Langmuir 1989, 5, 161-164
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A Study of the Mechanical Behavior of Surface Monolayers Using Orthogonal Wilhelmy Plates K. Halperin,+J. B. Ketterson,l and P. Dutta*** Department of Materials Science and Engineering and Department of Physics and Astronomy, Northwestern University, Euanston, Illinois 60208 Received March 25, 1988. I n Final Form: September 23, 1988 We have studied the stress-strain behavior of three types of carboxylic acid monolayers on the surface of water using orthogonal Wilhelmy plate measurements. Whether a monolayer supports shear (i.e., whether it is a solid) can be determined from these measurements, which were made with commonly available apparatus used for 11-a isotherm determination. We found that pentadecanoic acid monolayers do not support measurable shear at any pressure, while octadecanoic and tetracosanoic acid monolayers support shear at all pressures studied. The changes in the slope of the 11-a curves of the latter two materials may be solid-solid transitions or kinetic effects unrelated to phases; stress-relaxation results show the 11-a kinks to be the onset of new relaxation regimes.
Introduction A plot of the pressure (II) YS specific area ( a ) of an organic monolayer on the surface of water typically shows discontinuities in the slope, which are usually interpreted as phase Of course, pressure-area behavior by itself suggests the phases but does not determine them; numerous attempts have been made to independently corroborate the phases, for example, by using shear and viscosity measurement^.'^^*^^^ Very recently, some X-ray diffraction data have become available.6a Still, nothing has so far been generally accepted as conclusive. We have studied the mechanical behavior of three long-chain carboxylic acids: pentadecanoic or pentadecylic acid (henceforth referred to as C-15), octadecanoic or stearic acid (C-18), and tetracosanoic or lignoceric acid ((2-24). We have examined the n-a behavior of each simultaneously with a Langmuir balance9 and a Wilhelmy balance,l0J' where the Wilhelmy plate was suspended fist parallel to the Langmuir balance and then orthogonal to it. We have carried out an elastic analysis of the system, making quantitative the expectation that if the monolayer is a solid, the surface pressure in the two Wilhelmy plate directions will be different, and if a fluid, the same. Our data show that for C-15 there are no significant differences at any point on the II-a curve, while for C-18 and C-24 there are differences at all points, with a n especially striking deviation for C-24 in the higher pressure "phase".
Experimental Section A commercial Lauda film balance was filled with water purified in a Barnstead Nanopure 11. In the case of (2-15 the subphase was 0.01 M HCl at 30 "C;lZthe other two materials were spread on pure water at ambient temperature, 21 "C. Each carboxylic acid was dissolved in a spreading solvent: hexane for C-24 and a mixture of chloroform and heptane for the other two materials. The area was changed at the Lauda's Slowest speed,0.9 cm/min. The pressure was read by the built-in Langmuir balance and also by a filter paper Wilhelmy plate suspended from a Cahn RM microbalance. We modified the Wilhelmy balance so that the plate could be suspended with thin-walled stainless steel tubing (0.068-in. o.d., 0.010-in. thickness) with two hooks orthogonal to each other. This prevented free rotation of the plate and allowed it to be oriented either parallel or perpendicular to the direction of compression. The experiments were also performed with the plate suspended from the balance by a string; in the case of C-24 this gave the same resulta as with the tube, but in the other two cases the plate tended to turn parallel at high pressures. This t Department of
Materials Science and Engineering. *Departmentof Physics and Astronomy. 0743-7463/89/2405-Ol61$01.50/0
