J. Phys. Chem. 1985, 89, 3 173-3 179 the observed conductance and the theoretically predictable part of A(c), which, at very low concentrations, approaches
A" = A,, - Sc'f2
+ Ec In c
(32)
The difference also depends obviously on the mathematical formulation of the theoretical h(c) used in the analysis. Therefore, if two even slightly different theoretical functions are used to
3173
analyze data for a given system, different values of the parameters must be expected. However, if data for a set of systems (a given salt in various solvents, or various salts in a given solvent) are analyzed by using two different theoretical functions, A,(c) and Ab(c), the sequence of parameter values should not change: that is, if Ral > R,, > ... > R,,, then Rbl > Rb2 > ... > Rbnshould hold.
Enthalpies of Dilution of Aqueous Decyl-, Dodecyl-, Tetradecyl-, and HexadecyltrlmethylammoniumBromides at 10, 25, 40, and 55 O C Michael T. Bashford and Earl M. Woolley* Department of Chemistry, Brigham Young University, Provo, Utah 84602 (Received: January 16, 1985; In Final Form: February 18, 1985)
We have measured enthalpies of dilution of aqueous solutions of decyltrimethylammoniumbromide, dodecyltrimethylammonium bromide, tetradecyltrimethylammonium bromide, and hexadecyltrimethylammonium bromide at 10, 25, 40, and 5 5 O C , and at concentrations ranging from well below to well above the cmc. We have calculated A H o / n for the formation of micelles from our data as well as the corresponding values valid at the cmc using a mass-action model. Because of the effect of concentration on the enthalpy, we have tabulated values for the cmc from the literature and from our data. We also report values of ACpo/n and dJ.
Introductien A knowledge of thermodynamic properties is important in order to predict the behavior of surfactant solutions and also to test different theories or models. Because of this, the limited number of papers reportin-g actual measurements of the thermodynamic properties of surfactant solutions is somewhat surprising. Often thermodynamic properties are derived from measurements of the change in cmc with temperature. Because of the fact that the cmc is not well-defined, the use of this method is limited. In this paper we report a systematic study of enthalpies of dilution for a series of alkyltrimethylammonium bromides (TABS). Previous papers have reported enthalpies of dilution for C9 and C10 TABS at 25 'C at concentrations above and below the cmc, and for a range of TABS from C6 to C14 at concentrations below the c ~ c . ' - ~ Measurements of enthalpies of micellization have also been We have measured enthalpies of dilution for C10, C12, C14, and C16 TABS at 10,25,40, and 55 OC and at concentrations ranging from well below to well above the cmc. This type of systematic data shows the trends in AH and other thermodynamic properties and allows extrapolation to other temperatures and chain lengths. A mass-action model that includes the effects of activity coefficients to describe thermodynamic properties of micellar solutions has recently been r e p ~ r t e d . ~This model can be used to analyze our enthalpy data and to determine the apparent molar enthalpy, &, and other descriptive parameters for the surfactant (1) De Lisi, R.; Ostiguy, C.; Perron, G.; Desnoyers, J. E. J . Colloid Interface Sci. 1979, 71, 141. (2) Desnoyers, J. E.; De Lisi, R.; Perron, G . Pure Appl. Chem. 1980, 52,
433. (3) Birch, B. J.; Hall, D. G. J. Chem. Soc., Faraday Trans. 1 1972, 68, 2350. (4) Espada, L.; Jones, M. N.; Pilcher, G. J . Chem. Thermodyn. 1970, 2, 1.
(5) Adderson, J. E.; Taylor, H. J . Pharm. Pharmacol. 1971, 23, 311. ( 6 ) Evans, D. F.; Wightman, P. J. J. Colloid Interface Sci. 1982.86, 515. (7) Paredes, S.;Tribout, M.; Sepulveda, L. J. Phys. Chem. 1984.88, 1871. ( 8 ) Paredes, S.;Tribout, M.; Ferreira, J.; Leonis, J. Colloid Polym. Sci. 1976, 254, 631. (9) Burchfield, T. E.; Woolley, E. M. J . Phys. Chem. 1984, 88, 2149.
0022-3654/85/2089-3 173$01.50/0
solution. Our data can be used both to test this model where these parameters have been previously reported and to determine these parameters for new conditions not previously reported.
