J . Phys. Chem. 1986, 90, 3038-3046
3038
neglected, so that uncondensed free ions can be treated in the Debye-Huckel approximation. As predicted by Manning's theory and in agreement with the experimental finding on various polyelectrolyte solutions, the equivalent conductivity of samples with divalent counterions is markedly less than that of solution with monovalent counterions. Our results confirm these indications both for CMC-I and CMC-I1 in BaCI, and CaCI, electrolyte solutions when compared with samples in NH4C1 solutions. The A values line up in the order A(NH4+) > A(Ba2+) > A(CaZ+) which reflects the limiting mobility of the counterions, according to the prediction of the counterion condensation theory. On the other hand, marked deviations from the calculated values occur for all the samples investigated, suggesting that there must be specific effects for each counterion owing to its strong interactions with the polymer anion. These interactions depend probably on hydration properties of ions rather than their charge on concentration, while the size would have little or no effect. This possibility remains to be investigated. Finally, the large discrepancy between the experimental and the calculated values for A in NH4-CMC must be noted. Similar deviations of NH4+ from the limiting law have also been obtained
by Eisenberg et aI.l9 in the fraction of free counterions for salts of polyvinylsulfonate thus suggesting that ammonium counterions behave differently from other monovalent cations. The general trend emerging from these results is that the Manning theory provides a qualitatively correct description of the equivalent conduction of rodlike polyelectrolytes, but, when counterions strongly interact with polyion, as in the case of Ca2+ or Ba2+, specific effects dependent on the ion properties must be taken into account. Moreover, the molecular weight of the polyion may affect the conductance, especially for polyions of relatively low charge density and low counterion concentration, when the coiling does not modify the macromolecular conformation. These indications may be of importance in the transport properties of different polyelectrolytes and would have to be taken into account in the development of more elaborate conductivity theories. Registry No. NH,-CMC, 9086-60-6; Ca-CMC, 9050-04-8; BaCMC, 64936-94-3; "&I, 12125-02-9; CaCI2, 10043-52-4; BaCI,, 10361-37-2. (19) Eisenberg, H.; Mohan Ram, G.; J . Phys. Chem. 1959, 63, 671.
Enthalpies of DHution of Aqueous Decyl-, Dodecyi-, Tetradecyl-, and Hexadecyltrimethylammmtum BromMe Sodium Bromide Solutions at I O , 25, 40, and 55 OC
+
Earl M. Woolley* and Michael T. Bashford Department of Chemistry, Brigham Young University, Provo, Utah 84602 (Received: December 1 1 , 1985; In Final Form: February 6, 1986)
We have measured enthalpies of dilution of aqueous solutions containing sodium bromide plus decyltrimethylammonium bromide, dodecyltrimethylammonium bromide, tetradecyltrimethylammonium bromide, and hexadecyltrimethylammonium bromide surfactants at 10, 25, 40, and 5 5 O C and at surfactant molalities ranging from well below to well above the cmc. The ratios of molalities of surfactant to sodium bromide were held constant at 1:l in order to facilitate extrapolation to infinite dilution in both solutes to the usual standard states. Enthalpies of dilution were also measured for tetradecyltrimethylammonium bromide at 40 O C with ratios of molalities of surfactant to sodium bromide of 1:3 and 1:9. A mass-action model that includes activity coefficients of all components in the solution was used to correlate and interpret the data. The data are compared with predictions based on enthalpy data for the two binary systems consisting of water + surfactant and of water + sodium bromide.
Introduction
In an earlier paper we reported a systematic study of enthalpies of dilution for a series of alkyltrimethylammonium bromides (TABS) in water.' In this paper we report a similar study for the slightly different systems: water TAB NaBr. Previous studies of the effects of added strong electrolytes on the thermodynamic properties of aqueous ionic surfactant solutions have usually involved measurements with a constant background concentration of the electrolyte. We have measured enthalpies
+
+
(1) Bashford, M. T.; Woolley, E. M. J. Phys. Chem. 1985,89, 3173. Note that a factor of 2 was inadvertently omitted from the second term in the right-hand side of eq 5 in this reference and in ref 7. This factor of 2 is correctly shown in the osmotic coefficient equation of the current paper and in ref 2-4. Also note that, in Table IV of this reference, should be - 4 ~ ~ .
0022-3654/86/2090-3038$01.50/0
of dilution of aqueous C10, C12, C14, and C16 TABS at 10,25, 40, and 55 OC with constant concentration ratios of surfactant to NaBr. This means that, as the surfactant is diluted, the electrolyte is also diluted. This makes possible the extrapolation to infinite dilution in all solute components, to the usual standard state. A mass-action model that includes the effects of activity coefficients to describe the thermodynamic properties of ionic surfactant solutions has recently been The enthalpy data in our previous study of aqueous TABS were analyzed by using this model, and the descriptive parameters for these twocomponent TAB water systems were determined.' The model
+
(2) Burchfield, T. E.; Woolley, E. M. J. Phys. Chem. 1984, 88, 2149. (3) Woolley, E. M.; Burchfield, T. E. J. Phys. Chem. 1984, 88, 2155.
