MEASURING AREAS OF MOLECULES
28!)
A NEW METHOD FOR MEASURING THE EFFECTIVE AREAS OF FILM-FORMING MOLECULES NEVILLE F. MILLER Research Division, The New Jersey Zinc Company, Palmerton, Pennsylvania Received April 18, 1940 I. INTRODUCTION
Measurements of the effective areas of polar molecules are employed in industrial laboratories to standardize the substances to be adsorbed in measurements of the specific area of solids, to evaluate the efficiency of adsorption of surface-active agents, and to study the molecular structure of film-forming materials. For these purposes the area measurements obtained at zero film pressure are not as significant as those obtained at higher pressures, where the film is more consolidated. This paper presents a new method for measuring the effective areas of polar molecules at a film pressure of 10.3 f0.3 dynes per centimeter. The method is rapid and convenient and requires no surface balance. It is based on the equilibrium of tensions established a t the point where the pressure developed in the deposited monolayer has become large enough to prevent the spreading of a lens of solution on the substrate.’ This film pressure for a variety of polar substances dissolved in pure benzene a t congram-moles per cubic centimeter is 10.3 f 0.3 centrations of 0.5 to 2 X dynes per centimeter. The method consists in determining the exact amount of benzene solution required to form the first stable lens on a substrate of known area. At this point the surface is covered with a monolayer a t a film pressure of 10.3 f 0.3 dynes per centimeter. This investigation has shown that the equilibrium established at the lens cndpoint is not reversible but that, in the presence of excess solution, the equilibrium shifts toward the development of higher film pressures. This increase in film pressure is accompanied by an increase in the lens angle. Measurements of lens angles and of all tensions under conditions corresponding to the lens endpoint have been made for nine systems. The data obtained have been found to satisfy equations derived by applying Scumann’s theorem to these lens-film systems. 11. DESCRIPTIOE; OF THE EQUILIBRIUM LENS ENDPOINT METHOD
The apparatus required in this method consists of a 0.1-cc. serological pipet and a glass photographic tray. The tray contains the substrate * Langmuir and Schaefer (9) have already described this effect, but apparently no one has used it as the basis of a method for measuring the areas of molecules in films.
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NEVILLE F. MILLER
(either water or dilute acid) and should be well illuminated, The solution of film-forming substance is added dropwise to the surface of the substrate from the pipet. Each drop is allowed to spread before the mext drop is added. The first drops spread rapidly. Subsequently the drops spread more slowly, and at this point the solution is added in 0.002-cc. portions by allowing this amount to flow out on the end of the pipet and touching the pipet to the water surface. The endpoint is reached when the 0.002-c~. portion forms a stable lens on the surface of the substrate. This lens is the first one which is in equilibrium with the film and may be called the “equilibrium lens.’’ The equilibrium lens may be distinguished from all preceding lenses by the following six criteria: (1) The first drops added to the surface form lenses of relatively short life period. The equilibrium lens remains on the surface for a p preciable periods of time, which depend upon the temperature of the substrate. (2) The shadows of lenses just prior to the equilibrium lens are surrounded by dark halos. These halos are easily observed if the lens system is located directly beneath a ceiling light and a bright metallic surface is placed beneath the tray. As the equilibrium lens is approached, the halo moves inward until it disappears entirely for the equilibrium lens. (3) The equilibrium lens is definitely circular in outline and has a sharp boundary. Previous lenses have boundaries of definite widths, which occasionally show interference fringes or give reflected sparkles which indicate that the lens edge is vibrating. (4) Light is focused sharply by the equilibrium lens to form a small bright spot on the lower surface of the tray. Previous lenses are incapable of giving a sharp focus to the light, since they are not truly lenticular. With some systems the focal length of the equilibrium lens is too long to give a sharp point of light on the tray. The fact that these lenses are truly lenticular may be shown by placing a sheet of graph paper beneath the glass tray and observing the characteristic magnified image of the spacings. (6) The first lenses added to the substrate move more or l e a rapidly over the surface, since the surface tension of the substrate is reduced unevenly around them. The equilibrium lens remains relatively quiescent, since the formation of the complete film has established an equilibrium of tensions. (With some systems the completion of the film seems to be accompanied by a relatively large increase in surface viscosity, which entirely stops the motion of the lens.) (6) If two lenses are placed near to each other they are instable in each other’s presence if they are not equilibrium lenses. One lens (or
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291
both) will vibrate violently and assume a very irregular outline. Streamera of liquid will leave from between the two lenses in a fan-like sheaf. These lenses never merge together. However, a t the equilibrium point, two lenses may be placed very near to each other without showing any effect, one on the other. Both will remain perfectly circular in outline, give sharp foci of light, and remain relatively quiescent or slowly merge together. The formation of the equilibrium lens indicates the complete coverage of the substrate surface with a monolayer under a film presaure very close to the spreading prwure of the solution on the substrate. The calculation of the effective area of the polar molecules is obtained from the equation : A X 10'' Effective area = V X C X 6.06X loB where A = surface area of substrate in square centimeters, V = volume of solution required to reach the equilibrium lens endpoint in cubic centimeters, and C = concentration of solution in gram-moles per cubic centimeter.
