AARONN. FLETCHER AND CARLA. HELLER
3742
Self-Association of Alcohols in Nonpolar Solvents
by Aaron N. Fletcher and Carl A. Heller Chemistry Division, Research Departnzent, Naval Weapons Center, China Lake, California 93666 (Received March 10, 1967)
Studies were made of solutions of 1-octanol and 1-butanol in n-decane using the infrared absorption of the first overtone of the 0-H stretch vibrations of the monomer and selfassociation polymers. Evaluation was made on 1-octanol solutions from 5 to loo", without making use of a priori self-association models. Evaluations were performed by three methods involving comparisons of: (I) the monomer absorbance and the total alcohol concention, (11) the monomer absorbance and the polymer absorbance, and (111) a combination of I and 11. The following new assignments were made: (1) the end 0-H of linear selfassociation polymers do not contribute significant absorbance at the monomer peak in the first overtone region ; (2) the monomer molar absorptivity is constant with temperature; (3) the usual "dimer" peak at 1.528 p cannot be due to a 0-H . * 0-H dimer as its absorbance varies directly proportionally to that of the monomer (it is tentatively assigned to an alcohol-solvent interaction) ; (4) the remainder of the polymer absorption is assigned solely to tetramers; and (5) the tetramers give partially overlapping peaks which are due to 0-H bonds in two different tetramers. Thermodynamic values indicate a linear and a cyclic tetramer. The linear with three bonds has a AH of -16.5 kcal/mole and the cyclic with four bonds has a AH of -20.3 kcal/mole. Thus within the limits of error, all 0-H first overtone absorption is explained by assigning a monomer in equilibrium with two tetramers. This holds from lo-* M to neat 1-octanol over a 95" temperature range. Data from other workers for other alcohols in CCL are evaluated and found to be consistent with the present assignments. Much more self-association of alcohols was observed in n-decane than was observed in CCL In particular, kinetic data involving alcohols are explained by the physical model described.
Introduction The literature on the self-association of alcohols in nonpolar solvents does not present a uniform picture.1-a I n general, alcohols are considered to associate into a series of n-mema There have been many attempts at classifying the n-mers and at evaluating the equilibrium between the monomer and each n-mer' ultrasonic^,^ diele~tric,~ spectrophotometric,2sa vapor preSsUrel6 equation of state,' methyl radical abstraction,8 and nmr8 have been used with ambiguous results. Infrared spectra show a monomer 0-H stretch peak at low concentrations and polymer peaks which grow with concentration. Quantitative measurements have been made of the association of the monomer as shown by the monomer peak height. Assignments of polymer absorbances to dimer, trimer, and higher nmers have been made. Both linear (acyclic) and The Journal of Phvsieal Chemistry
cyclic n-mers have been postulated. A t the present time there is no agreed Physical Picture, much less quantitative constants, which can be used to describe an alcohol solution. (1)
(2)
F. Franks and D. J. G. Ives, Quart. Rev. (London), 20, 1 (1966). D. Hadzi, "Hydrogen Bonding," Pergamon Press, New York,
N. Y.,1959. (3) G. C. Pimentel and A. L. McClellan, "The Hydrogen Bond," W. H. Freeman and Co., San Francisco, Calif., 1960. (4) R.5. Musa and M. Eisner, J . Chem. Phys., 30, 227 (1959). (5) J. Malecki, ibid., 43, 1351 (1965). (6) E. Steurer and K. C . Wolf, Z . Physik. Chem. (Leipzig), B39, 101 (1938). (7) N. S. Berman and J. J. McKetta, J . Phys. Chem.. 66, 1444 (1962). (8) I. V. Berezin, K. Vatsek, and N. F. Kazanskaya, Dokl. Akad. Nauk sSSR, 144, 139 (1962). (9) v. s. Griffiths and G. Socrates, J . M ~ Zspectry., . 21, 302 (1966).
