AARONN. FLETCHER
1808
Self-Association of Methanol Vapor. Evidence for Dimers and Tetramers by Aaron N. Fletcher Chemistry Division, Research Department, Code 6059, Naval Weapons Center, China Lake, California 98555 (Received July 1 , 1970) Publication costs assisted by the Naval Weapons Center, China Lake
In an attempt to help resolve conflicting interpretations as to the major self-association species of alcohols, a spectrophotometric study of methanol vapor has been made from 2.5 to 3.0 ,um taking measurements every 0.1 nm. The interdependence of the absorption of monomer and polymers was determined making use of absorption spectra integrated over 501 different wavelength regions. Particular attention was given to the problem of band overlap in the assignments of absorption to the various species. After computer subtraction of the monomer spectra, polymer bands at about 2.775 and 2.950 pm were found to show second- and fourthorder relationships with the monomer concentration, respectively. The wavelength region from 2.80 to 2.90 pm, intermediate to the two bands, consisted only of overlaps of these bands. These results are interpreted as evidence for dimers and tetramers as the major self-association polymers of methanol vapor.
Introduction Previous workers, using heat capacity, P V T j 2and infrared absorption data,a concluded that the most probable major self-association species of methanol vapor were the dimer and the tetramer. This 1-2-4 model also has been used to explain heat capacity data of a number of other alcohols in the gas pha~e.~-lORecently, however, Tucker, et al. ,11 have reported that their data could be best explained by the existence of only monomer, trimers, and octamers of methanol in both the gas phase and in nonpolar solvents. The usual approach for the selection of models of self-association is to use some form of a material-balance equation. Material-balance equations, however, have an inherent limit to their range of application evoked by the saturation pressure in the gas phase and the neatsolution concentration in the liquid phase. Furthermore, condensation upon the walls of the container increases the possibility of significant experimental bias in the concentration range of greatest interest in selfassociation studies of vapors, i.e., the pressures just below saturation. The purpose of the present study is t o determine all the significant n-mers (n is the number of monomer units contained in each polymer molecule) formed in the self-association of methanol in the gas phase without using material-balance equations. By examination of both monomer absorption and polymer absorption in the wavelength region 2.5 to 3.0 pm, five major advantages will be achieved. First, it will be possible to determine monomer-polymer mathematical relationships at low concentrations where material-balance equations would be sensitive only to the monomer and thus provide a wider range of measurements. Second, it will be possible to check for interference in the determination of the monomer concentration by the presence of polymeric species. Retention of a mathematical The Journal of Physical Chemistry, Vol. 7 5 , No. 12, 1971
relationship between the monomer absorbance and a polymer absorbance, from low concentrations to high, will be used as evidence of an insignificant amount of polymer end-group absorbance at the wavelengths used to measure the monomer. Third, examination of all of the available polymer absorption wavelength region allows a comparison of polymer absorption at different concentrations and thus the detection of any new polymer species. This procedure detects wavelength regions (if they exist) where only polymers having the same value of n are found. This ensures not only that all measurable n-mers have been detected, but it also ensures against the introduction of a more complicated model which gives a better “fit” to the monomerpolymer relationship. Fourth, the relationships between the monomer and the n-mers can be determined for each individual sample. Thus, it is possible to determine the constancy of the equilibrium quotients over a wide range of absorbance values, temperatures, and concentrations. And fifth, since the quantitative measurements of the methanol are not, used in the determination of the self-association polymers, wall condensation errors are not a problem. (1) W. Weltner, Jr. and K. S. Pitzer, J . Amer. Chem. Soc., 73, 2606 (1951). (2) C. B. Kretschmer and R. Wiebe, ibid., 76, 2579 (1954). (3) R . G. Inskeep, J. M. Kelliher, P. E. McMahon, and B. G. Somers, J . Chem. Phys., 28, 1033 (1958). (4) G. M. Barrow, ihid., 20, 1739 (1952). ( 5 ) J. F. ,Mathews and J. J. McKetta, J . Phys. Chem., 65, 758 (1961). (6) N. 9. Berman and J. J. McKetta, ihid., 66, 1444 (1962). (7) E. T. Beynon, Jr. and J. J. McKetta, ihid., 67, 2761 (1963). (8) J. L. Hales, J. D. Cox, and E. B. Lees, Trans. Faraday Soc., 59, 1544 (1963).