result is a qualitative measure of the greater stiffness of the C-24. Voltages were read by three digital voltmeters, one each for area, Langmuir force, and Wilhelmy force; the first two voltages were also fed into an X-Y recorder. Pressures were calibrated by using the published value of the transition point of C-18, 25 mN/m (dyn/cm) (ref 1, p 220). While this means that our absolute accuracy was no better than about 1mN/m, our relative accuracy was about 0.025 mN/m, determined by the accuracy of the voltmeter (0.1 mV). (The difference between two curves is significant if it is greater than the relative accuracy.) Below 5 mN/m our curves were not very repeatable; this may be due to relative error, which is a greater percentage in that region, or to the material itself. We recorded the n-a curve for each material with the Wilhelmy plate suspended first parallel to the Langmuir balance and then perpendicular to it, and we then repeated both measurements in reverse order.'* Each direction was measured a minimum of 3 times. The n-a curves obtained with a Langmuir balance are shown in Figure 1. These may be compared to published W-a diagrams for C-15,3J3C-18,' and C-24.14J5 The Wilhelmy plate data are plotted in Figure 2. To highlight the differences, we have plotted the parallel Wilhelmy pressure minus the orthogonal Wilhelmy pressure (nw,, - IIwJ on the ordinate versus Langmuir pressure (nL) on the abcissa. We also performed relaxation experiments on all three materials. The monolayer was compressed to some surface pressure (1)See, e.g., Gaines, G. L., Jr. Insoluble Monolayers at Liquid-Gas Interfaces, Interscience Publishers: New York, 1966. (2)Adam, N. K. The Physics and Chemistry of Surfaces, 3rd ed.; Oxford University Press: London, 1941;Chapter 2. (3)Harkins, W. D. The Physical Chemistry of Surface Film; Reinhold Publishing: New York, 1952.. (4)Joly, M. In Recent Progress in Surface Science 1; Danielli, J. F., Pankhurst, K. G. A., Riddiford, A. C., Eds.; Academic Press: New York, 1964;pp 1-50. (5)Abraham, B.M.;Miyano, K.; Ketterson, J. B.; Xu, S. Q. Phys. Reu. Lett. 1983,51,1975.Abraham, B. M.; Miyano, K.; Xu, S. Q.,Ketterson, J. B. Reu. Sci. Instrum. 1983,54, 213. (6) Kjaer, K.; Als-Nielsen, J.; Helm, C. A.; Laxhuber, L. A.; Mohwald, H. Phys. Rev. Lett. 1987,58,2224. (7)Dutta, P.; Peng, J. B.; Lin, B.; Ketterson, J. B.; Prakash, M.; Georgopoulos, P.; Ehrlich, S.Phys. Reu. Lett. 1987,58,2228. (8)Barton, S.; Thomas, B.; Flom, E.; Rice, S. A,; Lin, B.; Peng, J. B.; Ketterson, J. B.; Dutta, P. J. Chem. Phys. 1988,89,2257. (9)Langmuir, I. J. Am. Chem. Soc. 1917,39,1848. (10)Wilhelmy, L. Ann. Phys. 1863,119, 177. (11)Lord Rayleigh Philos. Mag. 1899,48(Ser. 5),321. (12)We realized recently that since the difference between parallel and perpendicular measurements is the quantity of interest, a balance with two plates on opposite a r m s could be used to measure the difference directly and thus more sensitively. (13)Pallas, N. R.; Pethica, B. A. Langmuir 1985,1,509. (14)Sttillberg-Stenhagen,S.; Stenhagen, E. J.Biol. Chem. 1946,145, 599. (15)Lundquist, M. Suomen Kemistiseuran Tied. 1963,72,14.
0 1989 American Chemical Society
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162 Langmuir, Vol. 5, No. 1, 1989 D 33
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Figure 2. Difference between pressures recorded by a Wilhelmy plate parallel to a Langmuir balance (IIW~) and one that is perpendicular to it (IIwJ va pressure recorded by the Langmuir balance (IId. The open and solid points are from two different runs, shown to indicate the degree of reproducibility. (Data from other runs were similar). and area, and the pressure waa then recorded against time. This is a standard stress-relaxation Typically, we held the area constant for around 3 min, as this was long enough to achieve steady-state relaxation. In a few cases we held it for longer; no new information was gained by doing so. Our results are shown in Figure 3.
