J. Phys. Chem. 1994,98, 9115-9118
9115
Test of the Additivity Rule for the Estimation of Standard Partial Molar Heat Capacities and Volumes of Some Nonionic Surfactants in Aqueous Solutions Rameshwar Jha and J. C. Ahluwalia' Department of Chemistry, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India Received: January 7, 1994; I n Final Form: March 18, 1994"
(e,,)
The heat capacities of pure liquid nonionic surfactants Triton X-100 and n-decyl and n-dodecyl poly(oxyethylene glycol) monoethers C10E5, C ~ O EClOE8, ~ , C12E5, C12E6, and C12E8 have been measured using a differential scanning calorimeter. The partial molar heat capacities of these surfactants in water in the post micellar state (Cpp2,mic) have been evaluated from apparent molar heat capacities (Cp+)which are measured using a Picker Microflow calorimeter. The standard partial molar heat capacities have been obtained (i) by combining the heat capacities of the pure surfactants with the heat capacities of dissolution in the premicellar (Aq,,,,,) region and (ii) by combining the partial molar heat capacities in the post micellar state (cpp2,fic) with the heat capacities of micellization (ACp,m). The comparison of the estimated by using a group additivity rule with the experimental values indicates that the additivity rule for the estimation of the standard partial molar heat capacities in water holds reasonably well for nonionic surfactants for which it is difficult to obtain accurate z"p2 experimentally due to their low critical micelle concentration (cmc).
(q2)
(q,)
q2
Introduction The accurate values of partial molar heat capacitiesand volumes of surfactants in pre- and post-cmc regions are of importance in the evaluation of the thermodynamic parameters of micellization. It is well recognized that the direct calorimetric measurement of the partial molar heat capacity of surfactants in aqueous solution is more accurate than its evaluation from the temperature dependence of the solubility of surfactants in water. Desnoyers and co-workers,1-4 Woolley and Burchfield,5-6Rosenholm et al.? and Groliers have reported many papers in this field. But most of the reported data are for the ionic surfactants. The accurate partial molar heat capacity and partial molar volume data for aqueous nonionic surfactants of polyoxyethylene class are scarce.9-11 The lack of accurate data in the pre-cmc region is due to the very low cmc of these nonionic surfactants. At concentrations less than 10-3 mol L-1, the measurements of apparent molar heat capacities and volumes and their extrapolation to infinite dilution to obtain partial molar heat capacities and volumes at infinite dilution are associated with large uncertainties. The other calorimetric method for the evaluation of the partial molar heat capacities in the pre-cmc region involves the measurements of the temperature dependence of the enthalpies of solution and the heat capacity of the pure surfactant
c2
(e,,)
and
q 2 = Aq,mono + q
2
This method also results in large uncertainties in the AC and as the differences are usually small compared witR'%zlarge individual values of the enthalpies of solution, and calculation of AG,,,,, involves one differentiation step dAH1 d T. The volume changes for the micellization can be obtained by measuring the variation of cmc with pressure; again, it involves one differentiation step (d In cmc/dP)T resulting in error magnification. The direct density measurement method gives
qoPz
*Abstract published in Advance ACS Abstracts, August 15, 1994.
0022-365419412098-91 1 5$04.50/0
the best results,' but this method too has limitations for accurate measurements of apparent molar volume at very low concentrations. We therefore have estimated the standard partial molar heat capacities and volumes of the nonionic surfactants using group additivity rules of Nichols et al.l2and Cabani et al." and compared these with the experimentally determined values. For this we have measured the heat capacities of some pure liquid nonionic surfactants n-decyl and n-dodecyl poly(oxyethylene glycol) monoethers (CIOES,ClOE6r C I O E ~C, I ~ E S , C&6, C I ~ E Sand ) Triton X-100 at 298.15 K and combined with the heat capacities of dissolution (AC",,m,,no)in the pre-cmc region reported earlierI4 to obtain the partial molar heat capacities at infinite dilution We have also measured the apparent molar heat capacities (Cp4)and volumes (V,) of the above nonionic surfactants in the post micellar state and therefrom obtained the values of cpp2mi and c r2,mic. The cp2,micvalueshave been combined with the reported values of the heat capacity of micellization (ACP,,) to obtain the values of
(e2)
(c)
q2
(e,,)
c2.
c2.