Notes on procedure The pipet used in this work was calibrated in hundredths of a cubic centimeter, and since these calibrations were spaced 1.3 cm. apart, volumes could be estimated to thousandths of a cubic centimeter. The accuracy of the calibrations on the pipet was checked with a mercury column in the usual way. When making measurements, all excesesolution was wiped from the tip with a clean filter paper. Since more than one pipetful of solution was required for each measurement, it was necessary to clean the pipet between each addition of 0.1 cc. This was done by drawing pure benzene through the pipet and then drying by connecting to a vacuum line. The glass tray waa cleaned with warm sodium dichromate-sulfuric acid solution and rinsed with distilled water before each measurement. The surface of the substrate was freed from impurities in this way: A large sheet of clean filter paper waa laid on the substrate surface. After the paper was wet through, it waa held by the unwet edge and drawn rapidly across the surface and over the edge of the tray. This procedure was repeated a t least twice before each measurement. Since the sides of the tray were not truly perpendicular, the surface area of substrate varied slightly according to the volume of substrate used. The area of substrate was measured for each determination. 111. THEORY OF THE EQUILIBRIUM LENS METHOD
The theory of this method may be understood by reference to the vector diagram of figure 1.
292
NEVILLE F. MILLER
Here S3 = surface tension of pure substrate, Si = surface tension of substrate plus film at spreading pressure Fa, 8’’- surface tension of substrate plus film at “equilibrium endpoint” pressure F,, : :
:
I S;
s3 I
:
I
A.
f
-
SPREADING F, s-, -3-; s ,
: : I : I
s sa
’1
LENS ANGLE IS ZERO
,
C.
I
>
h
*
.
s23
CONTRACTION TO STABLE LENS LENS ANGLE FINITE
FIG.1
8: = surface tension of solution in contact with substrate, and S23= interfacial tension of solution and substrate. When a drop of solution is first added to the substrate (figure 1, A), it spreads with a force F, whose magnitude (in dynes per centimeter) is given by the well-known equation of Harkins:
F a = Ss
- S:
- Szs
(1)
XEASURING AREAS OF MOLECULES
293
Spreading continues until the film reaches the confines of the tray, when it begins to build up a film pressure ( F ) , thereby reducing the effective surface tension of the substrate and also the spreading force (F8). This film pressure continues to increase after the complete monolayer is formed, until Sa has been reduced to S: and F , has become zero (see figure 1, B). At this point, a fresh drop of solution is added to the substrate and shoys no spreading tendency. Since Fa= 0 and Sa has become equal to Sa, equation 1 reduces to
s: = s; +
823
The values of 8; and Szafor this equation are identical with those of equation l, since a fresh drop of liquid was added to form this last lens.2 ( F ) has become equal to the original spreading force of the solution (F,) and we may write, from equation 1:
The values of 8; and 82s of equations 2 and 3 are identical, and we may add these equations to obtain
This equation gives the film pressure a t the point where F = F, and corresponds to the equation used by Harkins and Anderson (7) for determining film pressures with the vertical-balance method. Equation 3 is similar to the equation derived by Cary and Rideal (4)for the equilibrium existing between a lens of pure liquid (not solution) and the deposited film. Equations 2 and 3 are unable to account for the conditions which obtain at the lens endpoint. Equation 2 requires no minimal suifaces for the i is equal to the sum of 8; and an extension lens of solution. (Since S of the surfaces of the lens due to spreading into any irregular shape would involve no change in total free surface energy of the system.) Equation 2 also implies that the lens angle is zero. The lenses actually obtained a t the endpoint are definitely circular in outline and have well defined angles of from 8' to 16'. The explanation for the formation of these lenses is as follows: This investigation has shown that in the presence of a lens of excess solution, the film pressure continues t o increase beyond the point where
* A small area of previously deposited film is covered by this last drop and dissolves in the lens, producing an insignificant fractional change in concentration AC/C equivalent to AAIAF,where AA is the area of film covcrcd by the lens and A p is the area which would be covered by the spreading of all the polar molecules contained in this lens into a monolayer a t a film pressure equal to F,. The change in Szs and in S Zdue to AC has been calculated as less than 0.1 dyne pcr centimeter.
