Langmuir 1991, 7, 2208-2212
2208
The "Time of Observation"of P A Isotherms. 2. A Possibility That So-called "Solid Films" in P A Isotherms of Monolayers of Long-chain Acids May Not Correspond to the Two-DimensionalSolids but to the First-Order Phase Transition Regions from Two-DimensionalLiquids to Solids Teiji Kato,' Yoshinori Hirobe, and Motoko Kat0 Department of Applied Chemistry, Faculty of Engineering, Utsunomiya University, 2753 Ishii-Machi, Utsunomiya, Tochigi 321, Japan Received December 7, 1990. In Final Form: March 25, 1991 Monolayers on the water surface are viscoelastic bodies and characteristictimes of measurement of r-A isotherms are necessary. The time of observation of r-A measurement is defined and a new method of measurement in which the time of observation can be kept constant is proposed. The drastic change of the shape of P A isotherms of arachidic acid monolayers even at a constant temperature by changing the time of observation widely and systematically is demonstrated. Some evidence for a possibility that so-called 'solid films" of monolayers of long-chain acids may not correspond to the two-dimensional solids but to the two-dimensional first-order phase transition regions from liquids to solids are presented and discussed.
Introduction
The a-A isotherm shows only a slope change a t this transition point and there is no discontinuous area change a-A isotherms are the most fundamental and the most with keeping surface pressure constant. This corresponds frequently measured property of monolayers of amformally to the second-order phase transition. Thermophiphilic materials, and enormous amounts of isotherm dynamics predicts, however, that the phase transition from data were accumulated since the early works of Adam, a liquid to a solid should be first order. There is a large Langmuir, Schaefer, and Harkins.' *-A isotherms have contradiction at this point of *-A isotherms. Many been treated as two-dimensional analogues of p-V isoinvestigators have made efforts to explain this contratherms of materials and were believed to be thermodydiction since the early works of Harkins: but no one could namical quantities. Recently, some investigators have solve this problem without ambiguity. This is a longreported the area relaxations of monolayers at constant standing contradiction about condensed monolayers (Harpressures or the pressure relaxations at constant area^.^-^ kins' paradox). Harkins has stated in his report without The relaxation behavior of insoluble monolayers is a rather actual proof that the change from three to two dimensions, general phenomenon. a-A isotherms are measured under or a decrease of one dimension, gives an increase of one continuous compression in general, and the relaxation in order of the phase transitions.6 processes in monolayers should affect the shape of T A The second objective of this paper is to discuss a isotherms. possibility that so-called "solid films" in F A isotherms of We have proposed the idea of "time of observation" of monolayers of long-chain acids may not correspond to the r - A isotherms as a characteristic time of measurements two-dimensional solids but to the two-dimensional firstand showed that the shape of T-A isotherms of arachidic order transion (liquid-solid coexisting)regions. There are acid monolayers was surprisingly changed by changing some other questions about this "solid" of monolayers: the time of observation even at a constant tem~erature.