SELF-ASSOCIATION OF ALCOHOLS IN NONPOLAR SOLVENTS
Our interest arose through studies of an alcoholcatalyzed autoxidation of tetrakis(dimethy1amino)ethylene'o in n-decane. The oxidation rate was found to be fourth order in alcohol monomer over four orders of magnitude of the rate constant and first order at the lower concentrations. We monitored the monomer by the absorbance at 1.405 p . We interpreted these results as indicating that the tetramer was the major alcohol polymer in the solution. Alcohol dimers and trimers should also have shown a catalytic effect, yet we found negligible evidence of their existence. A preliminary spectrophotometric evaluation" of a tetramer equilibrium constant for 1-octanol was made at 30" on the basis that only monomers and tetramers were present. The equilibrium constant was used to evaluate Stern-Volmer fluorescence quenching constants.12 From the kinetic study'O.'' we found that the tetramer had a much larger catalytic effect for the autoxidation than did the monomer. In the present work a examination has been given to the Self-aSS0CiatiOn Of alcohols where W e Start with no a priori assumption with respect to the combination Of n-mers. I n particular, 1-octanol has been studied since it was used in the autoxidation kinetic work. Through examination of the near-infrared absorption of the monomeric and polymeric species we now find evidence for only the monomer and two tetramers. This is in sharp contrast with a number of recent paper^'^-'^ where experimental evidence is attributed to the presence of 0-Ha -0-H dimers. We hope that our experimental evidence will correct the widespread concept that the self-association 0-H 0-H dimer is present in appreciable quantities in nonpolar solutions. It has become rather common practice to assume the presence of a dimer a t the start of alcohol self-association studies. Without a measurable dimer, these evaluations have no meaning. We have evaluated the extent of self-association of 1-octanol over a wide range of concentrations and temperatures. Through a short study of the selfassociation of 1-butanol in n-decane and the reevaluation of self-association data of other alcohols in carbon tetrachloride, we believe that the results of the present study can be extended to give approximate equilibrium quotients for alcohols in hydrocarbon or carbon tetrachloride systems.
-
Experimental Approach Because of its chemical reactivity, we could not use carbon tetrachloride as a solvent in our autoxidation studies."J Instead, we used n-decane because of its high boiling point and its chemical inertness. Since n-decane absorbs heavily in the fundamental
3743
IO,
f
031
I30
I35
140
143
150
155
I 60
165
I70
WAVELENGTH, P
Figure 1. Varying concentrations of l-octanol in n-decane at 450 with n-decane in the reference beam, cells, The n-decane absorbance measurements were made with CClr in the reference beam.
0-H stretch region, we were forced to use the region of the first overtone from 1.4 to 1.65 p for spectrophotometric examination. As can be seen in Figure 1, n-decane also absorbs in this region. However, the hydrocarbon functional groups which cause the absorption by n-decane also exist in n-aliphatic alcohols. Thus it is possible to physically replace one for the other, as shown in Figure 1 by the near-isosbestic point at 1.39 p for varying concentrations of n-decane and 1-octanol. By using a double-beam technique with n-decane in the reference, we cancel almost all of the absorbance due to the CH2 groups of the hydrocarbon solvent. Complete cancellation is not necessary as we do not measure peak heights from the zero absorbance line but rather perform measurements from selected base points in the absorption spectra. Some type of cancellation is necessary in order to evaluate alcohol polymerization in the overtone (10) A. N. Fletcher and C. A. Heller, J. Catalysis, 6, 263 (1966). (11) A. N. Fletcher and C. A. Heller, presented at the Symposium on Chemiluminescence, March 31-April 2, 1965, at Durham, N. C. (12) A. N. Fletcher and C. A. Heller, Photochem. Photobwl., 4, 1041 (1965). (13) L. J. Bellamy and R. J. Pace, Spectrochim. Acta, 22, 525 (1966). (14) A. B. Littlewood and F. W. Willmott, Trans. Faraday SOC.,62, 3287 (1966). (15) D. A. Ibbitson and L. F. hloore, J . C h m . SOC.,76 (1967). (16) (a) 5. Sin& and C. N. R. Rao, J. Phys. Chem., 71, 1074 (1967); (b) A. Kivinen and J. Murto, Suomen Kemistilehti, B40, 6 (1967).
