3529
INFLUENCE OF WATERSTRUCTURES O N SURFACE PRESSURES AND POTENTIALS
spectroscopic methodsIg indicate that the true polarity of the C-H bond in a saturated aliphatic compound
is Cf-H-, giving the C-H bond the same polarity as the C-X bonds.
Influence of Water Structures on the Surface Pressure, Surface Potential, and Area of Soap Monolayers of Lithium, Sodium, Potassium, and Calcium
by D. F. Sears Tulane University, School of Medicine, New Orleans, Louisiana
and Jack H. Schulman Columbia University, School of Mines, Stanleu Thompson Lahoralories, New York, New York (Received April 13,1964)
Force-area and surface potential-area curves were obtained atj 15, 25, and 37" for stearic acid on 0.1 N HC1 and 0.5 N hydroxides of lithium, sodium, and potassium. Differences In areas per molecule at the same temperature and surface pressure on the different. substrates indicated that the hydrated ion associated with the carboxyl group of the stearate determined the expansion of the monolayer. Areas per molecule increased in the sequence Li < Na < K. Trace amounts of calcium, when added to the hydroxide substrates, markedly decreased the expansion effected by the monovalent ions. On bicarbonate substrates of sodium and potassium, compression of the monolayer promoted removal of the respective cation. This removal allowed the area per molecule a t high surface pressures to compress to the area of stearic acid on 0.1 N HC1. Calculation of the surface compressional modulus indicated that the monolayers on the hydroxide substrates were liquid expanded. The effect of temperature was examined by determining the change in surface pressure with change in temperature a t constant area per molecule (AAnlAT). The values varied with temperature and with the compression of the monolayer. Stearic acid on the acid substrate gave A A r I A T values which increased with increasing areas per molecule, whereas on hydroxide substrates the monolayers gave decreasing values with increasing area. Within the same temperature range and for the same area per soap molecule, values for A A r / A T increased in the sequence Li < Na < K.
Intrduction Adam and >[iller1 reported expansion of fatty acid monolayers on alkali solutions of sodium and potassium. On 2 N hydroxides, limiting areas extrapolated to zero
compression were 31 and 38 Lk.2/moleculefor sodium aiid potassium soaps, respectively. Experiments with adsorbed monolayers of sodium and potassium oleate a t a benzene-water interface indicat,cd that potassium Volume 68, Number 1.9
Decemhw. 1964
D. F. SEARSAND JACK H. SCHULMAN
3530
oleate monolayers were more expanded than sodium oleate.* This paper examines to what extent this expansion is due to the size of the hydrated sodium or potassium associated with the fatty acid monolayer. Studies of ionic radii and hydration of ions have been reviewed by Stern and A r n i ~ . ~ The methods reviewed gave information concerning ion size in solution. It remains to be shown whether these measurements apply to ions a t an interface. Information concerning the relative sizes of Na+ and K + at an interface can be obtained from the monolayer technique after accounting for the effects of ionization and electrostatic repulsion between the molecules. The hydrated sizes of Na+ and K+ are of biological significance. Cell membranes accumulate K + in the cell interior while excluding Na +. Theories developed to account for the selectivity have been based in part on estimates of the size of hydrated ions derived from hydration numbers. Some values taken from the extensive study of Stokes and Robinson4 for n (the number of water molecules interacting with the cation with an energy large compared to k T ) and for d (the distance of closest approach to the hydrated cation by the anion, assumed to be unhydrated) are given in Table I. Values for
Table I Salt
n
d
LiCl
7.1 3.5 1.9
4.32 3 97 3.63
NaCl
KC1
Force-area ( ~ 1 1and ) surface potential-area (AV-A) curves of stearic acid spread on 0.5 N hydroxides of lithium, sodium, and potassium were examined. Care was taken to remove traces of Ca+2which might affect the results. At pH 13 saponification is essentially complete. The data reported here show that lithium, sodium, and potassium cause expansion of the monolayers of stearic acid and the limiting areas of these cations at the interface increase in the sequence L4 < Ka < K; this is the reverse of the sequence found for hydration sizes measured in the bulk solution.