Experimental Section Materials. The surfa,ctants were purified before use by previously reported methods.' Decyltrimethylammonium bromide (Kodak, lot A 10F) and dodecyltrimethylammonium bromide (Kodak, lot A9F) were recrystallized 3 times from acetone. Tetradecyltrimethylammonium bromide (Research Plus) was recrystallized twice from acetone. Hexadecyltrimethylamonium bromide (Fisher, Lot 716090) was recrystallized 3 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 OC prior to use. Solutions were prepared by weight with distilled water and used the same day. Equipment. Enthalpies of dilution were measured by using a Tronac 450 isoperibol calorimeter with a Tronac 1040 temperature controller, interfaced to an Apple IIe computer. The buret injection system consisted of a IO-mL Metrohm Herisau E415 piston buret driven by a synchronous motor located outside the calorimeter. The titrant surfactant solutions were thermally equilibrated after leaving the piston buret in a 15-mL glass coil immersed in the calorimeter bath. The temperature changes were measured by following the imbalance in a Wheatstone bridge circuit containing a sensing thermistor. The sensitivity of this circuit is about 25 mV/K at 25 'C. The voltages were measured by using a Hewlett-Packard 3450A multifunction meter with a sensitivity of 1 pV and recorded by the computer. Data were recorded every 10 s throughout the titrations. Time intervals were measured with a time-base pulse generator. The calorimetric calibration of the system was checked by titrating dilute HC1 into tris(hydroxymethy1)aminomethane (THAM). Averaging all the calorimetric values cited in ref 10 except the high and the low, we obtained a value of 47 482 f 102 J for AH for the protonation (10) Christensen, J. J.; Hansen, L. D.; Izatt, R. M. 'Handbook of Proton Ionization Heats and Related Thermodynamic Quantities"; Wiley: New York, 1916.
0 1985 American Chemical Society
3174 The Journal of Physical Chemistry, Vol. 89, No. 14, 1985
Bashford and Woolley
TABLE I: Representative Values of the Integral Enthalpies of Dilution of Aqueous Decyltrimethylamdum Bromide 10 oc 25 OC 40 OC
m,
m,
mmol/kg 8.24 13.66 19.03 24.34 29.60 34.82 39.98 45.09 50.15 55.16 60.13 65.05 69.92 74.75 79.53 84.26 88.96 93.61 98.21 102.78 107.30 111.78 116.22 120.63 124.99 129.31 133.60 137.84 142.06 146.23 150.37 154.47 158.53
J/mol -4733 -4794 -4802 -4796 -4745 -4708 -4653 -4602 -4549 -4490 -4432 -4367 -4236 -3943 -361 1 -3301 -3021 -2770 -2545 -2343 -2159 -1993 -1839 -1 702 -1576 -1459 -1353 -1252 -1 161 -1076 -996 -923 -854
1.0969"
mmol/kg 6.91 11.78 16.60 21.38 26.10 30.78 35.41 40.00 44.54 49.03 53.48 57.89 62.26 66.58 70.86 75.10 79.30 83.46 87.58 91.67 95.71 99.72 103.69 107.62 111.52 115.38 119.21 123.00 126.76 130.48
J/mol 360 407 446 498 550 607 663 728 787 855 922 996 1076 1173 1273 1354 1417 1468 1512 1547 1577 1603 1625 1641 1656 1670 1680 1690 1697 1704
mmol/kg 8.29 13.74 19.14 24.49 29.78 35.02 40.21 45.35 50.44 55.49 60.48 65.42 70.32 75.17 79.98 84.74 89.46 94.13 98.76 103.35 107.89 112.40 116.86 121.28 125.67 130.01 134.32 138.58 142.81 147.00 151.16 155.28 159.36
0.9578'
55
oc
m,
m, J/mol 4971 5041 5145 5207 5289 5345 5418 5505 5567 5656 5734 5815 5829 5753 5622 5477 5324 5181 5044 491 1 4788 4668 4558 4452 4354 426 1 4171 4088 401 1 3934 3863 3792 3727
mmollkp
Jhol
6.13 1 1.64 17.09 22.50 27.84 33.14 38.38 43.57 48.71 53.80 58.84 63.84 68.78 73.68 78.53 83.34 88.10 92.81 97.48 102.1 1 106.70 111.24 115.75 120.21 124.63 129.01 133.35 137.66 141.92 146.15 150.34 154.49 158.61
9 151 9 392 9 404 9 487 9 547 9 625 9 693 9 756 9 820 9 880 9 938 10013 10039 10 029 9 901 9 694 9431 9 155 8 885 8618 8 361 8 115 7 887 7 670 7 461 7 270 7 088 6913 6 757 6 596 6 447 6 310 6 176
I ,0966'
1.0971"
Initial concentration, mol/kg.