Experimental Section The nonionic surfactants used for the present study were pentaoxyethylene glycol mono-n-decyl ether (CloE5), hexaoxyethylene glycol mono-n-decyl ether (C1OE6), octaoxyethylene glycol mono-n-decyl ether (CloEa), pentaoxyethylene glycol monon-dodecyl ether ( C I Z E ~hexaoxyethylene ), glycol mono-n-dodecyl ether ( C I ~ E ~octaoxyethylene ), glycol mono-n-dodecyl ether (C12Es), and Triton X-100, ( C H J ) ~ C C H ~ C ( C H ~ ) ~ C ~ H ~ ( O C H ~ CH2)9.5OH. All these nonionic surfactants except Triton X-100 were monodisperse and more than 99%pure as evident from the gas chromatograms supplied by Nikko Chemical Co., Japan. Triton X-100 was obtained from Sigma. No moisture content was detected by a Karl Fischer Aquatest-IV moisture analyzer. The molar masses of CloE5, C10E6, CloEs, C12E5, C12E6,C12Es, and Triton X-100 are 378.5, 422.5, 510.6, 406.6, 450.6, 538.7, and 624.9 g mol-', respectively. The heat capacities of pure liquid nonionic surfactants were measured using a differential scanning calorimeter, Micro DSC (Setaram, France), which has a heat capacity resolution of 5 X 10-5 of the absolute value (0.2 mJ K-1 g-I). The scanning rate used for the measurement of was 2 O C h-I. The instrument has two identical detachable batch cells of about 1 cm3 volume. 0 1994 American Chemical Society
9116 The Journal of Physical Chemistry, Vol. 98, No. 37, 1994 TABLE 1: Apparent Molar Heat Capacities and Volumes of Some Nonionic Surfactants in Water in Post Micellar Region at 298.15 K m,mol kg-'
v,*
CP,
0.050 66 0.071 23 0.07745 0.110 1 1 0.18049 0.198 16 0.245 52
m - ~cm3 mol-' J K-'g-' Triton X-100 570.7 4.1391 0.999792 571.1 1 .OOO 930 4.1206 571.0 4.1174 1.001 159 571.3 4.0897 1.002953 571.1 4.0400 1.006 104 4.0257 57 1 .O 1.007236 570.7 1.009428 3.9928
0.02075 0.02985 0.03957 0.06272 0.07690 0.09732
0.997083 0.997099 0.997087 0.997089 0.997088 0.997 110
0.023 77 0.02730 0.03937 0.051 97 0.05680 0.701 18 0.07247 0.08461 0.101 95
0.997251 0.997273 0.997361 0.997452 0.997496 0.997610 0.997616 0.997698 0.997826
p, g~
CioE5
377.9 377.8 378.6 378.9 379.1 378.9
CIO&
415.1 415.4 415.7 415.5 415.7 451.7 415.7 415.8 415.8
CioEs
0.018 30 0.02866 0.041 41 0.053 90 0.086 1 1
0.997509 0.997748 0.998 044 0.998 340 0.999077
0.00658 0.00885 0.00909
0.997 030 0.997003 0.997 016
0.03275 0.03281 0.053 74 0.07727 0.084 18
0.997 164 0.997 131 0.997 184 0.997222 0.997239
0.00407 0.00486 0.007 05 0.00778 0.01092 0.01700 0.027 10 0.03641 0.04930 0.06960 0.09209
0.997125 0.997 142 0.997183 0.997205 0.997262 0.997379 0.997569 0.997 747 0.997997 0.998369 0.998789
,
486.6 487.3 487.5 487.4 487.5
412.7 411.3
Cl2E6 449.3 449.4 449.6 449.6
CI2&
521.0 520.6 520.9 519.8 520.4 520.5 520.7 520.7 520.5 520.6 520.4
capacity (CpQ)as
Cp9= MCP-
CN*
J K-l mol-'
1767 1768 1767 1767 1751 1765 1760
4.1716 4.1683 4.1637 4.1537 4.1472 4.1383
1193 1199 1174 1159 1148 1142
4.1696 4.1682 4.1626 4.1556 4.1539 4.1470 4.1466 4.1417 4.1332
1341 1344 1327 1294 1303 1295 1297 1302 1292
4.1700 4.1640 4.1577 4.1483 4.1308
1605 1582 1594 1538 1543
4.1759 4.1745 4.1744
1135 1121 1125
4.1638 4.1643 4.1549 4.1429 4.1406
1394 1410 1413 1392 1403
4.1769 4.1764 4.1749 4.1744 4.1722 4.1682 4.1621 4.1578 4.1480 4.1354 4.1220
1587 1591 1583 1580 1570 1575 1597 1586 1593 1593 1595
C12ES
Jha and Ahluwalia