Theory A solid may be defined as material which exhibits a static shear modulus. For a discussion of the definition of a solid, see, e.g., Scipio.21 We call anything that is not (16) Marcelin, A. Ann. Phys. 1925, 4 , (Ser. lo), 459. (17) Rabinovitch, W.; Robertson, R. F.; Mason, S. G. Can. J . Chem. 1960,38, 1881. (18) Munden, J. W.; Bloia, D. W.; Swarbrick, J. J . Pharm. Sci. 1969, 58,1308. (19)Sims, B.;Zogrdi, G. Chem. Phys. Lipids 1971,6,109. Sims, B.; Zografi, G.J. Colloid Interface Sci. 1972, 41, 35. (20)Abraham, B. M.; Miyano, K.; Ketteraon, J. B. In Ordering in Two Dimensions; Sinha, S.K. Ed.; North-Holland Amsterdam, 1980.
a solid a fluid. One need not do a shear experiment to determine the presence of a shear modulus for a monolayer; the presence or absence of a shear modulus emerges from the much simpler experiment of perpendicular Wilhelmy plates. This experiment is neither more nor less steady state than the standard II-a experiment; for that reason it compares well to the well-established body of knowledge and introduces no new experimental or definitional difficulties. We w u m e for ow monolayers that (a) the deformations are small enough that the equations of linear elasticity hold, (b) there are no relevant body forces, (c) the system is static (an assumption we explore a t length in a later section), (d) corner effects are negligible, and (e) the material is orthotropic (isotropic in the plane). The last assumption reduces the compliance tensor to five com(21) Scipio, L. A. Principles of Continua, with Applications; Wiley: New York, 1967.
Mechanical Behavior of Surface Monolayers
Langmuir, Vol. 5, No. 1, 1989 163
ponents, S1111,S1122, SI1339 83333, and 82323, with S1212 = /z(S1lll - S1122).There are no applied shears, thus eliminating all the off-diagonal terms of the stress (a) and strain (e) tensors. The surface at x 3 = 13, the air-monolayer interface, is free; this eliminates uQi. The direction of applied strain is xl, giving rise to the term ell. The pinned walls in the x 2 direction eliminate ea Thus we are left with only all, u22,ell, e33, and the five compliances of an orthotropic system. the x 3 direction is effectively uncoupled from the plane, and thus the problem reduces to a twodimensional one, given the simplifying assumptions we have introduced. A failure of the results to exactly fit the model (which indeed happens) means that we have oversimplified, but a more general model would preclude a closed form solution. For the purpose of distinguishing solidlike from fluidlike behavior, our model is sufficient. Note that the in-plane Poisson ratio determined will take values from 0 to 1 (in three dimensions, the maximum value is 0.5). The application of the remaining boundary conditions then leads to g22
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= - ( ~ ~ 1 / ~ 1 ) S 1 1 2 2 / ( S 2 1 1 2 2- S21111) =
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where l1 is the original length of the monolayer surface and All is the change in that length, that is, the distance the bar has been moved. Thus the measurement of force in two orthogonal directions determines the two elastic constants, Slllland Slim (Ideally, we would employ a trough with a Langmuir balance on each of two normal walls, as has recently been constructed by Miyano;22our alternative method, hanging the Wilhelmy balance in each of two orthogonal directions, was described above.) Young’s modulus E, Poisson’s ratio v, and the shear modulus G are related to our two compliances by E = l/Sllll,v = -S1122/Sllll, and G = 1/(2Sllll - 2Sl122). If ull = u22,then Sllll = SllZ2= 0, the familiar condition for a fluid. This simply means that if the principal stresses are equal than there is no shear stress, which is the definition of a fluid from which we are working. The slope of the standard n-a diagram is S1111/(s21122 - Gllll).Of course, this slope is expected only if the shear stress has not exceeded a critical value at which stress relaxation sets in; beyond this point, the II-a behavior is governed approximately by the bulk compressibilityaZ3
Results and Discussion As can readily be seen in Figure 2, each curve has a long flat region, centered around 0 for C-15,0.2 for C-18, and 0.7 for (2-24, all in mN/m (dyn/cm). Ignoring data below a Langmuir surface pressure of 5 mN/m due to irreproducibility and above 20 mN/m due to the change in the curves, we find the mean values for the difference (with standard deviations in parentheses) are -0.026 (0.057) for (2-15, 0.18 (0.052) for C-18, and 0.72 (0.10) for C-24. As we have stated before, our absolute accuracy is at best two digits. These numbers are the differences between two curves. As previously stated, such differences are governed by the relative accuracy, which is 0.025 mN/m. This accuracy, combined with a standard deviation of twice the mean, leads us to conclude that C-15 is indistinguishable from (22) Miyano, K., personal communication. (23) Abraham, B. M.; Ketterson, J. B.; Behroozi, F. Langmuir 1986, 2, 602.
