Role of Tail−Tail Interactions versus Head-Group−Subphase

Role of Tail−Tail Interactions versus Head-Group−Subphase Interactions in Pressure−Area Isotherms of Fatty ... Langmuir , 1997, 13 (20), pp 5440...
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Langmuir 1997, 13, 5440-5446

Role of Tail-Tail Interactions versus Head-Group-Subphase Interactions in Pressure-Area Isotherms of Fatty Amines at the Air-Water Interface. 2. Time Dependence P. Ganguly,* D. V. Paranjape, K. R. Patil, and Murali Sastry Physical and Materials Chemistry Division, National Chemical Laboratory, Pashan Road, Pune 411008, India

F. Rondelez Institut de Pierre et Marie Curie, 11 rue Pierre et Marie Curie, 75231 Paris Cedex 05, Paris, France Received October 8, 1996. In Final Form: July 11, 1997X The dependence of the surface pressure vs area (π-A) isotherms of fatty primary amine monolayers spread on a subphase of an aqueous solution of various Hn[MO4]n- acids (M ) S6+, P5+, Cl7+) under ionic conditions of low pH on several temporal parameterssincluding compression/expansion ratesshave been studied as a function of the chain length of the fatty amines. A parameter, RT/C, has been used as a qualitative measure of the relative strengths of the tail-tail interaction as compared to the subphasehead-group (acid-base) complex-forming interaction. The changes in the π-A isotherm due to waiting for different periods of time after spreading as well as the changes in the surface pressure, π, with time at various barrier positions have been studied. The results show an increase in the lift-off area, ALO, with time that is not due to an external contaminant. The compression/expansion curves always show hysteresis, the extent of which may decrease (for larger RT/C) or show a counterintuitive increase (for smaller RT/C) with decreasing compression/expansion rates. The results are analyzed in terms of a new two-state model involving clusters and individual complexed amine molecules.

I. Introduction 1

In the first part of this study on the pressure-area isotherms of Langmuir monolayers of various fatty amines, we have studied the influence of various acid counterions in the subphase in the initial stages after spreading of the monolayer. The π-A isotherm is a sensitive function of a parameter, RT/C, which is a qualitative measure2 of the ratio of the strengths of the tail-tail van der Waals interaction between the hydrocarbon chains and the strength of the head-group-subphase interaction (or the amine-acid interaction) at the air-water interface. Such an interface was also termed the airface-aquaface interface as the organization of the amines at the airface (or air side of the air-water interface) may influence or be influenced by the organization of the acid counteranions at the aquaface (or the water side of the air-water interface). A complex equilibrium

(1 - x)RNH2(airface) + (z - x)H+(bulk, solvated) + (z - y)X-(bulk, solvated) T (y - y′)RNH3+(airface)X-(aquaface, solvated) + y′RNH3+X-(bulk, solvated) + (x - y)RNH3+(airface) (1) between various species at the airface aquaface interface X Abstract published in Advance ACS Abstracts, September 15, 1997.

(1) Ganguly, P.; Paranjape, D. V.; Rondelez, F. Langmuir 1997, 13, 5433. (2) This ratio, RT/C, is at present only qualitative. For a given acid in the subphase and a given pH we may expect RT/C for various fatty RNH2 compounds to decrease in the order C20-NH2 > C18NH2 > C16NH2 > C16PhNH2. For a given fatty amine RT/C depends on the strength of the acid in the subphase. For the acid counterions MO4n- species in which M ) Cl, S, P with n ) 1, 2, and 3, respectively, we expect the acidity corresponding to the first ionization of the acid (and hence RT/C) to decrease in the order (see refs 1 and 5) HClO4 > H2SO4 > H3PO4.