(9) N. S. Berman, C. W. Larkam, and J. J. McKetta, J . Chem. Eng. Data, 9,218 (1964). (10) N. S. Berman, AIChE J . , 14, 497 (1968). (11) E. E. Tucker, S. B. Farnham, and S. D. Christian, J . Phys. Chem., 73, 3820 (1969).
SELF-ASSOCIATION OF METHANOL VAPOR
Experimental Section Equipment. Spectral measurements were made with a Cary 14RI spectrophotometer with the monochromator grating blazed for maximum efficiency at 1.6 pm and having a Cary 1490090 Universal OjoT Slidewire. The Universal Slidewire has the capability of expanding any 5, 10, 20, 50, or 100% transmission (%T) full scale starting at any specified integral %T within the range of O-lOO~oT. The output of slidewire was transferred to a 1000 unit digital readout, making a theoretical output scale of 20,000 units. I n practice, noise-time considerations limited the system to a maximum sensitivity of the 10%T range (10,000 units). The absolute value of the %T scale was checked at 5 different points with calibrated rotating sector disks (Beckman Instruments) and found to be within the 0.2% error rating. Measurements were made every 0.1 nm and both the wavelength and the slidewire output were punched onto paper tape. The calculated spectral resolution was 2 cm-' a t 3.0 pm and less than 1 cm-l at 2.5 pm. The insttrumerit was continuously flushed with dried air. An insulated stainless-steel gas cell with an 18.9-cm light path was used to take spectral measurements. The spectrophotometer cell used four calcium fluoride windows with an evacuatable separation between the end windows. A Lauda Type N constant-temperature bath was used to pump Union Carbide UCON HTF-10 fluid to a jacket around the length of the spectrophotometer cell. A Hewlett-Packard quartz thermometer was used to measure the temperature of the UCON HTF-10 in the cell jacket and inside the main constanttemperature bath. The outer portion of the spectrophotometer cell was insulated with polyurethane foam and epoxy-fiberglass. Quantitative measurements of gas concentration were made by breaking sealed glass ampules of methanol inside an additional chamber connected to 0.15-, 1-, and 9-1. tanks. The tanks and addition chamber were calibrated by weighing distilled water into them (using a 3-kg capacity balance accurate to 1 mg). Repeat measurements gave differences on the order of 0.02% relative error. Hoke stainless-steel bellow valves were used throughout the system. Except for a heated '/*in. 0.d. stainless-steel tube connecting to the spectrophotometer cell, the remaining portions of the all stainless-steel system (in contact with methanol) were submerged in a 50-gallon constanttemperature bath containing UCON HTF-10 bath fluid. A Bayley Inst. Co. Precision temperature controller (Danville, Calif.) allowed temperature control of the main bath in the range of fO.001 to 0.01" depending upon the absolute temperature. The spectrophotometer-cell temperature variation was f0.3". Pressure could be measured by a means of a Pace DifferGage (submerged in the Oil bath) sensitive to Oeol psi full scale. The Pace Gage drove a Texas Instrument CO. EO.150 LPC pressure controller. The
1809 gas pressure was measured with a Texas Instrument Co. 0-3000 Torr Quartz Precision Pressure Gage (readable to 0.01 Torr). Material. Spectroquality methanol from Matheson Coleman and Bell was distilled from calcium hydride at slightly greater than atmospheric pressure. Distillation and all transfers were made in the absence of air. The flask of methanol was cooled with solid COz and the pressure reduced to partially degas the methanol before its transfer by distillation to the glass ampules. Matheson Prepurified Grade (99.998% min) argon was used to preflush the distillation equipment and to pressurize the methanol system. Procedure. Weighed portions of methanol (corrected for air-density effects) were introduced into the evacuated stainless-steel system yielding a known concentration of methanol in the 1-and 9-1. tanks. Both tanks were in turn pressurized with argon so that expansion of either into the spectrophotometer cell would result in a total pressure of 2400 Torr. A 100-W heater was wrapped around the two tanks to create a hot band. Although 1 hr of mixing with the hot band appeared sufficient, quantitative measurements were always made with a minimum of 15 hr of mixing. Some of the nonquantitative high-concentration runs were mixed in the spectrophotometer cell by raising its temperature 20 to 30". A number of successive runs were made from a single weighing of methanol by expanding the known concentration of methanol in the 9-1. tank into the evacuated 1-1. tank. Evacuation to better than Torr measured with a Veeco Discharge Pressure Gage was possible. Spectrophotometric calibration runs were made for every two sample runs. Because of some of the high scale sensitivity-high pen dampening, some spectrophotometric runs from 3.0 to 2.5 pm required up to 4 hr to perform. In order to make full use of the OjoT scale expansion, a series of runs was necessary to obtain a complete absorption spectrum, e.g., 60 to 80OjoT combined with a 80-100%T run were common. Also, mixed-range runs were performed giving priority to values on the more sensitive range, e.g., 80-100%T combined with a 0-100%T run. These combinations as well as most of the other manipulations of the data were performed on a Univac 1108 computer.
