- Email: [email protected]
Effect of pressure and temperature on the partial molal volume and compressibility of sodium decanoate micelles
Effect of Pressure and Temperature on the Partial Molal Volume and Compressibility of Sodium Decanoate Micelles E. V I K I N G S T A D , A. S K A U G E , AND H. HOLLAND Department of Chemistry, University of Bergen, N-5014 Bergen-U, Norway Received December 6, 1978; accepted February 8, 1979 Ultrasound measurements have been carried out under high pressure for solutions of sodium decanoate above and below the critical micelle concentration (CMC) at 25°C. From these measurements the partial molal volumes and compressibilities of sodium decanoate in singly dispersed state and in micellar state have been determined in the pressure range 1-1600 bar. It was found that the partial molal volume and compressibility in the micellar state both decreased with increasing pressure, but the corresponding quantities in the singly dispersed state increased with pressure. These results have been interpreted from changes in hydrophobic interactions and in electrostriction of water molecules with increasing pressure. From density measurements and ultrasound measurements in the temperature range 10-40°C the partial molal volumes and compressibilities of sodium decanoate above and below the CMC have been determined as a function of temperature. The partial molal volumes and compressibilities increase with temperature for sodium decanoate both in singly dispersed state and in micellar state. INTRODUCTION
MATERIALS AND METHODS
In an earlier work (1) the change in partial molal volume, AVm, and partial molal compressibility, AK", in the formation of micelles were determined for the homologous series of sodium alkylcarboxylates at 25°C. It was found that both AV m and ~K m increased with increasing chain length of the surfactant, which has also been found for the alkylsulphates (2, 3) and for alkyltrimethylammonium bromides (4). We considered it of interest to extend the investigations of AWn and AKm to different temperatures and different pressures. In this work AV m and AKm have been determined for sodium decanoate (NaC~0) in the temperature range 10-40°C. By establishing a method for ultrasound measurements under high pressure we have been able to determine AV m and AKm in the pressure range 1-1600 bar. The pressure dependence of AV m and An m has been compared to the conductivity data from the earlier work (1).
The synthesis of sodium d e c a n o a t e (NaC10) from decanoic acid and N a O H has been described in earlier works (1, 5). Decanoic acid was supplied by Fluka, puriss grade, and the N a O H by E K A , Sweden. Ten solutions of NaC10 were made in the concentration range 0.04-0.4 mole kg-L The concentrations were determined by weight. The densities of the solutions were determined at 5-degree intervals between 10 and 40°C by a Paar density meter, and the isentropic coefficients of compressibility were determined at the same temperatures by ultrasound measurements. Details of these measurements have been presented elsewhere (6, 7). The temperature was measured with a H e w l e t t - P a c k a r d quartz thermometer and was controlled to _+0.005°C in a water bath. U l t r a s o u n d m e a s u r e m e n t s at high pressure. The " s i n g - a r o u n d " principle for ultra59 0021-9797/79/13005%09502.00/0
Journal of Colloid and Interface Science, Vol. 72, No. 1, October 15, 1979
Copyright © 1979 by Academic Press, Inc. All rights of reproduction in any form reserved.
60
VIKINGSTAD,
E
SKAUGE,
F
A
FIG.
1. T h e
cell for
ultrasound
measurements
under high pressure. (A) steel cylinder; (B) the end piece of the cell; (C) the piezoceramic transducer; (D) nylon isolating material; (E) copper metal; (F) cell openings for filling the cell. sound measurements used in our laboratory for the determination of isentropic coefficients of compressibility at atmospheric pressure has been described in detail elsewhere (7). This principle was also used to determine isentropic coefficients of compressibility at higher pressures. H o w e v e r , a new cell had to be constructed for these measurements. This cell is shown in Fig. 1. The cell was a 5-cm closed steel cylinder with a piezoceramic transducer at each end. The transducer was attached to a piece of copper metal with a t w o - c o m p o n e n t electrically conductive e p o x y adhesive. This copper metal was isolated from the steel of the end piece by a ring of nylon material (see Fig. 1). The outer part of the transducer was connected to the end piece by a thin copper thread, thus making a complete current loop. Oil was used as the pressure transmitting medium. Two pieces of PVC-tubings containing a volume greater than the compression volume of the cell content was attached to the cell openings. The pulse-frequency of the ultrasound radiation was determined at 1,200,400,800, 1200, and 1600 bars at 25°C. The pressure was determined by a high-pressure transducer with an accuracy of _+2 bar (see Ref. 8). Water was used to calibrate the cell, applying the data of Chen and Millero (9). The pulse-frequency of the ultrasound radiation is very dependent on pressure
AND HOILAND
(about 2 Hz/bar for the 5-cm long cell). It was therefore found necessary to employ two measuring cells simultaneously in the pressure compartment. One cell was filled with water, the other with the solution, and it was thus possible to determine the calibration pulse-frequency of water directly at each of the applied pressures. This increased the relative accuracy of the determination of pressure to better than _+0.5 bar. The main problem during the development of this method of measurement has been the nylon material isolating the copper metal from the steel of the end pieces of the cell. Occasionally it was found that this material was damaged by oil or pressure. The method is still under development and improvement, and new materials are being tested out. RESULTS
AND DISCUSSION
Partial Molal Volumes and Compressibilities at Different Pressures The speed of sound in pure water at different pressures at 25°C has been determined by several authors (10-12). We have used the data of Chen and Millero (9) to calibrate the measuring cells. The isentropic apparent molal compressibility, K~,~), can be expressed by: K.(~
1000 mdo (fl~ - ~o~) + [3~V.