of THAM. Averaging 33 of our data points, we obtained a value of 47478 f 44 J, which is consistent with the average of the literature values. We estimate that the total calorimetric uncertainty in measured heats during our dilution experiments is less than f0.05 J. Procedures. For each run, the 50-mL Dewar was filled with 40 g of distilled water and placed in the calorimeter. The buret and glass coil were filled with the surfactant solution. The system was allowed to thermally equilibrate and the temperature of the water in the Dewar was adjusted to the bath temperature. Approximately 9 mL of the surfactant solution was added to the Dewar during the course of the run. The mass of the solution added was calculated from the volume and the density of the solution. All calculations of AHdilwere done by the computer in the usual way. Results and Discussions All experiments except those with hexadecyltrimethylammonium bromide were done in triplicate. As the hexadecyltrimethylammonium bromide solutions approach room temperature, the solute precipitates, allowing time for only duplicate runs. Tables I-IV contain representative values for AHdilfor each of the four surfactants at each temperature. In these tables, AHdil is the integral enthalpy of diluting a solution from the indicated initial. concentration to the final concentration m. The mass-action model can be summarized by eq9 1-7. nPBr-
+ nTAB+ = Br,,,TAB,"('-@)
K = [ a / n ( l - Pa)"B(l
log
r
(1)
- a)n~(ng+rl)]r
+
+
+
+
= -AyZ1/'/(l bZ'/') (1/2) log (1 - a) log (1/2) log (1 - Ba) + B1,[m(2 - a - Ba)/21 + Bw[ma/2n1 (4) C#J
+
+
= 1 - a ( 1 B - l / n ) - (In 10)A,Z3/2a(bZ1/2)/3m Bl,[(l - a ) ( l - Ba)m(ln 10)/2] + Bw[a(l Ba)m(ln 10)/2nI (5)
ob)= 3[1 + Y - 1/(1 + y ) - 2 In (1 + y)]/y3
(6)
I = [2(1 - a) + n62(1 - p y a
(7)
+ (1 - j3)a]m/2
In eq 1-7, TAB' is the monomeric surfactant, Br- is the free counterion, Br,TAB,"('-8) is the micelle (including bound counterions), n is the aggregation number, no is the number of counterions bound to the micelle, K is the equilibrium constant for reaction 1, a is the fraction of the surfactant incorporated into micelles, r is the activity coefficient product for the equilibrium in reaction 1, A , is the Debye-Hiickel parameter for activity coefficients, m is the molality of the surfactant, Z is the ionic strength, b is an 'ion-size" parameter, B1,and B , are the Guggenheim ion interaction parameters for counterion-monomer and counterion-micelle interactions, ya and 4 are the activity coefficient and osmotic coefficient for the surfactant solution, and 6 is a "screening factor" for the micellar charge. Temperature derivatives of eq 2-7 lead to eq 8 . l l The coefficients k,L are given explicitly in terms of m,a,n, p, 6, b, A,,
(2)
+
= -n[d2n(l - p)2 - p - 1]Ay11/2/(1 b11/2) 4,[nm(2Pa - P - 111 + B,,[m(l - 2Pa)l (3)
(11) Woolley, E. M.;Burchfield, T. E. J . Phys. Chem. 1984, 88, 2155.
The Journal of Physical Chemistry, Vol. 89, No. 14, 198.5 3175
Enthalpies of Alkyltrimethylammonium Bromides
TABLE 11: Representative Values of the Integral Enthalpies of Dilution of Aqueous Dodecyltrimethylammonium Bromide 10 O m,
mmol/kg 1.55 3.36 5.15 6.92 8.67 10.39 12.10 13.79 15.45 17.10 18.74 20.35 21.94 23.52 25.08 26.63 28.15 29.66 31.16 32.64 34.10 35.55 36.98 38.40 39.80 41.19 42.56 43.92 45.27 46.60 47.92 49.23 50.52 51.17
25 O C
C
40
M d i h
m,
m d i l r
J / mol
m,
mmol/kg
J/mol
-4043 -4060 -4084 -403 1 -4000 -3954 -3909 -3887 -38 13 -3457 -3045 -267 1 -2359 -2098 -1866 -1672 -1497 -1345 -1205 -1086 -982 -882 -797 -717 -643 -580 -519 -466 -415 -368 -324 -289 -25 1 -234
1.10 2.92 4.72 6.49 8.25 9.98 11.69 13.39 15.07 16.72 18.36 19.98 2 1.58 23.17 24.74 26.29 27.82 29.34 30.84 32.32 33.79 35.24 36.68 38.1 1 39.51 40.9 1 42.29 43.65 45.00 46.34 47.67 48.98 50.28 50.92
2553 2657 2730 2797 2889 2945 3009 3053 3121 3067 2967 2851 2758 2668 2583 2512 2436 2383 2320 2266 2218 2172 2128 2089 205 1 2023 1984 1952 1924 1892 1866 1845 1814 1805
mmol/kg 2.85 4.65 6.44 8.21 9.95 11.68 13.38 15.07 16.74 18.39 20.02 21.63 23.22 24.80 26.36 27.90 29.43 30.94 32.43 33.91 35.37 36.82 38.25 39.67 41.07 42.45 43.83 45.19 46.53 47.86 49.18 50.49 5 1.78 53.06
0.3094"
0.3095'
55 OC
O C
AHdili J/mol 8722 8821 8931 9021 9073 9145 9237 9316 9209 8693 8164 7668 7226 6842 649 1 6178 5902 5647 5428 5230 5032 4867 4702 4550 4408 4288 4164 4062 3958 3858 376 1 3675 3590 3656
m, J/mol 14248 14364 14437 14 556 14647 14701 14806 14795 14 884 14 755 14 131 13 308 12 533 11 835 1 1 209 10614 10 113 9 650 9 235 8 838 8 499 8 177 7 883 7 606 7 345 7 109 6 896 6 682 6 487 6 305 6 129 5 969 5 824 5 744
mmol/kg 2.86 4.67 6.47 8.24 9.99 11.72 13.44 15.13 16.80 18.46 20.09 21.71 23.31 24.89 26.45 28.00 29.53 3 1.05 32.54 34.03 35.49 36.94 38.38 39.80 41.20 42.59 43.97 45.33 46.68 48.01 49.34 50.64 5 1.94 52.58
0.3100"
0.3096"
" Initial concentration, mol/kg. 1
4 000,
0
1500
i
-
5 0 E
I
7 -4
000
0
d I
1
-s' -0 000
i
\.
