monolayers were in a state of zero surface pressure. Figure 7 shows a sequence of BAM micrographs of octadecanol monolayers on water at 20 °C having different initial spreading conditions: 120, 100, 60, 30, and 20 Å2/ molecule. The conditions are similar to the initial conditions used in Figure 6: 2 µL, 73.1 Å2/molecule; 3 µL, 48.8 Å2/molecule; 4 µL, 36.6 Å2/molecule; and 5 µL, 29.3 Å2/molecule. As can be seen in the images shown in Figure 7, coexisting structures of 2D gaseous phase (dark) and 2D condensed phase (bright) are formed already after evaporation of the spreading solvent even at high areas per molecule of 120 Å2/molecule. The area ratio of the coexisting 2D phases depends on the amount of octadecanol spread on the water surface. As demonstrated by the BAM micrographs, the more spreading material, the larger the portion of the 2D condensed phase with higher density. Decreasing the amount of spread octadecanol should reduce the ratio of the condensed phase to the gaseous phase on the drop surface, and hence more gaseous “gaps” or holes should exist between the condensed phase structures. Thus, it becomes apparent what causes the differences between the two types of experiments: Initial differences of the amount of octadecanol on water drops of the same size cause differences of the area ratio between 2D expanded films. While it is easily possible to reach the same rate of molecular area compression by compressing the film containing fewer octadecanol molecules more slowly, the initial differences between the ratios of 2D condensed and expanded films will persist during compression and lead to different patterns of response. While the difference in collapse pressure is readily seen in Figures 4 and 6, other differences in the isotherms can also be readily documented. An example is given in Figure 8, where three isotherms are shown: one at a motor setting of 5 and a large amount of octadecanol (4.5 µL) and two motor settings of 4 with smaller amounts of octadecanol (2 and 2.5 µL of solution). The rate of molecular area change is 10.3 and 12.9 Å2/(molecule min) for motor setting 4 and 11.6 Å2/(molecule min) for motor setting 5. While the rates of motor setting 4 bracket the one at setting 5, the isotherm for the latter lies well outside the range of the former two. Other examples can be readily found in the data. It should be noted that the compressibilities of the upper parts of the π-A isotherms shown in Figures 4 and 6 are essentially the same, since the condensed phase structures are rather incompressible and closely packed. However, it seems that the limiting molecular area, by customary extrapolation, may be rate dependent. This question will be explored in a subsequent section. Rate Dependence of the Collapse Pressure. Overall the number of octadecanol molecules on the drop surface was varied from 0.58 × 1014 to 1.58 × 1014, and three

Kwok et al.

Figure 8. Surface pressure (mJ/m2) versus area per molecule (Å2/molecule) of pendant drops with octadecanol film. The compression rates for 10.3 and 12.9 Å2/(molecule min) were obtained, respectively, from 2.5 and 2 µL of octadecanol/heptane solution at motor setting 4. The compression rates for 11.6 Å2/(molecule min) were obtained from 4.5 µL of octadecanol/ heptane solution at motor setting 5.

Figure 9. Collapse pressure (mJ/m2) versus the rate of compression (Å2/(molecule min)) with the 95% confidence limits, for three motor speed settings: 4, 5, and 6. Each of the points represents an average of at least 4 and up to 15 repeat experiments. A student t distribution was used to calculate the 95% confidence limits.

motor speed settings were used, 4, 5, and 6. They correspond to a rate of drop surface area change of 0.0741, 0.151, and 0.296 cm2/min, respectively (cf. Figure 5). The rate dependence of the collapse pressure is shown in Figure 9 for the three motor speed settings. Each of the points in this figure represents an average of at least 4 and up to 15 different experiments; a total of 190 experiments, i.e. over 11 000 surface tension measurements, were performed in this rate dependent study. The 95% confidence limits are also included in this figure; a student t distribution was used. The experimental data

+

+

1-Octadecanol Monolayers

Langmuir, Vol. 12, No. 7, 1996 1857

Table 1. Results of the Mean Collapse Pressures at 0.0741 cm2/min (Motor Speed Setting 4) for Different Numbers of Octadecanol Molecules rate (Å2/(molecule min))

vol of octadecanol/n-heptane solution (µL)