Volume 71, Number 1.9 November 1067
3744
AARON N. FLETCHER AND CARLA. HELLER
region. The results of Ens and Murray," for example, peak. However, none of the polymer absorbance is who looked a t a number of alcohols in carbon tetraobserved to extend lower than the 1,405-p peak as chloride in this region, are invalid a t higher concenshown in Figure 1 for even neat alcohol, and the monotrations since they did not correct for the effect of the mer peak remains a t essentially the same wavelength. CH, groups of their alcohol polymers. Figure 2 shows the variation of the absorbance of Most of the attempts to evaluate quantitative neat 1-octanol with temperature. It is obvious that equilibrium constants for alcohol self-association using the relative shape of curves in the polymer region spectrophotometric techniques make use of the varia(1.42-1.65 p ) vary considerably with temperature tion of the monomer concentration, AI, with respect changes. Yet when the concentration changes for to the formal (added) alcohol concentration,Ao,inorder any specific temperature, the relative proportions of to determine the extent of polymerization. The majority the curves change similarly to that found in Figure 1. of the workers, however, use concentrations of alcohol Since the relative shapes (Figure 2) do not change from only up to a few tenths formal. Most of the previous 1.61 to 1.65 p , we have concluded that absorbance in infrared papers covered the fundamental region where this region is due only to one species while we shall the large molar absorptivity of the species requires test whether the absorbance at 1.43 p is due only to a very small path lengths and where the polymer has second species. a higher absorbance relative to the m ~ n o m e r ~ ~ , By ~ ~ using the above working hypothesis, we shall (and consequent possible interference with monomerevaluate monomer and polymer absorbances. The absorbance measurements) than it does in the overtone mathematical consistency of the results will be used region. By working in the overtone region and by to test the stated working hypothesis and to assist in the using a Beckman DK-2 spectrophotometer with full assignment of the absorption bands. scale ranges from 90 to 100% transmission up to 1-2 in absorbance, it was possible to use only a single 1-cm Experimental Details path length for a range of concentrations of low3M up Apparatus. A Beckman DK-2 spectrophotometer to above 6 M for pure 1-octanol or above 10 M for 1A was used to determine the absorption spectra. butanol. Beckman No. 92527 temperature-regulated cell holder Measurement of Absorbances. We make the hywas used to control the temperature of the sample and pothesis that the absorbance peak a t 1.405 p is due reference solutions to within * l o above 45". The solely to the monomer. We measure the 1.405-p solutions were controlled to =kO.lOo at 30°, and to peak from the solution absorbance at 1.39 p . The d=0.5" at the rema.ining temperatures by circulating CH, absorption at 1.39 p is almost an isosbestic point a tempering solution to the cell holder from a thermistorbelow 50" for solutions of 1-butanol and 1-octanol in controlled external source. The temperature of the n-decane. ;\lecke20 has shown an approximate 1-1 solutions were measured in their cells by means of relationship between the 1,405-p overtone absorbance a Digitec digital thermometer. and the 2.76-p fundamental absorbance associated Chemicals. The 1-octanol was reagent grade obwith the monomer. We measure the absorbance of tained from J. T. Baker Chemical Co. It was dried a polymeric species at 1.43 p from the 1.39-p base by Linde molecular sieve 4A and distilled under an point since 1.43 p also corresponds to a large amount atmosphere of purified helium. The n-decane was of n-decane absorption. For regions that have a low % obtained from the Phillips Petroleum Co. 95 mole n-decane absorption such as at 1.61 p, we use the It was digested with 30% fuming sulfuric acid, minimum solution absorption near 1.30 p where nwashed with concentrated sulfuric acid, water, and decane has another area of low absorption. sodium hydroxide