000
+ I
+
.
7
\
s'-1500
'
0.000
Ib!
+a
I
I
40
55
25 0.005
m
/
0.010 MOL KG-1
0.015
0.020
Figure 1. Relative apparent molar enthalpies of tetradecyltrimethylammonium bromide at 10 O C (0),25 OC (+), 40 O C (*), and 55 OC (A). The solid lines are least-squares fits using the parameters in Table VI.
the DebyeHuckel parameter for enthalpies AL, B1,! B,, T , and the gas constant R. In this equation, is the relative apparent molar enthalpy for the titrant solution. The values used for A , and AL are given in Table V. These values were obtained from the literature or by interpolati~n.~~' 1*12 The ion-size parameter, b, is equal to 1.9 Values of n and /3 were taken from the literature, and are given in Table VI. Values for 6, B , , and B,, for decyltrimethylammwium bromide were obtained as in ref 12. For (12) Woolley, E.
+25
40
i
-1 2 000
-16
-
M.;Burchfield, T. E. J. Phys. Chem. 1985, 89, 714.
-308Fi
30
0.0035
0.0040 0.0045 m / MOL K G - ~
00050
0
155
Figure 2. Relative apparent molar enthalpies of tetradecyltrimethylammonium bromide at 10 O C ( O ) , 25 O C (+), 40 OC (*), and 55 OC (A), showing only the region of the cmc. Arrows indicate the position of the break corresponding to the cmc.
the other three surfactants, 6 = 0.5, B , , = 0, and Bny = 0 were obtained by comparison with similar compounds because of the lack of reliable activity or osmotic coefficient data.'* Obviously, nonzero values of (dB,,/dT), are inconsistent with a constant BIy. Unfortunately, it is impossible to determine B,, without free energy data. Also, we have found that varying B,, and By does not have a large effect on calculated values of the parameters in eq 8. The value of K was chosen so that the relative apparent molar enthalpy described in eq 8 would "break" at the cmc in order to give a minumum in the root-mean-square deviation.
3176
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985
Bashford and Woolley
TABLE 111: Representative Values of the Integral Enthalpies of Dilution of Aqueous TetradecyltrimethylammoniumBromide 40 O C 25 O C 55 IO o c
m, mmollke
m, mmol I ka 0.688 1.334 1.973 2.603 3.226 3.842 4.450 5.051 5.645 6.231 6.81 1 7.384 7.951' 8.510 9.064 9.61 1 10.152 10.687 11.215 11.738 12.256 12.767 13.273 13.773 14.268 14.757 15.242 15.721 16.195 16.664 17.128 17.587 18.042 18.491
AHd,,,
Jlmol -2157 -2138 -2085 -2003 -1959 -1892 -1686 -1338 -1066 -822 -66 1 -512 -385 -302 -223 -153 -92 -42 3 30 59 81 105 123 140 152 156 166 172 174 176 175 165 166
0.533 1.117 1.695 2.266 2.829 3.386 3.936 4.479 5.016 5.547 6.07 1 6.589 7.101 7.608 8.108 8.603 9.092 9.575 10.053 10.526 10.994 1 1.456 11.913 12.365 12.813 13.255 13.693 14.126 14.554 14.978 15.398 15.813 16.223 16.630 0.09459O
JJmol
m, mmol 1ka
AH,,,. Jlmol
m, mmollkg
6159 6254 6261 6370 6404 6358 5782 5289 4850 4510 4232 4016 3788 3605 3454 3334 3213 3111 3006 2922 2828 2756 2679 2628 2552 2503 2452 2394 2360 2307 2270 2226 2191 2158
0.591 1.174 1.750 2.319 2.881 3.436 3.984 4.526 5.061 5.590 6.113 6.629 7.140 7.644 8.143 8.636 9.124 9.605 10.082 10.553 11.019 11.480 11.935 12.386 12.83 1 13.272 13.708 14.140 14.567 14.989 15.407 15.820 16.229 16.634
13468 13515 13 597 13 767 13843 13872 13872 13 103 11 845 10839 9971 9 277 8 637 8 101 7 648 7 252 6881 6 562 6 277 5 993 5771 5 552 5 344 5 169 5 000 4 837 4 700 4 580 4 455 4 300 4210 4 096 3 988 3916
0.623 1.209 1.788 2.359 2.923 3.481 4.032 4.576 5.113 5.644 6.169 6.688 7.200 7.707 8.207 8.702 9.192 9.675 10.153 10.626 1 1.094 11.556 12.013 12.465 12.913 13.355 13.792 14.225 14.653 15.077 15.496 15.91 1 16.321 16.727
AHd,i.