The instrument was first calibrated using the Joule effect and then tested by measuring the heat capacities of pure liquid heptane against water as the reference. The values obtained were found in excellent agreement with the reported values.1S-18 The apparent molar heat capacities and volumes of the above surfactants in post micellar region were measured with a Picker microflow calorimeter and an Anton Paar densimeter, respectively. The operational details and the working principles of these instruments have been described elsewhere.19-21 Results and Discussion Apparent Molar Heat Capacities in the Post Micellar Region. The specific heat capacity of solution measured with Picker microflow calorimeter was converted to apparent molar heat
lOO0(Cp m
ep)
and apparent molar volume VQ was calculated from the density as
where M i s the molar mass of the surfactant and m is the molality. The C, and c", are the specific heat capacities of the solution and the solvent, respectively. d and do are the densities of the surfactant solution and the solvent, respectively. The apparent molar heat capacities and volumes of the surfactants in the post micellar region are listed in Table 1. The partial molar heat capacities, Cp2,micrand volumes, V2,micr in the post micellar region have been evaluated22 from apparent molar heat capacities and volumes using the following relationships:
-
V2,mic= V,
+ m(dVQ/dm) = V, + A(mV,)/Am
(4)
The average of the nearly constant C,, values at high concentration (where dCN/dm and dVQ/dm are nearly zero) of the surfactant in the post micellar region was taken as the CP2,,ic and listed in Table 2. The standard deviations of CP2,dcand V2,,ic are within h20-60 J K-I mol-' and k0.5 cm3 mol-I, respectively. The V2,,ic values in the post-cmc region for the surfactants C12E~,C12&,andCl&arewithinfl cm3mo140fthereported"3J1 values while that of ClzE8 differs by about 4 cm3 mol-'. There are no reported values for the other surfactants, except for Triton X-100a t higher pressures.'O Heat Capacities of Pure Liquid Nonionic Surfactants. The heat capacities of pure liquid nonionic surfactants are listed in Table 2. In the literature the only reported values for c",, are 886 f 323and 881 f 524 J K-I mol-' for C12E5 at 328.51 and 298.15 K and 1328 J K-I mol-' for Triton X-100,2s which are in very good agreement with our values. Partial Molar Heat Capacitiesat Infinite Dilution. The values of partial molar heat capacities at infinite dilution were obtained by combining the heat capacities of pure nonionic surfactants (c",,) with the heat capacities of dissolution of surfactants in the premicellar region (Ac",,,,,,) and also by combining our heat capacities in the post micellar region (CPp2,,ic) with the heat capacities of micellization (ACP,,) as follows:
(q2)
c2
The experimental values of thus obtained are listed in Table 2. Estimation of Partial Molar Heat Capacitiesat Infiite Dilution. For nonionic surfactants, we have estimated the partial molar heat capacities a t infinite dilution from additivity methods of Nichols et a1.'2 and Cabani et al.I3 (Table 2) and partial molar volumes at infinite dilution from the additivity methods of Cabani et al.13 and by the method of Harada and Nakagawalo (Table 3). An illustration of estimation of is given below.