0 1986 American Chemical Society
Enthalpies of Alkyltrimethylammonium Bromides
+ NaBr
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986 3039
TABLE I: Representative Values of the Enthalpies of Dilution of Aqueous DecyltrimethylammoniumBromide and NaBr 25 OC 10 OC 40 "C 55 1OOOm, mol/kn
-68 -3 1 4 35 72 109 152 197 257 557 1007 1404 1753 2037 2276 2479 2653 2799 2925 3033 3127 3208 3279 3336 3388 343 1 3468 3502 3530 3555 3574 3591 3603
9.58 15.49 21.34 27.12 32.85 38.52 44.13 49.68 55.17 60.61 66.00 71.33 76.61 8 1.84 87.02 92.14 97.22 102.24 107.22 112.15 117.04 121.87 126.66 131.41 136.11 140.77 145.39 149.96 154.49 158.98 163.43 167.83 172.20
mol / kg
J/mol
1OOOrn, mol/kg
J / mol
9.26 15.16 21.00 26.77 32.48 38.14 43.74 49.28 54.76 60.19 65.57 70.89 76.15 81.37 86.53 9 1.65 96.71 101.73 106.69 111.61 1 16.48 121.31 126.09 130.82 135.51 140.16 144.76 149.32 153.84 158.32 162.75 167.15 171.51
3879 3968 4067 4135 4200 4267 4336 4404 4498 4596 4649 4690 4693 4692 4684 4668 4649 4623 4601 4573 4546 4517 4486 4459 4427 4396 4368 4337 4308 4277 4250 4219 4190
9.32 15.26 21.13 26.94 3'2.69 38.38 44.01 49.58 55.10 60.56 65.96 71.31 76.61 8 1.85 87.05 92.19 97.28 102.32 107.31 112.26 117.16 122.01 126.8 1 131.57 136.28 140.95 145.58 150.16 154.70 159.20 163.65 168.07 172.45
7669 7863 7946 8068 8113 8201 8293 8363 843 1 8289 8032 7156 7485 7246 7022 6820 6632 6460 6305 6162 6027 5902 5785 5678 5575 5480 5389 5305 5226 5147 5078 5005 4939
1000rn,
Mdil,
J/mol
AHdil,
M d i b
oc
~~
1OOOrn, mol/kg
J/mol
9.70 15.67 21.58 27.43 33.22 38.95 44.62 50.23 55.78 61.28 66.72 72.10 77.43 82.71 87.94 93.1 1 98.23 103.31 108.33 113.30 118.23 123.11 127.94 132.72 137.46 142.16 146.81 151.42 155.98
11092 11249 11422 11565 11632 11717 11800 11899 11944 11904 11578 11129 10643 10192 9774 9389 9036 8714 8425 8160 7913 7682 7479 7284 7099 6935 6778 663 1 6493
AHdiI,
Initial Surfactant Concentration, NaBr Concentration, mol/kg 1.1361, 1.1375
1.1310, 1.1351
1 7 500 I
1.1310, 1.1328 200
I
i
B E
0
: .-- 7 500
m < -200
S
w I -
-*
-Y
a
2 500
-2 500 0.000
1.1323, 1.1357
-400
0.015
0.030
0.045
0.060
rn. rnol/kg
-600doo
\ 0.015
0.030
0.045
J 0.060
rn. mol/kg
Figure 1. Enthalpies of dilution of equimolal dodecyltrimethylammonium bromide + sodium bromide solutions at 10 OC (n),25 OC (+), 40 OC (*), and 55 OC (A). The solid lines are least-squares fits using eq 14 with the parameters in Table VII.
Figure 2. Excess enthalpies of equimolal dodecyltrimethylammonium bromide + sodium bromide solutions at 10 OC ( O ) , 25 OC (+), 40 OC (*), and 55 'C (A). The solid lines are least-squares fits using eq 13a with the parameters in Table VIII.
has also been extended to include the description of activity coefficients and enthalpies for three-component systems of the type discussed in this papers4' In the current paper we will use this extended model to analyze our measured enthalpy data for the CIO, C12, C14, and C16 TAB NaBr +water systems. Our data present an interesting test of the versatility and limitations of the mass-action model.
viously reported methods.'V6 Decyltrimethylammonium bromide (Kodak, Lot AlOF) and dodecyltrimethylammonium bromide Kodak, Lot A9F) were recrystallized three times from acetone. Tetradecyltrimethylammonium bromide (Research Plus) was recrystallized twice from acetone. Hexadecyltrimethylammonium bromide (Fisher, Lot 716090) was crystallized three times from a mixture of acetone and less than 5% methanol. The recrystallized surfactants were washed twice with ethyl ether and dried in a vacuum oven at 60 O C prior to use. Sodium bromide (Allied Chemical, Reagent) was used as supplied. Solutions were prepared by weight with distilled water and used the same day.
+
Experimental Section Materials. The surfactants were purified before use by pre(4) Woolley, E. M.; Burchfield, T. E. Fluid Phase Equilib. 1985,20,225. ( 5 ) Burchfield, T. E.; Woolley, E. M. In Surfactants in Solution; Mittal,
K. L., Botheral, P., Eds.; Plenum: New York, in press.
(6) DeLisi, R.; Ostiguy, C.; Perron, G.; Desnoyers, J. E. J . Colloid Interface Sei. 1979, 71, 147. (7) Woolley, E. M.; Burchfield, T. E. J . Phys. Chem. 1985, 89, 714.
3040 The Journal of Physical Chemistry, Vof.90, No. 13, 1986
Woolley and Bashford
TABLE II: Representative Values of the Enthalpies of Dilution of Aqueous DodecyltrimethylnmmoniumBromide and NaBr 10 o c
25 O C
40 O C
55
oc
1OOOm, mollkg
J/mol
1OOOm, mollkg
J/mol
1OOOm, mollkg
AHdil, J/mol
1OOOm, mol/kg
J/mol
2.81 4.66 6.48 8.28 10.06 11.82 13.56 15.28 16.98 18.66 20.32 21.97 23.59 25.20 26.79 28.36 29.91 3 1.45 32.97 34.47 35.96 37.43 38.88 40.33 41.75 43.16 44.56 45.94 47.31 48.66 50.00 5 1.32 52.64
-1621 -1589 -1566 -1533 -1481 -1435 -868 -289 168 507 788 99 1 1164 1303 1412 1503 1577 1643 1694 1733 1768 1799 1824 1838 1855 1865 1875 1881 1885 1891 1891 1890 1889
3.00 4.85 6.67 8.48 10.26 12.02 13.76 15.48 17.18 18.86 20.52 22.16 23.79 25.40 26.98 28.56 30.1 1 3 1.65 33.17 34.67 36.16 37.63 39.08 40.52 41.95 43.36 44.76 46.14 47.50 48.86 50.20 5 1.52 52.83
4612 4683 4755 4855 4919 4952 473 1 4500 4285 4108 3961 3820 3697 3590 3488 3398 3310 3232 3160 3096 3035 2979 2924 2872 283 1 2780 2741 2700 2659 2621 2589 2551 2521
2.93 4.79 6.62 8.44 10.23 12.00 13.75 15.49 17.20 18.89 20.56 22.22 23.85 25.47 27.06 28.65 30.21 3 1.75 33.28 34.80 36.29 37.77 39.24 40.69 42.12 43.54 44.94 46.33 47.71 49.07 50.41 51.75 53.07
9984 10211 10424 10509 10590 10685 10131 9194 8394 7702 7154 6668 6259 5902 5596 5313 5073 4859 4667 4494 4335 4190 4058 3937 3823 3716 3624 3538 3450 3370 3299 3225 3157
3.03 4.89 6.73 8.55 10.35 12.13 13.88 15.62 17.33 19.03 20.70 22.36 24.00 25.62 27.22 28.80 30.37 31.92 33.45 34.96 36.46 37.94 39.41 40.86 42.30 43.72 45.12 46.52 47.89 49.25 50.60 51.94 53.26
15144 15498 15609 15754 15914 15979 16021 15054 13726 12490 11468 10608 9843 9192 8643 8134 7725 7312 6971 6656 6378 61 10 5892 5672 5476 5289 5121 4970 4825 4689 4566 4447 4339
AHdii.