[1]
where m is the molality of the solution, do is the density of the solvent, and fls and fl0s are the isentropic coefficients of compressibility of the solution and the solvent, respectively, fls is expressed by:
/3~ -
106 v2d
[2]
where d is the density of the solution, and v is the speed of sound in the solution. By measuring the ultrasound frequencies for
Journal of Colloid and Interface Science, Vol. 72, No. 1, October 15, 1979
VOLUMES AND COMPRESSIBILITIES OF SURFACTANTS the solution v can be determined at each pressure, using the data for the speed of sound in water. In order to determine K~s~ at different pressures the quantities d, do, /3s, fi0~, and V . must be known at each pressure. The quantities do and /30s are known from the literature (13). /3~ can be determined from the ultrasound measurements but it requires that d be known as well. By an iteration process it is possible to determine d and consequently V . at different pressures from the ultrasound measurements. The relation between the apparent molal volume and the isothermal apparent molal compressibility can be expressed by: K~ = _ ( 0 V ° t
\ OP }r
.
[3]
Desnoyers and Philip (14) have shown that the relation between isothermal and isentropic apparent molal compressibility, K. and K.~s~ is given by the equation: R = K ~ - K.(s)
61
singly dispersed state, E~, was determined as 0.29 ___ 0.02 cm a K -1 mole -1, and the corresponding quantity in the micellar state, Eg~, was determined as 0.19 _+ 0.02 cm 3 K -1 mole-L Assuming that the contribution from C . was small, the isothermal apparent molal compressibilities in the singly dispersed state and micellar state, K~, and KS, was determined as - 5 2 . 1 0 -4 and 58.10 -4 cm 3 bar -~ mole -1, respectively. The isothermal values of the compressibilities are about 15% higher than the isentropic values (see Table II). H o w e v e r , it can be shown that if this difference is neglected and if we put K. = ~:.(s~ in Eq. [3] this will change the final results for V® and •. only within the estimated experimental uncertainty. The difference R in Eq. [4] must be known at different pressures in order to use Eq. [3]. The pressure dependence of the expansitivity can be expressed by:
OE. ] _ 02Vo OP Jr
OTOP = _ ( O K ~ t ---(OK~'s~l • [51 \ OT )e \ OT )e
= coefficient of thermal expansion cr = volumetric specific heat = 13-/~s, the difference between isothermal and isentropic coefficients of compressibility E . = apparent molal expansitivity C . = apparent molal heat capacity The subscripts refer to the pure solvent. It can be shown (14) that the major contribution to the difference R for surfactants comes from the expansitivity. F r o m our measurements of V . at different temperatures the apparent molal expansitivities for the solutions were calculated. F r o m the plot of E . versus concentration the apparent molal expansitivity in the
The temperature dependence of K.(s~ for the solutions has been determined in the second half of this work, and E . at different pressures can be obtained. These values of E® are calculated on the assumption that E . is linearly dependent on the pressure, which is valid to about 800 bars. H o w e v e r , even above this pressure Eq. [5] gives a good estimate for E . . In order to integrate Eq. [3] the pressure dependence of ~:. must be known. H o w e v e r , we can make a first guess and assume that OK./OP ~ O. Integration of Eq. [3] then gives:
V . ( P ) = V®(1) - ( P - 1)K®(1). [6] V . ( P ) is the apparent molal volume at pressure P. F r o m the well-known equation relating V® and the density of the solution, d, a first value of d at the pressure P can Journal of Colloid and Interlace Science, Vol. 72, No. 1, October 15, 1979
62
VIKINGSTAD, SKAUGE,AND HOLLAND
be calculated: d(P)=
concentration of the surfactant at each pressure. These plots turned out to be similar ( )1000 --+Mm in form to those presented in earlier works (1, 5, 15). The change in partial molal volume during micelle formation, AVTM, can ( _ 1000 _ ) be expressed by: x V . ( P ) + mdo(P) " [7] AVm = V~ - V~
The isentropic apparent molal compressibility K~s)(P) can now be determined:
[131
where V$ and V~ are the partial molal volumes of the surfactant in the singly 1000 K¢(s)(P) dispersed state and in the micellar state, mdo( P) respectively. V~, is equal to V. at the CMC, × (flu(P) + flos(P)) + fls(P)V¢(P) [8] and V~ is determined by using a saturation function to the plot of V. above the where CMC (5, 15). The obtained results for V~, 10~ V$, V~, and AVm at different pressures fis(P) [91 v2(P)d(e) are shown in Table I. AVm can also be determined as a funcValues of K.(s)(P) can now be calculated at each pressure for the solution. K.(~)(P) tion of pressure by conductivity measureis then assumed to be described by a ments, determining the CMC as a function of pressure: polynomial in P: ~C~(s)(P) = ao + a , P + a2P 2 + a3P a.
[10]
From the obtained values of ~:.(s)(P) the constants a0, a,, a2, and a3 were calculated by a polynomial regression. Using this equation and Eq. [4] to calculate K.(P), integration of Eq. [3] gives: V . ( P ) = V.(1) - (aoP+ V2alP 2 + V3azP 3 + ¼a3P 4 + R ( P ) )
+ (a0 + 1/5al + ½a2 + ¼a3 +R(1)).