(c2)
(e)
c2
Surfactant: Cl0E5= CH,(CH2)9(CH2CH20)50H
The Journal of Physical Chemistry, Vol. 98, No. 37, 1994 9117
Test of the Additivity Rule
TABLE 2: Heat Capacities of Some Pure Liquid Nonionic Surfactants, Their Partial Molar Heat Capacities in the Micellar State, and Experimental and Estimated Values of Partial Molar Heat Capacities at Inifdte Dilution at 298.15 K (All Values in J K-1 mol-') surfactant
e,
AG, mono
TX-100
1284 f 8 1328 f lob 822 f 8 918 f 8 1108 f 8 883 f 4 886 f 3r 881 f 5f 982 f 5 1172 f 5
864 f 30 824 f 60e 828 f 16 872 f 40 979 f 33
CioEs CioE6 CioEs CIA C12E6 CnEs
CP2, mic
A Gm
1766 f 1 1 421 f 50e 1169 f 23 1297 f 14 1540 f 20 1127 f 24 1085 f 17f
-410 f 80b -335 f 10Sd -605 f 508
1402 f 18 1586 f 12
1019 f 36
-634 f 40h -670 f 75'
eXDt
est
2148 f 30 2152 f 62b 1650 f 16 1790 f 40 2087 f 37 1732 f 55 1690 f 53
2147
2036 f 44 2191 f 36
1887 2133
1587 1710 1956 1764 1759
a From ref 14 at 25 OC for Clo& and at 30 OC for other surfactants. From ref 25. From ref 25; the average of the values at 20 and 30 'C. ref 26. e From ref 23 at 30.36 OC. f From ref 27 at 25 OC. g From ref 27 at 17.5 "C. From ref 27 at 18.5 OC. From ref 27 at 25 'C.
TABLE 3: Partial Molar Volumes in the Post Micellar State and Estimation of Partial Molar Volumes at Infinite Dilution and Volumes of Micellization of Some Nonionic Surfactants in Water at 298.15 K (All Values in cm3 mol-') surfactant i%est) P2.mideXDt) AVdest) TX- 100 CioEs CioE6 CioEs CnEs CnE6 c I 2Es
565.5 366.7 403.8 477.8 398.3 435.4 509.4
570.9 378.7 415.8 487.5 412.5 449.6 520.8
5.4 12.4 12.0 9.7 14.2 14.2 11.4
Method Nichols et ala"
c = 19.06 + (15.8
5
+ 9 = 1591 J K-'mol-'
where the contributions of CH3, CH2,0, and OH groups toward are 157,90,-57 and 9 J K-' mol-', respectively.
q2
Method: Cabani et
2"p2 = 110.1 + (87.5 X 9) + (87.5 X 2- 51.9) X 5 - 10.1 + 79.6 N 1583 J K-'mol-' where the contribution of CH3, CH2,0, and OH groups toward the are 110.1,88.5,-51.9, and -10.1 J K-I mol-', respectively. The value 79.6J K-I mol-' is the correction factor. The values obtained by the two methods are very close to each other; hence, an average value of 1587 J K-l mol-' is taken as The values of other surfactants have been evaluated in the same fashion. The values of (Table 2) estimated from the group additivity rule agree reasonably well with the experimental values within the experimental uncertainty. It may therefore be concluded that the group additivity rule may be used to obtain partial molar heat capacities of nonionic surfactants, particularly for those which have very low cmc and are not amenable to accurate measurements of partial molar heat capacities in the pre-cmc region. Furthermore, the values of estimated from the group additivity rule may be used to estimate heat capacity of micellization (ACP,,) from the relationship
11)
+ (38.88 X 8)- (1.84X 8) + 6.74 + 13.41 = 509.33 cm' mol-'
where thecontributions of CH3, CH2, CH2CH20, and OH toward are 19.06,15.8,38.88,and 6.74cm3 mol-'. The value f1.84 cm3 mol-' is the correction factor per CHzCHzO group, and 13.41 cm3 mol-' is the overall correction factor.
Method Harada and Nakagawa" of C,,E8 =
2"p2 = 157 + (90 X 9) + (90 X 2 - 57) X
X
From
+
e Of C4HgOH
= 55.12 (15.8X 8)
4-
(CH,),
+ (CH2CH20)8
+ (38.88 X 8)- (1.84X 8) = 509.44cm3 mol-'
where 55.12cm3 mol-' is the partial molar volume of C4H90H and the other values are the same as given in the method of Cabani et al.13 The two values are very close to each other, and hence we have taken an average of these values. Since to the best of our knowledge the experimental values of partial molar volumes of the above nonionicsurfactants are not reported in the literature, it is not possible to verify the additivity rule. However, from the estimated values of and V2,,ic, we have derived the volume of micellization (AV,) from the relationship
q2
q2. q2
q2
q2
Estimation of
Values.