0.09408n
0.10503"
O C
AHdd,
Jlmol 20 976 20961 20771 20 746 20 789 20 866 21 026 21 017 20 249 18618 17079 15869 14738 13766 12 952 12 151 11 524 10861 10364 9916 9 486 9 094 8 777 8 404 8 079 7 796 7 589 7 288 7111 6 860 6 673 6513 6 285 6 159
0.094 12"
Initial concentration, mol/kg. 10
000
I
... 7
\
CI
C
' 0
I
a
h
h
-1C
17
,.
--
5c3 n-~
-vu
3005
,
__-_
3 0'"
m
/ vo
3C'5
COO
__ '313
c325
JS-'
Figure 3. Relative apparent molar enthalpies of decyltrimethylammonium bromide ( O ) , dodecyltrimethylammonium bromide (+), tetradecyltrimethylammonium bromide (*), and hexadecyltrimethylammonium bromide (A)at 40 OC. The solid lines are least-squaresfits using the parameters in Table VI.
The results of fitting our experimental data to eq 8 are given in Table VI, along with the values for n, p, 6, B,,, and Bn7. The A values are a sum of the average of the standard deviation of the replicate runs for a given parameter and the standard deviation for the average value of that parameter. Values of (dB,,!dT), were not determined for those runs with insufficient premicellar data. Values of (dB,,/dT), were not determined for any of the runs. The contribution of (dB,,/dT), only becomes significant at concentrations higher than our experimental data. Values obtained for the fitting parameters from data reported by De Lisi
t /
oc
Figure 4. A H o / n vs. T for decyltrimethylammoniumbromide (a),dodecyltrimethylammonium bromide (+), tetradecyltrimethylammonium bromide (*), and hexadecyltrimethylammonium bromide (A). Slopes of lines are equal to ACpo/n.
et al. for decyltrimethylammonium bromide at 25 "C are also included in Table VI. These values agree very well with our experimental values. As stated above, the type of systematic data we have collected emphasizes certain properties of these surfactant solutions. I n Figure 1 we show relative apparent molar enthalpies for tetradecyltrimethylammonium bromide. As can be seen from this figure and from the data in Table VI, A H " / n decreases, or becomes more negative, as the temperature increases. The same
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985 3177
Enthalpies of Alkyltrimethylammonium Bromides
1350
TABLE I V Representative Values of the Integral Enthalpies of Dilution of Aaueous Hexadecyltrimethylammonium Bromide
0.331 0.643 0.95 1 1.255 1.555 1.851 2.144 2.433 2.719 3.001 3.280 3.556 3.828 4.098 4.364 4.627 4.887 5.144 5.398 5.649 5.898 6.143 6.386 6.627 6.864 7.099 7.332 7.562 7.789 8.014 8.237 8.457 8.675 8.891
10824 11 188 11078 9 176 7722 6750 5954 5421 4948 4640 4289 4071 3831 3611 3469 3263 3145 3020 2907 2767 2684 2583 2514 2418 2337 2307 2242 2181 2123 2062 2011 1962 1928 1877
0.335 0.650 0.961 1.269 1.572 1.872 2.168 2.460 2.749 3.034 3.316 3.595 3.870 4.142 4.411 4.677 4.940 5.199 5.456 5.710 5.961 6.209 6.454 6.697 6.937 7.174 7.409 7.641 7.871 8.098 8.323 8.545 8.765 8.983
0.049 86'
19340 19626 19814 17414 14407 12293 10692 9642 8722 7890 7294 6850 6376 6061 5744 5467 5184 4949 4192 4550 4442 4314 4137 4046 3907 3806 3737 3611 3541 3405 3346 3268 3195 3147
27 936 28 759 28 649 28 297 24 573 20 743 17890 15854 14085 12753 11 586 10754 9 985 9 202 8 695 8 089 7 707 7 172 6 878 6614 6 333 6 077 5 764 5 552 5 394 5213 5 010 4 821 4175 4 575 4418 4 299 4 159 4 027
0.319 0.634 0.945 1.253 1.556 1.856 2.152 2.444 2.733 3.018 3.300 3.578 3.854 4.126 4.394 4.660 4.923 5.182 5.439 5.692 5.943 6.191 6.436 6.678 6.918 7.155 7.390 7.622 7.851 8.078 8.303 8.525 8.744 8.962
10 25 40 55
A,* kg1/2/moll/2 0.4988 0.5108 0.5242 0.5393
1350
-
UI
n
.