10-14 × no. of molecules

mean collapse pressure (mJ/m2)

no. of drops

95% confidence limits

4.68 5.14 5.71 6.43 7.35 8.57 10.29 12.86

5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0

1.5847 1.4406 1.2966 1.1525 1.0084 0.8644 0.7203 0.5762

43.2 47.6 53.0 56.0 59.1 61.2 60.3 60.6

7 14 7 6 4 7 6 8

0.2 0.8 0.3 0.7 0.4 0.5 0.9 0.4

Table 2. Results of the Mean Collapse Pressures at 0.151 cm2/min (Motor Speed Setting 5) for Different Numbers of Octadecanol Molecules rate (Å2/(molecule min))

vol of octadecanol/n-heptane solution (µL)

10-14 × no. of molecules

mean collapse pressure (mJ/m2)

no. of drops

95% confidence limits

9.52 10.47 11.63 13.08 14.95 17.44 20.93 26.17

5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0

1.5847 1.4406 1.2966 1.1525 1.0084 0.8644 0.7203 0.5762

43.0 47.3 52.6 55.9 58.8 60.9 61.1 61.1

8 6 6 7 6 6 6 10

1.1 0.7 1.1 0.7 0.3 0.5 0.8 0.4

Table 3. Results of the Mean Collapse Pressures at 0.296 cm2/min (Motor Speed Setting 6) for Different Numbers of Octadecanol Molecules rate (Å2/(molecule min))

vol of octadecanol/n-heptane solution (µL)

10-14 × no. of molecules

mean collapse pressure (mJ/m2)

no. of drops

95% confidence limits

18.67 20.53 22.81 25.66 29.33 34.12 41.07 51.33

5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0

1.5847 1.4406 1.2966 1.1525 1.0084 0.8644 0.7203 0.5762

43.0 47.1 52.6 56.1 58.6 60.0 60.8 61.6

13 15 8 11 11 6 7 5

0.8 0.8 0.4 0.5 0.4 0.9 0.4 0.6

Figure 10. Collapse pressure (mJ/m2) versus the number of octadecanol molecules on the drop surface for the data in Figure 9, with the 95% confidence limits. Each of the points represents an average of at least 4 and up to 15 repeat experiments. A student t distribution was used to calculate the 95% confidence limits.

underlying Figure 9 are shown in Tables 1, 2, and 3, respectively, for the three different rates. It should be noted that the collapse pressures shown in Figure 9 and Tables 1-3 were obtained graphically, by drawing a

straight line along the upper region of the π-A isotherm. The collapse pressure was identified as the point where the upper part of the π-A isotherm starts to deviate from the straight line (see Figure 2). As can be seen in Figure 8, the rate dependence of the collapse pressure shows a similar shape for the three different motor speed settings: increasing the rate of molecular area compression by providing fewer and fewer molecules at the same setting for the rate of drop volume and hence drop surface area change increases the collapse pressure until a plateau at about 61 mJ/m2 is reached. It is obvious from this figure that the collapse pressure is not uniquely dependent on the rate of molecular area compression. As a result, the rate of molecular area compression cannot be used to specify the collapse pressure. In light of the BAM results, this is not surprising. These results also provide a hint how to proceed further in the description of the collapse pressure. Since the main implication of the BAM study is the significance of the ratio of 2D condensed and expanded phases, and since this ratio depends directly on the initial molecular area, the existence of a relation between the latter and the collapse pressure should be explored. This is done in Figure 10, where the collapse pressure is plotted over the number of octadecanol molecules initially present on the drop surface (of constant area). A unique collapse pressure dependence on the amount of octadecanol is obtained. ANOVA statistics were performed to study whether the collapse pressure is indeed independent of the motor speed settings; it was found that the collapse depends only on the amount of surfactant, at >99.5% confidence. Details of the statistics can be found in ref 34. In fact, this result

+

+

1858

Langmuir, Vol. 12, No. 7, 1996

Kwok et al.