294
F
NEVILLE F. MILLER
= F,. Evidentk the escaping tendency of the polar molecules from the lens to the film s somewhat greater than the solution tendency of the film in the lens. Thus the equilibrium established at the lens endpoint is not a truly reversible equilibrium but one which slowly shifts toward the development of higher film pressures. This slow shift in the equilibrium pressure does not preclude the use of the lens endpoint for area determinations, since careful measurements have shown that the film pressure developed at the lens endpoint is highly reproducible (10.3 f 0.3 dynea per centimeter). Equations 2, 3, and 4 may be rewritten to conform to the condition that F has increaaed by a small amount (AF) to F,, whil; Si has decreased by the same amount (AF) to 8’;(see figure 1, C). (SS and S p a for a fresh drop of solution have their original values.) On the wumption that Neumann’s theory may be applied to these lens-film systems, equations 2 and 3 become
T
s”3 - S:
COS
a
+
6
(5)
- SB COS /3
(6)
SB COS
F. = Ss - S i COS a
Here the angle y is omitted, since observations have shown it to be zero €or these small lenses. Equation 4 may be revised to:
F,
= Sa
- Sy
(7)
This equation is used to calculate Si from measurements of SI and F, and involves no assumption regarding Neumann’s theory. IV. EXPERIMENTAL METHODS
In order to ascertain how closely actual systems conform to the theory of equations 5, 6, and 7, this investigation was confined to measurements of surface area and the related tensions for solutions of six polar compounds in benzene on water or dilute acid. Kine systems were studied. Purity of materials The be& grades of myristic acid, palmitic acid, cetyl alcohol, and cholesterol obtainable from the usual supply houses were recrystallized from suitable solvents. The stearic acid was obtained by saponifying a good grade of methyl stearate with alcoholic potassium hydroxide, acidifying with hydrochloric acid, and then subjecting the stearic acid to several purification steps. The glyceryl trioleate was a sample prepared in connection with another investigation (6). The benane was C.P. material redistilled to remove non-volatile impurities. The surface tension and interfacial tensions of the benzene against water were found to agree closely with published values for these
MEASVFUNG W OF MOLBCULES
295
tensions. Fresh distilled water was used in all experiments but was not redistilled except for a few special experiments.
Surface area m e a s z c r m These measurements were made by the lens endpoint method exactly 88 described above. Memurements of Si and Sa These measurements were made by the capillary-rise method in an apparatus similar to that Uses by Bartell, Caee, and Brown (3). The accuracy of these measurements waa estimated a t f O . l dyne per centimeter. The surface tensions of the solutions saturated with a few drop of substrate were not noticeably different from the surface tensions of the dry solutions or of the dry benzene for determinations made at the same temperature. Measurements of 828 These measurements were made in a double capillary apparatus similar to that described by Mack and Bartell (11). The benzene solutions and substrates were not previously saturated with each other, since this might have caused separation of polar molecules in a water film on the walls of the container. The accuracy of these measurements waa estimated at f0.2 dyne per centimeter, except in the case of the glyceryl trioleate solution, which did not establish a true equilibrium. Measurements of F, Measurements of the film preasure in equilibrium with the first stable lens were made by the vertical-balance method of Harkins and Anderson (7). To prevent vibrations of the liquid surface by air currents, the lens system waa formed in a dish of 8.4 cm. diameter contained in the balance case. The microscope slide was dipped into the substrate contained in this dish. Very small drops of solution were added from a micropipet until the first stable lens having a sharp edge was formed. Thsslide waa immediately allowed 'to rise to ita new equilibrium position. Duplicate values of F, thus obtained for any one system checked within h O . 1 dyne per centimeter. No contact angles of the liquid with the slide were observed.