d
c10
J kg1/2/mo13/2
A,," J kg'l2/K mo13/2
1620 1973 2395 2903
24.18 28.95 33.81 39.39
AL,
\
,
I
0.01
0.02
0.03
m / MOL KG-1
is true of &. Figure 2 shows that the cmc also increases for the same surfactant as the temperature increases. This is consistent with the trends in &, W / n , In K,and the van't Hoff relationship. Figure 3 shows 4Lfor all four surfactants at 40 OC. From this figure and Table VI, it can be seen that &, and thus AHo/% decreases as the chain length increases. The slope in the premicellar region also becomes more steep. Through the application of simple thermodynamic relationships, we can also obtain information about heat capacities. The temperature derivative of eq 8 leads to eq 9.l' With all of the
4J = 4c - c p z o =
+ klc(a2Bl,/ap)p + k n C ( a 2 ~ , , / a ~(9) ),
parameters known, this equation can be used to predict &. Figure 4 is a graph of A H o / n vs. T for all four surfactants. The slope of each line is equal to ACpo/n. We approximated this slope using a linear least-squares method. For the C10 TAB, ACpo/n= -302 f 12 J/(K mol), for C12 TAB it is -406 f 10 J/(K mol), for C14 TAB it is -499 5 J/(K mol), and for C16 TAB it is -573 f 12 J/(K mol). With this information, plus the parameters listed
*
m / MOL K G - '
O C
"Values of A, were obtained from the literature or by interpolation."J2
koc + k , ~ c ;
1
0 020
0.015
Figure 5. Relative apparent molar heat capacities of tetradecyltrimethylammonium bromide at 10, 25, 40, and 55 OC calculated from eq 9. The intercepts have been arbitrarily fixed to separate the lines from each other so that the concentration and temperature dependencies are more visible.
658.i0
TABLE V A 7y A L, and A E at 10,25,40, and 55 O C
0 010
0 005
0.049 95'
0.050 18'
'Initial concentration mol/kg.
7'.
'
550 0 000
Figure 6. Relative apparent molar heat capacities of decyltrimethylammonium bromide, dodecyltrimethylammonium bromide, tetradecyltrimethylammonium bromide, and hexadecyltrimethylammonium bromide at 40 O C calculated from eq 9. The intercepts have been arbitrarily fixed to separate the lines from each other so that the concentration and structure dependencies are more visible.
in Tables V and VI, Figures 5 and 6 were produced. Figure 5 shows 4, for tetradecyltrimethylammonium bromide at all four temperatures. As the temperature increases, the height of the "hump" increases. This hump is caused by the perturbation in the micellization equilibrium induced by the temperature change that is inherent in a measurement or calculation of heat capacity. The magnitude of the hump increases because the magnitude of A H o / n increases with increasing temperature. The break in 4J also occurs at increasingly higher concentrations for the same reason. The abrupt drop in dJ beyond the cmc reflects the contribution of large negative values of ACpo in eq 9. Figure 6 shows $, for all four surfactants at 40 O C . From this figure it can be seen that, as the chain length increases, the concentration at which the hump occurs decreases, the magnitude of the hump increases, and the overall decrease in $J gets larger. These facts are all consistent with the previously discussed information and the data in Table VI. To obtain a value of A H / n for reaction 1 valid at the cmc, eq 1 0 was used.12
AH = AHO
- R p ( a In
r/aT),
(10)
obtained Values of the cmc and corresponding values of from eq 10 are given in Table VI1 and compared with values from
3178
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985
Bashford and Woolley
TABLE VI: Parameters for Fitting Enthalpy Data to Eq 8"**
4.;)
IO 25 2S1 40 55
172 171d 170d 171 170
(aBl,/aT),, AHo/n, RMSD,C J/mol kg/K mol J/mol Decyltrimethylammonium Bromide, n = 36,9J2p = 0.73,17 6 = 0.5 -5 142.6 i 48.0 6452.8 f 46.3 -3.5 x 10-3 f 3.1 x 10-4 26.0 -36.5 f 20.7 1857.7 f 39.4 -7.0 x IO-' i 2.4 x 10-4 49.0 1973 f 96 -8.0 x 10-3 f 8.0 x 10-4 92 4662.9 f 20.3 -3 188.2 f 32.1 -4.8 x 10-3 1.3 x 10-4 29.2 8897.6 f 122.3 -6 944.4 f 99.4 -3.3 x 10-3 f 6.3 x 10-4 50.3
IO 25 40 55
380 37 1 371 361
Dodecyltrimethylammonium Bromide, n = 52: = 0.77,' 6 = 0.5 5 144.6 i 26.4 -4 153.0 i 48.0 -4.5 x 10-3 i 1.7 x 10-3 30.4 2 502.4 i 35.5 -1 473.3 i 45.8 -0.0137 f 2.0 X 29.0 8 503.8 f 48.3 -7531.5 f 102.9 -0.0175 i 3.1 X 46.0 14090.3 i 222.2 -13 119.6 i 132.1 -0.0111 i 5.1 X 66.8
0 0 0 0
IO 25 40 55
709 686 678 66 1
Tetradecyltrimethylammonium Bromide, n = 70,a p = 0.8,* C = 0.5 -2041.8 f 76.9 2 763.7 f 96.2 61.6 6235.8 i 80.4 -4954.2 i 25.0 53.4 13581.7 f 264.0 -12416.8 i 202.0 75.5 20686.3 f 89.7 -19685.7 f 143.0 74.9
0 0 0 0
25 40 55
1090 1079 1047
Hexadecyltrimethylammonium Bromide, n = 87,' p = 0.84,176 = 0.5 11 002.4 f 247.8 -9706.4 f 183.1 165.9 19698.1 i 319.9 -17993.8 i 396.3 139.2 28 102.9 f 223.1 -26909.2 f 235.1 112.2
0 0 0
T, "C
In K
J/mol
BIT, kg/mol
B",, kg/mol
-0.42 -0.575 -0.575 -0.68 -0.75
5.5 8.0
8.0 11.3 14.6 0 0 0 0
0 0
0 0 0
0 0
Superscript numbers indicate references. Values of (BB,,/BT), are zero at the 95% confidence limit in all cases over the concentration ranges of the experimental data. 'RMSD is the root-mean-square division of the fit to eq 8. dThese values do not correspond to the minimum in the RMSD. Values were calculated at a In K value consistent with the other temperatures. The data show very little break near the cmc. 'This value is the average of 14 values from ref 18-26. fThis value is the average of 3 values from ref 17 and 20. 8This value is the average of seven values from ref 17, 19, 21, 22, 24, and 27. *This value is the average of four values from ref 17 and 28. 'This value is the average of six values from ref 19, 21, 22, and 24.