~ Why two-dimensional compressibilities of monolayers in The first of the two objectives of this paper is to "solid films" are much larger for an order of magnitude or demonstrate change of the shape of a-A isotherms of more than those estimated from compressibilities of threearachidic acid monolayers in more detail when the time dimensional solids of organic materials, or why one can of observation is changed widely and systematically. deposit amphiphilic materials in the "solid" regions with It is said that a long-chain acid, stearic acid for example, the vertical dipping method which inevitably accompanies in a monolayer changes its phase from a two-dimensional flow of monolayers during deposition, and why areas of liquid to a solid with compression a t about 25 mN/m at monolayers decrease with time when the surface pressures a certain low temperature on an acidic subphase. The are kept constant in the 'solid" regions. Our idea in this steepest slope (with the smallest compressibility) part of paper can reply to all of these questions, and we can propose the r-A isotherm is called a 'solid film" because the film a unified explanation of these long-standing questions. exhibits the shear elasticity, which is a feature of a solid. Experimental Section Author to whom correspondenceshould be addressed. Materials. Arachidicacid (99%),behenicacid (99%),ateatic (1) Gains,G.L., Jr. Insoluble Monolayersat the Air/ Waterlnterface; acid (99%),palmitic acid (99%),andpentadecanoic acid (99%) Interscience Publishers: New York, 1966; Chapter 5. were purchased from Sigma Chemicals and they were wed (2) Huhnerfw, H.; Alpera, W. J. Phys. Chem. 1983,87,5251. Huwithout further purification. Spectrogradebenzene was wed as heduma, H.; Walter, W. J. Colloid Interface Sci. 1984,97, 476. (3) OBrien, K.C.; Lando, J. B. Langmuir 1986,1,453. a spreading solvent. Water for the subphase was distilled with (4) Bois, A. G.J. Colloid Interface Sci. 1986, 105, 124. Bois, A. G.; an all-Pyrexdistillingapparatus. Guaranteed grade sulfuricacid Ivanova,M. G.;Panaitov, I. I. Langmuir 1987,4215. Boie, A. G.;Baret, (Wako Chemicals) was used to adjust subphase pH to 2. MonoJ. F.; Kulkami,V. S.;Panaitov, I. I.; Ivanova, M. G.Langmuir 1988,4, 1358. (6) Kato, T . Langmuir 1990,6,870.
0743-7463/91/2407-2208$02.50/0
(6) Harkins, W. D.; Copland, L. E. J. Chem. Phys. 1942, 10, 272,
0 1991 American Chemical Society
Langmuir, Vol. 7, No. 10, 1991 2209
Time of Observation of AA Isotherms of Monolayers layers were spread with a Cloehn microsyringe of gas-tight type. Compressionof monolayersstarted 15minafter spreading.Gains' and Barnes et al.8 have shown that even relatively nonvolatile hydrocarbons disappear completelyfrom a monolayerwithin 1015 min, and the usual spreading solvents (such as hexane and benzene) evaporate rapidly and completely. Therefore, 15min of standing before the s t a r t of compression is enough to assure complete evaporation of benzene from the monolayer systems. F A isothermswere measured with a microcomputer-controlled instrument developed in our laboratory. Details of the instrument are reported else~here.~J~ The most important feature of this instrument is that two barriers confining a monolayer are driven symmetrically in all compressionmodes of monolayers including the constantstrain rate compression. Temperatureof subphase water was controlled by circulating water from a thermostated water bath into a double-bottomed Langmuir trough. Two control modes were used: the short term-control was to circulate strictlytemperature-controlled water, and the long term-control was that using feedback of the surface temperature detected to the temperature of circulating water. Temperature fluctuation of the surface in these modes were less than fO.O1 "C for the former controland less than i0.05 OC for thelatter. The response time of the feedback control was about 8 min. When experiments take longer than 30 min, the latter control mode was used. To detecttemperature change of the water surface with compression of monolayers, the short-termcontrol was used because the temperature change was cancelled by the feedback control of the latter mode. The size of the tip of a platinum wire resistance sensor (100 Q), which was sealed in a glass bead and was used for detection of the surface temperature,was 0.8 mm diameter and 2 mm length. The glass bead was set horizontally on the water surface. The surface temperature was converted into voltage with a voltage converter and was taken into a microcomputer through an A/D converter after amplification.