solution, and dried with activated The problem of considering whether polymeric It was then distilled from sodium under an alumina. species absorb at the same region as the monomer is atmosphere of purified helium. The 1-butanol was very vital to the mathematical evaluation. Pimentel A.C.S. grade obtained from Allied Chemical Co. and McClellan3 conclude that the absorbance associated Methanol and toluene were Spectroquality reagent with the monomer cannot be directly related to the concentration of the monomer if linear polymeric (17) A. Ens and F. E. Murray, Can. J . Chem., 3 5 , 170 (1957). species are present. This conclusion is based upon the (18) F. A. Smith and E. C. Creitz, J . Res. Natl. Bur. Std., 46, 145 assumption that an 0-H group with a hydrogen(1951). bonded oxygen will absorb a t or near the wavelength (19) 9. C. Stanford and W. Gordy, J . A m . Chem. Soc., 6 2 , 1247 of the monomer. There is, indeed, a large absorbance (1940). at wavelengths only slightly higher than the 1.405-p (20) R. Mecke, Discusawns Faraday Soc., 9, 161 (1950). The Journal of Physical Chemistry
SELF-ASSOCIATION OF ALCOHOLS IN NONPOLAR SOLVENTS
1.1
3745
100
I
v)
a W
t-
80
I-
W -I
0d
0 W
z 0.7
P In
0.6
zz
0,s
tt-
V,
e
a
z
a a
Y
P a
E a
60
u a
0.4
100
5-
v)
c
40
W
rL
90
5z a t" I-
0.3
z
20
W
u a
0.2
W
t
0. I
1
80 e
0 1.60
q.30
0.0
1.40
1.50
WAVELENGTH, p -0.1
L-.-
' WAVELENQTH,
Figure 3. Methanol in toluene solutions at about 30". Concentrations are: A, 2.5 F; B, 0.5 F; C, 0.25 F; D, 0.1 F; and E, 0.0 F. A prime is used for spectra of the solution when it is examined using the 75-125% transmission mode.
p
Figure 2. Neat 1-octanol in the sample beam and n-decane in the reference beam at various approximate temperatures in 0.5-em cells.
grade from Matheson Coleman and Bell. The last three chemicals were used without further purification.
Results The absorbances assigned to distinct species are calculated by the differences a1 =
a'1.406
- a'l.39
(1)
atria =
a'1.43
- a'i.ae
(2)
=
a'1.61
+
(3)
a1.61
a'1.30
where primed values indicate values measured from the zero absorbance line. The absorbance a1 is considered as representing the monomer at concentration A1, where the formal (added) alcohol concentration is Ao. Tables of our data are available elsewhere.2l Figure 3 shows the spectra of solutions of methanol in toluene at about 30". Here an example of the scale expansion of the Beckman DK-2 can be seen.
Calculations Method I--Graphical. A molar absorptivity, €1, can be calculated for the alcohol monomer from the relationship, e1Ao = al since a plot2*of al/Ao us. AO gives a constant value as A . + 0. For 30"we found e1
to be 1.65 as reported earlier.1a-'2 Using this el we can calculate the monomer concentration, AI, in any sample from the relationship A1 = al/el. The total polymer will be (Ao- A1) formal. The concentration of each n-mer, A,, will be given by the thermodynamic equilibrium constant
(4)
If any one n-mer is predominant it will show on a log plot of (Ao- Al) os. AI. When such a plot is made2' we find a fourth-order relationship between A1 and (Ao- A1) for concentrations down to the region where A1approaches the value of Ao,making the value of (AoA1) inaccurate. Since this method does not yield easily accessible information concerning small amounts of other n-mers, we tested our data further in the following section. Method I- Computer Pit. One can also express t,he (21) Tables containing data supplementary to this article have been deposited as Document No. 9555 with the AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington, D. C. 20540. A copy may be secured by citing the document number and by remitting $2.50 for photoprints or $1.75 for 35-mm microfilm. Advance payment is required. Make checks or money orders payable to Chief, Photoduplication Service, Library of Congress.
Volume 71 Number 12 -?'orember 1967 ~
AARON N. FLETCHER AND CARLA. HELLER
3746
Table I : Variation of the Coefficients" of the Regression Equation With Some Terms Set to Zero for 30'
0.25 -0.32
x x
104 104
x
104
-0.22 x 104 0.0 -0.29 x 104 -0.18 X 10' 0.0 0.0 0.0 0.0 0.0 0.0
0.0
0.0 -0.30 0.0 0.0 0.0
0.0 0.0 a
Ci = iK1,ijqi.