TABLE VII: Valws of A H l n Valid at the cmc cmc, A H * / n , J/mol T, 'C mollkg eq 9 lit. 10 25 40 55
IO 25
40
55
T, O C
Decyltrimethylammonium Bromide 0.064' 5 656 5 145' 0.065" 5 679 0.057' 377 2501,-12812 0.062' 258 541' 0.065b 205 0.064' -4 581 -6 462' 0.068" -4 666 0.070' -4 739 0.069' -8251 -10890' 0.072' -8 315
5 25 40 55 25
Dodecyltrimethylammonium Bromide 0.015".C,' 4 839 4 366' 0.014 5b -2 243 0.0147' -2251 -2 446' 0.015 84 -2 304 -1 3934 0.0164" -2 335 0.015 7' -8661 -9 875' 0.0163" -8 709 0.O16Sc -8 734 0.017 5' -14 104 -17 172' 0.018 5" -14181
40 55
cmc, mollkg
A H * / n , J/mol
eq 9
Tetradecyltrimethylammonium o.ooj3a 2775 0.003 86,d -4 860 0.004 0" -4 899 0.004 22" -12 343 0.004 24" -12357 0.0049"36 -19941
lit. Bromide -20 8786 -25 9836 -31 3806
Hexadecyltrimethylammonium Bromide 0.000 897 -9 761 -9 1637 0.00092b -9 762 -9 764 -9 288' 0.000 96' 0.001 00" -9 767 0.001 08" -1 8 079 0.001 32b -27018 0.001 33" -27 039
"These are our experimentally determined values. They correspond to the first significant break in a curve of concentration vs. A H , , . bThese are recommended values from ref 29. 'These are values reported in ref 29. dThe values for cmc and A H * / n from ref 6 are not at exactly the same temperatures. Values were reported at 25.2, 40.3, and 54.2 O C .
the literature. It can be shown from eq 10 that it is important be the reason for our disagreement with some of the literature to specify precisely the molality in any discussion of properties values given in Table VI1 that were obtained in this ~ a y . ~ . ~ at or near the cmc, since A H / n can be changing significantly in that region.I2 There is generally quite good agreement between our values and calorimetric values reported in the l i t e r a t ~ r e . ~ * ~ * ~ ~1965. * J(16) ~ King, E. J. "Acid-Base Equilibria"; Pergamon Press: New York, The difficulty in obtaining AH*/n values from cmc measurements (17) Zana, R.; Yiv, S.;Strazielle, C.; Lianos, P. J . Colloid Interface Sci. as a function of temperature has been d i s c ~ s s e d . ' ~ - 'This ~ may 1981, 80, 208. (13) Rasenholm, J. B.; Burchfield, T. E.; Hepler, L. G. J. Colloid Interface Sri. 1980, 78, 191. (14) Muller, N. 'Micellization, Solubilization, and Microemulsions"; Mittal, K. L., Ed.; Plenum Press: New York, 1977; Vol. 1. (15) Holtzer, A,; Holtzer, M. F. J . Phys.Chem.1974, 78, 1442.
(18) Ozeki, S.; Ikeda, S.Bull. Chem.Soc. Jpn. 1981, 54, 552. (19) Lianos, P.; Zana, R. J. Colloid Interface Sci.1981, 84, 100. (20) Guveli, D. E.; Kayes, J. B.; Davis, S. S.J. Colloid Interface Sci. 1981, 82, 307.
(21) Guveli, D. E.; Kayes, J. B.; Davis, S.S.J. Colloid Interface Sci. 1979, 72, 30.
(22) Leibner, J. E.; Jacobus, J. J. Phys.Chem. 1977, 81, 130.