[11]
From this equation new values of V . ( P ) and d ( P ) have been determined, and the values of K¢(s)(P) can be redetermined by using Eq. [8]. This iteration process (Eqs. [31, [6[-[111) can then be continued until:
tge(sl(P)n+l
1 ~< 0.001
[12]
I K.(s)(P)n where n is the number of iterations. From this iteration process values of V. and K.(s) for each solution where determined at different pressures from the ultrasound measurements. V. has been plotted as a function of the
A v m = ( 1 + f i ) R T ( O In CMC) OP r
[14]
where fi is the fraction of associated counterions. Previously (1) AVTM has been determined by this method, and the results have been included in Table I. Plots of AVm as a function of pressure from the two methods are shown in Fig. 2. It turns out that AVm decreases with increasing pressure, and the two different methods of measurements are in good agreement. Figure 3 shows V~ and V~ as functions of the pressure. The results are similar to those obtained by Tanaka et al. (16) for alkylsulphates by density measurements under high pressure. V~ increases with increasing pressure. This can be explained by the changes in electrostriction of water molecules with pressure. At higher pressure the water structure is already somewhat disordered, and the negative contribution to V. from electrostriction at the ionic head group of the surfactant thus decreases with increasing pressure (16). The group partial molal compressibility
Journal of Colloid andlnterface Science, Vol. 72, No. 1, October 15, 1979
VOLUMES AND COMPRESSIBILITIES OF SURFACTANTS TABLE I A p p a r e n t Molal V o l u m e s and the C h a n g e in Partial Molal V o l u m e during Micelle F o r m a t i o n for Sodium D e c a n o a t e at Different P r e s s u r e s at 25°C ( V . -+ 0.3) c m 3 m o l e - ' P(bars)
1 200 400 800 1200 1600
V=
V%
V~
164.7 166.0 167.0 168.0 168.8 169.2
165.4 166.4 167.2 168.6 169.3 169.8
175.2 173.8 173.1 172.0 170.3 169.3
( A V m -+ 0.4) c m ~ m o l e - ' Ultrasound
Conductivity'
9.6 7.4 5.9 3.4 1.0 ± 1.0 - 0 . 5 ± 1.0
9.5 7.2 5.8 3.0 0 -1.0
a Ref. (1).
of a CH2 group in aqueous solution, K(CH2,aq), is about - 2 . 0 . 1 0 -4 cm 3 bar -~ mole -~ at 25°C (17). This means that V(CH2,aq) increases slightly at lower pressures, but at higher pressure V(CHz,aq) decreases (16) as a result of increased hydrophobic interactions. However, this
i(
63
decrease in V. from the hydrophobic part of the surfactant molecule is small compared to the increase in V. at the ionic head group. V~ shows the opposite trend to V~ and decreases with pressure. This must be a result of changes in the interior of the micelle, as the partial molal volume of the charged micelle surface probably increases with pressure as a result of reduced electrostriction. The decrease in V~ can be ascribed to the loss of free space between the molecules in the interior of the micelles when the pressure increases. The partial molal compressibility of a CH2 group in the micellar core, K(CH2,mic), is about 10.10 -4 cm 3 bar -1 mole -1 at atmospheric pressure (18). This means that V(CH2,mic) decreases rapidly with increasing pressure, and this explains the decrease in V~. It should be noticed that the decrease in AVm with pressure is a result of changes in the partial molal volumes both below and
)
AV TM cm3mol -It
6'
-2
:
L
400
~00
1200 pressure,
4
1600
t
2000
Dar
FIG. 2. AVm as a function of p r e s s u r e for s o d i u m d e c a n o a t e at 25°C. O, ultrasound m e a s u r e m e n t s ; [3, conductivity m e a s u r e m e n t s . Journal of Colloid and Interface Science, V o l . 72, N o , 1, O c t o b e r 15, 1979
64
VIKINGSTAD, SKAUGE, A N D HOLLAND
I
V¢
174
cm3mol -I 172'
170
168.
166"
164
I
I
I
I
400
800
1200
1600
!
2000
pressure, bar
FIG. 3. The pamiH molH volume of sodium decanoate in the singly dispersed state (V~,©) and in the micellar state (V~,D) as a function of pressure at 25°C.
above the CMC, V% increases and V~ decreases. The change in partial molal compressibility during micelle formation, At
where t<¢(s)Sand t
singly dispersed state and in the micellar state, respectively. Plots of K.(s) as a function of concentration are similar to the corresponding plots of V.. From these plots o0 S t
T A B L E II
T A B L E III
Apparent Molal Compressibilities and the Change in Partial Molal Compressibility during Micelle Formation for Sodium Decanoate at Different Pressures at 25°C
Apparent Molal Volumes and the Change in Partial Molal Volume during Micelle Formation for Sodium Decanoate at Different Temperatures
~K~n = K~<~) - x~(s)
(K,~
[15]
( V . -+ 0.2) c m 3 m o l e
± 3 ) . 10 4 e m 3
bar x mole-a (A~csnl ± 5). 104 c m z P(bars)
1 200 400 800 1200 1600
K~
~)
K,%~
-78 -58 -44 -27 -18 -8
-63 -45 -37 -22 -11 -4
51 35 27 13 6 4
b a r -~ m o l e
T (°C)
V~
V~,
V~
10 15 20 25 30 35 40
159.5 161.0 163.0 164.2 165.8 167.2 168.7
160.2 161.8 163.9 165.4 166.8 168.1 169.3
171.9 172.7 173.9 175.0 175.8 176.7 177.7
(AV m -+ 0.4) c m 3 m o l e
t
114 80 64 35 17 8
Journal of Colloid and Interface Science, Vol. 72, N o . 1, O c t o b e r 15, 1979
11.7 10.9 10.0 9.6 9.0 8.6 8.4
VOLUMES AND COMPRESSIBILITIES OF SURFACTANTS
65
result of the reduced free space between the molecules. This can explain the decrease in K,(~)mwith pressure.