Results and Discussion We have proposed the "time of observation" of measurement of u-A isotherms of monolayer^.^ The time of observation (tab) is defined by the reciprocal of the strain rate of compression of monolayers. Therefore, a monolayer should be compressed under a constant strain rate to measure a r-A isotherm at a constant time of observation. The speed of compression barriers change exponentially with time in this case. The is a characteristic time of P A measurement and the shape of a u-A isotherm is governed by balance of the relaxation times of molecular motions in monolayers which occur during compression and the time of observation. If the relaxation times of the molecular processes are much shorter than the time of observation, all the molecular processes relax completely during compression and the surface pressure does not rise with compression by them. The surface pressure detected under compression is given by the superposition of a series of partially relaxed pressures up to that instance. Figure 1shows F A isotherms of arachidic acid monolayers at 10 "C on a pH 2 subphase, measured at rather shorter times of observation (tab = 200-3000 s). Figure 2 shows also those measured at medium times of observation (tab = 6000-70600 9). Figure 3 summarizes P A isotherms of arachidic acid monolayers measured at the same conditions as to those in Figures 1and 2 except that the times of observation were very long (70600-400000 8). As seen from these three figures, the shape of P A isotherms of arachidic acid monolayers measured even at the same temperature changes drastically by changing the time of observation systematically and widely as if we changed the film material. The P A isotherm measured at shorter (7)Gains, G. L.J. Phys. Chem. 1961,65,382. (8)Barnes,G.T.; Elliot, A. J.;Grigg, E. C. M. J. ColloidZnterface Sci. 1968,26, 230. (9) Kato, T.; Watanabe, T. Nippon Kagaku Zasshi 1987,1987,954. (10) Kato, T. Jpn. J . Appl. Phye. 1987,26, L1377.
I
2 \
k .IW
rn
e
n.
W
0
rcI
cn 3
Molecular Area A/nm%olec.-l
Figure 1. u-A isotherms of arachidicacid monolayers measured at the shorter times of observation (pH 2.10 OC). The times of
observation are shown in the figure. BDDl
7
80-
P 50c
I'
"
s".
\
PI ' O -
I
30-
a
8 20- '
Gg
100 0.10
I
0.20
b
,
I
0.20
.20
Holecular Area A/ni*iolec.-'
Figure 2. *-A isotherms of arachidicacid monolayersmeasured at the medium times of observation (pH 2, 10 "C). The times of observation are shown in the figure.
30
A/nmamolec.-l Figure 3. u-A isothermsof arachidicacid monolayersmeasured at the longer times of observation (pH 2,lO O C ) . The times of observation are shown in the figure. Molecular Area
time of observation, t&,= 200 s for example, in Figure 1 is composed of six parts, a-b, b-c, c-d, d-e, e-f, and f-g, as illustrated in the figure. Part a-b is the gas/liquid coexisting region. Part b-d corresponds to the liquidcondensed region, and there is a phase transition of a small scale detected at point c. It is said that arachidic acid becomes a two-dimensional solid at point d with compression and part d-e is called a "solid film". The "solid film" collapses at point e. We consider now that part e-f
Kat0 et al.
2210 Langmuir, Vol. 7,No. 10,1991
Table I. Comparison of the Surface Compressibility of So-called 'Solid Film" of an Arachidic Acid Monolayer with Those Estimated from the Three-Dimensional Compressibilities of Organic Liquids or Crystals, Assuming That the Film Thickness of These Materials Is the Same as That of the Arachidic Acid Monolayer in the 'Solid Film", 2.77 nm. R,mN/m K". m/mN Two-Dimensional 1 x 103 1 x 10-3 arachidic acid ('solid film", 10 "C, 25-60 mN/m) 1 x 102 1 x 10-2 arachidic acid ("liquid-condensed film", 10 "C,0-25 mN/m)
diphenylamine (30"C, triclinic, 1 x 106 to 2 x 107 Pa) tartaric acid (30"C, triclinic, 1 X lo6 to 8 X lo7 Pa) ethylene glycol (25 "C,106-107Pa) pentadecane (60 "C, l@-107 Pa) palmitic acid (65 "C,106-107Pa)
a axis b axis c axis a axis b axis c axis
K , m2/N K , N/m2 Three-Dimensional (Solids) 5.0 X lo-" 2.0 x 10'0 4.9 x 10-11 2.0 x 10'0 1.8 X 10'0 5.6 X lo-" 8.4 X 10-l2 1.2 x 1011 1.9 x 1010 5.2 X lo-" 1.1 x 10-11 9.1 x 1010 Three-Dimensional (Liquids) 3.7 x 10-10 2.7 x l o g
K8,b
'
mN/m
5.5 x 5.5 x 5.0 X 3.3 x 5.3 x 2.5 X
104 104 10' 106 104
106
K", m/mN
1.8 X 1.8 X 2.0 x 3.0 X 1.9 x 4.0 X
loa 10-6 10-6
1o-B 10-5 lo4
7.5 x 103
1.3 X lo4
1.0 x 104
1.0 x 109
2.8 x 103
3.6 X lo4
9.2 X 10-lo
1.1 x 109
3.0 x 103
3.3 x 10-4
are estimated a Key: K , bulk compressibility; K , bulk modulus;K8,area modulus; K', surface compressibility. Two-dimensional moduli (R) from bulk moduli ( K )assuming the film thickness of the materials is the same as that of an arachidic acid monolayer in the 'solid film", 2.77 nm, and using a relation, 1.8 X lo7 N/m2 = 50 mN/m.