Table
2
Ci
CS
0.90 0.32 0.40 0.34 0.31 0.24 0.26 0.27 0.28 0.0
x 10' X 10' X 10' x 103 X loa X 10' X 10% X 10' X 10'
* Average relative standard deviation.
-0.62 X -0.15 X -0.12 x 0.0 0.0 0.16 X 0.59 X 0.0 0.0 0.11 x 0
10' 10' 10%
10* 10'
10'
0.23 X 101 0.81 x 10-1 0.51 -0.14 -0.12 -0.91 0.0 0.43 0.0 -0.83 X 10'
0.5866 0.6055 0.6017 0.6085 0.6065 0.6156 0.6022 0.5981 0.6127 0.7079
0.0482 0.0492 0.0490 0.0492 0.0493 0.0500 0 .050gC 0.0521 0.0545 0.1013
Best fit with no negative coefficients.
II: Best-Fit Equations with No Negative Coefficients from 5 to 100" for l-Octanol
C4
100 75 45 30 15 5 0
0.26 0.21 0.34 0.0 0.0 0.0
0.0 0.0 0.0 0.59 X 10' 0.11 x 10% 0.13 X 10'
0.84 0.53 X 10' 0.62 X 10' 0.26 X 10' 0.12 x 104 0.30 x 104
Average relative standard deviation.
0.6176 0.6227 0.5908 0,6022 0.6811 0.5381
0.0463 0.0578 0.0611 0.0509 0.1298 0.1079
30 25 31 38 20 23
j = number of paired values of added alcohol concentration, Ao, and monomer absorbance,
at.
relationship between A. and the monomer absorbance, ai, in an algebraic equation. First we write
A0 = A1 + 2Az + 3A3 + + nA, ( 5 ) where A, is the molar concentration of the n-mer or the sum of several subforms of the n-mer. Then by making use of eq 4 between the monomer and each nmer, it is possible to rewrite eq 5 as
Ao
=
Ai
+ 2K1,2-4i2 + n&,nAin * * *
(6)
Substituting the absorbance and molar absorptivity for the concentration of the monomer, we obtain
Ao
+
+
= U ~ / E I 2Ki,2ai2/(~1)'
* *
was minimized. The program was written so that it was possible to set any coefficient equal to zero or to some other fixed value. This made it possible to eliminate results which yielded negative coefficients, and also to evaluate results from different temperatures using the samemolar absorptivity for the monomer. We searched for the mathematical best fit of eq 7, using an IBM 7094 computer, using the chemical criterion that no coefficient could be negative. Of the valid (no negative coefficients) solutions, we used the one with the smallest average relative standard derivation
+ nKi,naln/(dn (7)
The coefficients, Cf, of the power series in a1 were obtained by fitting a regression line to the data in which the square of the relative difference between the summation of j observed and calculated values of the added alcohol
k([Ao(obsd) - Ao(ca1cd) ]/Ao(obsd))2 1
The Journal of Physical Chemistry
as the closest approach to the correct polymer picture. This search was done a t each temperature for which we had data, using as high as sixth-order terms. Table I shows an example of how the coefficients varied at one temperature as we searched for a best solution. Table I1 shows the coefficients for the valid best-fit equations for each temperature. The predominance of the fourth power is evident from this table.
