Ind. Eng. Chem. Res. 1998, 37, 4823-4827
4823
GENERAL RESEARCH Intra- and Intermolecular Hydrogen Bonding of 2-Methoxyethanol and 2-Butoxyethanol in n-Hexane Ray L. Brinkley and Ram B. Gupta* Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849-5127
Glycol-ether compounds such as 2-methoxyethanol (CH3OCH2CH2OH) and 2-butoxyethanol [CH3(CH2)3OCH2CH2OH] form both intra- and intermolecular hydrogen bonds. Using Fourier transform infrared spectroscopy, we have measured extent of intra- and intermolecular hydrogen bonding in these compounds dissolved in n-hexane at varying concentrations and temperatures. Intramolecular hydrogen bonds are present at all conditions, whereas intermolecular bonds appear at higher concentrations. Using lattice-fluid-hydrogen-bonding theory, equilibrium constants for the formation of intra- and intermolecular hydrogen bonds are determined. The results show that the equilibrium constant for intermolecular bond formation is approximately 6 times the intramolecular equilibrium constant for 2-methoxyethanol systems at 35 °C. Experiments at higher temperature, 45 °C, with 2-methoxyethanol show less hydrogen bonding as expected due to higher thermal energy. Due to steric hindrance, 2-butoxyethanol has a lower degree of hydrogen bonding than 2-methoxyethanol at the same temperature and concentration. Introduction Hydrogen bonding (h-bonding) plays an important role in fundamental sciences and in industrial applications (Lammers, 1991; Ikhlaq, 1992; Bestani and Shing, 1989; Bourrel and Schechter, 1988). The h-bond is a weak attractive interaction, yet it is stronger and has a much longer lifetime than the ordinary van der Waals interaction. In fact, the phase behavior of nonionic polar fluids is usually dominated by h-bonding (Prausnitz et al., 1986). The h-bond is perhaps the most important interaction to humans after the carbon-carbon bond since life on earth is based on water and other h-bonding compounds (Pimentel and McClellan, 1960). There are two main types of hydrogen bonds: intermolecular and intramolecular. Intermolecular hydrogen bonds occur between separate molecules while intramolecular bonds occur when a molecule bonds with itself (Figure 1). These two types have different bonding energies and different effects on solution properties. Much of the work concerning intramolecular hydrogen bonding has dealt with the qualitative study of its effect on solution properties (Singleburg et al., 1991; Rutkowski and Koll, 1994). However, little effort has been devoted to quantitative measurements of the degree of each type of hydrogen bonding in mixtures. The purpose of this study is to contribute toward our understanding of h-bonding interactions in fluid phase equilibria encountered in industrially important systems: glycol-ether + n-alkane binary mixtures. Accurate quantitative measurements can now be performed with recent advances in spectroscopy and * To whom correspondence should be addressed. E-mail:
[email protected]. Phone: (334) 844-2013. Fax: (334) 844-2063.
Figure 1. Intra- (a) and intermolecular (b) h-bonding arrangements in 2-methoxyethanol.
computers. The concentration of nonbonded (free) and h-bonded, both intra- and intermolecular, can be obtained using Fourier transform infrared (FTIR) spectroscopy. Free and h-bonded species have molecular vibrations at different infrared frequencies. For the systems studied here, the typical free OH stretching frequency is at 3648 cm-1 and the intramolecular h-bonded stretching frequency is at 3612 cm-1. The intermolecular h-bonded peaks occupy the region of 3100-3600 cm-1. Experimental Section Apparatus and Material. The experimental apparatus (Figure 2) consists of a mixing chamber, a pump (Fluid Metering Inc., model QG400), a six port injection valve (Rheodyne model 7012 loop filler port), a temperature controller (Cole Palmer Digi-Sense model 218620), and an IR cell (constructed in-house). The mixing chamber is initially charged with a known amount of n-hexane. The six-port injector allows the addition of fixed volumes of the h-bonding compound without the risk of loss of solution or contamination by atmospheric moisture. A temperature controller maintains the solution temperature passing through the IR cell within 0.1 °C.
10.1021/ie970740p CCC: $15.00 © 1998 American Chemical Society Published on Web 11/06/1998
4824 Ind. Eng. Chem. Res., Vol. 37, No. 12, 1998
Figure 2. Apparatus for hydrogen bonding measurements using FTIR spectroscopy.