Results and Discussion Measurement of the Monomer Concentration and Xpectra. Quantitative measurements of the formal methanol concentration were made only high enough to ensure that Beer's law was applicable and t o determine when the formal12 polymer concentration was significant, i e . , was high enough so as to make more than a (12) The term formal ( F ) is used t o express the mathematical concentration of the added material without consideration of any chemical reaction within the solution. Molar ( M ) is used to express known (tentative 01 real) concentrations. The Journal of Physical Chemistry, Vol. 76,N o . 13, 1971
1810
AARONN. FLETCHER
possible 1% error in the determination of the monomer concentration. Since over '/z million absorption measurements were recorded and used in calculations, it was necessary to transform the data to a reduced form. The spectral absorbance values of data measured up to and including k0.5 nm from each integral nanometer were integrated using the trapezoid formula and associated with the integral nanometer. This transformation reduces the 5011 absorption measurements used for each run down to 501 integrated absorbance values, I x . Figure 1 shows a semilog plot of these condensed values for the monomer of methanol at 80". The condensed spectrum has the appearance of that expected from an instrument of lower spectral resolution. In order to test for the applicability of Beer's law, the relationship
-zr
10.0
3 W
0
2z a 8
9
Q
1.0
0.1
W
2W
n
= 0.01 2.6
2.7 2.8 2.9 WAVE LENGTH ((1 METERS)
3.0
Figure 1. Condensed absorbance curve for 0.0033 mol L-1 of methanol vapor a t 80".
A test will be described in a later section, however, that
indicates a negligible interference is possible when shifting monomer determinations over the 2.652.70-pm spectral region. Because of the great emphasis to obtain monomer measurements free from end-group absorption, a major portion of this study was performed at concentrations where the polymers represented only a small proportion of the total methanol present. At EA-+ ~ ~ (as1 A) O---f AI (2) higher concentrations, where the polymer concentration where ~ ~ (is1the ) molar absorptivity of the monomer at was significant, the monomer absorption was too intense wavelength X and AI is the monomer concentration in for accurate measurement in the wavelength region moles liter-l. If Ex is a constant for a range of formal where end-group absorption would be expected. For alcohol concentrations when the polymer concentration this reason it was not possible, with the present specis low, we can then use Beer's law to determine the trophotometer cell, to determine whether absorption of monomer concentration, AI, at all concentrations. acyclic species was present near the Q band. It was found convenient to make use of the sum of the The monomer concentrations were measured, where integrated absorbance units, I A , for ten successive h possible, with ~ ( h values ) in the prime range of 10 to values in this and other tests. A unit y(X) is defined 100 (corresponding to average absorbance values of 0.1 to 1.0) shifting to different wavelength regions as (3) necessary. The validity of this procedure was confirmed by the constancy of y(h) e.g., a relative where h is measured in nanometers as a subscript and in error of 0.36% was found for 14 values of ~ ( 2 . 6 7 ) / micrometers in the parentheses. Values of r(2.67)/Ao ~ ( 2 . 6 6for ) the prime results of 80". Values outside the along with other basic data are presented e1~ewhere.l~ prime region are still usable as the ratios using y(X) These ratios at 40, 80, and 120" were observed to be values from 1 to 230 were in reasonable agreement with constant at low concentrations confirming that our those in the prime region of 10to 100. spectrophotometer-computer system had the resolution Determination of Polymer Absorbance from 2.76 to needed to make use of Beer's law and thus measure the 3.00 pm. The absorbance a t wavelength X can be exmonomer concentration. pressed by Although Beer's law may be valid at low concentraIA = b[€x(l) x A1 EX(2) x tions, absorption from the nonhydrogen-bonded 0-H proton of acyclic polymers, if they are present, could A, . . . €A(%) x An1 (4) interfere with the determination of