AHdil,
Initial Surfactant Concentration, NaBr Concentration, mol/ka I
0.3117, 0.3118
0.3113, 0.3114
,
1 7 500 1
-
0.3120, 0.3121
0.3119, 0.3121
12 500
i
10 000
500
1
7 500
5
50 0
$
5
000
a 2 500 500
i -* 5 0 8I .~~ 0
9 0000
0.015
0.030
0.045
0.0' 6 0
0.05
rn. mol/kg
Enthalpies of dilution of equimolal dodecyltrimethylammonium bromide + sodium bromide solutions at 10 O C ( O ) , 25 O C (+), 40 O C (*), and 55 "C (A). The solid lines were obtained via eq 14 with the least-squares parameters from eq 13a given in Table VIII.
F i g u r e 3.
Equipment and Procedure. Enthalpies of dilution were measured by using a Tronac 450 isoperibol calorimeter with a Tronac 1040 temperature controller, interfaced to an Apple IIe computer. Details of the buret injection system, data collection system, experimental prwedure, and calibration methods were identical with those described earlier.' W e estimate that the total calorimetric uncertainty in measured heats during our dilution experiments is less than *0.05 J. Solutions of aqueous NaBr were also prepared and diluted a t 25 and 40 OC. These enthalpy data were used subsequently, along with data from the literature,'** (8) Pitzer, K. S.; Brewer, L. Thermodynamics, 2nd ed.; McGraw-Hill: New York, 1961 (revision of: Lewis, G. N.; Randall, M. Thermodynamics, 1st
ed.).
0.10
0.15
0.20
rn, mol/kg
Figure 4. Enthalpies of dilution of equimolal decyltrimethylammonium bromide + sodium bromide solutions at I O O C (a), 25 O C (+), 40 O C (*), and 5 5 O C (A). The solid lines are least-squares fits using eq 14 with the parameters in Table VII.
in the interpretation of the enthalpy data for the ternary water + TAB + NaBr systems. Model. The derivation of the mass-action model which we have used to describe the thermodynamic properties of aqueous ionic surfactant solutions has been given in detail elsewhere.*' Application of the model to activity coefficients of aqueous ionic surfactant solutions containing an added strong 1: 1 electrolyte has also recently been d i s c u ~ s e d .This ~ ~ ~extension involves the inclusion of terms to account for the added electrolyte in the fundamental equations as summarized in eq 1-9.
n@M*
+ nAi
= MnBAnTn(l-B)
(1)
Enthalpies of Alkyltrimethylammonium Bromides
+ NaBr
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986 3041
TABLE III: Representative Values of the Enthalpies of Dilution of Aqueous Tetradecylbimethylamnmonium Bromide and NaBr with m,/m = 1 10 o c 1OOOm, mol/kg 0.89 1.47 2.05 2.62 3.18 3.74 4.29 4.83 5.37 5.90 6.42 6.94 7.45 7.95 8.45 8.95 9.43 9.92 10.39 10.87 11.33 11.79 12.25 12.70 13.15 13.59 14.03 14.46 14.89 15.31 15.73 16.14 16.55
25 O C 1000m, mol/kg 1.02 1.67 2.31 2.94 3.56 4.18 4.79 5.39 5.99 6.57 7.15 7.73 8.29 8.85 9.41 9.96 10.50 1 1.03 11.56 12.09 12.60 13.12 13.62 14.12 14.62 15.11 15.59 16.07 16.55 17.02 17.48 17.94 18.39
AHdiI,
J / mol 21 68 186 217 590 867 1041 1218 1363 1484 1565 1629 1705 1744 1768 1791 1809 1826 1862 1860 1851 1865 1855 1847 1837 1825 1818 1800 1786 1768 1757 1736 1720
,
40 O C Mdil,
J/mol 7845 7960 81 10 7965 6865 6079 5448 4985 4576 4278 4003 3780 3596 3432 3279 3155 305 1 2974 2867 2799 2715 2660 2598 2534 2482 243 1 2384 2333 2290 2240 222 1 2179 2146
1OOOm, mol/kg 0.92 1.51 2.09 2.66 3.22 3.78 4.33 4.87 5.41 5.94 6.46 6.98 7.50 8.00 8.50 9.00 9.49 9.97 10.45 10.92 11.39 11.85 12.31 12.76 13.20 13.65 14.08 14.52 14.94 15.37 15.79 16.20 16.61
55
Initial Surfactant Concentration. NaBr Concentration. mol/ka 0.1051, 0.1041 0.09442, 0.09417 I
0.09467, 0.09406
1OOOm, mol/kg 0.93 1.52 2.10 2.68 3.24 3.81 4.36 4.91 5.45 5.98 6.51 7.03 7.55 8.06 8.56 9.06 9.55 10.04 10.52 10.99 11.46 1 1.93 12.39 12.84 13.29 13.74 14.18 14.61 15.04 15.47 15.89 16.30 16.72
Mdil,
J/mol 15040 15473 15543 15630 15197 13102 11365 10072 9065 8247 7556 6973 6487 6020 5690 5388 5120 4880 4664 4469 4283 4113 3980 3835 3716 3618 3488 3424 3340 3248 3174 3081 3033
oc AHdiI, J/mol 21697 22013 21886 22 168 22020 21303 18377 16181 14304 12862 1 1667 10659 9763 9019 8368 7822 7415 6950 6532 6221 5916 5637 5422 5204 4945 4797 4605 4443 4275 41 17 4049 3906 3787
-
0.09445, 0.09469
2 0 000
i
20 000
000
1 6 000
'ij 1 2
E
000
3
000
5
h
a ooo
000 4 000
0
I
0.005
0.010
0.015
0.020
0.005
rn. rnol/kg
Figure 5. Enthalpies of dilution of equimolal tetradecyltrimethylammonium bromide sodium bromide solutions at 10 O C ( O ) , 25 OC (+), 40 O C (*), and 55 O C (A). The solid lines are least-squares fits using eq 14 with the parameters in Table VII.