Methods VA curves were obtained using a Wilhelmy balance which had a sensitivity of 0.2 dyne/cm. Both fused silica troughs and aluminum troughs coated with Teflon were used. No difference in the force-area curves could be detected because of differences in the troughs. Stearic acid was obtained from K and K Laboratories and was recrystallized six times, m.p. 68-69'. Xormal hexane used for diluting the stearic acid was chromatographically pure. Substrate solutions were made with Pyrex distilled water. Sodium hexametaphosphate (Calgon) was added to the substrates (0.5 g./l.) to bind any calcium present. The acid and bicarbonate solutions were filtered over activated charcoal. Substrates mere allowed to stand in the trough to accumulate any surface-active contaminants at the surface. The surface was then cleaned with a paraffined glass slide and suction. The temperature was regulated by surrounding the trough with water circulated from a water bath and was measured with a thermometer submerged in the substrate. Surface potentials were determined by the method described by Schulman and Rideal.' A Keithley electrometer with an input impedance of l O I 4 ohms was used.
other salts of the same cations vary as a function of the anion size, but the same order, Li > Na > K, for n and d was maintained. Results Since it is at the cell membrane-water interface that Figure 1 shows the n-A and AV-A curves for stearic ion transport occurs, knowledge of the properties of acid on 0.1 N HC1 and on 0.5 N solutions of lithium, the cations in an interfacial region rather than in the sodium, and potassium hydroxides a t 15'. Each bulk of a solution is pertinent for biological consideration. Structuring of water at interfaces is i n d i ~ a t e d . ~ (1) N. K. Adam and J. G. F. Miller, Proc. Rov. Sac. (London), A142, The work of Derjaguin and Titijevskayas on free films 401 (1933). and froths showed that water layers adjacent to sodium (2) D. F. Sears and R. M . Eisenberg, J . Gen. Physiol., 44, 869 (1961). oleate-adsorbed films were oriented to as much as ten (3) K. H. Stern and E. 9. Amis, Chem. Rev., 5 9 , 1 (1959). molecules thick and were characterized by a low (4) R. H. Stokes and R . A. Robinson, J . Am. Chem. Sac., 70, 1870 dielectric constant. At an interface, the hydration (1948). numbers given by Stokes and Robinson4 for n may be (5) J. T. navies and E. K. Rideal, "Interfacial Phenomena," 4cademic Press, New York, N. Y . , 1962. expected to increase due to a reduction in thermal (6) B. F. Derjaguin and A. 5 . Titijevskaya, Proc. Intern. Congr. agitation. Surface + t i d y , and, London, 1, 211 (1957). This investigation was undertaken to measure the (7) J. H. Schulman and E. K. Rideal, Proc. Rou. Sac. (London), relative ion sizes with the monolayer technique. A130, 259 (1931); A138, 430 (1932). The Journal o j Physical Chemistry
3531
INFLUENCE OF WATERSTRUCTURES ON SURFACE PRESSURES A N D POTENTIALS
15°C Stearic acid on D 0.1 N HCI 0.5 N LiOH 0 0 . 5 N NaOH 0 . 5 N KOH
30
4
361 34-
AV in mV
25Oc Stearic acid on
32-
AV in mV 400 350
26
300
24-
250
22
200
30-
00,lN HCI a0.5 N LiOH o 0.5 N NaOH 0.5 N KOH
2826-
24i
iP
\\
- 450
-400 -350
-300 -250 -200
I50 P
I00
187
50
0 -50
-100
4 '\
1-150
-150
0 IO 20 30 4 0 50 60 70 80 90 100 I10 %'per molecule
i12 per molecule
Figure 1. Force-area (bold lines) and surface potentialarea (light lines) curves for stearic acid on various substrates a t 15". Each curve represents the average of three or more experiments on the respective substrates. The pH values for the alkali substrates a t 15" were: LiOH, 12.6; NaOH, 13.2; and KOH, 13.4.
Figure 2. Forcearea (bold lines) and surface poteotialarea (light lines) curves of stearic acid on substrates at 25". Each curve represents the average of three or more experiments. The pH values for the alkali substrates were: LiOH, 12.6; NaOH, 13.2; KOH, 13.4.