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and in the bulk is envisaged1 with z being the initial bulk amount of the acid in the bulk. y e x so that there are (x - y) moles of another anionic species, X′-, produced at the interface for charge neutrality. The amphiphilic fatty amine molecules in the monolayer could be in “clusters” or as “individual” molecules of a two-state model that is somewhat different from that proposed earlier.3 In our model, the “individual” state is likely to be RNH3+ (airface)X-(aquaface), solvated) complex species involving the protonated amine and the subphase X- acid counterions that occupy areas per molecule close that observed for the liquid-expanded (LE) region.3a The formation of “clusters” is favored at low areas per molecule (Amol ∼ Aperp ∼ 20-25 Å2, where Aperp is the cross-sectional area of the hydrocarbon chain perpendicular to its axis) in the so-called liquid-condensed (LC) region. The changes in the surface concentration of these two states requires a reorganization of the species at the airface and aquaface, which in turn may be associated with different time scales. The important feature at the airwater interface is that this surface, by its very definition, has no components in the bulk. This restriction of a degree of freedom in the third dimension may have dramatic influence on the time scales of the reorganization. It is with this in mind that we have reinvestigated in this communication the “bizarre” temporal behavior4 of the amine monolayers, especially in terms of a possible “twostate” model. (3) (a) Israelchavili, J. Langmuir 1994, 10, 3774. (b) Ruckenstein, E.; Li, B. Langmuir 1995, 11, 3510; J. Phys. Chem. 1996, 100, 3108; Langmuir 1996, 12, 2308. (4) Adam, N. K. Proc. R. Soc. London A 1930, 126, 526. (5) Albert, A.; Serjeant, E. P. Ionization Constants of Acids and Bases; Wiley: New York, 1962. We consider only the monovalent anion being attached to the protonated -NH3+ group at the airface. We have not specifically examined the possibility of polyvalent anions “condensing” onto the charged ammonium head groups just as the polyvalent cations condense onto carboxylate groups (see ref 10).

© 1997 American Chemical Society

π-A Isotherms of Fatty Amines. 2

Figure 1. Pressure-area isotherms of n-docosylamine on an aqueous subphase of perchloric acid (pH ) 2) at various temperatures (curly brackets, in °C) and times (square brackets, in minutes) after spreading: long dashes (HCOC2O1a), {15} [25]; long and short dashes (HCOC202a), {60} [25]; dashes and dots (C20Cl02a), {15} [20]; short dashes (C20Cl02b), {60} [20].

II. Experimental Section The pressure-area isotherms were carried out on a NIMA trough with a trough area of 600 cm2. Unless otherwise mentioned, the pressure-area isotherms were carried out on aqueous solutions using double-distilled water, because of the limited availability of millipore water. A few experiments were carried out with millipore water to confirm the nature of changes observed. The boundary conditions such as the initial number of molecules spread per unit area, the syringe size, and the position of the barrier (fully opened) before spreading were kept constant. The temperature of the experiments was the ambient room temperature, which varied mainly between 298 and 303 K.

III. Results III.1. Short-Time Effects. III.1.1. Time Dependence. The π-A isotherms of C20NH2 spread on an aqueous subphase of perchloric acid solution (pH ) 2) is shown in Figure 1 at various temperatures and at various times of spreading. These isotherms are characterized by their lift-off area, ALO, and an area, Akink, at which the pressurearea isotherm shows signs of collapse. ALO and Akink are both much larger than Aperp at low pH when the equilibrium in eq 1 is expected to be shifted to the right. The isotherms show an expansion as a function of time especially at higher temperatures, all other conditions being the same. Such a dependence indicates that external contaminants are not the likely cause for the changes with time. III.1.2. Influence of Compression Rates. The π-A isotherms for n-octadecylamine spread on aqueous solutions of bulk pH ) 2 of perchloric acid obtained at various uniform compression rates are shown in Figure 2. We compress to areas above Aperp (20 Å2/mol of amine) to avoid possible collapse of the amphiphile monolayer at lower areas and the formation of multilayers. The compression is carried down to an area ∼30 Å2/mol of amine and then expanded rapidly at ∼60 (Å2/mol of amine)/min to the fully expanded position (Amol > Aperp). On immediate recompression, the π-A isotherm is shifted to lower areas. This is not due to dissolution.6 After some period, the original value of the lift-off area, ALO, is recovered.7 The plots for various compression rates (Figure 2) are nearly superimposable at low pressures or areas close to ALO but deviate considerably at higher pressures (or lower areas) during compression with a reduction in π (at a given area) (6) Berg, J. M.; Eriksson, L. G. T. Langmuir 1994, 10, 1213.