AI at higher concenby applying Beer's law for each possible self-association trations. Bellamy and PaceI4 have shown by difspecies. eA(n)is the apparent molar absorptivity of ferential spectroscopy that the polymer end-group aball polymers made up of n monomer units at wavelength sorption peak of methanol in ccl4 is shifted to 2.750 pm from the monomer peak at 2.745 pm. I n order to re(13) Tables of basic data and statistical correlations will appear duce the chances of end-group interference, all monomer following these pages in the microfilm edition of this volume of the determinations in the present study were made on the journal. Single copies may be obtained from the Reprint Dept., ACS Publications, 1155 Sixteenth St., N.W., Washington, D. C. R-rotational band in the wavelength region 2.65 to 20036. Remit $4.00 for a photocopy or $2.00 for microfiche. 2.70 pm. It should be noted that no assumption is (14) L. J. Bellamy and R. H. Pace, Spectrochim. Acta, 22, 525 made here as to the absence of end-group absorption. (1966). b X EA X Ao (1) can be written where Ex is the formal absorptivity observed at wavelength A, A0 is the formal added methanol concentration in moles l i t e r 1 , and b is the cell length. At low alcohol concentrations
Ix
+
The Journal of Physical Chemistry, VoL 75, No. 12,1971
+
1811
SELF-ASSOCIATION OF METHANOL VAPOR Equation 4 can also be expressed using the mass-law equilibrium constant, &,, relating the concentration of the monomer, Ai, with the concentration of each n-mer, An A.
+
4
4.0
.
Ix = b [ ~ , ( l ) X Ai ex(2) X Ki,2 X Ai2 . . . eh(n)X K 1 , n X Ain] ( 5 )
+
By using one of the low-concentration monomer curves (0.00058 F at 120") 0.0012 F at 80", and an average composite at 40") expanded so that its absorbance matches the monomer absorption [usually y(2.68)] of the sample of interest, it is possible to subtract the monomer absorption. The polymer absorption curves can be represented by Ah
=
Ih - b X
eh(1)
=
b [ ~ h ( 2X )
K1,2
X AI X Ai2 . . .
2.5
2.6
2.7
2.8
3.0
2.9
WAVE L E N G T H (1.1 M E T E R S )
Figure 2. Polymer absorption of methanol vapor at 40".
+
eh(n) X K1,n X Ai"] (6) An example of a plot of A may be seen in Figure 2 where two prominent absorption peaks at 2.775 and 2.950 pm are found for methanol vapor a t 40". The region from 2.65 to 2.75 pm is illustrative of the efficiency of this procedure. All of this region is reasonably flat except for the very sharp spike of the Q band at 2.716 pm showing very little change in the shape of the monomer absorption band over a wide range of absorbance values. Determination of the First Significant n-Mer and Testing for End-Group Interference. Since a major problem in the evaluation of infrared data for selfassociating species is to ensure that absorption is really caused by the species ascribed to it, the absorption data of this report were examined in several ways. Figure 1 shows that the monomer absorbs throughout the 2.53.0-pm region. That the spectra were due to the monomer was confirmed by the constancy of band shapes using overlays of log absorbance plots at different low concentrations. A trial subtraction of the "monomer" absorption using eq 6 results in the A(2.75 to 2.80) values shown in Figure 3. Of the results at the three different temperatures, the 120" curves showed essentially no 2.95-pm absorption, the 80" curves showed 2.95-pm absorption at the higher concentrations, and the 40" curves showed the 2.95-pm peak only at the two highest concentrations. We are concerned with this 2.95-pm absorption region, since end-group absorption, associated with it, if there is some, might absorb in the 2.75-2.80-pm region. Since the slope of the data in Figure 3 remains the same for data both with and without 2.95-pm absorption, however, it would appear safe to conclude that any high-polymer end-group absorption is not significantly affecting absorption from 2.75 to 2.80 pm. The presence of measurable polymer end-group absorption at wavelengths where the monomer was determined would cause A1 values to be too large. This
0.001
0.01
0.1
MONOMER CONCENTRATION (MOLE LITER->)
Figure 3. Determination of the n-mer responsible for the 2.775-pm absorption band. Solid lines are second order in monomer concentration.