a fluid throughout the isotherm. For the other two materials, we observe a difference between the parallel and perpendicular orientations which is significant throughout the n-a diagram. The thickness of the monolayer is not known, but as an approximation we use the layer spacing in corresponding LangmuirBlodgett multilayers, 2.5 nm for (2-18 and 3.3 nm for C-24, which we assume to be the lengths of the molecules. The choice of l1 is also not straightforward; we took it to be the length at the onset of a measurable difference between IIw,, and nW,, that is, the onset of solidlike behavior. (Because of stress relaxation, this choice is somewhat arbitrary.) In practice, for both C-18 and (3-24, this was the onset of measurable pressure IIL,which we defined as pressure exceeding 10 times the relative error. This pressure is 0.25 mN/m. We may now calculate some values for elastic compliances. But first a further discussion of the features of Figure 2 is necessary. Above point C on the C-24 curve, and point B on the C-18 curve, there are few data points. This is due to the steep rise of the corresponding section of the E a diagram; the pressures are changing too fast with area to allow for much data to be taken; furthermore, the behavior is not repeatable from one run to another. Thus the shapes of the curves in those regions are suspect. Below this point the curves of Figure 2 are flat for C-15 and C-18 but show a remarkable change in the behavior of C-24. This change for C-24 occurs a t point B. If our assumptions of linear elasticity were valid, the curves in Figure 2 for C-18 and for C-24 would show a gentle positive slope corresponding to a constant ratio g 2 2 / ~ 1(Poisson’s 1 ratio for this experiment). Instead, the curves are basically flat. Thus the model is only partly correct; it shows the difference between solid and fluid but does not correctly predict the slopes of the curves. To report some numbers, which are good at least for order of magnitude, we choose the point nL= 15 mN/m and calculate the constants. For C-24, the values are Sllll= 0.29 X lo4 m2/N, SllZ2 = -0.28 X lo+ m2/N, v = 0.95, E = 3.5 GPa, and G = 0.88 GPa. For C-18 the corresponding values are 1.02 and -1.01 X lo* m2/N, 0.99,0.98 GPa, and 0.25 GPa, respectively, with a curve slope of 43 GPa. The young’s moduli of these carboxylic acid monolayers compare well to those for multilayered Langmuir-Blodgett films of similar materials. The multilayer films have an in-plane Young’s modulus of around 6 GPa.u,25 A typical polyester, for comparison, has a Young’s modulus of around 2 GPa.26 Both monolayers show almost no resistance to flow, having Poisson ratios close to the theoretical limit in two dimensions, which defines a fluid. And yet the results are unambiguous: the materials support shear throughout their measurable II-a diagrams. If the material were prefectly elastic, it would hold its shape under pressure: held a t constant strain, its stress would not relax with time. The converse is also true. If it can be shown that there is relaxation within the material, then the material is not perfectly elastic. Thus relaxation experiments are indicated (Figure 3). As can be seen clearly, the kink point marks a change in the relaxation behavior for both C-18 and (2-24. Each is quite stable for 5 min in the low-pressure region and quite unstable in the high-pressure region. C-18 in the high-pressure region relaxes to the pressure at B. This result was also reported (24) Zanoni, R.; Naselli, C.; Bell, J.; Stegeman, G. I. Seaton, C. T. Phys. Reu. Lett. 1986, 57, 2838-40. (25) Halperin, K.; Sailor, M.; Gadwood, R.; Peng, J. B.; Ketterson, J.; Dutta, P., submitted to J. Polym. Sci. (26) van Krevelen, D. W. Properties of Polymers: Correlation with Chemical Structure; Elsevier: North-Holland, Amsterdam, 1972.