Figure 4. Curvefit for a 2-methoxyethanol + hexane mixture at 35 °C. The top curve is the summation of the hydrogen bonded and free peaks. The small peak at 3648 cm-1 corresponds to the free -OH stretch. The sharp peak at 3612 cm-1 is due to intramolecular bonding, and the remaining peaks are due to intermolecular bonding.
Figure 3. FTIR spectra of 2-methoxyethanol + n-hexane mixture at 35 °C with varying 2-methoxyethanol concentration.
n-Hexane (Fisher cat. no. H303-4, Optima grade) was used as received. 2-Methoxyethanol (Aldrich cat. no. 28,446-7) and 2-butoxyethanol (Aldrich cat. no. 25,6366) were dried with 4 Å molecular sieves (Fisher, cat. no. M514-500) to remove any trace amounts of water prior to use. The IR cell, built at Auburn University, consists of two sapphire windows separated by a 0.5 mm thick stainless steel spacer and sealed with Teflon rings in an aluminum body. The cell is placed in the sample compartment of the FTIR spectrophotometer (PerkinElmer FTIR Spectrum 2000). Background moisture is removed by purging the compartment with nitrogen (BOC grade 5.0) for 1 h. The cell and all tubing are insulated to aid in temperature control. Spectral Analysis. A background spectrum is recorded after the sample compartment has been purged and the solution has reached its set-point temperature. The background consists of 100 spectra averaged over a 6-min interval. Multiple scans increase the signalto-noise ratio and improve the accuracy of the peakfitting process. After the glycol-ether has been injected and the system is allowed to reach equilibrium, the sample scan is performed in the same manner. FTIR spectra (Figure 3) are recorded with increasing glycolether concentration. At the low concentrations (mole fraction, xglycol-ether < 0.0007) only two OH stretch peaks, one at 3648 cm-1 and one at 3612 cm-1, are observed. The former is due to non-h-bonded and the latter is due to intramolecularly h-bonded -OH. As the glycol-ether concentration increases, peaks due to intermolecularly h-bonded -OH groups begin to appear in the range of 3100-3600 cm-1. A commercial software package, PeakSolve (Galactic Industries Corp.), is used to curve-fit the collection of peaks and to obtain their separate areas as shown in
Figure 4, for illustration. The peaks are fit according to the Voigt peak shape, and the parameters of the peaks’ center, height, width, and Lorentzian width are optimized to match the calculated and experimental spectra. The amount of free and intramolecularly bonded -OH groups is calculated from a two-point calibration generated at low concentrations where no intermolecular h-bonds are present. Spectra at two concentrations, using simple algebra, allow determination of two extinction coefficient, using for free and intramolecular h-bond peak areas AFree and AIntra, respectively,
(
AFree ) 1
)
Aintra N NT 2
(1)
where 1 and 2 are extinction coefficients for free and intramolecularly h-bonded peaks, respectively, N is number of glycol-ether molecules, and NT is total number of molecules in the mixture. The number of intramolecular h-bonds, B, is calculated as
B)
NTAIntra 2
(2)
New Experimental Data. New FTIR experimental data at ambient pressure are obtained for 2-methoxyethanol at 35 and 45 °C and for 2-butoxyethanol at 35 °C. n-Hexane, a non-h-bonding fluid, is used as the solvent in all cases. These data are reported in Tables 1 and 2 with an error of less than 5% for peak areas. Theory Recent theories of h-bonding are based on chemical equilibria approach (Heidemann and Prausnitz, 1976), perturbed-hard-chain theory (Walsh and Donohue, 1989; Economou and Donohue, 1991), statistical association (Huang and Radosz, 1990, 1991, 1993), mobile and static molecular disorder (Huyskens, 1992), and lattice-fluidhydrogen-bonding (Veytsman, 1990; Panayiotou and Sanchez, 1991; Gupta et al., 1992; Gupta and Johnston, 1994; Gupta and Prausnitz, 1996; Gupta and Brinkley, 1998). Here we have used lattice-fluid-hydrogen-bonding theory because its general formalism is valid for multicomponent systems of molecules having any num-