+
0.010
0.015
0.020
m. rnol/kg
+
Figure 6. Enthalpies of dilution of sodium bromide tetradecyltrimethylammonium bromide solutions at 40 O C and at molality ratios m,/m = 0 @),I 1 (+), 3 (*), and 9 (A). The solid lines are least-squares fits using eq 4 with the parametefs in Table VI1 (ref 1 for m,/m = 0).
r = 1 + m,/m I = {[nS2(1- P)2 - @ - 1 1 .
a b ) = 3[1 + y - 1 / ( 1
(7)
+ 2r)m/2
+ y ) - 2 In ( 1 + y ) ] / y 3
(8) (9)
In eq 1-9, m is the stoichiometric molality of surfactant, MA, and m, is the stoichiometric molality of the added strong 1 : l electrolyte, MX. These equations also include a new term, Bxy, which represents the Br~msted-Guggenheiminteraction coefficient for the ions M*:XT. The new term, r, is defined in terms of m, and m in eq 7 . All other symbols are the same as those used in the original fundamental equation^.^-^ The excess free energy, GE,is defined in the traditional manner in terms of the mean ionic activity coefficients and the osmotic coefficient in eq 10, where M , is the molar mass of the solvent.
3042
Woolley and Bashford
The Journal of Physical Chemistry, Vol. 90, No. 13, I986
TABLE IV: Representative Values of the Enthalpies of Dilution of Aqueous TetradecyltrimethylammoniumBromide and NaBr with m,/m = 3 and 9 at 40 OC mJm = 2.9874 m,/m = 8.9254 1OOOm, mol/kg 0.94 1.54 2.13 2.71 3.28 3.85 4.41 4.96 5.51 6.05 6.59 7.11 7.63 8.15 8.66 9.16 9.66 10.15 10.64 11.12 11.59 12.06 12.53 12.99 13.44 13.89 14.33 14.77 15.21 15.64 16.06 16.48 16.90
iw,il,
J/mol 15585 15665 15854 14105 11431 9472 8160 7249 6495 5932 5451 5088 4792 4490 4239 4070 3862 3734 3619 3491 3366 3277 3197 3101 3027 2974 2885 2841 2794 2720 268 1 2622 2589
1OOOm, mollkg 0.94 1.57 2.20 2.81 3.42 4.03 4.62 5.21 5.79 6.36 6.92 7.48 8.03 8.58 9.1 1 9.64 10.17 10.69 11.20 11.71 12.21 12.70 13.19 13.67 14.15 14.62 15.09 15.55 16.01 16.46 16.90 17.34 17.78
TABLE V: Representative Values of the Enthalpies of Dilution of Aqueous Hexadecvltrimethvlammonium Bromide and NaBr 55 o c 40 OC 1000m, mol/kg 0.36 0.62 0.87 1.11 1.36 1.60 1.84 2.07 2.31 2.54 2.76 2.99 3.21 3.43 3.65 3.86 4.07 4.28 4.49 4.69 4.89 5.09 5.29 5.49 5.68 5.87 6.06 6.25 6.43 6.62 6.80 6.98 7.15
udil,
J/mol 16128 16580 12645 9881 8297 7396 6741 6336 5989 5712 5555 5390 5264 5148 509 1 5006 4932 4896 4841 4817 4744 4724 4687 4654 4619 4620 4586 4574 4558 4516 4506 4476 447 1
AHdil, J/mol 27649 28189 28318 26857 22558 19333 16749 14869 13296 12182 11114 10354 9515 8969 8495 7918 7558 7141 6765 6470 6244 5957 5772 5490 5265 5092 4897 4814 4577 4479 4358 4214 4106
1000m, mol/kg 0.48 0.79 1.10 1.41 1.71 2.00 2.30 2.59 2.88 3.16 3.44 3.72 3.99 4.26 4.53 4.79 5.05 5.31 5.57 5.82 6.07 6.31 6.56 6.80 7.04 7.27 7.51 7.74 7.97 8.19 8.41 8.64 8.85
Initial Surfactant Concentration, NaBr Concentration, mol/kg
Initial Surfactant Concentration, NaBr Concentration, mollkg 0.09497,0.2838
AHdih J/mol 21831 21523 19376 14890 12057 9864 8412 7392 6378 5667 5145 4609 4179 3778 3530 3286 2998 2805 2630 2470 2363 2208 21 19 2036 1941 1885 1785 1783 1676 1590 1578 1470 1462
0.04052, 0.04015
0.04049, 0.04014
0.09687.0.8646
+
G E / R T = 2m In (yIMA) 2m, In (Y*MX) - 2mr4 (1000/M,) In ((lOOO/M,)/[(lOOO/Ml) m m,]) (10)
+ +
TABLE VI: Values of the Parameters for NaBr Used in Fitting Enthalpy Data with Eq 13 and 14"
Application of the defining equation for the excess enthalpy, HE,given in eq 11 to eq 10 gives eq 12 directly. HE = - p [ a ( G E / V / a q ,
T, O C 10 25
B,,, kg/mol (0.136) 0.152d
40
(0.163)
55
(0.169)
(11)
(dB,,/dT),,* kg/(mol K) (0.001 200) 0.000882 10.000 043 0.000564 10.000 044 (0.000246)
RMSD,'
m, mol/kg final
J/mol
initial
6.5
0.9417
5.6
0.9243 0.002-0.16
0.002-0.17
"Values in parentheses were calculated or extrapolated. *The 1 values are the standard deviations. cRoot-mean-squaredeviation in the fit of NaBr enthalpy data as explained in the text. "Obtained from ref 8.