Method Cabani et
The volumes of micellization AV, which are listed in Table 3 are positive and increase with the increase in the number of CH2 groups. The contribution of one CH2 appears to be 16.8 cm3 mol-1. References and Notes (1) Desnoyers, J. E.; Perron, G.; Roux, A. H.In Surfactant Solutions, New Methods of Inuesfigation; Zana, R., Ed.; Marcel Dekker: New York,
1987; Vol. 22, p 1 . (2) Desnoyers, J. E.; DeLisi, R.; Ostiguy, C.; Perron, G. In Solufion Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum: New York, 1979; Vol. 1, p 221. (3) Leduc, P. A.; Fortier, J. L.; Desnoyers, J. E. J . Phys. Chem. 1974, 78, 1217. (4) Desnoyers, J.E.;Caron,G.;DeLesi,R.;Roberts,D.;Roux,A.;Perron, G. J . Phys. Chem. 1983,87, 1397. ( 5 ) Woolley, E. M.; Burchfield, T. E. J . Phys. Chem. 1984, 88, 2155; 1985, 89, 714. (6) Burchfield, T. E.; Woolley, E. M.Fluid Phase Equilib. 1985, 20, 207 (7) Rosenholm, J. B.; Grigg, R. B.; Hepler, L. G. J . Chem. Thermodyn. 1986, 18, 1153. (8) Grolier, J. P. E. 2nd Czechoslovak ConferenceonCalorimetry; Prague and Liblice, Sept 1982; p 95. (9) Kaneshina, S . J . Colloid Inferface Sci. 1980, 73, 124. (10) Harada, S.; Nakagawa, T. J. Solution Chem. 1979, 8, 267.
9118
The Journal of Physical Chemistry, Vol. 98, No. 37, 1994
(11) Herrigton, T. M.; Sahi, S. S.J . Chem. SOC.,Faraday Trans. 1 1985, 81, 2693.
(12) Nichols, N.; Skold, R.;Spink, C.; Suurkuusk, J.; Wadso, I. J . Chem. Thermodyn. 1976,8, 1081. (13) Cabani, T.; Gianni, P.; Mollica, V.; Lepori, L. J . Solution Chem. 1981, 10, 563. (14) Jha, R.;Ahluwalia, J. C. J . Surf. Sci. Technol. 1991, 7, 73. (15) Ginnings, D. C.; Furkawa, G. T. J . Am. Chem. Soc. 1953,75,552. (16) Van Miltenberg, J. C.; Vanden Berg, G. J. K.; Bommel, M. J. J . Chem. Thermodyn. 1987, 19, 1129. (17) McCullough, J. P.; Mwserly, J. F. Bur. Mines Bull. 1961, 596. (18) Dougles, T. B.;Furukawa, R.E.; McCloskey, R.E.; Ball, R. F. J . Res. Natl. Bur. Stand. 1954, 53, 139. (19) Picker, P.; Leduc, P. A,; Philip, P. R.; Desnoyers, J. E. J. Chem. Thermodyn. 1971, 3, 631.
Jha and Ahluwalia (20) Kell, G. S.J. Chem. Eng. Data 1967,1Z, 66. (21) Picker, P.; Tremblay, E.; Jolicoeur, C. J . Solution Chem. 1974, 3, 377. (22) Musbally, G. M.; Perron, G.; Desnoyers, J. E. Can. J. Chem. 1976, 54, 2163. (23) Suurkuusk, J.; Wadso, I. J. Chem. Thermodyn. 1974, 6, 667. (24) Olofsson, G. J . Phys. Chem. 1983, 87, 4000. (25) Andersson, B.;Olofsson, G. J . Chem. SOC.,Faraday Trans. I 1988, 84, 4087. (26) Corkill, J. M.;Goodman, J. F.;Tate, J. R.Trans. Faraday Soc. 1964, 60, 996. (27) Olofsson, G . J. Phys. Chem. 1985, 89, 1473.