J. Phys. Ckem. 1985,89, 3 179-3 182 for C10, In conclusion, the measurements we made of C12, C14, and C16 TABS provide information about 4L,cmc, AHo/n, AH*/n, ACpo/n,and 4,. Generally speaking, the values we obtain are in good agreement with literature values, where (23) Anacker, E. W.; Rush, R. M.; Johnson, J. S. J. Phys. Chem. 1964,
68, 81. (24) Tartar. H.V. J. Colloid Sei. 1959. 14. 115. (25j Debye,'P. Ann. N . Y. Acad. Sci. 1949151, 575. (26) Debye, P. J. Phys. Chem. 1949, 53, 1. (27) Llanos, P.; Zana, R. J. Colloid Interface Sei. 1982, 88, 594. (28) Venable, R. L.; Nauman, R. V. J. Phys. Chem. 1964, 68 3498. (29) Mukerjee, p.; ~ ~K, J. "Critical ~ ~ ~ i l ~Concentrations ~~ l l , ~ of
Aqueous Surfactant Systems", Natl. Stand. Ref: Data Ser. (US.Natl. Bur. Stand.) 1971, NSRDS-NBS 36.
3179
literature values are available. We have also shown that the model described above is applicable to our data and provides useful information about trends in the thermodynamic properties of these alkyltrimethylammonium bromide surfactants. Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund. administered bv the American Chemical Society, for support 'of this research: Registry No. Decyltrimethylammonium bromide, 2082-84-0; dodecyltrimethylammonium bromide, 1 1 19-94-4; tetradecyltrimethylammonium bromide, 1 1 19-97-7; hexadecyltrimethylammonium bromide, 57-09-0.
Mechanism of Tritium-Atom Promoted Isotope Exchange in the Benzene Ring: 2. Substituent Effects and a Crossover in Labeling Mechanism M. F. Powellt and R. M. Lemmon* National Tritium Labeling Facility, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 (Received: November 5, 1984)
Reaction of tritium atoms, generated by microwave activation of T2 gas, with substituted benzenes was studied at - 4 0 O C . The tritiations were usually carried out with a 1:l mole mixture of the desired phenyl compound and toluene. Both relative labeling yields (with benzene = 1 as a reference) and product isotope effects were determined; these were used to support a crossover in labeling mechanism from predominantly addition-elimination (as in benzene-?) to a hot-atom multiple-tritium addition (as takes place in xylene-t). The contribution of each labeling pathway could be controlled by varying the distance between the microwave discharge cavity and the sample; shorter distances gave "hotter" tritium atoms at the sample, resulting in less selectivity but higher labeling yields.
Introduction
T
Tritium labeling of biological compounds by microwave activation of T2is one of the simplest of labeling procedures devised and, yet, is not used routinely because of the lack of general understanding of reaction mechanism(s) and conditions required for enhanced labeling selectivity. We have turned our attention to this and have recently delineated some of the factors for the For example, the effect of tritiation of aromatic sample temperature and isotopic substitution in the labeling of benzene demonstratd that the main labeling pathways are T. addition to give the cyclohexadienyl radical followed by either Ha elimination (yielding benzene-t, eq 1) or reaction of this radical
with additional T. atoms (resulting in saturated side products such as cyclohexadiene-t2 and cyclohexane-t,, eq 2). There was little indication from these previous studies of the reaction between T.* (translationally hot) and benzene, such as (i) H.abstraction by T.* to give HT followed by reaction of the phenyl radical with another T. atom (eq 3 and 4) or, (ii) a concerted substitution reaction (eq 5 ) . It may be possible, however, to identify hot T-* H (3)
Institute of Pharmaceutical Sciences, Syntex Research, 3401 Hillview Ave., Palo Alto, CA 94304.
0022-3654/85/2089-3 179$01.50/0
@+ T-6 ,H
(4) T
atom labeling in substituted benzenes because labeling by the addition-elimination pathway of substituted benzenes (eq 1) should decrease due to the higher stability of the intermediate cyclohexadienyl radical3 formed. Since most substituents on benzene are thought to stabilize aryl radicals (vide i ~ ~ f r a almost ) , ~ , ~ all substituted phenyl compounds should exhibit lower tritium labeling yields than in benzene (due to eq 2 predominating over eq 1) with concomitant increases in the amounts of saturated products formed. We have demonstrated this herein and found that by changing the geometry of the labeling apparatus-specifically, varying the distance between the microwave cavity and the sample holder-we were able to show evidence for a change in the major labeling mechanism from addition-elimination (eq 1 and 2) to a translationally "hot-atom" reaction ( eq 3,4, and/or 5) in microwave-T. labeling of aromatic compounds. Experimental Section and Results All phenyl compounds were spectral grade or chromatography standards and were used without further purification. Deuterated (1) Powell, M. F.; Morimoto, H.; Erwin, W.R.; Gordon, B. E.; Lemmon, R. M. J. Phys. Chem. 1985, 88, 6266-71. (2) Gordon, B. E.; Peng, C. T.; Erwin, W. R.; Lemmon, R. M. Int. J. Appl. Radiar. Isot. 1982, 33, 721-24. ( 3 ) Nelson, R. F.; Adams, R.N. J. Am. Chem. Sor. 1968, 90, 3925-30. (4) Nelsen, S. F.; Landis, R. T.; Kiehle, L. H.; Leung, T. H. J. Am. Chem. Sor. 1972, 94, 1610-14.
0 1985 American Chemical Society