AHdil= -4Lt + k,,
+ kLLAHa+ klL(dBly/dT)p+ kr.L(aB",/aT),
+ kxL(aBXy/aT)p (14)
These equations can be applied to the same enthalpy of dilution data in order to obtain the fundamental parameters: AH", (aBl,/aT)p, (6Bn,/aT)p, and (aB,,/aT),. Treatment of data by eq 13a tends to give more weight to enthalpy data corresponding to high molalities, whereas treatment of data by eq 14 tends to give more weight to enthalpy data corresponding to low molalities. The coefficients qij in eq 13a are explicit functions of m ,m,,K , a,n, @, b, 6,A,, BIT,Bq, Bxy,and T. The coefficients kij are equal to the coefficients qij divided by m. The second term in eq 13a and the third term in eq 14 result directly from the derivative (a In KIBT),. The quantity dLtis the relative apparent molar en-
thalpy of the initial solution, and AHdilis the experimentally determined integral enthalpy of diluting the initial surfactant + NaBr solution to final molalities m and m,. Equations 13a and 14 are of the form of the equation for dL for aqueous ionic surfactants derived earlier,3 but they include the additional parameter (aB,,/aT),. One can use eq 13a or 14 to predict or AHdilfor the ternary system H 2 0 M A + MX by using the enthalpy parameters obtained from the binary systems H,O MA and HzO + MX.
+
+
Results and Discussion All experiments except those with hexadecyltrimethylammonium bromide were done in triplicate. As the hexadecyltrimethylammonium bromide solutions are cooled to near room temperature the surfactant precipitates, allowing time for only duplicate runs and making it impossible to make measurements at all at 10 and 25 "C. All surfactants were studied with a 1:l ratio of concentrations of surfactant to NaBr. In addition, tet-
Enthalpies of Alkyltrimethylammonium Bromides
+ NaBr
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986 3043
TABLE VII: Parameters for Eq 14 for TABS + NaBeb
w,/a
Moln,
4L',
qp,e
RMSD,~ Jlmol
T, O C
m,lm
10 40 55
1.0012 1.0036 1.0016 1.0030
J/mol J / mol DecyltrimethylammoniumBromide (n = 36,/3 = 0.73)l 7714 f 219 163 471 f 9 1 64c -3 553 f 74 2 142 f 448 -7 139 f 139 -3745 f 130 160 158 -10416 27 -6778 f 378
0.231 f 0.021 0.207 f 0.027 0.098 f 0.010 0.146 f 0.025
25 47 29 33
10 25 40 55
1.0003 1.0003 1.0003 1.0006
Dodecyltrimethylammonium Bromide (n = 52,@ = 0.77)' 375 1878 f 21 6831 f 94 1.135 f 0.035 -2366 f 37 0.433 0.021 369 -4378 f 28 367 -9905 f 41 -10360 f 54 358 -15 029 f 67 -16999 f 48
17 24 66 75
10 25 40 40 40 55
0.9936 0.9905 0.9979 2.9874 8.9254 1.0025
TetradecyltrimethylammoniumBromide (n = 70,/3 = 0.80)I 695 80 f 153 3212 f 81 2.96f 0.46 687 -7770 f 78 -7398 f 88 -0.18 f 0.11 -17634 f 192 -2.41 f 0.40 678 -15066 f 215 678 -15092 t 212 -18 932 f 297 -1.69 f 0.16 681 -14017 f 299 -17 924 f 462 0.27 f 0.04 657 -21 688 f 137 -27013 f 193 -3.43 f 0.25
40 55
0.9909 0.9914
25
kn/(mol K)
In K
*
*
38 36 65 111 203 82
Hexadecyltrimethylammonium Bromide ( n = 87,6 = 0.84)' 1077 -21 268 f 190 -26 742 f 205 -19.0 f 0.8 1036 -28 172 f 170 -37065 f 500 -27.1 f 1.0
134 310
'Values of (aB,,/ar), are zero at the 95% confidence interval for this fit. bThe f values given are the standard deviations. See discussion in ref 1. cValues of parameters not given are zero at the 95% confidence limit. dRoot-mean-squaredeviation of the fit to eq 14. eValues were calculated at a K value consistent with other values. The data show very little break near the cmc. See ref 1. 35 000
28
ooo
2
rn
+ " +
2 000
i
'0°
t
--- I
"
'
"
+ * 0
1
'
+
*
1
A
I
-a ooo v
X
I
a
-10 000
in. rnol/kg
Figure 7. Enthalpies of dilution of equimolal hexadecyltrimethylammonium bromide + sodium bromide solutions at 40 O C (*) and 55 OC (A). The solid lines are least-squares fits using eq 14 with the parameters in Table VII.