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Figure 2. Pressure-area isotherms of n-octadecylamine (C18NH2) spread on an aqueous (double-distilled water) solution of perchloric acid (bulk pH ) 2) at various compression rates (in (Å2/mol of amine)/min, given in square brackets) with the compression commencing at various times after spreading (in minutes, given in curly brackets). c18aci31 (filled squares), [36] {3}; c18aci32 (filled circles), [∼18] {18}; c18aci33 (triangles), [∼9] {35}; c18aci34 (squares), [∼4.5] {50}; c18aci35 (open circles), [∼18] {65}.

Figure 3. Pressure-area isotherms of n-octadecylamine (C18NH2) spread on an aqueous (ion-exchanged millipore water) solution of perchloric acid (bulk pH ) 2) at various compression rates (in (Å2/mol of amine)min, given in square brackets) with the compression commencing at various times after spreading (in minutes, given in curly brackets): c18aci41 (filled squares), [∼36] {3}; c18aci42 (filled circles), [∼9] {18}; c18aci43 (triangles), [∼4.5] {35}; c18aci44 squares), [∼2.3] {50}; c18aci45 (open circles), [∼18] {110}. Inset: pressure-area isotherm of n-hexadecylamine on an aqueous (millipore water) solution of perchloric acid (bulk pH ) 2). c16hclo5 (full line), [∼4.5] {30}; c16hclo7 (broken line), [∼2.3] {60}.

as the compression rate is decreased. The experiments in Figure 2 were reproduced with millipore water (Figure 3). The extent of the changes in the pressure-area isotherm due to changes in the compression rate depends on RT/C, the relative strengths3 of the tail-tail interaction between the hydrocarbon chains and the head-group-subphase interaction determined by the acid strength5 for a given amine. The influence of the compression rate becomes more pronounced as RT/C increases or the length of the hydrocarbon chain (compare C18NH2 with C16NH2 shown (7) In order to do this, we have carried out compression/expansion cycles restricting ourselves to a maximum surface pressure of 5 dynes/ cm until the original value of ALO is recovered, after which the full compression was carried out again at the desired rate.

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Figure 4. (a) Pressure-area isotherms during compression/ expansion cycle of n-hexadecylamine spread on an aqueous subphase of perchloric acid with bulk pH ) 2: c16hclb1 (circles), [∼12] {15}; c16held1 (triangles), [∼3] {45}. (b) Pressure-area isotherms during compression/expansion cycle of n-hexadecylamine spread on aqueous subphase of phosphoric acid with bulk pH ) 2: c16hpo3 (circles), [∼12] {15}; c16hpo4 (triangles), [∼3] {45}; c16hpo5 [∼1.2] (75). See Figure 3 for the significance of the meaning of the figures in square and curly brackets.