3747
SELF-ASSOCIATION OF ALCOHOLS IN NONPOLAR SOLVENTS
~~
4.0 1
~
Table III : Equilibrium Quotients for 5-100" Polymerization of 1-Octanol Using l/a Equal to 0.6065. Only All Positive Combinations of K's Are Shown Kls4
Ki,r
Kl,a
3.0
-
2.0
-
1.0
-
8 0.0
-
Ua
looo 1.887 0.968 1,523 0.0 0.0
0.0 0.940 0.0 0.188 X 101 0.0
0.0 0.0 0.408 0.0 0.149 X 10'
0.0776 0.0618 0.0478 0.0784 0.2093
75O
1.064 x 10' 0.801 X 101 0.966 X 101 0.0 0.0
0.0 0.165 X 10' 0.0 0.622 X 10' 0.0
0.0 0.0 0.396 0.0 0.236 X 101
0.0743 0.0638 0.0597 0.1276 0.3153
1.179 X lop 1.106 X loz 1.157 X loz 1.106 x 102 0.0 0.0
45" 0.0 0.241 X 101 0.0 0.237 X 101 0.331 X lo2 0.0
0.0 0.0 0.234 0.416 0.0
0.464 X 101
0.0643 0.0628 0.0629 0.0628 0.2028 0.4087
0.518 X loa 0.480 X lo8 0.507 X 108 0.0 0.0
30 " 0.0 0.0 0.774 X 101 0.0 0.0 0.397 0.843 X 108 0.0 0.0 0.608 X 101
0.0550 0.0511 0.0526 0.2340 0.4257
0.241 X lo4 0.209 x 104 0.229 X lo4 0.0 0.0
15" 0.0 0.459 X lo2 0.0 0.280 X 108 0.0
0.0 0.0 0.226 X 101 0.0 0.1821 X loa
0.1444
0.701 X lo4 0.611 X lo4 0.692 X lo4 0.0 0.0
5" 0.0 0.994 X loz 0.0 0.590 X 108 0.0
0.0 0.0 0.875 0.0 0.167 X 102
0.1323 0.1224 0.1315 0.3145 0.5709
a
Y -I
A
x
10-3
0.1352 0.1360 0.3220 0.5680
Average relative standard deviation.
We next looked at the values of 1/61 (=CI).The values of Table I1 indicate no specific drift with temperature, so we decided to use one value at all temperatures. To do this we used j-weighted averages of the values of 1/61 in Table I1 and obtained an average of 0.6065. This value compares closely with the 30" value of 0.60606 we obtained by measurement of the 30"molar absorptivities at low alcohol concentrations.10-12 Fixing this coefficient we again solved for the valid combination of eq 7. Table I11 shows the calculated value of K1,,
-3.0
2.6
I
I 2.8
I
I I I 3.0 3.2 1OW/T, KELVIN"
I
I 3.4
I
3
Figure 4. van't Hoff plot of method I equilibrium quotients of 1-octanol. Curve A represents the leastrsquares line for the monomer-tetramer equilibrium quotient, Kt,,, calculated by considering the tetramer as being the only polymer while curve B represents KI,I from the beatrfit data where other polymers are allowed. Curves C and D represent the monomer-trimer and the monomer-dimer equilibrium quotients, respectively,from beat-fit equations.
obtained in this fashion, making use of a constant value of 0.6065 for 1/01 at all temperatures. The mathematical fit of the data in Table 111can be given an additional chemical restraint by a comparison of the various chemically valid equilibrium quotients with changing temperatures. Figure 4 shows a van't Hoff plot of the equilibrium constants for the best-fit data of Table 111. The dimer values are obviously scattered and yield a positive AH. The trimer line looks good but the slope is almost the same as that of the tetramer and probably represents just errora from the tetramer line. General Evaluation of AH Values Determined from Method I Type Calculations. Values of AH from method I type calculations have been used to support a particular equilibrium model if the AH/bond value falls near values found in other studies. We started to use this approach by dividing AH by either n or n - 1. Surprisingly, we found that the AH/bond values varied from -4 to - 6 kcal for ahnost all of the alcohol selfassociation models which gave positive equilibrium quotients from our data. In order to test the validity of this type of evaluation, we took the absorbance values from our 5, 45, and V d u m 71, Number 1% Nmstnber 1987
AARONN.FLETCHER AND CARLA. ME,,
3748
~
100" data, and used the K I , equilibrium ~ quotients for the monomer-tetramer(on1y) model from Table III to calculate synthetic formal 1-octanol concentrations to 10 significant, digits. These values would thus correspond closely to the actual concentrations and yet would represenC a precise tetramer(on1y)-monomer equilibrium with the same number of data points and ahsurbance values as the real data. We then fit secondthrough sixth-order equations where we evaluated oniy the constant of the highest order terms and the :nonomer terms from the synthetic data. Sixth-order eqiiations eralcating all terms were calculated which gave very good checks on the computer. At 100", fur exampie, we obtained
i t o =- -0.23>