Lens angle measurmenta Lens angles (e) were measured by a new method which will be published soon. This method depends on measuring the diameter of a lens of known volume and is quite accurate for lens angles up to 20'. These angles gradually increase in size from about 8" to over 20" aa the equilibrium
296
NEVILLE F. MILLER
slowly shifts. Measurements were made on fresh drops of solution added to the substrate a t the point where the first stable lens was formed. V. SURFACE AREA DATA
The data for the surface area measurements obtained by the lens endpoint method, together with the corresponding film pressures, are given in table 1. The last column of the table contains the surface area measurements for these substances a t corresponding temperatures and film pressures obtained by other investigators, using the Langmuir film-balance TABLE 1 Surface area data
-
EX
BUB8TANCBI
ad
BWBBTBATB
ij
Y
[
! li
P
E
d
j
c -
'C.
5 B c g i i -g
cc.
m.2
I.,
A.1
Myristic acid.. . . . . . . . . . . 2 Myristic acid.. . . . . . . . . . . 2
0.01 N HCl 0.01 N HC1
8 10.50.130 530 33.t 33.8 (1) 2 . : 10.50.126 528 34.t 34.7 (1)
Palmitic acid.. . . . . . . . . . . 2 Palmitic acid.. . . . . . . . . . . 2
HzO 0.1 N H C l
6 6
.0.50.210 516 20.1 19.8 (8) .0.60.203520 21.1 20.8 (10)
Glyceryl trioleate.. . . . . . . 0.5
HoO
6
0.30.155 528112
Cetyl alcohol.. . . . . . . . . . .
Hz0
6
0.10.220 528 19.1 19.4 (8)
Stearic acid.. . . . . . . . . . . . 2 Stearic acid.. . . . . . . . . . . . 2
HzO 0.1% HCl
6 6
0.40.215 516 19.8 19.3 (8) 0.40.173 507 24.2 24.1 (8)
Cholesterol. . . . . . . . . . . . . 1
Hi0
2 j
.09
(8)
3 0.20.212 522 4o.e 40.6 (2) -
method. The surface area measurements obtained@by the lens endpoint method agree within f 3 per cent of the measurements obtained by other investigators, using the film-balance method. Adam and Jessop (1) have discussed variations in results encountered during an extensive series of surface area measurements made by the horizontal film-balance method. They concluded that the errors of their measurements were &3 per cent. Thus the accuracy of the lens endpoint method appears to compare favorably with that of the horizontal-balance method.
297
MEASURING AREAS OF MOLECULES VI. TEST OF EQUATIONS 5,
6, AND 7 WITH LENS EQUILIBRIUM DATA
The lens angles and related tensions of the nine systems (presented in table 2) were used to test the suitability of the derived equations in this way: Values of 8'; were calculated by equation 7. These values and the TABLE 2 Lens equilibrium data*
SUBSTANCE
SOB6TRATE
c
c
8
-
4
I
B 0
s
+
L _
Glyceryl trioleate .
H20
s
3 2
__
10.0 1 O . l 10.0 10.l
14.5 14.5 14.5 14.6
16 16
.o.o 1 0 . l .o.o 1o.z
15.0 14.4 .5.5 15.8
116
.o.ol10.2
11.011.2
kU
~
0 1 N HC1
"
$
_
Myristic acid.. . . . . Myristic acid.. . , . . Palmitic acid.. . , . . Palmitic acid. . . , . .
9
Q
HzO
I
B
B
~
Cetyl alcohol.. . . . .
Hz0
116 134.2 '20.573.:
9.6 10.1
.4.5 14.4
Stearic acid.. . . . . . Stearic acid.. . . . . .
Hz0
O.l%HCI
116 134.0 29.473.: 116 133.8 29.573.:
9.9 10.4 9.9 10.4
.4.0 14.4 :4.5 14.5
9.810.2
.4.0 13.1
Cholesterol. . . . . . . .