curve represents the results from three or more experiments, Highest force values plotted for each curve are the breaking pressures with the exception of stearic acid on 0.1 N HC1 which gave breaking pressures as high as 44 dynes/cm. AV-A values for stearic acid on 0.1 N HC1 increased with compression to +390 mv., air with respect to water. For stearic acid spread on hydroxide solutions, AV was negative, air with respect to water. Erratic fluctuations of AV occurred a t areas less than about 20 A.2/rnolecule for the acid on LiOH, about 30 A.2/molecule on NaOH, and 40 A.2/molecule on KOH, which suggests that the monolayers had broken a t these areas. For KOH, the n-A curves dido not show an indication of breaking until about 25 A. 2/molecule. At pressures where coherent monolayers were obtained for all substrates, the area per molecule increased in the order H 5 Li < Na < K, and the surface potentials were negative for the hydroxide solutions in the order Li > Na > K. Figure 2 shows the results from experiments performed a t 25" with the same group of solutions. F A curves indicated that the monolayers were more expanded a t this temperature than a t 15". The same order of expansion on the different substrates was ob-
served. The highest pressures shown are the breaking pressures, except for stearic acid on HCl. Fluctuations of AV values suggested that breaks occurred a t larger areas than indicated by n-A curves. AV values for the monolayers on hydroxides were still negative, air with respect to water, but, in the case of the sodium and potassium hydroxide substrates, they showed a tendency to become positive with compression. Figure 3 shows the results from experiments performed a t 37". Further expansion was observed for each monolayer a t this temperature as compared with 25"; however, the increase was slightly less than bctween 15 and 25'. The same order of expansion between the different substrates was observed, ie., Li < Na < K. At this temperature the AV-A curves were negative a t large areas per molecule, but on sodium and potassium hydroxide the values became positive with compression. Since the n-A curves still showed the expansions associated with the respective cations, we ascribed the surface potential values to changes in the orientation of water about the acidcation association. Further evidence for the assumption that the orienVolume 6'8, Number 12
December, 1964
D. F. SEARSAND JACK H. SCHULMAN
3532
3634-
Stearic acid on 0.1 N HCI 0 . 5 N LiOH 0 0.5 N NoOH h0.5 N KOH
0
323028-
$
g
bV in mV 400
350
so
26-
250
241
200
22-
I50
20-
IO0
18-
50
3
16--
0
&'C
14-
-50
12-
-100
10-
-150
8-
- 200
64-
2-
O
I
IO
io
h
30 40 & $0I70 00
sb
153 IiO
2 p e r Molecule
Figure 3. Force-area (bold lines) and surface potentialarea (light lines) curves for stearic acid on substrates a t 37'. Each curve represents the average of three or more experiments. The pH values for the alkali substrates a t this temperature were; LiOH, 12.6; NaOH, 13.2; and KOH, 13.5.
strates. Values obtained varied within the range of 12.5 to 50, indicating that the monolayers were liquid expanded. Figure 4 shows the effect of Ca+2on monolayers with NaOH or KOH substrates a t 25'. When approximately 0.006 g./l. of Ca(OH), was added to 0.5 N NaOH or KOH, sufficient Ca+*was present to condense the monolayers. Greater amounts of C a f 2 added to NaOH caused greater compression of the monolayer. At larger areas per molecule the effect of calcium was less marked than a t smaller areas per molecule. Breaks in the force-area curves suggest different proportions of calcium to sodium or potassium associated with the stearate radical with progressive compression. Experiments with 0.5 N Na and KHC03as substrates were performed. The pH of these substrates was 8.5. Figure 5 shows curves on NaHC03 and KHC08 a t 25". At low surface pressures these T-A curves were expanded to resemble the curves on hydroxides. Surface potentials were negative. Compression resulted In limiting areas which were only slightly more expanded than stearic acid on 0.1 N HC1. Thus sodium or potassium was removed from the monolayer with Increasing compression and the surface potential became positive in this case indicating the formation of
34. 32-
tation of water caused the surface potential values was found when the millivolts per molecule was determined from the surface potential data. This was obtained from A V / N , where N is the number of molecules/cm.2. With compression a t 1 5 O , the electrical potential per molecule approached zero and the values were similar for all three hydroxide substrates. For the acid substrate the value decreased from a maximum value a t 22 &.2/molecule of 86 X mv. to 68 X mv. a t 17.5 &.2/molecule. This corresponds to a decrease 'In the dipole moment from 254 to 201 mD. due to compression. Since compression causes an alignment of molecules, it was expected that higher values of dipole moments would be obtained with compression rather than a decrease. The observed decrease of potential which occurred with both the acid and the hydroxide substrate could be explained on the basis of disorder in orientation of water molecules about the carboxyl end of the molecule. The surface compressional modulus (C8-l) defined as
CS-'= (-l/A(dA/dn)T)-l was calculated for each monolayer on hydroxide subThe Journal of Phusical Chemietru
30-
\
Stearic acid an 0.5 N 0.5N o 0.5 N A 0.5 N A
NoOH KOH NOOH e 0.006 q i i C O ( O H ) ~ KOH E 0.007 q l l C O ( W 1 2
temp. 25" C
A*
per molecule
Figure 4. Effect of Ca+2 in the substrate without the addition of Calgon. Force-area curves for Na and K substrates from Fig. 2 were included for comparison. These two curves represent actual data from representative experiments and not averages as repeats of the experiments with calcium present agreed only qualitatively.