Ind. Eng. Chem. Res., Vol. 37, No. 12, 1998 4825
ber of hydrogen bond donor and acceptor groups and is applicable over a wide range of conditions. In this theory the chemical contribution of the partition function is derived by determining the number of ways of distributing the hydrogen bonds among the donor and acceptor groups in the system. The donor and acceptor must be in close spatial proximity as described by a mean field probability. The mean field probability that a specific acceptor will be near a given donor depends on the system volume or total number of lattice sites and entropy loss (intrinsically negative) associated with the formation of a hydrogen bond. In general, there are three types of h-bonds in etherglycol mixtures: (1) intramolecular, (2) OH- - -OH intermolecular, and (3) OH- - -ether intermolecular. But here for simplicity, we have assumed last two types of the bonds to have no difference. Though it is known that alcohol-alcohol h-bonds are stronger than alcoholether h-bonds, but for the low concentrations where cooperativity effect is small, the alcohol-alcohol h-bonds are much weaker than at high concentrations (Gupta and Brinkley, 1998). In addition, the proposed assumption reduced number of equilibrium constants to be regressed from 3 to 2. This will yield a more unique set of equilibrium constants for which theory can correlate the data. The Helmholtz free energy of h-bonding, FH, for a system containing B intramolecular and M intermolecular h-bonds, is given by
FH ) ∆FBB + ∆FMM - kT ln Ξ
cMF˜ NT
pB ) cB
(5)
The probability, pB, of intramolecular pairs being neighbors is a constant for a given molecular structure. The constant, cM, depends on the geometry of the molecule and groups on it, NT is the total number of molecules, F˜ and is the reduced density of the mixture (Sanchez and Lacombe, 1976). The expression for Ξ0 is calculated by accounting for B intramolecular h-bonds followed by M intermolecular h-bonds. Each glycol-ether molecule is considered to have one proton donor site and three proton acceptor sites (one due to alcohol and two due to methoxy group). There is only one way of forming intramolecular h-bond on each molecule. After the B donors have been used in intramolecular h-bonding, N - B remain to form M intermolecular h-bonds. Therefore, intermolecular h-
(N - B)!(3N - B)! (N - B - M)!(3N - B - M)!M!
(6)
Using the above expression with Stirling’s approximation eq 3 is rewritten as
FH ) -B ln KB - M ln KM kT (N - B)(3N - B)3 N ln (N - B - M)(3N - B - M)3 (N - B - M)(3N - B - M) B ln (N - B)(3N - B) (N - B - M)(3N - B - M) M ln (7) eMNT
( (
) )
(
)
where e has the value of 2.71828 and KB and KM are equilibrium constant for intra- and intermolecular hbonding, respectively. These are given as
KB ) cB exp(-∆FB/kT)
(8)
KM ) cBF˜ exp(-∆FM/kT)
(9)
Now, to obtain an equilibrium state, the free energy, FH, is minimized with respect to number of h-bonds, B and M, as
( (
(4)
where Ξ0 is the number of ways to distribute h-bonds disregarding the fact that acceptor and donor molecules must be neighbors, pB and pM are the probabilities that the given donor/acceptor pairs are neighbors for intraand intermolecular h-bonding, respectively. The probability terms are given as (Gupta and Brinkley, 1998)
pM )
Ξ0 )
(3)