proach zero at the highest pressures. Plots of K.(s)S and K.(~)m as functions of pressure are similar to the volumes (Fig. 3) and the obtained results for the compressibilities are in good agreement with the slopes of the curves in Fig. 3. The increase in K.(s)s with increasing pressure must be understood from the changes in electrostriction mentioned in the discussion of VS. The electrostriction has a negative contribution to the compressibility, and the compressibility thus increases when the electrostriction is reduced. It is probable that the partial molal compressibility of the CH2 groups in the interior of the micelles decreases with pressure as a
Partial Molal Volumes and Compressibilities at Different Temperatures The partial molal volumes of the sodium decanoate solutions were calculated at different temperatures from density measurements, and plots of V . as a function of concentration were obtained at each temperature. F r o m these plots V ~, V%, Vg~, and AV m were determined, and the results are shown in Table Ill. It turns out that AVm decreases with in-
178
176
174
172
7
g
170
166
164
162
160 i0
I
I
I
15
20
25
temperature,
I
30
I
35
I
40
°C
FIG. 4. The partial molal volume of s o d i u m decanoate in the singly dispersed state (V%,©) and in the micellar state (Vg~,[]) as a function of temperature. Journal of Colloid and Interface Science, Vol. 72, No. I, October 15, 1979
66
VIKINGSTAD, SKAUGE, AND HOILAND TABLE IV
duced hydrophobic interactions with temApparent Molal Compressibilitiesand the Change in perature, thus reducing the negative contriPartial MolalCompressibilityduringMicelleFormation bution to V . from hydrophobic hydration. for Sodium Decanoate at DifferentTemperatures The partial molal volume of the ionic head group of the surfactant molecules also (K¢~ ± 2). 104 cm a bar-1 mole-t tends to increase with temperature (20). T (AK~ _+ 5)' 104 cm :~ V~ shows a linear increase with tempera(°C) K7 K$~ ~(~ bar -~ mole-' ture. This can be explained from the in10 -115 -99 38 137 creased kinetic movements of the mole15 -101 -88 43 131 cules in the interior of the micelles, thus 20 -91 -76 47 123 increasing the free space between the mole25 -78 -63 51 114 cules. The volume of the ionic head groups 30 -68 -50 55 105 at the micelle surface will also increase with 35 -54 -38 59 97 40 -43 -28 63 91 temperature. As mentioned under the discussion of the pressure effects, the partial molal expansicreasing temperature, and this decrease tivities of the surfactant in the singly disseems to be linear in the temperature persed state, E~, and in the micellar state, range 20-40°C. Similar results have been E~, can be determined from the slopes of found by Kaneshina et al. (2) for alkylsul- Fig. 4. E~ is determined to about 0.29 fates and by Musbally et al. for NTABr _+ 0.02 cm 3 K -1 mole -1, but seems to demicelles (n-nonyltrimethylammonium bro- crease slightly with temperature. This demide) (19). crease can be ascribed to the decreased The relation between the temperature expansitivity of the ionic head group of the dependence of AVm and the pressure de- surfactant at higher temperatures (20). The pendence of the entropy change of micelli- quantity E~ is determined to about 0.19 zation, AS TM, is given by: _+ 0.02 cm 3 K -1 mole -~ and seems to be constant in the temperature range investi0Arm I = -(OAsrn I . [16] gated. This is in good agreement with the observation that E(CH2) for pure liquids is The results obtained thus imply that the almost independent of temperature (21). entropy change of micelle formation inFrom the ultrasound measurements and creases with pressure, at least at low pres- plots of K~s~ as a function of concentrasures. Kaneshina et al. (2) have ascribed tion at each temperature, the quantities this result to the sharp decrease in partial KS , K~(s), s K~(s~,and AKm were determined. molal entropy below the CMC at in- The results are shown in Table IV. Both K ~m( s ) and K s~ ( s ) increase with creased pressure. Figure 4 shows plots of V~ and V~ as temperature, but the increase in K~(s~ is functions of temperature. V$ increases with much larger. Thus the observed decrease in temperature, but this increase is smaller at AKTM can be ascribed mainly to changes in the highest temperatures. This result is in the compressibility of the surfactant below good agreement with the results of Musbally the CMC. Cabani et al. (22) have shown et al. for NTABr. Also, Sakurai (20) has that this increase in compressibility with determined the temperature dependence of temperature is a result of both decreased V. for sodium heptanoate below the CMC hydrophilic and hydrophobic interactions, and has obtained similar results. The in- as the resistance to pressure of the increase in V. for hydrophobic solutes with creased water structure around the hydrotemperature is usually ascribed to the re- phobic part of the surfactant molecule and Journal of Colloid and Interface Science, Vol. 72, No. 1, October 15, 1979
VOLUMES AND COMPRESSIBILITIES OF SURFACTANTS
the electrostricted water structure around the hydrophilic end of the molecule both decrease with increasing temperature. As mentioned in the discussion of Vg~ the free space between the molecules in the interior of the micelle increases with temperature, and this can explain the increase in K(I)(s). m REFERENCES 1. Vikingstad, E., Skauge, A., and H0iland, H., J. Colloid Interface Sci. 66, 240 (1978). 2. Kaneshina, S., Tanaka, M., and Tomida, T., J. Colloid Interface Sci. 48, 450 (1974). 3. Musbally, G. M., Perron, G., and Desnoyers, J. E., J. Colloid Interface Sci. 48, 494 (1974). 4. Corkill, J. M., Goodman, J. F., and Walker, T., Trans. Faraday Soc. 63, 768 (1967). 5. Brun, T., H0iland, H., and Vikingstad, E., J. Colloid Interface Sci. 63, 89 (1978). 6. H¢iland, H., J. Chem. Soc. Faraday Trans. I 71, 797 (1975). 7. H¢iland, H., and Vikingstad, E., J. Chem. Soc. Faraday Trans. 1 72, 1441 (1976). 8. H0iland, H., J. Chem. Soc. Faraday Trans. I 70, 1180 (1974).
67
9. Chen, C. T., and Millero, F. J., J. Acoust. Soc. Amer. 60, 1270 (1976). 10. Wilson, W. D., J. Acoust. Soc. Amer. 31, 1067 (1959). 11. Barlow, A. J., and Yzgan, E., Brit. J. Appl. Phys. 18, 645 (1967). 12. Fine, R. A., and Millero, F. J., J. Chem. Phys. 59, 5529 (1973). 13. Chen, C. T., Fine, R. A., and Millero, F. J., J. Chem. Phys. 66, 2142 (1977). 14. Desnoyers, J. E., and Philip, P. R., Canad. J. Chem. 50, 1094 (1972). 15. Kale, K. M., and Zana, R., J. Colloid Interface Sci. 61, 312 (1977). 16. Tanaka, M., Kaneshina, S., Shin-No, K., Okajima, T., and Tomida, T., J. Colloid Interface Sci. 46, 132 (1974). 17. H0iland, H., and Vikingstad, E., Acta Chem. Scand. A 30, 692 (1976). 18. Vikingstad, E., J. Colloid Interface Sci. 68, 287 (1979). 19. Musbally, G. M., Perron, G., and Desnoyers, J. E., J. Colloid Interface Sci. 54, 80 (1976). 20. Sakurai, M.,Bull. Chem. Soc..lap. 46, 1596(1973). 21. Cabani, S., Conti, G., and Matteoli, E., J. Solution Chem. 5, 751 (1976). 22. Cabani, S., Conti, G., and Matteoli, E., J. Solution Chem., in press.