Figure 8. Differences between M 0 / n values obtained in sodium bromide solutions (Table VII) and in water (ref 1) for decyl- (+); dodecyl- (*); tetradecyl- at m,/m = 1 ( O ) , 3 (A), and 9 (0); and hexadecyltrimethylammonium bromide (X).
radecyltrimethylammonium bromide was studied at 40 OC with surfactant to NaBr concentration ratios of 1:3 and 1:9. Tables I-V contain representative data for each of the four surfactants at each temperature. The enthalpies of dilution, m d i l (J/mol of surfactant), given in these tables are for the process of diluting the initial solution (composition given at the bottom of the table) to the indicated final surfactant molalities, m . Enthalpies of dilution of 0.9 m aqueous NaBr solutions were also measured in triplicate at 25 and 40 OC. Treatment of these data using a form of eq 14 valid for a strong 1:l electrolyte (K = 0, a = 0, A P = 0) leads to the values of Bxy and (aB,,/aT), given in Table VI. The value of Bxy = 0.152 kg/mol for NaBr at 25 OC was taken from ref 8. Our average value of (aB,/aT), = 0.000882 kg/(mol K) at 25 "Ccompares well with values from ref 8 that range from 0.00100 to 0.00070kg/(mol K) in the range of molalities of our data. Furthermore, one can estimate (a2Bxy/aF'),= -2.1 x kg/(mol K2) from our values of (aBx,/aT) at 25 and 40 OC. This value compares with the ( a 2 B X , / a f i )values , from ref 8 that range from -3.7 X to -2.4 X kg/(mol K2) at 25 OC and in the range of molalities of our data. The values of n, & 6, BI,, Bm, b, and the Debye-Huckel constants A , and At used in all the calculations for this paper are the same as those used in our earlier studv of the enthaluies of the binary water + TAB systems.I
With the two-component aqueous ionic surfactant systems previously studied, we have fit an equation equivalent to eq 14 to experimental enthalpy data.1*3*4v7 In order to apply eq 13a, one effectively fits (mAHdil)vs. m . This procedure thus gives very little weight to enthalpy data at small m. Consequently, it is possible to obtain a rather poor representation of m d i l data at low m (in the premicellar region) when eq 13a is used. This representation gets much worse for surfactants with very low cmc values, as expected. On the other hand, the use of eq 14 to fit AHdilvs. m tends to provide a better representation of the data at low m, since it weights every value of AHa equally. The above points are illustrated in Figures 1-3 with parameters obtained by fitting eq 13a and 14 to data for the dcdecyltrimethylammonium bromide sodium bromide systems. Another factor had to be considered when we began to analyze the data using either eq 13a or eq 14. We have available to us six fitting parameters: K,$Lt, W ,(aBIy/aT),,(aB,/aT)p, and (aBXy/aT),.The behavior of the added electrolyte I S described by (aB,,/aT),, and it seems reasonable to fix that parameter to the values in Table VI obtained from our experimental data and from the literature.* Because there are very few premicellar data and also because the magnitude of (aBl,/a7'), is very small,'^' we have set this parameter either to zero or to the values obtained previously from ihe twc-component aqueous surfactant data.' This leaves the four remaining parameters, which we have used to fit
.
+
3044 The Journal of Physical Chemistry, Vol. 90, No. 13, 1986
Woolley and Bashford
TABLE VI11 Parameters for Eq 13a for TABS + NaBr"
4L',
AHo/n,b (aBl,/ar),,b J/mol kg/(mol K) Bromide (n = 36, P = 0.73)' 6453 -0.003 5 1858 -0.0070 -3 188 -0.0048 -6944 -0.0033
(aBn-,/anp kg/(mol K)
RMSD,C J/kg
0.117 f 0.004 0.147 f 0.007 0.1 14 f 0.005 0.1 15 f 0.005
5.3 5.2 3.9 4.5
0.593 f 0.029 0.659 0.009 0.753 f 0.049 0.982 i 0.061
2.4 1.6 4.5 6.5
Tetradecyltrimethylammonium Bromide (n = 70, = 0.80)' -304 f 140 2764 0 -6486 f 128 -4954 0 -12417 0 -12970 f 279 -11500 f 141 -12417 0 -9856 f 195 -12417 0 -19489 f 324 -19686 0
2.85 f 0.46 1.66 f 0.25 2.29 f 0.45 0.24 f 0.20 0.63 f 0.04 3.33 f 0.44
0.4 1.3 2.6 2.5 1.5 3.8
Hexadecyltrimethylammonium Bromide (n = 87, @ = 0.84)I -16968 f 1475 -17994 0 -24658 f 2500 -26909 0
of d
2.7 4.0
T, "C
mx/m
In K
10 25 40 55
1.0012 1.0036 1.0016 1.0030
163 164d 165 160
10 25 40 55
1.0003 1.0003 1.0003 1.0006
376 377 372 362
Dodecyltrimethylammonium Bromide (n = 52, = 0.77)I 1574 f 44 5145 -0.0045 -3771 f 17 -1473 -0.01 37 -8788 f 102 -7532 -0.0175 -14059 f 7 -13120 -0.01 11
10 25 40 40 40 55
0.9936 0.9905 0.9979 2.9874 8.9254 1.0025
677 676 674 667 663 657
40 55
0.9909 0.9914
1070' 1035e
J/mol Decyltrimethylammonium 860 f 36 -2368 f 19 -6390 f 128 -9807 f 87
*
The f values given are standard deviations. See discussion in ref 1. These values are taken from ref 1. e Root-mean-square deviation of the fit to eq 13a. "Values were calculated at a K value consistent with other values for this surfactant. The data show very little break near the cmc. See ref 1. eValues were calculated at a K value adjusted to be consistent with those for the other surfactants in this table when compared with K values given in ref 1. There is no minimum in a curve of RMSD vs. In K for these data because of the small number of premicellar data. JValues of (dB,,/dT), are zero at the 95% confidence interval for this fit.