in inset of Figure 3) increases for a given head-groupsubphase interaction. III.1.3. Compression-Expansion Cycles. All the pressure-area isotherms of the fatty primary amines spread as a monolayer on a subphase of low pH are dependent on the boundary conditions such as the rate of compression, the initial area, Ainit, before compression, and final area, Afin, after compression. The dependence on Ainit is not important in the initial (short time) stages after spreading as long as Ainit > ALO. The extent of hysteresis is strongly dependent on Afin (which is also the area at which expansion is started in a compression-expansion cycle), increasing as Afin is decreased. Such a marked hysteresis is usually observed in the case of Langmuir monolayers of fatty acids when Afin < Aperp (15-20 Å2; after collapse). In this case, multilayers of the fatty amphiphile are formed. In our experiments, Afin is usually greater than 20 Å2/mol of amine (∼Aperp). Since Afin > Aperp, it is unlikely that the observed hysteresis is due to amphiphile multilayer formation due to collapse of the amphiphile monolayer. We distinguish two distinct types of behavior that depend on the ratio of RT/C. In the case of C16NH2 spread on perchloric acidswhen RT/C is expected to be smallsthe hysteresis increases as the rate of barrier movement decreases (Figure 4a) for a given Afin. On the other hand as RT/C is increased2, as in the case of the C16NH2/H3PO4 system (bulk pH ) 2), we find (Figure 4b) that the extent of hysteresis increases as the compression (expansion) rate increases. Similar dependence on RT/C is also observed when the length of the hydrocarbon chain is varied.2 Accordingly, we find that with the C20NH2/HClO4 subphase system, the dependence on the compression rate (Figure 5a) is similar to that observed with the C16NH2/H3PO4 system (Figure 4b). In the case of the C20NH2/H3PO4 system (Figure 5b) the initial compression-expansion cycle shows the pressure going to zero at a low value of the area per mole of amine on expansion. Subsequent compression (curves 12e and 12f of Figure 4b) does not reproduce the original behavior even after 5 h of waiting. III.2. Long-Time Effects. The π-A isotherms of the C20NH2/H3PO4 system at short times after spreading (c20hpo11 in Figure 5b) show completely different behavior when measured after standing overnight (isotherms c20hp13a and c20hp13b of Figure 5b). The sharp “kink”like feature in the original isotherm obtained immediately after spreading (curve c20hpo11 of Figure 5b) is smoothed

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Figure 5. (a) Pressure-area isotherms during compression/ expansion cycle of n-docosylamine spread on perchloric acid solution (bulk pH ) 2): hcoc20 (circles) [∼12] {15}; hcoc201a (squares), [∼3] {30}. (b) Pressure-area isotherms during compression/expansion cycle of n-docosylamine spread on phosphoric acid solution (bulk pH ) 2): c20hpo11 (circles), [∼12] {15}; 12e (filled squares), [∼12] {∼180}; 12f (triangles), [∼12] {250}; c20hp13a (full line), [∼12] {1200}; c20hp13b (dashed line), [∼3] {1230}. See Figure 3 for the significance of the meaning of the figures in square and curly brackets.

Figure 6. Pressure-area isotherms during compression/ expansion cycle for (a) C20NH2 and (b) C18NH2 spread on aqueous perchloric acid solution (bulk pH ) 2) with barrier speed of.

out considerably and the extent of hysteresis is considerably reduced. There is also a small increase in ALO with time in this case. We show in Figure 6 the differences in the π-A isotherms for both the n-docosylamine (Figure 6a) and n-octadecylamine (Figure 6b) measured 15 min after spreading and nearly 20 h after spreading. Features due to liquid-expanded/liquid-condensed (LE/LC) coexistence region are seen as the area is reduced. The area, ALE/LC (or Akink), at which the “kink” in the pressure-area isotherm is observed at short times, is somewhat unchanged (for the given compression rate) even after standing for long times, as seen in Figures 5b and 6a,b. There is a marked increase in ALO for the pressure-area isotherm measured after ∼1200 min relative to that measured after 15 min. The π-A isotherm obtained at long times after spreading when RT/C is varied (for the same subphase conditions) (Figure 6) are nearly the same for both C18NH2 and C20NH2. For larger RT/C (phosphoric acid; Figure 5b) the kink becomes less prominent and there is a smaller extent of increase in ALO compared to that with low RT/C (perchloric acid; Figure 6b). In the C20NH2/H2SO4 system (Figure 7) there is a continuous change in the pressure-area isotherm with time extending over days. Because of the large areas involved (.Aperp), we may attribute the increase in ALO with time (Figure 7) to the formation of the acid-base complex, RNH3+ (airface)X- (aquaface, solvated), in eq 1 involving “individual” amine molecules. The equilibrium in eq 1,

π-A Isotherms of Fatty Amines. 2

Figure 7. Pressure-area isotherms of C20NH2/H2SO4 system (bulk pH ) 2) obtained after long periods. The isotherms have been obtained under uniform compression/expansion rates: h2sc20a (one long and two short dashes), [∼12] {15}; h2sc203 (one long and one short dashes); [∼0.6] {1200}; h2sc208 (full line), [∼0.6] {∼2500}. See Figure 3 for the significance of the meaning of the figures in square and curly brackets.