would in turn cause A to be smaller and AI" to be larger than their true values. Both effects would have caused measured AIAI" values to become smaller at high concentrations than at low. No such trend is observed in Figure 3 as the data do not show curvature, i.e., A/ AI" = constant.I8 Since the data fit a second-order line we appear to be observing the first (and only the first) term in eq 6. The 2.775-pm band is consequently assigned to the dimer. Note should be taken that the constancy of A/Aln does not show that no end-group absorbance occurs from 2.65 to 2.70 pm. The lowest concentrations were measured where at least 99% of the formal concentration was monomer so that no measurable end-group absorption could have been seen. These results consequently only show that any endgroup absorption was not sufficient to change the A/ Aln relationship from the lowest to the highest concentrations examined remembering that we sometimes shifted wavelengths in order to use prime absorption values.13 There are four factors that reduce the end-group absorption by methanol polymers in the gas phase in the wavelength region 2.65 to 2.70 pm. First, the increased mass of the polymers reduces the intensity of the rotaThe Journal of Physical Chemistry, Vol. 76, N o . 12, 1971
1812 tional P and R bands compared with those of the monomer. A loss of rotational bands occurs in Figure 2 although experimental "noise" may not make this too apparent. Second, the change in electron density of the 0-H group caused by hydrogen bonding has been observed to shift the end-group absorption of the polymer to longer wavelengths in the liquid-phase study of Bellamy and Pace.14 Third, some of the polymeric material may be cyclic and consequently introduce no end-group absorption. Fourth, the polymer must have reduced end-group absorption from that of the equivalent formal amount of monomer units since at least n - 1 monomer units must be involved in the hydrogen bonds that hold the polymer together. Thus, the tetramer at the very most mould have 1/4 the endgroup absorption of the four monomer molecules from which it is formed. The first three factors n~ouldact to reduce even further the end-group absorption at the wavelengths used to determine the monomer in the present study. On the basis of the frequency shift and band width of mixed dimers, Reece and Werner15 also concluded that the 2.775-pm band (which they measured as peaking at 2.778 pm for methanol vapor) was due to the dimer. Similar arguments were made by i\Iurty16for the existence of dimers of methanol and other alcohols in the liquid phase. Starting with this band-position information as evidence for the existence of the dimer, then the constancy of the A(2.75 to 2.80)/A12data serves to confirm the validity of the mass-action equations, the applicability of the spectrophotometer-computer system to separate absorption curves of the self-association species of methanol vapor, and the absence of endgroup interference in the determination of all of the Al values in this study. The 120" absorbance values for A a t wavelengths greater than 2.8 pm were found to be quite low when the formal polymer concentration was measurable. l 3 Hence, not only is the 2.775-pm peak formed by a dimer but its concentration is large enough to be detected by material-balance equations at 120". Since the dimer equilibrium quotient should increase with decreasing temperature, and since its absorption band was still quite significant at 40" (Figure 2)) it is concluded that the dimer is a significant species for a general model of the self-association of methanol vapor over a range of temperatures. The Ratio Test and Determination of the Xecond Significant n-Mer. Studies of hydrogen bonding of mixed dimers in solution show that the bound 0-H. . has a shift from the wavelength of the monomer towards longer wavelengths with increasing heats of reaction.17-20 A simplified explanation for this is: The stronger the hydrogen bond, the weaker the 0-H bond, and hence the shift of the 0-H stretch vibration to longer wavelengths. The recent evidence by Barnes and Hallam21r22 on alcohols in an argon matrix strongly The Journal of Physical Chemistry, Vol, 76, N o . 12, 1971
AARONN. FLETCHER
6.0
0
4.0
2.0
2.75
2.80 2.85 2.90 2.95 W A V E LENClTH ( p METERS)
3.0
Figure 4. Example of ratio of polymer absorbances, A, 80'. Results labeled by monomer concentrations: curve A, 0.0358/0.0343; curve B, 0.0358/0.0284; curve C, 0.0390/0.0284; curve D, 0.0368/0.0238; curve E,
0.0440/0.0284.