where ∆FB and ∆FM are the change of free energy upon intra- and intermolecular h-bond formation, respectively, and Ξ is the number of ways to distribute B intramolecular and M intermolecular hydrogen bonds among N glycol-ether molecules. In the mean field approximation, Ξ is given as (Marsh and Kohler, 1985) B Ξ ) Ξ0pM MpB
bond donors can be chosen in (N - B)!/(N - B - M)! ways. Since B acceptors have been used in intramolecular h-bonding, the remaining 3N - B can used to form M intermolecular h-bonds in (3N - B)!/(3N - B M)! ways. To avoid overcounting, due to M identical intermolecular h-bonds, the result is divided by M!. Finally
) )
∂FH/kT ∂B
M,N,NT
∂FH/kT ∂M
M,N,NT
)0
(10)
)0
(11)
Equations 10 and 11 yield expressions for B and M
B)
[
KB(N - M) 1 + KB
M ) N(1 - R)(4 - 2R) +
x(
N(1 - R)(4 - 2R) +
(12)
NT + KM
NT KM
)
2
]/
- 4(1 - R)3(3 - R)N2 2
[2(1 - R) ] (13)
where
R ) KB/(1 + KB)
(14)
Calculations. The equilibrium constants KB and KM are estimated by fitting the theory to the experimental data in Tables 1-3 for mole fraction h-bonding, B/NT and M/NT. A good agreement between theory and experiment is obtained as shown in Figures 5-7. For 2-methoxyethanol, at 35 °C, the values of KB and KM are 25 and 184, respectively. This represents that
4826 Ind. Eng. Chem. Res., Vol. 37, No. 12, 1998 Table 1. FTIR Data for H-Bonding in 2-Methoxyethanol + n-Hexane at 35 °C mole fraction 2-methoxyethanol 0.0004 0.0008 0.0011 0.0015 0.0019 0.0023 0.0027 0.0030 0.0034 0.0038 0.0042 0.0045 0.0049 0.0053 0.0057 0.0060 0.0096 0.0131 0.0165 0.0200 0.0235 0.0269 0.0303 0.0337 0.0371 0.0404 0.0438 0.0471 0.0504 0.0537
peak area free intramol 0.0213 0.0631 0.1207 0.1801 0.2409 0.3057 0.3400 0.3963 0.4165 0.4689 0.4418 0.4754 0.4845 0.5396 0.5675 0.5755 0.5736 0.6937 0.7684 0.5237 0.4709 0.4720 0.4083 0.3669 0.3564 0.3439 0.2833 0.2323 0.2009 0.1672
0.3306 0.6692 1.0040 1.3528 1.6914 2.0172 2.3548 2.6758 3.0004 3.3322 3.6459 3.9725 4.2750 4.6577 5.0105 5.3405 8.2784 11.0470 13.4290 15.5689 17.5632 19.4130 20.7505 22.0817 23.5660 24.8960 25.7213 26.4979 27.3867 28.1376
mole fraction h-bonds intramol intermol 0.0003 0.0007 0.0010 0.0014 0.0017 0.0020 0.0024 0.0027 0.0030 0.0033 0.0036 0.0040 0.0043 0.0047 0.0050 0.0053 0.0083 0.0110 0.0134 0.0156 0.0176 0.0194 0.0207 0.0221 0.0235 0.0249 0.0257 0.0265 0.0274 0.0281
0.0004 0.0009 0.0019 0.0036 0.0052 0.0068 0.0089 0.0111 0.0130 0.0150 0.0176 0.0203 0.0228 0.0254
Table 3. FTIR Data for H-Bonding in 2-Butoxyethanol + n-Hexane at 35 °C mole fraction 2-butoxyethanol 0.0002 0.0005 0.0007 0.0009 0.0012 0.0014 0.0016 0.0018 0.0021 0.0023 0.0044 0.0066 0.0087 0.0109 0.0130 0.0151 0.0172 0.0193 0.0214 0.0236 0.0256 0.0277 0.0298 0.0319
peak area free intramol 0.0086 0.0160 0.0267 0.0313 0.0476 0.0577 0.0666 0.0754 0.0860 0.1766 0.1962 0.4274 0.4693 0.4504 0.3906 0.4706 0.4629 0.5093 0.5310 0.5568 0.5958 0.6460 0.6887 0.7227
0.1948 0.3805 0.5689 0.7491 0.9616 1.1607 1.3626 1.5539 1.7498 1.9442 3.8374 5.4906 6.9801 8.6081 9.9638 11.5993 12.6404 13.9845 15.1516 16.2725 17.4517 18.6576 19.7943 20.8602
mole fraction h-bonds intramol intermol 0.0002 0.0004 0.0006 0.0007 0.0009 0.0011 0.0013 0.0015 0.0017 0.0019 0.0037 0.0053 0.0068 0.0084 0.0097 0.0113 0.0123 0.0136 0.0147 0.0158 0.0169 0.0181 0.0192 0.0203
0.0011 0.0012 0.0024 0.0029 0.0038 0.0046 0.0054 0.0061 0.0068 0.0076
Table 2. FTIR Data for H-Bonding in 2-Methoxyethanol + n-Hexane at 45 °C mole fraction 2-methoxyethanol 0.0004 0.0008 0.0011 0.0015 0.0019 0.0023 0.0027 0.0030 0.0034 0.0038 0.0073 0.0108 0.0142 0.0177 0.0210 0.0214 0.0248 0.0282 0.0315 0.0350 0.0383 0.0416 0.0449 0.0482 0.0515
peak area free intramol 0.0133 0.0385 0.0737 0.1013 0.1249 0.1594 0.2210 0.2368 0.3885 0.4488 0.7372 0.9369 1.0844 1.1160 0.8325 0.7654 0.7626 0.7622 0.7400 0.6756 0.6788 0.6209 0.6004 0.5490 0.5214