corresponds to the region of nucleation of three-dimensional crystallites and the number of nuclei increases with compression at this part. This was revealed by the electron microscopic observation of one-layer LB films deposited a t the region, using a new replica method of plasma po1ymerization.ll The results will be reported elsewhere.12 The nuclei begin growing at point f and part f-g is the growing region of three-dimensional crystallites of arachidic acid with compression in the collapsed monolayer. At the gas/liquid coexisting region, a-by as all of the relaxation times of molecular motions in the monolayer are shorter than the shortest time of observation (200s), molecular motions are fully relaxed and the surface pressure does not rise with compression, but at a constant of equilibrium two-dimensional vapor pressure of arachidic acid at 10 "C. Some of the relaxation times become longer with increasing molecular density of the monolayer than the time of observation at point b and the surface pressure begins rising with compression at this point. In the liquidcondensed state of monolayers, relaxation times are very long, as shown in Figure 3, and the surface pressure increases monotonically with compression. Recently, Kawai and his collaborators have estimated from the change of linewidth of symmetric CD2 stretching band of deuterated stearic-d3~acid in a monolayer measured by the nonresonance Raman spectra that the order of lateral chain packing is much improved, being accompanied by an increased amount of the trans conformation changed from the gauche one, with compression in the liquidcondensed state.13 Stearic acid and arachidic acid are the next members of the long-chain acid homologue having even-numbered hydrocarbon chains and it is natural to consider that the molecular conditions are almost the same in the liquid-condensed states of both materials. A small scale phase transition is detected a t point c and the relaxation mechanism in the monolayer may change here, but we do not know much about this transition yet. From all of the P A isotherms shown in Figures 1,2,and 3, we can predict that the surface pressure of the arachidic (11)Iriyama, K.; Araki, T.; Kato, T. Membrane 1991,16,43. (12)Kato, T.;Iriyama, K.; Araki, T. To be published elsewhere. (13)Kawai, T.; Umemura, J.; Takenaka, T. Chem. Phys. Lett. 1989, 162,243.
acid monolayer during compression will be at the limit of the ESP of this material a t this temperature when T-A isotherms are measured a t the infinitely long time of observation. Thus, a-A isotherms observed above the ESPs of amphiphilic materials at certain temperatures can be measured by virtue of the fact that relaxation times of the molecular processes are longer than the time of observation. As the pressure deviation from ESP increases, the free energy of a monolayer deviates positively from zero and becomes large, and the relaxation times of the molecular processes toward an equilibrium become short. Collapse of monolayers will occur when the relaxation times of the collapse processes become comparable to the time of observation. These conditions are shown clearly in Figures 2 and 3. At point d, the surface compressibility of the monolayer changes from about 0.01 m/mN for a liquidcondensed film to about 0.001 m/mN for a "solid film". It has been a question for a long time whether surface compressibilities of "solid films" of the order of 0.001 m/mN in general are much larger than those estimated from the three-dimensional compressibilities of organic crystals. Table I summarizes two-dimensional compressibilities of some organic compounds which were estimated from three-dimensional compressibilities of solids or liquids of these materials.14 Two-dimensional moduli are calculated from bulk moduli of the materials assuming that the thicknesses of films of these materials are the same as that of an arachidic acid monolayer, 2.77 nm. Even the surface compressibilities estimated from the values of three-dimensional organic liquids are much smaller than the surface compressibility of an arachidic acid monolayer in the "solid film". Those estimated from the values of three-dimensional crystals are smaller for 2 orders of magnitude or more than that of an arachidic acid monolayer in the "solid film". Figure 4 shows temperature change of the water surface with rapid compression of an arachidic acid monolayer, (14) Landolt-Bornstein Zahlenwerte und Funktionen a w Physik, Chemie,Astronomie, Geophysik und Technik; Springer-Verlag: Berlin, 1971. 6 Aufl. I1 Band, 1 Teil, S. 632-718.