INFLUENCE OF WATERSTRUCTURES ON SURFACE PRESSURES AND POTENTIALS
361 I
25"c Stearic acid on
34
0 0.01 N HCI o 0 5 N NoHCO~ A 0.5 N KHCO3
3533
AAll AT
aJ
I AVin mV - 400
aJ
&) 20-
-350
-8 kQ
-300
9 5
- 250
9
0
- 200
- 100 -50
0 --50
--IO0
00.1N HCI 0.5N LiOH o 0.5N NaOH A 0.5N KOH
181614-
l2
.s
-150
Stearic acid on
aJ
'?
*
1086-
P O'
-150
1'0
2b i o 40
io QO i o
80
&
Ibo
$per Molecule
"
O'
IO
20
i o 40
50
$0 i o
eb i o
3 per Molecule Figure 5. Forcearea and surface potential-area curves of stearic acid on 0.5 N NaHCOa and KHCO,. The pH of the bicarbonate substrates was 8.5 a t 25". The curves for stearic acid on 0.1 it' HC1 were included for comparison from Fig. 2. The sodium curve is more expanded than the potassium. Surface potentials on the bicarbonate substrates reverse sign during compression which did not occur with compression on 0.5 N hydroxides a t this temperature.
the acid stearate. The sodium curves were more expanded than the potassium curves; similar results, i.e., Xa > K, were reported by Rogers and Schulman* for the alkyl sulfates. The effect of temperature on the monolayers was examined on the basis of the relation A A n / A T , the change in surface pressure a t constant area a t two different temperatures. Since values for r corresponding to area from our experiments were available only a t 15, 21i, and 37") the data are sufficient only to show the direction of the changes. The term A A r / A T may be compared to hark in^'^ expression for the entropy of expansion of a film on water se
= (aS/duf)T,c,. =
-@Tf/aT)#,
where s, is the entropy per unit area, S is the total entropy, uf is the molecular area of the film molecule, uWis the area of the water, and y f is the surface tension of thc film. Values for A An/AT were determined from curves a t 15 and 37"; for stearic acid on the acid sub-
Figure 6. Plot of AATIAT values a t different areas per molecule. The temperatures used were 15 and 37" to give AT as 22" and pressures a t these two temperatures were measured a t the areas indicated to give A T . The 'sniall arrows indicate the estimated hydrated sizes of the \ations baaed upon the assumptions discussed in the text. The magnitudes of the values are dependent upon the choice of temperatures aa greater expansions, hence greater AT values, were obtained between 15 and 25" than between 25 and 35'. Thus measurements based upon AT of 10" between 15 and 25" would have given larger values for A A K I A T . However, the same relation between the curves is maintained.
strate the values increased with increasing area per molecule, for the hydroxide substrates the values decreased with increasing area. Values obtained from data at 15 and 37" are shown in Fig. 6. On the acid substrate, stearic acid shows an increase in A A T / AT which corresponds to increasing entropy, since
- (dr/dT),
=
+(dr/dT).
Values are shown in ergs X 10-16/n~oleculedeg.-l. The decrease in values with increasing area per molecule on the hydroxide substrate indicates a decrease in the randomness of the orientation as expansion occurs.
Discussion Stearic acid monolayers are expanded on hydroxide solutions in agreement with earlier reports in the literature. The degree of expansion varies with the specific cation. Adamlo attributed the loss of adhesion (8) J. Rogers and J. H. Schulman, Proc. Intern. Congr. Surface Activity, snd, London, 3 , 243 (1957). (9) W. D. Harkins, "The Physical Chemistry of Surface Films," Reinhold Publishing Corp., New York, N. Y . . 1952. (lo) N. K. Adam, "The Physics and Chemistry of Surfaces." Oxford University Press, London, 1941.