Figure 8. Pressure-area isotherms of n-octadecylamine spread on an aqueous perchloric acid solution (bulk pH ) 2) at various times: hcoc18a (open circles), [∼12] {15}; hcoc183 (long and short dashes), [∼12] {∼1300}; hcoc182 (inset), [∼12] {∼1200}. See Figure 3 for the significance of the meaning of the figures in square and curly brackets.

if established at all, may take a very long time.8 This is consistent with the usually long characteristic relaxation times seen in our studies (Figure 11; see section III.5). The marked changes in the pressure-area isotherms after long times raises the important question of whether such a behavior is due to an effect of some contamination. Such a possibility may be strongly discounted if it can be shown that the starting behavior may be regenerated after long times in some way without in any way changing the contents of the trough or its environs. We have achieved such a behavior in the following manner. The pressurearea isotherm of the C18NH2/HClO4 system measured 15 min after spreading is shown in Figure 8. That obtained ∼20 h after spreading is shown in the inset of Figure 8. The film is then recompressed and the barrier held at a (8) Much of the temporal characteristics observed by us are similar to those other fatty amphiphiles such as fatty acids, alcohols, and esters. Such time-dependent behavior (see for example: Smith, R. D.; Berg, J. C. J. Colloid Interface Sci. 1980, 74, 273. Claesson, P. M.; Hevder, P. C.; Berg, J. M. J. Colloid Interface Sci. 1990, 136, 541. Perzon, E.; Claesson, P. M.; Berg, J. M.; Vollhardt, D. J. Colloid Interface Sci. 1990, 138, 245), however, is characteristic of low-area (Amol ∼ 20 Å2/ hydrocarbon chain) condensed phases due to collapse of the monolayer (see: Ries, H. E., Ries, Swift, H. Langmuir 1987, 3, 853. Ries, H. E., Jr. Nature 1979, 281, 287. Ries, H. E., Jr.; Albrecht, G.; Ter-MinassianSarago, L. Langmuir 1985, 1, 135) to multilayer phases. The area per hydrocarbon chain is very large in our case.

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Figure 9. Quasistatic compression/expansion cycling experiments with n-hexadecylamine spread on an aqueous perchloric acid solution (bulk pH ) 2). Barrier moved at ∼3 (Å2/mol of amine)/min and then held a the same position for 15 min. The compression-expansion cycles were carried out between ∼20 and ∼80 Å2/mol of amine. Key: c16hclo7 (broken line), uniform compression isotherm obtained ∼400 min after spreading; c16hl121 (full line), first cycle; c16hl122 (squares), second cycle; c16hl123 (triangles), third cycle. There is no waiting period between the cycles.

fixed position (∼20 Å2/mol of amine ∼Aperp) for nearly 1 h. The pressure decreases slowly during this period. The expansion was then carried out. The π-A isotherm during expansion is close to that obtained 15 min after spreading. The subsequent π-A isotherm during the compressionexpansion cycle (hcoc184) is now very similar to that obtained (hcoc18a) in the first expansion-compression cycle obtained after 15 min of spreading. The above results clearly indicate that the time-dependent changes in the π-A isotherms are not due to external impurities or contamination. III.3. Quasistatic Experiments. The very long time scales over which changes in the pressure-area isotherm take place appear to exclude any possibility for obtaining reliable equilibrium information for such systems using the conventional measurement procedures.9 We have used quasistatic experiments in which the barrier is moved in each step at a given rate over a fixed distance and then held at a fixed position for the time required to obtain the desired effective compression rate. In such quasistatic experiments, it is found that, when the barrier is held at a fixed position, there is always an increase in the pressure following an expansion and a decrease in the pressure following a compression, confirming that equilibrium is reached at a slower rate than the rate of barrier movement. We show in Figure 9 the results of three compressionexpansion cycles of the C16NH2/HClO4 (bulk pH ) 2) system with low RT/C with a quasistatic motion of the barrier. There is no waiting period at the end of each cycle. The values of Ainit an Afin were ∼80 and ∼20 Å2/mol of amine, respectively. The area of the subphase was decreased by ∼3 Å2/molecule in 1 min and the barrier then held at a fixed position for 15 min. The average expansion/compression rate is then ∼0.2 (Å2/mol of amine)/ (9) One of the anomalous but reproducible features that requires further investigation in this system with high RT/C is that on the expansion cycle the pressure at the first stage of expansion becomes higher than that obtained during the compression cycle (see curve h2sc203 of Figure 7, for example). The area over which such a behavior is observed decreases with decreasing compression rate. In the curve H2sc208 of Figure 7 there is no such crossover for the given compression rate although there is a region in the expansion isotherm in which the pressure increases with increasing area.

