COMMUXICATIONS TO THE EDITOR
1837
3600 I
I
I
3400 I
electrolytes, the use of the Katchalsky equationgfor the mean activity coefficient has been recommended by us. Even at infinite dilution of the macro-ions, t and + may have effective contribution due to the segment-segment interaction and other factors. The nonideality in the equation given by Miller and Frommer is taken care of by the factor &. As pointed out in our paper,2 the flexible polyelectrolyte at higher concentration binds a considerable amount of counterions. The extent of such counterion binding in the surface and bulk phases is expected to be significantly different. Seither our equation nor that given by RIiller, et al., can take full account of this complex situation. The applicability of the Gibbs equation for such a case will be discussed in our subsequent calculation.
I
.... ........ . l .: '
A
145 i
135 ;\,
f* stands for the mean activity coefficient. For small ions, the Debye-Huckel expression for fi is used for the solution of f and 4. For the case of long-chain poly-
E
C
B
145
140
n
. . . ... . ... . . . . ................ . . . .........f .I
D
.. .. ..
~
igO
F
Figure 1. Spectra of free O H stretching overtone bands near 7100 em-1 and OH stretching fundamental bands near 3300 cm-1 (2.86 p) for the three systems methanol (MeOH), t-butanol (t-BuOH), and di-t-butylcarbinol (DTBC) in carbon tetrachloride solution. All spectra were recorded as per cent transmission (except DTBC band near 7100 as absorbance) us. linear wavelength (except DTBC band near (9) J. Bockris, Ed., "Modern Aspects of Electrochemistry," Butter3500 cm-1 as linear cm-l) using the following instruments: worth and Co., Inc.., Washington, D. C., 1954, pp 18-20, RleOH and t-BrtOH, 7100-em-' bands on Beckman DK-2, CHEMISTRY DEP.4RTMENT D. K. CHATTORAJ 3500-cm-lbands on Baird 4-55; DTBC, 7100-cm-l band on JADAVPUR IrPiIVEElSITY Gary 14R, 3500 em-' band on Perkin-Elmer 221PG. CALCUTTA 32, INDIA Additional details of the individual spectra are: A, DTBC F l NOVEMBER ~ 27, 1967 ~ ~ ~ ~ m, lo", ~ 2.0-cm ~ quartz cell; B, DTBC 0.073 m, lo", 0.073 1.0-ern quartz cell; C, bIeOH 0.049 M,25", 1.0-ern quartz cell; D, PlIeOH 0.049 X , 25', 1.1-em rock salt cell; E, t-BuOH 0.063 X , 25", 1.0-ern quartz cell; F, t-BuOH 0.063 M , 25', 1.1-ern rock salt cell. The solvent us. solvent curves Hydrogen-Bonded Dimers and the are shown as solid lines (dotted for A ) . For D and F alternate calculations using a corrected background obtained by 2.86-p Band in Alcohols assuming the free OH stretching band near 3650 ern-1 to be symmetrical gave the same conclusions as shown in Table 11. Sir: Fletcher and Heller' have recently reported For A, the small peak at lower frequency (-1.41 p ) is evidence for only monomers and two tetramers (linear always present in DTBC and its absorbance relative to the main peak is unaltered over a 40" temperature range. and cyclic) when l-octanol self-associates in n-decane.
A major point of their paper is an admonition against making a priori decisions as to the stoichiometry of the self-association and designing the mathematical analysis for this stoichiometry. These authors found a plot of absorbance a t 1.405 p (7117 cm-l) (free OH stretching overtone) us. absorbance a t 1.528 p (6544 cm-l) to be linear over a wide range of temperature and concentration shownng that the 1.528-p band is not due to an OH- . .OH dimer. Taking the 1.528-p band as an overtone of the 2.86-p band customarily assigned to dimers2 casts doubt on the reliability of work where the 2.86-p band furnished the major evidence that dimerization was occurring. We concur in the admonition of Fletcher and Heller on the dangers of a priori assignments of association stoichiometry. In addition, it seems clear that the 1.528-p band in the l-octanol-n-decane system is not due to an OH. -OH dimer. However, the assignment of the 1.528-p band as an overtone of a 2.86-p band might possibly be in error, and the apparent absence of dimer in the 1-
octanol-n-decane system might not result for other alcohols in other solvents. Table I lists the absorbance per unit path length (cm-l) for the free OH stretching overtone band near 7100 cm-l and the OH stretching fundamental near 3500 cm-l (2.86 p ) for the three systems methanol (MeOH), t-butanol (t-BuOH), di-t-butylcarbinol (DTBC)-CCL at several temperatures. Figure 1 shows representative spectra. Plots of absorbance near 7100 cm-I 21s. absorbance near 3500 em-* give parabolic curves consistent with dimerization in all cases. For methanol and t-butanol the situation is complicated by a band at 3350 cm-l which appears at the higher concentrations in Table I and overlaps the 3500-cm-l band. In the 7100-cm-' region there are no overlap difficulties for any of the alcohols. For (1) A. N. Fletcher and C. Heller, J . Phys. Chem., 71, 3742 (1967). (2) U. Liddell and E. D. Becker, Spectrochim. Acta, 10, 70 (1957).