Langmuir, Vol. 7,No. 10, 1991 2211
Time of Observation of P A Isotherms of Monolayers
1
End of Compression
Compression
I
9.00
100
200
300
400
Time
500
600
700
800
ti3
Figure 4. Change of the surface temperature of the subphase water with compression of an arachidic acid monolayer at 40 mm min (pH 2, 10 "C). Marks, a-g, correspond to the same mar s in Figure 5.
k
0.15
'4
ob
0 15
Figure 6. P A isotherms of arachidicacid monolayers measured at tob = 6000-70600 5 (PH 2,10"e). SO-cded "solid fih"parte
f
I
\
20t 10
0.20 Molecular Area A/R.lolec.-l
Y
h a
\i \I
0.10 0.20 0.30 Holecular Area A/nm%olec.-l Figure 5. PA isotherm of arachidic acid monolayer measured at a constant speed of compression of 40 mm/min (pH 2,lO "C).
40 mm/min around 10 "C. Despite our assertion of compression of monolayers under constant strain rates, the monolayer was compressed under a constant speed in this case because we wish to know the temperature change with unit change of the monolayer area per unit time. Figure 5 shows a T-A isotherm of an arachidic acid monolayer measured at the same conditions. Corresponding points, a-g, are marked in both figures. The strain rate of the monolayer changed from 10% /min at the beginning to 50%/min at the end of compression. This means that the time of observation changes continuously from 600 s at the start to 120 s at the end of compression. The shape of the T-A isotherm is almost the same from point a to point e with that measured at the time of observation of 600 s in Figure 1,but the slope of part e f and the pressure at part f-g are larger than those in Figure 1. This is because the strain rate is high (time of observation is short) at these parts. Before compression is started, temperature of the water surface fluctuates within fO.O1 "C around 9.96 "C, but it begins increasing gradually with compression. The temperature increases abruptly at part d-e and it shows a plateau at part e-f. The temperature increases considerably again at part f-g. The temperature increase continues for a while after compression stops. This may
are enlarged. be due to the spontaneous growing of crystallites in the collapsed film. It is reasonable to consider that enthalpy release being accompanied with the first-order phase transitions in the monolayer should be responsible for the marked increases of the surface temperature a t parts d-e and f-g. There is another possibility of temperature increase with compression of a monolayer, i.e., depression of water vaporization with increasing the surface density of the film material with compression. This effect may overlap on the temperature increase by the enthalpy release of the monolayer. If depression of water vaporization is the main cause of the surface temperature increase, however, it is difficult to explain why the surface temperature increase stopped at part e-f or why the temperature returned its original value within about 10 min after stopping compression. A t 20 mm/min compression, the surface temperature increase was also observed but the maximum temperature increase was only less than about 0.2 "C. This fact also supports the idea that exotherms with first-order phase transitions in an arachidic acid monolayer should be the main cause of the temperature increase. Data are not shown here but all of the monolayers of behenic acid, stearic acid, palmitic acid, and pentadecanoic acid showed temperature increase at regions corresponding to gas/liquid coexistingregions and collapsed regions and abrupt increase at so-called "solid films" regions with rapid compression. The degree of temperature rising is material dependent, but the phenomena are rather general, for monolayers of long-chain acids at least. These facts indicate that the temperature increases are due to the enthalpy release from monolayers at the first-order phase transitions of them. Then, a question arises of why "solids" release enthalpy by compression. Figure 6 summarizes enlarged parts of P A isotherms measured at the medium times of observation, showing the "solid films" of arachidic acid monolayers at 10 "C. Note the slopes of the parts of so-called "solid films". It can be clearly seen that the slope of the "solid film" decreases with increasing the time of observation. If the "solid film" is a true two-dimensional crystalline solid, the surface compressibility of it should not depend on the time of observation and the value should be of the order of 10-6 m/mN at most as described above. The surface pressure of the "solid film", however, relaxes considerably
Kato et al.