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164 Langmuir, Vol. 5, No. I , 1989
fire
(Tin)
Figure 3. Relaxation results, surface pressure vs time, starting at various initial pressures as shown.
by Sims and Zografi.l9 (2-15 also undergoes a change in its relaxation behavior not related to its transition points B or C. In the low-pressure region for both (2-18and C-24, we can safely say there is no relaxation, and thus the material is behaving elastically. It need not be linear elasticity; indeed, the shapes of the curves in Figure 2 lead us to believe that it is not. The relaxation effects a t high pressure are not permanent in that there is no permanent deformation; if the surface is expanded and then recompressed, the same stress behavior is encountered again. This is in contradistinction to the behavior above the collapse point D (not shown), in which the slope is lower, consistent with plasticity, and there are nonrecoverable effects. Other possibilities do present themselves. One is that the material is leaking through the barrier; another is that it is soluble. The former explanation requires that a leak open up a t a threshold pressure, which we consider unlikely. The latter was first proposed by MarcelinlGand is an attractive explanation. The solubility of octadecanoic acid in water a t 20 "C is 0.0003 g/100 g. Thus 1L could dissolve lo'* molecules. A 100-cm2surface holds around 4 X 10l6molecules; all of them could go into solution under suitable conditions, say, high pressure. The solubility of C-24 is 3 orders of magnitude less than that of C-18 for a solubility of 10l6 molecules/L. This could explain why the C-24 does not immediately relax to the pressure a t B; it has a slower relaxation time due to decreased solubility. Solubility is also indicated by irreproducibility in the n-a behavior. If the material is compressed and expanded and compressed again, the new II-a curve is identical with the first one, only displaced to smaller areas. Thus material must have been lost. This is much more evident in C-18 than in (2-24 and even more so in C-15.
Recently, Barton et a1.* have reported detailed X-ray diffraction studies of heneicosanol monolayers. (This material has an isotherm with the same qualitative appearance as that of C-18). They find a solidlike diffraction peak whose height is independent of pressure above the kink but begins to drop continuously as the pressure is reduced below the kink. This would imply continuous melting, except that the width of the peak does not change; they therefore propose that increasing numbers of gauche configurations reduce the diffraction peak intensity as they increase the area/molecule. In other word, the monolayer below the kink is a highly defective solid rather than a liquid. Such a monolayer should still support shear and may also relax much less easily because of the tangled chains. An alternative explanation is that the chains tilt away from the vertical; if the tilt is not toward one of the neighboring chains, the first-order X-ray peak will slowly vanish. In any case both our data, and the X-ray results, are in agreement that kinks do not necessarily indicate solid-liquid transitions.
Conclusions Octadecanoic acid and tetracosanoic acid monolayers on water deform as elastic solids. Within our accuracy, pentadecanoic acid appears to be a fluid. The transition point, B, on the surface pressure-specific area diagram for the two solids signals a transition in the stress-relaxation behavior. Acknowledgment. We thank Professor E. Reiss of the Department of Applied Mathematics, Northwestern University. This work was supported by the U S . Department of Energy under Grant No. DE-FGO284ER45125. Registry No. C-15,1002-84-2; C-18,57-11-4; C-24,557-59-5.