Volume 72, Number 6
Mag 1968
COMMUNICATIONS TO THE EDITOR
1838 Table I : Absorbance per Unit Path Length for 7100- and 3500-Cm-l Bands
---A7l00, om-1 - 6
Concn,a
M
110
0.020 0.025 0.049 0.074 0.098 0.147
0.03793 0.04683 0.08884 0.1203
0.021 0.032 0.042 0.063 0.105 0.210
0.04357 0.06434 0.08493 0.1219
0,04333 0.06385 0,08493 0.1248 0.1970
100
200
250
r
110
56'
Aaaoo, crn-l' 25'
7
56'
MeOH-CCla 0.04635 0.08884 0.1316 0,1599
0.08941 0.1353 0 .4291d 0,8518d
0.1230 0.1632 0.2313
0.1045 0.3212 0.7346d 1,104d
0.4337 0.6917 1.399d
t-BuOH-CCld 0.06198 0.08243 0.1219 0.1970 0.3613
0.08197 0.1707 0.2804 0.6402d
0.05621 0.1208 0.1989 0.4188 1.074d
100
200
0.05586 0.1150 0.2412 0.6455 2.008d
Concn, 112
DTBC-CC14 0.042 0 053 0.054 0.063 0.073 0.078 0.089 0.105
0.136 0.171 0.173 0.203 0.234 0.252 0,285 0.338
0.137 0.173 0.175 0.206 0.237 0.255 0.289 0.341
0.1225 0.174 0.193 0.276 0.336 0.375 0.485 0.682
0.106 0.165 0.171 0,256 0.284 0.350 0.428 0.631
The concentrations for MeOH and t-BuOH are given for 25'. Multiplication of these concentrations by 1.017 and 0.9617 will give concentrations a t 11 and 56", respectively. The measurements for MeOH and ~-BLIOHwere made in 10- and 1-em cells. For DTBC, 2- and 5-cm cells were used a t 10 and 20°, respectively. ' The measurements for MeOH and ~-BLIOHwere made in 1.10-, 0.935-, and 0.0772-cm cells. For DTBC, a 1-em cell was used. Cases where 3350-cm-1 band appears to overlap 3500-cm-' band.
DTBC no new bands occur in the fundamental OH stretching region up to 3.0 m since steric factors cause the self-association to ierminate at the species responsible for the 3500-cm-' band.3 The 3651-cm-l free OH band and the 3523-cm-l band for DTBC do not overlap at the concentrations in Table I. Complete deuteration of the OH group in DTBC reveals no absorbance other than OH stretching in the region 3700-3300 cm-1. There seems to be little chance that the DTBC absorbance values in Table I are in error due to unrecognized contributions in addition to the OH-containing species responsible for the band. The constancy of A3600/An7100 with changing concentration for a particular value of n identifies the stoichiometry between the species causing the 7100and 3500-cm-1 bands since A 3 5 0 0 / R n 7 1 0 0 is proportional to the overall equilibrium constant, Kn, for nM Mn (if several structures for M n occur, K n is the sum of the K's for the individual structures). Table I1 lists the average value of A3500/fin7100 over the concentrations in Table I for n = 1, 2, 3 as well as the 90% confidence probable error in this average4 and the percentage of the average given by the 90% confidence probable error. The criterion of this percentage as a minimum assigns the 3500-cm-' band to a dimer in each casea5 The Journal of Physical Chemistry
Two factors which could conceivably affect the constancy of A3m,/An7m sufficiently to cause an erroneous (3) L. K. Patterson and R, M. Hammaker, Spectrochim. Acta, 23, 2333 (1967). (4) H. A. Laitinen, "Chemical Analysis," McGraw-Hill Book Co., Inc., Kew York, N.Y., 1960, pp 546, 547. (5) Since dimerization is strongly indicated, it is tempting to use Aamo/A27ioo values in Table I1 to calculate AHD for dimer formation.
This calculation assumes that the absorption coefficients for all bands are temperature independent so that a In K cs. 1 / T plot is faithfully reproduced by a In (A3500/A27100) us. 1 / T plot. However, the data for these systems indicate that this assumption is not justified and that A H o deduced from a In (A3500/A27100) vs. 1/T plot may be seriously in error. Measurements in dilute solution where there is no band near 3500 cm-1 (2.86 p ) show that the absorption coefficients of the bands in the 7 1 0 0 - ~ m -region ~ for all three alcohols decrease with increasing temperature after correction for the variation of solution density with temperature. Absorption coefficients for the 3500-em-1 region bands, although not directly measurable, can be obtained either by a least-squares technique (ref 3) or using a dimer concentration estimated by subtraction of the monomer concentration calculated from the 7100-em-1 band absorbance and the absorption coeffirient for the 7100-cm-1 band (measured in dilute solution where there is no band near 3500 cm-1) from the stoichiometric alcohol concentration. I n any case, the dimer absorption coefficient increases with increasing temperature. Unfortunately, the precision of these determinations often leaves something to be desired. However, these temperature variations of absorption coefficients are capable of changing A H o by more than a factor of 2 from the result of a In (A8500/A27100) 5s. 1 / T plot. (The values in Table I1 give A H o - 3 . 3 , -4.0, and - 2 . 1 for MeOH, t-BuOH, and DTBC, respectively. Introduction of the temperature dependence of the absorption coefficient changes A H o to -7.1, - 6 . 5 , and - 3 . 8 for MeOH, t-BuOH, and DTBC, respectively. All values are in kcal/mole.)