2212 Langmuir, Vol. 7,No. 10,1991 IO(
8
fne
10 T
Holecular Area A / d m ~ l e c . - ~
40
Figure 7. Dependence of F A isotherms of arachidicacid monolayers on the time of observation at 20 "C (pH2).
Molecular Area A/Reolec.-l
Temperatamdependenceof PA isotherms of arachidic acid monolayers measured at a constant time of observation of 3000 s (pH2). because the temperature dependence of the relaxation times of the molecular processes is different. In other words, activation energies of the relaxation processes are different from molecular process to process. We will confirm next what molecular processes occur at part d-e by more direct proof such as X-ray diffraction using synchrotron radiation from monolayers compressed under suitable constant times of observation. Figure 8.
with time. This fact strongly suggests that part d-e of the T-A isotherm may not correspond to a one-phase region but to a two-phase coexisting region. Thus, all of these facts described above lead us to a conclusion that so-called "solid films" of monolayers are not the true two-dimensional solids of film materials but two-phase regions where two-dimensional liquids and solids in monolayers coexist. They appear as so-called "solid films" in PA isotherms with compression because of the longer times of relaxation than the times of observation of the usual compression speeds. It is expected that at a suitable time of observation, a phase transition from a liquid to a solid in two-dimensions should be observed in a T-A isotherm of an arachidic acid monolayer as a horizontal line, d-e' as shown in Figure 6. A true two-dimensional solid film, e'-e, will appear with surface compressibility of the order of lom5m/mN under ideal compression conditions, but this may be very difficult to be observed because the film will collapse as soon as the two-dimensional solid film being completed. Figure 7 showsdependenceof T-A isotherms of arachidic acid monolayers on the time of observation at 20 OC. Other experimental conditions are the same as those in Figures 1,2,and 3. As seen from this figure, part e-f disappeared at tob between 200 and 6008, and the so-called "solid f i " disappeared at tob between 30 000 and 60 O00 s at this temperature. These critical times of observation are much shorter than those at 10 O C . Moreover, collapse behavior at point e and the phase transition features at point c are something different from those at 10 OC. Figure 8 shows temperature-dependence of PA isotherms of arachidic acid monolayers, keeping the time of observation constant at 3000 s. By comparison of change of PA isotherms in these two figures, it can be said that increasing the time of observation at a constant temperature and increasing the temperature at a constant time of observation give almost the same effect on the change of T-A isotherms of arachidic acid monolayers. Two effects, however, are not quite the same, especially on the collapse behavior at point e and the transition behavior around point c. This is
Conclusions Insoluble monolayers at the air/ water interface show piessure relaxation at a constant area or area relaxation at a constant pressure. Insoluble monolayers are viacoelastic bodies, and it is necessary to consider a characteristic time of measurement of T-A isotherms. This is the time of observation. The time of observation of T-A measurement is defined by the reciprocal of the strain rate, and to keep the time of observation constant during measurement, monolayers should be compressed at a constant strain rate rather than a constant speed. The shapes of u-A isotherms are determined by the balance of the relaxation times of the molecular processes which occur during compression and the time of observation. Some experimental evidence shown in this paper indicates a possibility that so-called "solid films" of monolayers of long-chain acids may not correspond to the true two-dimensional solids but to the two-phase coexisting regions of a liquid and a solid. This working hypothesis can explain all of the long-standing contradictions about so-called "solid films" (including Harkins' paradox). Acknowledgment. This work was supported partially by the Grant in Aid for Scientific Study from the Ministry of Education (No. 02555167)and from the Iketani Science and Technology Foundation (No. 22004), which were given to T.K. in 1990. These were much appreciated. Thanks are due to Mr. T. Tanaka for his assistance in the experimental work.