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Figure 10. Quasistatic compressing/expansion cycling experiments with the 4-hexadecylaniline/H2SO4 system (bulk pH ) 2). The same conditions as in Figure 9 were employed. The experiments were commenced after standing overnight after spreading. Key: 4hda352 (small and large dashes), first cycle; 4hda351 (dashes), second cycle.

min. The following features are seen (Figure 9) for the C16NH2/HClO4 (bulk pH ) 2) system: (i) The pressurearea isotherm shifts to lower areas with successive cycles when the waiting time between each cycle is small (minutes). The behavior observed in the first cycle is qualitatively and almost quantitatively retrieved only after waiting for several hours at the end of each cycle provided the area at the end of the expansion stage is greater than the value of ALO(I), the lift-off area in the compression stage of the first cycle. (ii) The extent of the decrease in surface pressure during the compression stage at low areas ( Amol > Aperp, the deproteonation of the head group (eq 4) leads to a decrease in the extent of solvation per amine molecule at the interface. The estimated area AH+ is close to the experimentally observed value, Akink (also referred to as ALE/LC), the area at which there is a marked break in the slope of the π-A isotherm characteristic of the LE/LC coexistence region. When Aperp < Amol < Akink, a deprotonation of the -NH3+ groups is likely with the formation of free amines and eventually the nucleation and growth of condensed clusters, the size of which increases with decreasing Amol and increasing time. The value of the surface pressure, πkink, obtained from the π-A isotherms at the area, Akink (onset of the LE/LC-like coexistence region), during compression (at short times after spreading), is decreased not only when RT/C is increased by increasing the chain length (Figure 6)swhich is only expectedsbut also by decreasing the strength of the acid in the subphase (Figures 4 and 5). The high-area complex (the LE-like region) is favored when the head-group-subphase interaction is strong relative to the chain-chain interaction. In the conventional models (see ref 3b and references therein) the large area per molecule in the liquid-expanded region is thought to be due to the presence of gauche defects in each chain of the individual molecules, although it is not clear how the gauche defects become favored because of increased head-group-subphase interaction. The two-state model accounts naturally for the two different characteristic times observed in the relaxation studies (section III.5). From the observed dependence of t1 and t2 on RT/C it is likely that t1 is associated with the tail-tail interaction or with kNclusters (eq 4) while t2 is associated with the time scales for the formation of the complex or kcomplex (eq 3). We may therefore associate t1 and t2 with the time scales tcluster and tcomplex for the formation of clusters and complex, respectively. The large values of t2 account for the anomalous “bizarre” timedependent behavior of the pressure-area isotherm of fatty amines observed so early by Adam4 and the extremely long times over which changes are seen to take place in the pressure-area isotherm (Figure 9). Such considerations are important in judging the temporal dependence of the surface pressure such as those observed by Bodalia and Duran13 for pentadecylaniline monolayer spread on the sulfuric acid subphase as compared to that of hexadecylaniline monolayer. IV.2. Hysteresis in Compression-Expansion Cycles. The “expanded” individually complexed amine molecules are expected to originate from the perimeter of a condensed cluster. Increasing the number of molecules, N, in the clusters (see eqs 3 and 4) then leads to an increase in tcluster, simply because the fraction of molecules at the perimeter of a two-dimensional cluster would decrease. This accounts for the increased hysteresis as RT/C is increased (see section III.1.3) at a given compression rate since an increase in the chain-chain interaction favors the growth of clusters. When RT/C is large (as in the C16NH2/H3PO4 system in Figure 4 or the C20NH2/H3PO4 system in Figure 5), we expect kNcluster (eq 4) to be greater than kcomplex (eq 3) for a given amine-head-group/subphase system and N is expected to increase. For a given set of boundary conditions, the extent of hysteresis is expected to depend not only the time scales, (12) Damodaran, K. V.; Merz, K. M., Jr. Langmuir 1993, 9, 1179. (13) Bodalia, R. R.; Duran, R. S. J. Am. Chem. Soc. 1993, 115, 11467.