Journal of Colloid and Interface Science, Vol. 72, No. 1, October 15, 1979
MATERIALS AND METHODS
In an earlier work (1) the change in partial molal volume, AVm, and partial molal compressibility, AK", in the formation of micelles were determined for the homologous series of sodium alkylcarboxylates at 25°C. It was found that both AV m and ~K m increased with increasing chain length of the surfactant, which has also been found for the alkylsulphates (2, 3) and for alkyltrimethylammonium bromides (4). We considered it of interest to extend the investigations of AWn and AKm to different temperatures and different pressures. In this work AV m and AKm have been determined for sodium decanoate (NaC~0) in the temperature range 10-40°C. By establishing a method for ultrasound measurements under high pressure we have been able to determine AV m and AKm in the pressure range 1-1600 bar. The pressure dependence of AV m and An m has been compared to the conductivity data from the earlier work (1).
The synthesis of sodium d e c a n o a t e (NaC10) from decanoic acid and N a O H has been described in earlier works (1, 5). Decanoic acid was supplied by Fluka, puriss grade, and the N a O H by E K A , Sweden. Ten solutions of NaC10 were made in the concentration range 0.04-0.4 mole kg-L The concentrations were determined by weight. The densities of the solutions were determined at 5-degree intervals between 10 and 40°C by a Paar density meter, and the isentropic coefficients of compressibility were determined at the same temperatures by ultrasound measurements. Details of these measurements have been presented elsewhere (6, 7). The temperature was measured with a H e w l e t t - P a c k a r d quartz thermometer and was controlled to _+0.005°C in a water bath. U l t r a s o u n d m e a s u r e m e n t s at high pressure. The " s i n g - a r o u n d " principle for ultra59 0021-9797/79/13005%09502.00/0
Journal of Colloid and Interface Science, Vol. 72, No. 1, October 15, 1979
Copyright © 1979 by Academic Press, Inc. All rights of reproduction in any form reserved.
60
VIKINGSTAD,
E
SKAUGE,
F
A
FIG.
1. T h e
cell for
ultrasound
measurements
under high pressure. (A) steel cylinder; (B) the end piece of the cell; (C) the piezoceramic transducer; (D) nylon isolating material; (E) copper metal; (F) cell openings for filling the cell. sound measurements used in our laboratory for the determination of isentropic coefficients of compressibility at atmospheric pressure has been described in detail elsewhere (7). This principle was also used to determine isentropic coefficients of compressibility at higher pressures. H o w e v e r , a new cell had to be constructed for these measurements. This cell is shown in Fig. 1. The cell was a 5-cm closed steel cylinder with a piezoceramic transducer at each end. The transducer was attached to a piece of copper metal with a t w o - c o m p o n e n t electrically conductive e p o x y adhesive. This copper metal was isolated from the steel of the end piece by a ring of nylon material (see Fig. 1). The outer part of the transducer was connected to the end piece by a thin copper thread, thus making a complete current loop. Oil was used as the pressure transmitting medium. Two pieces of PVC-tubings containing a volume greater than the compression volume of the cell content was attached to the cell openings. The pulse-frequency of the ultrasound radiation was determined at 1,200,400,800, 1200, and 1600 bars at 25°C. The pressure was determined by a high-pressure transducer with an accuracy of _+2 bar (see Ref. 8). Water was used to calibrate the cell, applying the data of Chen and Millero (9). The pulse-frequency of the ultrasound radiation is very dependent on pressure
AND HOILAND
(about 2 Hz/bar for the 5-cm long cell). It was therefore found necessary to employ two measuring cells simultaneously in the pressure compartment. One cell was filled with water, the other with the solution, and it was thus possible to determine the calibration pulse-frequency of water directly at each of the applied pressures. This increased the relative accuracy of the determination of pressure to better than _+0.5 bar. The main problem during the development of this method of measurement has been the nylon material isolating the copper metal from the steel of the end pieces of the cell. Occasionally it was found that this material was damaged by oil or pressure. The method is still under development and improvement, and new materials are being tested out. RESULTS
AND DISCUSSION
Partial Molal Volumes and Compressibilities at Different Pressures The speed of sound in pure water at different pressures at 25°C has been determined by several authors (10-12). We have used the data of Chen and Millero (9) to calibrate the measuring cells. The isentropic apparent molal compressibility, K~,~), can be expressed by: K.(~
1000 mdo (fl~ - ~o~) + [3~V.
[1]
where m is the molality of the solution, do is the density of the solvent, and fls and fl0s are the isentropic coefficients of compressibility of the solution and the solvent, respectively, fls is expressed by:
/3~ -
106 v2d
[2]
where d is the density of the solution, and v is the speed of sound in the solution. By measuring the ultrasound frequencies for
Journal of Colloid and Interface Science, Vol. 72, No. 1, October 15, 1979
VOLUMES AND COMPRESSIBILITIES OF SURFACTANTS the solution v can be determined at each pressure, using the data for the speed of sound in water. In order to determine K~s~ at different pressures the quantities d, do, /3s, fi0~, and V . must be known at each pressure. The quantities do and /30s are known from the literature (13). /3~ can be determined from the ultrasound measurements but it requires that d be known as well. By an iteration process it is possible to determine d and consequently V . at different pressures from the ultrasound measurements. The relation between the apparent molal volume and the isothermal apparent molal compressibility can be expressed by: K~ = _ ( 0 V ° t
\ OP }r
.