TABLE I X Effects of Changing n and 6 on the Parameters for Eq 14 for DodecyltrimethylammoniumBromide T , "C 10
25
40
55
n
P
52 67 52 67 52 67 52 67 52 67 52 67 52 67 52 67
0.77 0.77 0.82 0.82 0.77 0.77 0.82 0.82 0.77 0.77 0.82 0.82 0.77 0.77 0.82 0.82
In K 375 485 387 500 369 477 381 493 367 473 379 489 358 46 1 369 477
&Lt,
AHo/n,
J/mol 1862 1871 1865 1862 -4386 -4390 -4387 -4389 -9880 -9875 -9888 -9873 -1 5065 -1 5046 -1 5029 -15045
J/mol 6 869 6 685 7 203 7 139 -2 338 -2 281 -2 370 -2 327 -10 375 -10379 -10796 -10792 -16999 -16971 -17 778 -17710
+ Sodium
1.15 1.43 1.17 1.50 0.44 0.62 0.46 0.63
RMSD,d Jlmol 16 15 11
11 24 25 26 27 69 75 14 76 76 79 81 86
"These parameters are for the data in Table 11. bValues of (dBl,/aT)p are zero at the 95% confidence interval for this fit. CValuesof parameters not given are zero at the 95% confidence interval. dRoot-mean-square deviation of the fit to eq 14.
eq 14 to the data. The value of K is chosen so that the function described by eq 14 "breaks" at the c ~ c . ~ . ~The , ~ values ,' of K and AHo should be the same as they were in the binary aqueous surfactant systems at each temperature for each surfactant if the model is to give a completely true representation of the binary and ternary systems. Table VI1 contains the results of fitting eq 14 to all our data by using the four parameters K,$ J ~AHo, ~ , and (aB?,/a n p . Figures 1 and 4-7 show AHdildata and the lines obtained from the fitting parameters given in Table VII. As can be seen from those figures and from the values of the root-mean-square deviations (RMSD) in Table VII, the parameters in Table VI1 represent the experimental enthalpy data very well. However, when we compare the parameters in Table VI1 with those obtained from the binary TAB + water data in our previous paper,' an apparent inadequacy in the model becomes apparent. According to the mass-action model, A H o / n should not change for a given surfactant at a given temperature, even in the presence of an added electrolyte. However, as shown in Figure 8, the values of A H o / n obtained from enthalpy data for a given TAB in the presence of added NaBr are generally somewhat different from corresponding
values of A H o / n obtained from enthalpy data for the same surfactant in the absence of NaBr. Others have previously reported a decrease in AH/n for micelle formation of decyltrimethylammonium bromide in the presence of NaBr as the temperature is increased, relative to decyltrimethylammonium bromide in the absence of NaBre9 The differences illustrated in Figure 8 are probably the result of some of the simplifying assumptions we initially made when deriving eq 13 and 14.*v3 (1) Only one micellar aggregate can exist in a given surfactant solution. (2) The stoichiometry of that aggregate ( n and 8) is fixed under all conditions of a given experiment ( T , P, m, mJ. (3) The Br~nsted-Guggenheimequations for activity coefficients, and the resultant equations derived for enthalpies, are adequate to describe the ion-ion and ionsolvent interactions not attributable to formation of micelles. The analysis of experimental data with a model based on these three simplifying assumptions was justified earlier.2s3 Although a multiple-equilibrium model is recognized as being a more nearly (9) Espada, L.; Jones, M. N.; Pilcher, G.J . Chem. Thermodyn. 1970, 2, 1.
Enthalpies of Alkyltrimethylammonium Bromides 1 0 000
+ NaBr
The Journal of Physical Chemistry, Vol. 90, No. 13, I986 3045
1
TABLE X: Values of AH*/n Valid at the erne’ mx! cmc,b.c AH*/n, J/mol
~~~
T,‘C
J
--______--------
E : I
-_____-_------
a -10 000
10 25 40 55 10 239
-20
0.015
0.030
0.045
0.080
Figure 9. A H / n for dodecyltrimethylammonium bromide from eq 15 with the parameters from Table VI1 for NaBr solutions (solid lines) and from ref 1 for pure water solutions (broken lines).
correct description of micelle formation, the simplicity of a single equilibrium model permits the inclusion of activity coefficients for each species and the subsequent application of rigorous thermodynamic definitions. One is not permitted to allow for variation of n and /3 with temperature and/or pressure when one uses our rigorous singleequilibrium model, since this creates a thermodynamic inconsisten~y.~ Furthermore, we have already shown that if one chooses to ignore self-consistency by letting n and /3 change with temperature and/or pressure in the single-equilibrium model, there is only a very small effect on the derived thermodynamic quantities AHo/n, A P / n , and ACpQ/m3There is also evidence that n and /3 can change significantly upon addition of larger amounts of added strong e l e ~ t r o l y t e . ~ “ -However, ~~ at the rather low concentrations of surfactant and added strong electrolyte we report in this paper, it is unlikely that n and /3 change very much. Even so, we have tested our eq 13 and 14 with significantly larger values of n and p to determine the effects that changing these quantities have on our least-squares parameters in Tables VI1 and VIII. The results of this analysis using eq 14 are illustrated in Table IX for dodecyltrimethylammonium bromide NaBr data. The differences in A H o / n are not enough to explain the trends seen in Figure 8, nor are they sufficient to justify the inclusion of significantly smaller n values at higher temperatures as recent measurements suggest.*O The general decrease in the differences in W / n seen in Figure 8 indicates that ACpo/nfor formation of micelles is more negative in the added strong electrolyte solutions than it is in water. This could possibly indicate that (a) the micelles are more extensively hydrated in pure water than they are in the salt solution and/or (b) the monomeric surfactant is more extensively hydrated in the salt solution than it is in pure water. Measurements of heat capacities of surfactant solutions containing added strong electrolytes will be useful in helping to resolve the cause of the trends seen in Figure 8. When we used eq 13a to fit the data, we found that fewer of
+
(IO) Gelbart, W. M.; Ben-Shaul, A.; McMullen, W. E.; Masters, A. J. Phys. Chem. 1984,88,861. McMullen, W. E.; Gelbart, W. M.; Ben-Shaul, A. J. Phys. Chem. 1984.88.6649. (11) Porte, G. J. Phys. Chem. 1983, 87, 354.1. (12) Porte, G.; Appell, J. In Surfacfants in Solution; Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1984; Vol. 2, p 805. (13) Candau, S. J.; Hirsch, E.; Zana, R. J. Phys. (ksLrlis, Fr.) 1984,45, 1263. (14) Liana, P.; Lang, J.; Zana, R. J. Colloid InterfaceSci. 1983, 91, 276. (15) Ikeda, S . In Surfactants in Solufion;Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1984; Vol. 2, p 825. (16) Ozeki, S.; Ikeda, S . J. Colloid Interface Sci. 1982, 87, 424. (17) Mazer, N. A,; Benedek, G. B.; Carey, M. C. J. Phys. Chem. 1976, 80, 1075. (18) Vold, M. J. Langmuir 1985, I , 501. (19) NBgele, G.; Klein, R.; Medina-Noyola, M. J. Chem. Phys. 1985,83, ~
eq 15 Bromide 5 938 217 -5 358 -9 496
Dodecyltrimethylammonium Bromide 0.0120 0.0120 5 497 e (0.0175) (0.050) e (0.100) e 0.0130 0.0130 -3 140 (0.0175) 0.0104 (0.023) 0.0093 (0.050) 0.00656 (0.100) 0.00434 e (0.0175) (0.050) e (0.100) e 0.0130 0.0130 -10643 0.0145 0.0145 -17 383
1
oaoooo
rn. mol/kg
2
mol/kg mol/kg Decyltrimethylammonium 0.05401054 0.055 0.055d 0.060 0.060 0.063 0.063
.