COMMUNICATIONS TO THE EDITOR Table 11: Average Values for
1839
A360O/A"?lOO
MeOH-CC14
-----Average value for
n = l
110-----_. n = 2
n - 3
n = l
n = 2
n = 3
n = l
n = 2
n = 3
4.29
59.3
1014
4.59
43.7
525
4.60
26.9
168
564 56
2.10 46
3.5 8
366 70
1.79 39
2.1 8
82 49
-----56"--
-----250--
A 3$0O/A7100 Probable errora
(PE/AVG)~x 100%
2.18 51
3.64 6
t-BuOH-CC14
Average value for
3.27
41.6
611
2.87
28.2
367
2.62
15.9
140
1.70 52
2.4 6
329 54
1.55 54
1.3 5
208 57
1.78 68
0.9 6
77 55
A3$00/~"1lOO
Probable errorn (PE/AVG)~x 100%
___--Average value for
DTBC-CCI4
-100--
n = l
n = 2
n = 3
----2o n = l
n = 2
n = 3
1.38
6.21
30.2
1.23
5.46
26.3
0.37 27
0.33 5
10.2 34
0.21 17
0.19 4
5.4 20
_--o
A3S00/An7100
Probable error' (PE/AVG)~ x 100% a
Calculated a t the 90% confidence level.
Probable error/average.
choice of n are activity coefficients and contributions to the monomer band by the free end groups of linear associated species. The low concentrations of alcohol and the small percentage of total alcohol present as the species causing the 3500 cm-l make interference from these sources seem unlikely. The work of Fletcher and Heller serves as a warning that the assignment of the 3500-cm-' (2.86-p) band should be carefully considered for each system studied. However, it appears that an OH. .OH dimer (cyclic or linear or both) is responsible for the 3500-cm-' (2.86-p) band for the systems treated here.
2.86-pm band. We have made a similar evaluation for methanol in carbon tetrachloride and collaborate the findings of Hammaker, et al. (curve AA in Figure 1). The evidence now clearly indicates that the 2.86-pm (2.82 pm for methanol in CCL) band is indeed due to the self-association dimer. These results would then suggest that the first-overtone region between the monomer and the cyclic tetramer bands should also show a second-order relationship for methanol in carbon tetrachloride in contrast to the first-order relationship that we found for 1-octanol in n-decane.2 I n Figure 2 it can be seen that for methanol in carbon tetrachloride, two definite peaks can be found near Acknowledgments. R. 11.C. and S. L. R. acknowl1.53 pm, one at 1.515 and the other at 1.535 pm. The edge the supporl of the XSF Undergraduate Research relative absorbance of these two peaks remains conParticipation Program, and P. E. R. acknowledges the stant and they show a first-order relationship (curve support of an NSF Summer Fellowship for Teaching CC in Figure 1) to the monomer absorbance indeAssistants. pendent of temperature when measured in the same DEPARTMENT OF CHEMISTRY R. M. HAMMAKER manner as our previous paper.2 When measured from KANSAS STATEUNIVERSITY ROBERTM. CLEGG the zero absorbance line (curve BB, Figure a), an MANHATTAN, KANSAS 66502 LARRYK. PATTERSON approximate first-order relationship is seen until the pan^ E. RIDER tetramer becomes predominant. Even with dimer STEVENL. ROCK absorbance per unit length as high as 1.0 cm-1 in the RECEIVED DECEMBER 18, 1967 fundamental, the formation of a measurable secondorder peak in the first-overtone region is not observed. The Alcohol Self-Association Dimer and We thus conclude that the 1.53-c~mband(s) is not an overtone of the 2.86-pm band. It is also not due to an the Absorption Band(n) near 1.53 pm alcohol-solvent interaction as its wavelength is no Sir: The communication of Hammaker, et d . , l is the (1) R. M. Hammaker, R. M. Clegg, L. K. Patterson, P. E. Rider, first direct evidence of a second-order relationship and 8 . L. Rock, J.Phys. Chem., 72, 1837 (1968). between an alcohol monomer absorption band and the (2) 8 . N. Fletcher and C. A. Heller, ibid., 71, 3742 (1967). Volume 72,Number 6 M a y 1968