[3]
Desnoyers and Philip (14) have shown that the relation between isothermal and isentropic apparent molal compressibility, K. and K.~s~ is given by the equation: R = K ~ - K.(s)
61
singly dispersed state, E~, was determined as 0.29 ___ 0.02 cm a K -1 mole -1, and the corresponding quantity in the micellar state, Eg~, was determined as 0.19 _+ 0.02 cm 3 K -1 mole-L Assuming that the contribution from C . was small, the isothermal apparent molal compressibilities in the singly dispersed state and micellar state, K~, and KS, was determined as - 5 2 . 1 0 -4 and 58.10 -4 cm 3 bar -~ mole -1, respectively. The isothermal values of the compressibilities are about 15% higher than the isentropic values (see Table II). H o w e v e r , it can be shown that if this difference is neglected and if we put K. = ~:.(s~ in Eq. [3] this will change the final results for V® and •. only within the estimated experimental uncertainty. The difference R in Eq. [4] must be known at different pressures in order to use Eq. [3]. The pressure dependence of the expansitivity can be expressed by:
OE. ] _ 02Vo OP Jr
OTOP = _ ( O K ~ t ---(OK~'s~l • [51 \ OT )e \ OT )e
= coefficient of thermal expansion cr = volumetric specific heat = 13-/~s, the difference between isothermal and isentropic coefficients of compressibility E . = apparent molal expansitivity C . = apparent molal heat capacity The subscripts refer to the pure solvent. It can be shown (14) that the major contribution to the difference R for surfactants comes from the expansitivity. F r o m our measurements of V . at different temperatures the apparent molal expansitivities for the solutions were calculated. F r o m the plot of E . versus concentration the apparent molal expansitivity in the
The temperature dependence of K.(s~ for the solutions has been determined in the second half of this work, and E . at different pressures can be obtained. These values of E® are calculated on the assumption that E . is linearly dependent on the pressure, which is valid to about 800 bars. H o w e v e r , even above this pressure Eq. [5] gives a good estimate for E . . In order to integrate Eq. [3] the pressure dependence of ~:. must be known. H o w e v e r , we can make a first guess and assume that OK./OP ~ O. Integration of Eq. [3] then gives:
V . ( P ) = V®(1) - ( P - 1)K®(1). [6] V . ( P ) is the apparent molal volume at pressure P. F r o m the well-known equation relating V® and the density of the solution, d, a first value of d at the pressure P can Journal of Colloid and Interlace Science, Vol. 72, No. 1, October 15, 1979
62
VIKINGSTAD, SKAUGE,AND HOLLAND
be calculated: d(P)=
concentration of the surfactant at each pressure. These plots turned out to be similar ( )1000 --+Mm in form to those presented in earlier works (1, 5, 15). The change in partial molal volume during micelle formation, AVTM, can ( _ 1000 _ ) be expressed by: x V . ( P ) + mdo(P) " [7] AVm = V~ - V~
The isentropic apparent molal compressibility K~s)(P) can now be determined:
[131
where V$ and V~ are the partial molal volumes of the surfactant in the singly 1000 K¢(s)(P) dispersed state and in the micellar state, mdo( P) respectively. V~, is equal to V. at the CMC, × (flu(P) + flos(P)) + fls(P)V¢(P) [8] and V~ is determined by using a saturation function to the plot of V. above the where CMC (5, 15). The obtained results for V~, 10~ V$, V~, and AVm at different pressures fis(P) [91 v2(P)d(e) are shown in Table I. AVm can also be determined as a funcValues of K.(s)(P) can now be calculated at each pressure for the solution. K.(~)(P) tion of pressure by conductivity measureis then assumed to be described by a ments, determining the CMC as a function of pressure: polynomial in P: ~C~(s)(P) = ao + a , P + a2P 2 + a3P a.
[10]
From the obtained values of ~:.(s)(P) the constants a0, a,, a2, and a3 were calculated by a polynomial regression. Using this equation and Eq. [4] to calculate K.(P), integration of Eq. [3] gives: V . ( P ) = V.(1) - (aoP+ V2alP 2 + V3azP 3 + ¼a3P 4 + R ( P ) )
+ (a0 + 1/5al + ½a2 + ¼a3 +R(1)).
[11]
From this equation new values of V . ( P ) and d ( P ) have been determined, and the values of K¢(s)(P) can be redetermined by using Eq. [8]. This iteration process (Eqs. [31, [6[-[111) can then be continued until:
tge(sl(P)n+l
1 ~< 0.001
[12]
I K.(s)(P)n where n is the number of iterations. From this iteration process values of V. and K.(s) for each solution where determined at different pressures from the ultrasound measurements. V. has been plotted as a function of the
A v m = ( 1 + f i ) R T ( O In CMC) OP r
[14]
where fi is the fraction of associated counterions. Previously (1) AVTM has been determined by this method, and the results have been included in Table I. Plots of AVm as a function of pressure from the two methods are shown in Fig. 2. It turns out that AVm decreases with increasing pressure, and the two different methods of measurements are in good agreement. Figure 3 shows V~ and V~ as functions of the pressure. The results are similar to those obtained by Tanaka et al. (16) for alkylsulphates by density measurements under high pressure. V~ increases with increasing pressure. This can be explained by the changes in electrostriction of water molecules with pressure. At higher pressure the water structure is already somewhat disordered, and the negative contribution to V. from electrostriction at the ionic head group of the surfactant thus decreases with increasing pressure (16). The group partial molal compressibility
Journal of Colloid andlnterface Science, Vol. 72, No. 1, October 15, 1979
VOLUMES AND COMPRESSIBILITIES OF SURFACTANTS TABLE I A p p a r e n t Molal V o l u m e s and the C h a n g e in Partial Molal V o l u m e during Micelle F o r m a t i o n for Sodium D e c a n o a t e at Different P r e s s u r e s at 25°C ( V . -+ 0.3) c m 3 m o l e - ' P(bars)
1 200 400 800 1200 1600
V=
V%
V~
164.7 166.0 167.0 168.0 168.8 169.2
165.4 166.4 167.2 168.6 169.3 169.8
175.2 173.8 173.1 172.0 170.3 169.3
( A V m -+ 0.4) c m ~ m o l e - ' Ultrasound
Conductivity'
9.6 7.4 5.9 3.4 1.0 ± 1.0 - 0 . 5 ± 1.0
9.5 7.2 5.8 3.0 0 -1.0
a Ref. (1).