~
(Pure benzene). . . . (Pure benzene). , , ,
8.81 9.11
__
* All tensions are expressed in dynes per centimeter and are averages of a t least two measurements. t not constant but tended to fall t o lower values.
corresponding values of S i and a and @ by the equations :
823
were used to calculate the lens angles
Equations 8 and 9 were obtained by applying a theorem of elementary geometry to Neumann's triangle of forces, as indicated by Coghill and An-
e98
NEVILLE F. MILLER
derson (5). By addition of the corresponding values of a and 8, values for the total lens angles 0 were obtained. These computed values of e are listed in the last column of table 2. It may be observed that the agreement between the computed values of 0 and the values found by measurement is very good. The separate angles a and /3 were not measured but observations showed that a was always larger than &-the upper segment of the lens being larger than the lower segment. This agrees with Neumann’s theory and with the calculated values of a and 8, since the values of S; are smaller than the corresponding values of Ssa. The values of F, exceed, by 0.3 to 0.5 dyne per centimeter, the corresponding values of F, (calculated from equation 1). This tends to support the theory (advanced in this paper) that the existence of true lenses of finite angles depends on a slight increase (AF) in the film pressure above the point where F = Fa. Unfortunately, the sum of the experimental errors involved in measuring 528,S;, 88,and F,for any one system is large enough to account for the differences between F, and F,. However, these errors would have to be systematic for the nine systems in order to allow F, to equal F.. The tension data for pure benzene shows that the values of F, for the solutions are about 1.5 dynes per centimeter higher than the spreading coefficient of the pure solvent. Another consideration supporting the theory advanced in this paper arises from the minimal surfaces required for the stable lens by equation 5. A rather striking experiment has been devised which demonstrates that these surfaces are minimal, The surface of a substrate contained in a large g l w tray is covered with a monolayer by adding the solution d r o p wise in the usual way. When the first equilibrium lens is obtained, a large lens of the solution is added to the substrate and, by means of a glass rod, this lens is drawn out into an irregular shape. On removing the rod, the lens immediately contracts back to the perfectly circular shape required for minimal lens surfaces. From the considerations of finite lens angles, minimal lens surfaces, and the data of table 2, it is concluded that the theory and equations presented in thie paper adequately explain the equilibrium of lens-film systems on neutral or acid substrates. No work has been done with more complicated systems involving alkaline substrates or substrates containing insolubilizing ions, such as barium or aluminum ions. Such systems might require an entirely different theory to account for their tension equilibria. It is possible that the lens endpoint method for measuring surface areas of molecules could be extended to other film preseures by using solvents which would give solutions with spreading pressurea above or below those of benene solutions.
MEASURING AREAS OF MOLECULES
290
SUMMARY
1. A new method has been described for measuring the cffective surfacc areas of film-forming molecules at film pressures of 10.3 f 0.3 dynes per centimeter. This method (called the equilibrium lens method) is rapid, convenient, and requirea no complicated apparatus. 2. A theory has been presented to explain the formation of stable lenses of solutions composed of polar substances in non-polar liquids on neutral or acid substrates. It has been shown that the equilibrium of such lensfilm systems is not truly reversible but shifts in the direction of higher film pressures and larger lens angles. 3. Equations derived by application of Neumann’s theory to these lensfilm systems on neutral or acid substrates have been found to satisfy the data obtained for nine systems at the equilibrium lens endpoint. 4. Six criteria are described for distinguishing the equilibrium lens from all preceding lenses. REFERENCES
(1) ADAM,N. K., AND JESSOP, G.: Proc. Roy. SOC. (London) A112, 362 (1926). (2) ADAM,N. K., AND ROSENREIM, 0.: Proc. Roy. SOC. (London) AlM, 25 (1929). (3) BARTELL,F. E., CASE, L. O., AND BROWN,H.: J. Am. Chem. SOC. 56, 2769 (1933). (4) CARY,A., AND RIDEAL,E. K.: Proc. Roy. SOC. (London) A M , 318 (1925). (5) COGHILL, W.H., AND ANDERSON, C. 0.: U. S. Bur. Mines, Tech. Paper KO.262, 54 pp. (1923). (6) GAMBLE,D. L., AND BARNETT, C. E.: Ind. Eng. Chem. 32, 375 (1940). (7) HAREINS,W. D., AND ANDERSON, T. F.: J. Am. Chem. SOC. 69, 2189 (1937). (8) LANGMUIR, I.: J. Am. Chem. SOC.39, 1848 (1917). (9) LANGMUIR, I., AND SCHAEFER, V. J.: J. Am. Chem. SOC.69, 2400 (1937). (IO) LYONS,C. G., AND RIDEAL,E. K.: Proc.Roy. SOC. (London) AlM, 322 (1929). (11) MACE,G.L., AND BARTELL,F. E.: J. Am. Chem. SOC.64, 936 (1932).