Figure 11. Schematic of a π-A isotherm; extrapolations for the limiting molecular area and molecular area at collapse are shown.

is, in principle, obvious from the first experiment, i.e. the procedure described in section 1, which showed that no speed dependence with respect to the collapse pressure was found (cf. Figure 4). The results in Figure 10 suggest that collapse pressure will increase with decreasing amounts of surfactant on the surface. This is readily understood from the BAM results: Decreasing the amount of surfactant decreases the fraction of the condensed phase and improves the regularity of the condensed phase, which is conducive to increasing the strength of the film. Rate Dependence of the Limiting Molecular Area. In view of the results of the film compression experiments and the BAM study discussed above, questions also arise with respect to the molecular area at close packing. The limiting molecular area is determined conventionally by extrapolation to the upper part of the π-A isotherms to zero pressure π. This procedure may possibly be justifiable for compression of a homogeneous film. However, the BAM study has shown that the octadecanol films comprise at least two phases. The standard procedure might therefore be questionable; it was therefore decided to consider an alternative concept, the molecular area at collapse. The procedures for establishing both conventional limiting molecular area and the molecular area at collapse are shown schematically in Figure 11. For the first type of experiment, by varying only the motor speed settings (i.e. area/minute), the π-A isotherms for different molecular area compressions are shown in Figure 4. It can be seen that, at different compression rates, the limiting molecular areas are different, varying from about 20.2 to 21.0 Å2/molecule: Increasing the rate of compression increases the limiting molecular area, while

the molecular area at collapse is essentially constant at about 19.4 Å2/molecule. For the second type of experiment, the π-A isotherms were obtained by keeping the motor speed settings (i.e. area/minute) constant and varying the amount of octadecanol (see Figure 6). In this figure, the limiting molecular areas were found to vary from about 20.4 to 22.0 Å2/molecule. In general, increasing the rate of molecular area compression also increases the limiting molecular area, while the limiting molecular area at collapse is essentially constant at about 19.5 Å2/molecule. These results suggest that the limiting molecular area is rate dependent. A summary of all the results of the mean molecular area at collapse and the limiting molecular area is shown in Tables 4 and 5, respectively. The 95% confidence limits are also included; a student t distribution was assumed and used. It can be seen in Table 4 that the molecular area at collapse shows little scatter; the collapse area and its 95% confidence limits vary from 19.0 to 20.3 Å2/molecule and from (0.2 to 0.7 Å2/molecule, respectively. No trends of any kind are apparent. The limiting molecular area in Table 5 shows larger scatter; the limiting area and its 95% confidence limits vary from 20.4 to 22.9 Å2/molecule and from (0.3 to 1.7 Å2/molecule, respectively. These results suggest that the determination of the former is more consistent, while the latter is less reproducible and may be speed dependent, as can be seen in Figures 4 and 6. To illustrate this point, an analysis of variance (ANOVA) was performed, on the basis of the hypothesis that these molecular areas are dependent on the molecular area at spreading and the motor speed settings. Details of these ANOVA statistics can be found in ref 34. It turns out that the values of the molecular area at collapse given in Table 4 are statistically identical at >95% confidence. Therefore, the molecular area at collapse is, statistically, unique and reproducible, independent of the number of molecules and the motor speed settings at >95% confidence. The limiting molecular area, by customary extrapolation, was found to be different for different numbers of molecules at >95% confidence. At ≈88% confidence, the limiting molecular area was also found to be significantly different for different motor speed settings. The above results suggest that the limiting area is dependent on both the number of molecules, i.e. the molecular area at spreading (at >95% confidence), and the motor speed settings (at ≈88% confidence). Hence, statistically, the limiting molecular area should not be considered as unique for octadecanol and, presumably, other multiphase monolayers. From the statistics in ref 34, the collapse areas in Table 4 are statistically identical; we can, therefore, average these values. This procedure yields a molecular area of

Table 4. Results of the Mean Molecular Areas at Collapse (Å2/molecule) Compressed at 0.0741, 0.151, and 0.296 cm2/min (i.e. Motor Speed Settings 4, 5, and 6) for Different Numbers of Octadecanol Molecules on the Drop Surfacea compression speed (motor speed setting) 0.0741 cm2/min

0.151 cm2/min

0.296 cm2/min

× no. of molecules

molecular area at collapse (Å2/molecule)

no. of drops

molecular area at collapse (Å2/molecule)

no. of drops

molecular area at collapse (Å2/molecule)

no. of drops

0.5762 0.7203 0.8664 1.0084 1.1525 1.2966 1.4406 1.5847

20.1 ( 0.5 19.6 ( 0.4 19.7 ( 0.6 19.5 ( 0.6 19.6 ( 0.5 19.3 ( 0.4 19.6 ( 0.3 19.4 ( 0.2