of a CH2 group in aqueous solution, K(CH2,aq), is about - 2 . 0 . 1 0 -4 cm 3 bar -~ mole -~ at 25°C (17). This means that V(CH2,aq) increases slightly at lower pressures, but at higher pressure V(CHz,aq) decreases (16) as a result of increased hydrophobic interactions. However, this
i(
63
decrease in V. from the hydrophobic part of the surfactant molecule is small compared to the increase in V. at the ionic head group. V~ shows the opposite trend to V~ and decreases with pressure. This must be a result of changes in the interior of the micelle, as the partial molal volume of the charged micelle surface probably increases with pressure as a result of reduced electrostriction. The decrease in V~ can be ascribed to the loss of free space between the molecules in the interior of the micelles when the pressure increases. The partial molal compressibility of a CH2 group in the micellar core, K(CH2,mic), is about 10.10 -4 cm 3 bar -1 mole -1 at atmospheric pressure (18). This means that V(CH2,mic) decreases rapidly with increasing pressure, and this explains the decrease in V~. It should be noticed that the decrease in AVm with pressure is a result of changes in the partial molal volumes both below and
)
AV TM cm3mol -It
6'
-2
:
L
400
~00
1200 pressure,
4
1600
t
2000
Dar
FIG. 2. AVm as a function of p r e s s u r e for s o d i u m d e c a n o a t e at 25°C. O, ultrasound m e a s u r e m e n t s ; [3, conductivity m e a s u r e m e n t s . Journal of Colloid and Interface Science, V o l . 72, N o , 1, O c t o b e r 15, 1979
64
VIKINGSTAD, SKAUGE, A N D HOLLAND
I
V¢
174
cm3mol -I 172'
170
168.
166"
164
I
I
I
I
400
800
1200
1600
!
2000
pressure, bar
FIG. 3. The pamiH molH volume of sodium decanoate in the singly dispersed state (V~,©) and in the micellar state (V~,D) as a function of pressure at 25°C.
above the CMC, V% increases and V~ decreases. The change in partial molal compressibility during micelle formation, At
where t<¢(s)Sand t
singly dispersed state and in the micellar state, respectively. Plots of K.(s) as a function of concentration are similar to the corresponding plots of V.. From these plots o0 S t
T A B L E II
T A B L E III
Apparent Molal Compressibilities and the Change in Partial Molal Compressibility during Micelle Formation for Sodium Decanoate at Different Pressures at 25°C
Apparent Molal Volumes and the Change in Partial Molal Volume during Micelle Formation for Sodium Decanoate at Different Temperatures
~K~n = K~<~) - x~(s)
(K,~
[15]
( V . -+ 0.2) c m 3 m o l e
± 3 ) . 10 4 e m 3
bar x mole-a (A~csnl ± 5). 104 c m z P(bars)
1 200 400 800 1200 1600
K~
~)
K,%~
-78 -58 -44 -27 -18 -8
-63 -45 -37 -22 -11 -4
51 35 27 13 6 4
b a r -~ m o l e
T (°C)
V~
V~,
V~
10 15 20 25 30 35 40
159.5 161.0 163.0 164.2 165.8 167.2 168.7
160.2 161.8 163.9 165.4 166.8 168.1 169.3
171.9 172.7 173.9 175.0 175.8 176.7 177.7
(AV m -+ 0.4) c m 3 m o l e
t
114 80 64 35 17 8
Journal of Colloid and Interface Science, Vol. 72, N o . 1, O c t o b e r 15, 1979
11.7 10.9 10.0 9.6 9.0 8.6 8.4
VOLUMES AND COMPRESSIBILITIES OF SURFACTANTS
65
result of the reduced free space between the molecules. This can explain the decrease in K,(~)mwith pressure.