favors an acyclic form of the dimer. If the dimer were cyclic, the marked wavelength separation from the higher polymers could be attributed to a weak, bent, hydrogen bond. But an acyclic dimer far removed from the wavelength position of the higher polymers suggests a marked sensitivity of the 0-H bond strength to the relative location of the 0-H group within the self-association polymer. Thus the acyclic tetramer should have four different "types" of 0-H groups which should absorb in four different wavelength regions.Z3 It is consequently unlikely that the band position of the smaller self-association polymers would be identical. In order to test whether wavelength regions, in addition to the dimer, exist where only a single polymer absorbs, a ratio of A values for two different concentrations of monomer was made from 2.75 to 3.0 pm. In wavelength regions where absorption of a single n-mer is predominant, the ratio of two A values from eq 6 reduces to A(j)/A(lc)
=
[Al(j)/Al(lc)]" = constant
(7)
where the letters in the parentheses designate different concentrations. As the hydrogen bonds are expected (16) I. H . Reece and R. L. Werner, Spectrochim. Acta 24A,1271 (1968). (16) T. S. S.R. -Murty, Can. J . Chem., 48, 184 (1970). (17) M. D. Joesten and R. 5 . Drago, J . Amer. Chem. Soe., 84, 3817 (1962). (18) K. F. Purcell and R. 5. Drago, ibid., 89,2874 (1967). (19) G. Sellier and B. Wojtkowisk, J . Chim. Phys. Physicochim. Biol., 65, 936 (1968) (20) E. M. Arnett, L. Joris, E. Mitchel, T. S. S. R. Murty, T. M . Gorrie, and P. v. R . Schleyer, J . Amer. Chem. Soc., 92, 2365 (1970). (21) A. J. Barnes and H. E. Hallam, Trans. Faraday Soc., 66, 1920 (1970). (22) A. J. Barnes and H. E. Hallam, ibid., 66, 1932 (1970). (23) A. N. Fletcher and C. A. Heller, J . Phgs. Chem., 71, 3742 (1967).
1813
SELF-ASSOCIATION OF METHANOL VAPOR looo.o
T
31 80
o
I
I
I
I
I
I
I
I
I
I
I
IO
20
30
40
60
60
70
a0
80
loo
110
IIIY 123
PRESSURE. ITORAI
-
1.0 0.01
MONOMER CONCENTRATION (MOLE
0.1
LITER-^)
Figure 5. Determination of the 7t-mer responsible for the 2.95-pm absorption band. Curve A, 0 , summation of A values from 2.90 to 2.985 pm, solid line is fourth order in monomer. Curve B, A, summation of A values for 2.985 to 3.00 pm, aolid line is fourth order while dashed line C is fifth order in monomer.
to increase in strength with an increasing amount of self-ass~ciation,~~ the higher polymers are expected to be observed a t increasingly longer wavelengths. Figure 4 shows a range of constant ratios of A values with the higher ratios, corresponding to the higher value of n in eq 7, found a t the longer wavelengths. The intensities of the small “peaks” common to the ratios in Figure 4 do not change enough to be an indication of new species. They are believed to be artifacts due to the use of a common monomer “blank.” Disregarding these experimental errors, a region showing little change in the A ratio values with changing wave-
Figure 6. Data of Cheam, Farnham, and Christian26 for methanol vapor a t 25’. Curve A has a root mean square deviation (RMSD) of 0.047 for data up to 90 Torr using the trimer model with a K1,3 of 4.38 X 10-7 Torr-2. Curve B has a RMSD of 0.048 for data up to 90 Torr using the monomer-dimer-tetramer model with a Kl,zof 3.5 X Torr-‘ and K1,4 of 2.0 X 10-8 Torr-3 (personal communication from S. D. Christian, 1970). Curve C is calculated using the equilibrium quotients reported by Tucker, Farnham, and Christian” for the monomer-trimer-octamer model.