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tcomplex and tcluster, for complex and cluster formation (eqs 3 and 4) but also on the time scale, tbarrier, for driving the changes in area or barrier motion. When tcomplex > tbarrier > tcluster (high RT/C), the π-A isotherm is controlled by the rate of complex formation with the individual amine molecules. The extent of hysteresis in the π-A isotherm then decreases as the compression rate is decreased for high RT/C (see section III.1.3). Such a behavior is the normal behavior. The behavior is anomalous when tcluster > tbarrier > tcomplex (low RT/C). As the compression rate is decreased, one may expect the number of molecules, N, in a cluster to increase during the compression stage so that tcluster is increased. The rate of formation of the complex is expected to be controlled by the rate of release of the free amine molecule from the periphery of the clusters. tcomplex is not expected to depend on the size of the clusters, however. The increase in tcluster on decreasing the compression rate, decrease the number of free amine molecules available for complexation so that the rate of formation of the individual, complexed amine molecules decreases. Such an increase in tcluster leads to the counterintuitive increase in the hysteresis with decreased expansion/compression rate (Figure 4) for systems with low RT/C (see section III.1.3). The marked decrease in the pressure on holding the barrier at a fixed position at low areas in the second (c16hl122) and third (c16hl23) compression/expansion cycles of the C16NH2/HClO4 system (Figure 9) is consistent with an incomplete conversion of the low-area condensed clusters to expanded complexed amines at high areas at the end of the cycle. This leads to a decrease in the number of complexed molecules so that ALO decreases on compression. On expansion, the newly formed clusters are not all recoverted to the complexed state. The residual clusters act as nucleation centers and accelerate the growth of the clusters on recompression so that the cluster size is further increased and the rate of formation of the free amine (eq

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4) available for complexation (eq 3) is further decreased. The above dependence on the number of compression/ expansion cycles clearly demonstrates the dependence on boundary conditions and is consistent with a two-state model. The value of RT/C of C16PhNH2/H2SO4 is expected to be greater than that of the C16NH2/HClO4 system. Accordingly, the rate of formation of the cluster in the former system is expected to be fast and independent of the rate of movement of the barrier so that the hysteresis behavior becomes not much dependent on the time taken for expansion and compression. There is thus little change in the extent of hysteresis on cycling (Figure 11). At long times after spreading, when the equilibrium conditions have been approached, one expects the size of the clusters to have become small. tcluster is then small and does not contribute to the rate-determining steps. The extent of hysteresis in the compression and expansion stages of π-A isotherms measured at long times after spreading is then expected to decrease as in the C20NH2/H3PO4 system (Figure 5). The observed dependence of the hysteresis of π-A isotherms of fatty amines on RT/C should also be useful in further understanding the nature of changes in the pressure-area isotherms of other systems including lung surfactants.14 In the presence of the protein (smaller RT/C) the extent of hysteresis in the compression/expansion curves increases while in the absence of the protein (larger RT/C) the extent of hysteresis decreases. Acknowledgment. We acknowledge funding from CEFIPRA in the Indo-French program. LA960982E (14) Longo, M. L.; Bisagno, A. M.; Zasadzinski, J. A. N.; Bruni, R.; Waring, A. J. Science 1993, 261, 453 and references therein.