proach zero at the highest pressures. Plots of K.(s)S and K.(~)m as functions of pressure are similar to the volumes (Fig. 3) and the obtained results for the compressibilities are in good agreement with the slopes of the curves in Fig. 3. The increase in K.(s)s with increasing pressure must be understood from the changes in electrostriction mentioned in the discussion of VS. The electrostriction has a negative contribution to the compressibility, and the compressibility thus increases when the electrostriction is reduced. It is probable that the partial molal compressibility of the CH2 groups in the interior of the micelles decreases with pressure as a
Partial Molal Volumes and Compressibilities at Different Temperatures The partial molal volumes of the sodium decanoate solutions were calculated at different temperatures from density measurements, and plots of V . as a function of concentration were obtained at each temperature. F r o m these plots V ~, V%, Vg~, and AV m were determined, and the results are shown in Table Ill. It turns out that AVm decreases with in-
178
176
174
172
7
g
170
166
164
162
160 i0
I
I
I
15
20
25
temperature,
I
30
I
35
I
40
°C
FIG. 4. The partial molal volume of s o d i u m decanoate in the singly dispersed state (V%,©) and in the micellar state (Vg~,[]) as a function of temperature. Journal of Colloid and Interface Science, Vol. 72, No. I, October 15, 1979
66
VIKINGSTAD, SKAUGE, AND HOILAND TABLE IV
duced hydrophobic interactions with temApparent Molal Compressibilitiesand the Change in perature, thus reducing the negative contriPartial MolalCompressibilityduringMicelleFormation bution to V . from hydrophobic hydration. for Sodium Decanoate at DifferentTemperatures The partial molal volume of the ionic head group of the surfactant molecules also (K¢~ ± 2). 104 cm a bar-1 mole-t tends to increase with temperature (20). T (AK~ _+ 5)' 104 cm :~ V~ shows a linear increase with tempera(°C) K7 K$~ ~(~ bar -~ mole-' ture. This can be explained from the in10 -115 -99 38 137 creased kinetic movements of the mole15 -101 -88 43 131 cules in the interior of the micelles, thus 20 -91 -76 47 123 increasing the free space between the mole25 -78 -63 51 114 cules. The volume of the ionic head groups 30 -68 -50 55 105 at the micelle surface will also increase with 35 -54 -38 59 97 40 -43 -28 63 91 temperature. As mentioned under the discussion of the pressure effects, the partial molal expansicreasing temperature, and this decrease tivities of the surfactant in the singly disseems to be linear in the temperature persed state, E~, and in the micellar state, range 20-40°C. Similar results have been E~, can be determined from the slopes of found by Kaneshina et al. (2) for alkylsul- Fig. 4. E~ is determined to about 0.29 fates and by Musbally et al. for NTABr _+ 0.02 cm 3 K -1 mole -1, but seems to demicelles (n-nonyltrimethylammonium bro- crease slightly with temperature. This demide) (19). crease can be ascribed to the decreased The relation between the temperature expansitivity of the ionic head group of the dependence of AVm and the pressure de- surfactant at higher temperatures (20). The pendence of the entropy change of micelli- quantity E~ is determined to about 0.19 zation, AS TM, is given by: _+ 0.02 cm 3 K -1 mole -~ and seems to be constant in the temperature range investi0Arm I = -(OAsrn I . [16] gated. This is in good agreement with the observation that E(CH2) for pure liquids is The results obtained thus imply that the almost independent of temperature (21). entropy change of micelle formation inFrom the ultrasound measurements and creases with pressure, at least at low pres- plots of K~s~ as a function of concentrasures. Kaneshina et al. (2) have ascribed tion at each temperature, the quantities this result to the sharp decrease in partial KS , K~(s), s K~(s~,and AKm were determined. molal entropy below the CMC at in- The results are shown in Table IV. Both K ~m( s ) and K s~ ( s ) increase with creased pressure. Figure 4 shows plots of V~ and V~ as temperature, but the increase in K~(s~ is functions of temperature. V$ increases with much larger. Thus the observed decrease in temperature, but this increase is smaller at AKTM can be ascribed mainly to changes in the highest temperatures. This result is in the compressibility of the surfactant below good agreement with the results of Musbally the CMC. Cabani et al. (22) have shown et al. for NTABr. Also, Sakurai (20) has that this increase in compressibility with determined the temperature dependence of temperature is a result of both decreased V. for sodium heptanoate below the CMC hydrophilic and hydrophobic interactions, and has obtained similar results. The in- as the resistance to pressure of the increase in V. for hydrophobic solutes with creased water structure around the hydrotemperature is usually ascribed to the re- phobic part of the surfactant molecule and Journal of Colloid and Interface Science, Vol. 72, No. 1, October 15, 1979
VOLUMES AND COMPRESSIBILITIES OF SURFACTANTS
the electrostricted water structure around the hydrophilic end of the molecule both decrease with increasing temperature. As mentioned in the discussion of Vg~ the free space between the molecules in the interior of the micelle increases with temperature, and this can explain the increase in K(I)(s). m REFERENCES 1. Vikingstad, E., Skauge, A., and H0iland, H., J. Colloid Interface Sci. 66, 240 (1978). 2. Kaneshina, S., Tanaka, M., and Tomida, T., J. Colloid Interface Sci. 48, 450 (1974). 3. Musbally, G. M., Perron, G., and Desnoyers, J. E., J. Colloid Interface Sci. 48, 494 (1974). 4. Corkill, J. M., Goodman, J. F., and Walker, T., Trans. Faraday Soc. 63, 768 (1967). 5. Brun, T., H0iland, H., and Vikingstad, E., J. Colloid Interface Sci. 63, 89 (1978). 6. H¢iland, H., J. Chem. Soc. Faraday Trans. I 71, 797 (1975). 7. H¢iland, H., and Vikingstad, E., J. Chem. Soc. Faraday Trans. 1 72, 1441 (1976). 8. H0iland, H., J. Chem. Soc. Faraday Trans. I 70, 1180 (1974).
67
9. Chen, C. T., and Millero, F. J., J. Acoust. Soc. Amer. 60, 1270 (1976). 10. Wilson, W. D., J. Acoust. Soc. Amer. 31, 1067 (1959). 11. Barlow, A. J., and Yzgan, E., Brit. J. Appl. Phys. 18, 645 (1967). 12. Fine, R. A., and Millero, F. J., J. Chem. Phys. 59, 5529 (1973). 13. Chen, C. T., Fine, R. A., and Millero, F. J., J. Chem. Phys. 66, 2142 (1977). 14. Desnoyers, J. E., and Philip, P. R., Canad. J. Chem. 50, 1094 (1972). 15. Kale, K. M., and Zana, R., J. Colloid Interface Sci. 61, 312 (1977). 16. Tanaka, M., Kaneshina, S., Shin-No, K., Okajima, T., and Tomida, T., J. Colloid Interface Sci. 46, 132 (1974). 17. H0iland, H., and Vikingstad, E., Acta Chem. Scand. A 30, 692 (1976). 18. Vikingstad, E., J. Colloid Interface Sci. 68, 287 (1979). 19. Musbally, G. M., Perron, G., and Desnoyers, J. E., J. Colloid Interface Sci. 54, 80 (1976). 20. Sakurai, M.,Bull. Chem. Soc..lap. 46, 1596(1973). 21. Cabani, S., Conti, G., and Matteoli, E., J. Solution Chem. 5, 751 (1976). 22. Cabani, S., Conti, G., and Matteoli, E., J. Solution Chem., in press.
Journal of Colloid and Interface Science, Vol. 72, No. 1, October 15, 1979