Volume 68,Number I2 December, 1964
D. F. SEARSAND JACKH. SCHULMAN
3534
between the fatty acid molecules on the alkaline substrate and, consequently, the expansion of the monolayer to repulsion between the similar electrical charges on thc adjacent end groups. Our experiments do not support this explanation. The reaction H(FA)
+ B(0H) +B(FA) + HOH
1s essentially complete a t a pH which is three unfts higher than the pK of the acid. For the experiments a t pH 13 on the hydroxides, the saponification of the fatty acid by the alkali would be complete. At a lower pH on the bicarbonates (8.5) the degree of association between the cation and the fatty acid could be less than complete, the actual degree of association depending upon two values, the pK of the anion and the pH a t the interface. On the substrates a t pH 8.5 compression was accompanied by the removal of cations as demonstrated by the forcearea and surface potential-area curves. Both of these curves approached the values obtaincd for stearic acid spread on 0.1 N HC1 with compression. The similarity of the curves a t the two different regions of pH values (pH 1 and 8.5) indicate that the difference in degree of ionization of the fatty acid plays only a small role in determining the forcearea relations of the monolayer as compared with the specific cation effect. The question also arises with respect to the magnitude of the electrical field which would produce the repulsion of adjacent soap molecules. We found no information concerning the dipole moment of soap molecules other than the values obtained from the surfacc potential mcasurernents. These measurements indicatc that this moment is small. This also suggests that electrostatic repulsion between adjacent soap molccules was not an important factor in determining the expansion of the monolayer. Rcplacenient of Naf or K + by C a f 2 a t pH 13 with compression of the monolayer as shown in Fig. 4 further demonstrates a specific effect which is attributable to characteristics of the cation. At large areas per molecule the Naf or K + could compete with the calcium for thc stearate; however, with reduction of the arca per molcculc, calcium predominated by virtue of its two valences and finally replaced monovalcnt cations that due to hydration size could not compress to thc arca available. Taking the diarncter of a water molecule to be 2.7 A. and assuming a sheath of water one molecule thick to be arrangcd about the cation with thc crystallinc radii given by Pauling,lLthe following areas per cation
The Journal of Physical C h e m i s l r ~
would be obtained: Li+, 35.7 Naf, 42.3 k.2; and K f , 51.5 A.2. I n the bulk solution, thermal agitation does not allow a complete saturation of the sphere of water about the cation. Thus Stokes and Robinson4 consider the water associated with the cation with an energy greater than k T . The size of the ions in the bulk would be related to the energy of hydration of the ion. However a t the interface, in a layer of “soft ice,”6reduction in thermal energy may allow a more complete filling of the hydration region about the ion. Thus a t the interface the size of the hydrated ion would be related to its actual crystalline size rather than to the energy of hydration. Figure 6 shows that the disorder in the soap monolayer decreased a t areas per molecule greater than that required f o r a completely +filled hydration shell. BoydI2 stated that hydration of the polar carboxyl groups in the monolayer gives a negative entropy contribution. The data presented in Fig. 6 suggest that increasing the area per molecule allows the orientation of water about the polar region which decreases the disorder in the soap monolayer. This did not occur in the case of the stearic acid spread on 0.1 N HCl where the interaction between the hydrocarbon groups played the major role in the structuring of the monolayer and increasing the area per molecule allowed greater disorder. Comparison of the values for the different soaps a t the same area per molecule shows that A A a / A T is less for lithium than for sodium and less for sodium than for potassium. These results are consistent with a high degrce of order between the head group and water which decreases in the sequence Li > Na > K. In water a t 25”, the partial molal entropies according to the values listed in Gurneyla are: Li, 4.7 e.u.; Na, 14.0 e.u.; and K, 24.2 e.u. Thus the order which exists in the soap monolayer is related to the order which exists between the water and the cations. The results indicate that cation size is an important factor in characterizing soap monolayers, that the size is due to the hydration of the cation, and that the hydrated size in the surface region where structuring of water occurs leads to the size sequence Li < Na < K.
rlcknowledgments. This work was supported by PHS Grants GM-07072-05 and NB-02067-05. We wish to thank Mr. Karl Dreher for his assistance. (11) I,. Pauling, “The Nature of the Chemical Bond,” Cornel1 University Press, Ithaca, N. Y . , 1960. (12) G . E. Boyd, J. Phu3. Chem., 62, 536 (1958). (13) R. W. Gurney, “Ionic Processes in Solution,” Dover Publications, Inc., New York, N. Y . , 1962.