0.2509 0.5567 0.8596 1.1583 1.4759 1.7917 2.0759 2.3812 2.6688 2.9215 5.8539 8.5940 11.2328 13.7837 14.8962 15.9727 18.2261 20.2780 22.1304 23.5678 25.5302 26.8019 28.3428 29.5536 30.9476
mole fraction h-bonds intramol intermol 0.0003 0.0006 0.0009 0.0012 0.0015 0.0018 0.0021 0.0024 0.0027 0.0029 0.0059 0.0089 0.0112 0.0138 0.0149 0.0160 0.0182 0.0203 0.0221 0.0235 0.0255 0.0268 0.0283 0.0295 0.0309
Figure 5. Hydrogen bonding in 2-methoxyethanol + n-hexane mixtures at 35 °C. Point are new experimental data, and lines are theory with KB ) 25 and KM ) 184. 0.0007 0.0013 0.0021 0.0049 0.0043 0.0054 0.0068 0.0083 0.0103 0.0117 0.0139 0.0157 0.0178 0.0198
intermolecular h-bonds are thermodynamically favored over intramolecular. At 45 °C, these values decrease to 20 and 119, reflecting decrease in h-bonding due to the increased thermal energy; i.e., the donor/acceptor groups are able to overcome the electrostatic attraction due to higher molecular motion. FTIR data suggest that the 2-butoxyethanol at 35 °C has lower h-bonding than 2-methoxyethanol at the same temperature. This is due to the presence of more steric hindrance by the butyl group than the methyl group, for h-bonding. For 2-butoxyethanol, at 35 °C, the values of KB and KM are 5 and 28, much lower than those for 2-methoxyethanol. It should be noted that for multiple sets of values for KB and KM, the theory can match the experiment.
Figure 6. Hydrogen bonding in 2-methoxyethanol + n-hexane mixtures at 45 °C. Point are new experimental data, and lines are theory with KB ) 20 and KM ) 119.
However, in all cases, essentially the same trends, as discussed above, are obtained. Heat of mixing data can confirm a unique set of equilibrium constant, but these data are not available at present. Using above equilibrium constants, for 2-methoxyethanol at 35 °C, h-bonding is calculated for the whole mole fraction range. As shown in Figure 8, the theory
Ind. Eng. Chem. Res., Vol. 37, No. 12, 1998 4827
work supported by the U.S. Civilian Research and Development Foundation under Award No. RC1-170. Literature Cited
Figure 7. Hydrogen bonding in 2-butoxyethanol + n-hexane mixtures at 35 °C. Point are new experimental data, and lines are theory with KB ) 5 and KM ) 28.
Figure 8. Prediction for h-bonding in 2-methoxyethanol + n-hexane at 35 °C. The intramolecular h-bonding curve reaches a maximum of 6%, and the intermolecular h-bonding curve reaches 93%.
predicts almost 100% total h-bonding for pure 2-methoxyethanol. Intermolecular h-bonding is of the order of 90%, close to the total h-bonding for pure ethanol and methanol (Gupta et al., 1992). Additional h-bonds are due to intramolecular h-bonding which are absent in pure ethanol and methanol. In 2-butoxyethanol, since almost all the donors are occupied, it may have more nonpolar behavior than corresponding n-alkanols, for molecules that are only proton acceptor. Inverse behavior may be expected for molecules that are only proton donor, due to additional nonoccupied acceptor sites on the 2-butoxyethanol. Conclusion We have presented new FTIR h-bonding data for 2-methoxyethanol and 2-butoxyethanol binary solutions in n-hexane at 35 and 45 °C. To correlate data, we have developed a new theoretical expression for this system where both intra- and intermolecular h-bonds are present. Obtained equilibrium constants suggest that intermolecular h-bonds are favored over intramolecular. 2-Butoxyethanol has lower h-bonding than 2-methoxyethanol due steric hindrance by the butyl group. Acknowledgment The authors are grateful to Mr. Joe Aderholdt for the construction of the IR cell. This material is based upon
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Received for review October 22, 1997 Revised manuscript received September 16, 1998 Accepted September 16, 1998 IE970740P