lengths is observed from 2.90 to 2.985 pm in Figure 4. This range defines the region where primarily a single n-mer absorbs in addition to the monomer if the assumption about the wavelength sensitivity of small self-association fipecies holds. A log plot of A against A1 is given in Figure 5 where it is seen that a fourthorder plot fits the data over a 1000-fold range of Z ~ S O Ovalues. ~ ~ ~ ~ItAis~ concluded that the tetramer is the second significant n-mer. Evidence for the Rejection of the Trimer as a Major Self-Association Species of Methanol Vapor. A curvesubtraction technique for the dimer was used in the Eame fashion as for the removal of the monomer abEorption. The wavelength region from 2.80 to 2.90 pm was then found to have about the same ratio as from 2.900 to 2.985 pm. After two curve subtractions, we are making an appreciable demand upon the accuracy of the spectrophotometric results to then perform a ratio test. One of the better ratio tests gave an average estimated standard deviation of 0.64 for the 201 ratio values from 2.80 to 3.0 pm with an average ratio The Journal of Physical Chemistry, Vol. 76,N o . 12, 1971
1814 of 2.6. Although the deviations were high, they were random, so it is concluded that no significant absorption occurs within the region 2.80 to 2.90 pm that cannot be attributed to the dimer or the tetramer absorption bands. This lack of trimer absorption band is in agreement with previous material balance studies11a23where it was not found possible to fit equations that included the trimer along with the dimer and tetramer. The polymer spectra indicate that the trimer is present only in concentrations too low to be detected by the present system. The lack of a flat region for high concentration ratios from 2.75 to 2.80pm is the result of subtracting two very large measurements from each other and then taking a ratio of two sets of these subtractions. It appears that a portion of the original I h curves reached the maximum absorbance values that could be measured with a %T instrument near 2.75 pm and that part of the high polymer band absorbs near 2.80 pm. The plot in Figure 5 for Z298~3000Ax suggests the possibility of an n-mer higher than fourth. As this wavelength region has a low total absorption (Figures 1 and 2 ) ) it is subject to increased experimental errors as is evidenced by the cross-over of curves D and E of Figure 4. A small amount of a higher n-mer cannot be rejected, however, from the 2.985-3.000-pm results. Testing for n-iVers Using a Power Series. Values of y(A) from the 80" results were tested every 50 nm from 2.80 to 3.0 pm and a t 2.78 pm using the equivalent of eq 5.13 The purpose of this was to double check the curve-subtracting techniques. All combinations of fits using the monomer and up to two n-mers were examined going up to sixth order comparing the integrated absorbance values, y (A), with the monomer concentration. The least-squares computer program used for this test has been described p r e v i ~ u s l y . ~A~ number of combinations of n-mers using as high as five in addition to the monomer were also tested, Except for a few cases 'Vith more than three Of the 1-2-4-6 terms showed one or more negative coefficients. Using
The Journal of Physical Chemistry, Vol. 7 5 , No. 13, 1971
AARONN. FLETCHER the F - t e ~ to t ~compare ~ variances of the valid (no negative coefficients) regression equations, all models other than the dimer were rejected for the y(2.78) values.l* In a similar fashion, it was found that all models other than the monomer-tetramer had to be rejected using y(2.95) at 80" if only l-n models were considered (as is suggested by the lack of band shape change from 2.90 to 2.985 pm shown by the ratio test). Rejection of the Monomer-Trimer-Octamer Model. Using a vapor-density balance that compensates for wall condensation (except near saturation pressure) , Cheam, et have recently reported evidence favoring the trimer as the major self-association polymer for methanol vapor up to 90 Torr at 25". They found an insignificant difference between the fit of the 1-3 model from the fit of the 1-3-8 model at pressures up to 116 Torr. This insignificance places particular doubt upon the previous P V T evidence for the octamer. As shown in Figure 6, a plot using the equilibrium quotients for the 1-3-8 model reported by Tucker, et does not fit the vapor-density data. This writer suspects that condensation of methanol upon the container walls introduced a significant experimental error into the results of Tucker, et al. The present study, of course, indicates that the monomer-dimertetramer model should be given preference to the monomer-trimer model. Certainly the results of Cheam, et al. (Figure 6)) do not present any evidence to the contrary. Acknowledgment. The computer programming performed by James R. Nichols, John B. Garber, and John E. Anderson is gratefully acknowledged. I also wish to thank Professor Hans B. Jonassen for a helpful criticism of the manuscript and Professor S. D. Christian for supplying his 1-2-4 equilibrium quotients and RNISD values for the data of Cheam, et (24) P. G. Hoel, "Introduction to Mathematical Statistics," 2nd ed, Wiley, New York, N. Y . , 1954. (25) V. Cheam, S. B. Farnham, and S. D. Christian, J. Phys. Chem., 74, 4167 (1970).