8 6 7 4 6 7 14 7

19.7 ( 0.4 19.4 ( 0.4 19.0 ( 0.5 19.4 ( 0.2 19.8 ( 0.6 19.6 ( 0.6 19.7 ( 0.3 19.6 ( 0.3

10 6 6 6 7 6 6 8

19.7 ( 0.3 19.9 ( 0.5 20.3 ( 0.7 19.6 ( 0.3 19.5 ( 0.4 19.6 ( 0.3 19.9 ( 0.2 19.7 ( 0.2

5 7 6 11 11 8 15 13

10-14

a

Experiments were performed at least 4 and up to 15 times; a student t distribution was used to calculate the 95% confidence limits.

+

+

1-Octadecanol Monolayers

Langmuir, Vol. 12, No. 7, 1996 1859

Table 5. Results of the Mean Limiting Areas (Å2/molecule) Compressed at 0.0741, 0.151, and 0.296 cm2/min (i.e. Motor Speed Settings 4, 5, and 6) for Different Numbers of Octadecanol Molecules on the Drop Surfacea compression speed (motor speed setting) 0.0741 cm2/min

0.151 cm2/min

0.296 cm2/min

× no. of molecules

limiting molecular area (Å2/molecule)

no. of drops

limiting molecular area (Å2/molecule)

no. of drops

limiting molecular area (Å2/molecule)

no. of drops

0.5762 0.7203 0.8664 1.0084 1.1525 1.2966 1.4406 1.5847

22.9 ( 1.4 22.0 ( 0.9 21.0 ( 1.5 22.0 ( 1.5 21.5 ( 0.9 20.9 ( 0.7 20.9 ( 0.4 20.3 ( 0.3

8 6 7 4 6 7 14 7

22.3 ( 1.0 21.8 ( 1.3 20.8 ( 1.2 20.8 ( 0.3 21.4 ( 0.5 21.3 ( 0.7 20.4 ( 0.4 21.4 ( 1.5

10 6 6 6 7 6 6 8

22.9 ( 1.6 21.9 ( 1.0 22.9 ( 1.7 21.7 ( 0.8 20.9 ( 0.7 22.0 ( 1.6 21.0 ( 0.4 21.5 ( 0.5

5 7 6 11 11 8 15 13

10-14

a

Experiments were performed at least 4 and up to 15 times; a student t distribution was used to calculate the 95% confidence limits.

19.6 ( 0.1 Å2/molecule at collapse. We conclude that the collapse area is more consistent and reproducible than the limiting molecular area for octadecanol. While the BAM study makes the deficiencies of the limiting molecular area concept for this insoluble multiphase monolayer quite apparent, it does not guarantee that the molecular area at collapse is an entirely unique quantity. A different ratio of the two phases at collapse could well cause a difference in the effective molecular area. All that can be said is that, statistically, the present large body of data contains nothing that would mitigate against averaging the results from all runs. Conclusions (1) Axisymmetric drop shape analysis (ADSA) can be operated as a film balance and is very suitable for obtaining large amounts of information with respect to the π-A isotherms. (2) The collapse pressure of 1-octadecanol is found to be not a unique function of the rate of molecular area compression; but it depends on the amount of material spread on the drop surface, i.e. the molecular area at spreading.

(3) The shape of the π-A isotherms changes with the rate of molecular area compression; increasing the compression rate shifts the lower part of the isotherm to the right. (4) The values of the molecular area at collapse are more reproducible and consistent than the limiting area; the former was found to be 19.6 ( 0.1 Å2/molecule. (5) The conventional extrapolated molecular area was found to be dependent on both the spread amount of octadecanol, i.e. the initial area per molecule, and the motor speed settings, i.e. the rate of drop surface area change. Thus, this molecular area will change from one compression rate to another. (6) The results of the surface pressure measurements can be understood qualitatively by considering the morphological properties of the octadecanol monolayers as visualized by Brewster angle microscopy (BAM). Acknowledgment. This research was supported by a grant from the Medical Research Council of Canada (Grant No. MT-5462) and a University of Toronto Open Fellowship (D.Y.K.). LA950562+