(20) Malliaris, A,; Le Moigne, J.; Sturm, J.; Zana, R. J . Phys. Chem. 1985, 89, 2709.
25 259.21
309 40 55 10 25 40 55 252223
40 55
lit.
-67g9 -9009 -1 2259 -15829 -16322‘ -1 8499 -20549 -39209 -400g9 -4 1429
Tetradecyltrimethylammonium Bromide 0.0027 0.0027 2 601 0.0029 0.0029 -7 480 0.0032 0.0032 -17 229 0.0024 -1 8 406 0.0072 0.0143 0.0016 -18409 0.0037 -26 094 0.0037 Hexadecyltrimethylammonium Bromide (0.002) (0.000409) (0.005) (0.000230) (0.05) (0.0001 24) 0.00082f (0.001)’ 0.00049/ (0.010)’ 0.00023/ (0.100)’ 0.00082 -25 697 0.00082 0.00115 -35 300 0.001 15
-774022 -7 19722 -489522 -882823~ -589923.‘ -33602’J
“Superscript numbers are literature references. Values in parexperimentally determined valentheses are given in mol d&. ues correspond to the first significant break in plots of AHdilvs. m. “Estimated to be consistent with other values, since there was no significant break in the AHdilvs. m plot. ‘cmc not reported. fThese values are for measurements in NaCl solutions.
the fitting parameters were required to give an adequate representation when the data are presented as a plot of HE vs. m. This is illustrated in Figure 2. In fact, we obtained a good fit to the data merely by setting values of AHo and (BB,,/dT), to those previously reported for the binary surfactant-water systems, and (dB,,.,/aT), to be determined thereby leaving only values of from the present ternary system data. Values of K and (aB,,/aT), were set as was done with the use of eq 14 as described above. The fitting parameters obtained by using eq 13a are given in Table VIII, and a plot of HEvs. m for the dodecyltrimethylammonium bromide sodium bromide system is in Figure 2. Similar plots were given previously4 for aqueous decyltrimethylammonium bromide sodium bromide and for some of the tetradecyltrimethylammonium bromide sodium bromide data. Values of the root-mean-square deviations in Table VI11 are not unrealistically large when compared to our estimated calorimetric uncertainty of about f1.2 J/kg (f0.05J in 40 g).’ The appeal of the above method of applying eq 13a is that we can use parameters obtained from the binary surfactant + water and sodium bromide water systems in order to “nearly” predict properties of the ternary systems. Only the values of dLtand (BB,,/BT), are treated as fitting parameters. The use of (aB,,,/aT)), can be justified by the fact that it accounts for micelle-counterion interactions, which become more important in the ternary systems, because of the added common-counterion strong electrolyte, sodium bromide. Similarly, the value of $Lt also depends upon these micelle-counterion interactions.
&‘
+
+
+
+
3046 The Journal of Physical Chemistry, Vol. 90, No. 13, 1986
The problem with using eq 13a is that it yields values of GL1 that are not consistent with the AHdildata. This point, which is illustrated in Figure 3 for dodecyltrimethylammonium bromide sodium bromide, is also obvious when one compares values of (bLt in Tables VI1 and VI11 with data shown in Figures 1 and 4-7. We suggest that it is preferable to use eq 14 and the resulting parameters in Table VI1 rather than eq 13a and the parameters in Table VI11 for the present ternary systems, not only because eq 14 represents the premicellar data better but also because the use of eq 14 more closely corresponds to our earlier analysis of enthalpy data for binary aqueous surfactant^.^^^^^^^ We have used the parameters in Table VII, along with the definition in eq 1 53 applied to eq 2, 3, 7, and 8, to obtain values of AH/n for reaction 1 valid at finite concentrations of surfactant and sodium bromide.
+
AH = AHo - R P ( 8 In r/aT),
(15)
Values of AH/n are shown for the dodecyltrimethylammonium bromide NaBr system, along with values for this same surfactant containing no NaBr, in Figure 9. Values of AH*/n valid at the cmc are listed in Table X for each surfactant and at the conditions reported in this paper. The cmc values are those corresponding
+
Woolley and Bashford to the first significant break in plots of AHdilvs. m as in Figures 1 and 4-7. Also given in Table X are calorimetrically determined values from the literature obtained from measurements in solutions containing a constant background concentration of strong elect r ~ l y t e . * ~ - *The ~ differences between our AH*/n values and literature values are not inconsistent with the differences reported earlier for surfactants in pure ~ a t e r . I ~ ~ ~ ~
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. Registry No. NaBr, 7647-1 5-6; decyltrimethylammonium bromide, 2082-84-0; dodecyltrimethylammonium bromide, 1 1 19-94-4; tetradecyltrimethylammonium bromide, 1 1 19-97-7; hexadecyltrimethylammonium bromide, 57-09-0. (21) Jones, M. N.; Pilcher, G.; Espada, L. J . Chem. Thermodyn. 1970,2, 333.
(22) Paredes, S.; Tribout, M.; Sepulveda, L. J. Phys. Chem. 1984, 88, 1871. (23) Paredes, S.; Tribout, M.; Ferreira, J.; Leonis, J. J . Colloid Polym. Sei. 1976, 254, 637.
