J. Phys. Chem. 1996, 100, 3959-3964
3959
Density and Temperature Effects on the Hydrogen Bond Structure of Liquid Methanol S. L. Wallen, B. J. Palmer, B. C. Garrett, and C. R. Yonker* EnVironmental and Energy Sciences DiVision, Pacific Northwest National Laboratory, Richland, Washington 99352 ReceiVed: August 17, 1995; In Final Form: NoVember 27, 1995X
The hydrogen bond structure of liquid methanol was investigated as a function of pressure and temperature up to 2.8 kbar and from 297 to 413 K. Chemical shifts of the CH3 and OH groups were monitored throughout this pressure and temperature regime, and the chemical shift difference between these two groups was used to describe changes of the hydrogen bond network in methanol. The hydrogen bond equilibrium was investigated using molecular dynamics simulations and a phenomenological model describing clustering in liquid methanol. Results are presented concerning the size and distribution of hydrogen-bonded clusters in methanol as a function of pressure and temperature. The results indicate that the extent of hydrogen bonding decreases upon an increase in temperature. The results for pressure are equivocal, the phenomenological model suggests that hydrogen bonding decreases with increasing pressure, which supports earlier interpretations regarding the measured self-diffusion coefficients in deuterated methanol as a function of pressure. The molecular dynamics simulations, however, show an increase in hydrogen bonding with increasing pressure.
Introduction The hydrogen bond structure of methanol and the effect of pressure on this liquid are of recurring interest. There have been various theoretical and experimental efforts describing the effect of temperature and pressure on the hydrogen bond strength and structure in methanol.1-7 Various spectroscopic techniques, such as Raman, X-ray, and neutron scattering have been used to study this system.4-6 NMR has also established itself as a method for probing the dynamics and structure of this hydrogenbonding liquid.8-10 Oldenziel and Trappeniers studied the chemical shifts of the OH and CH3 groups in methanol as a function of pressure at room temperature.10 Jonas and Akai investigated the self-diffusion coefficient of deuterated methanol over densities ranging from 0.8 to 1.0 g/cm3 and temperatures ranging from 223 to 323 K.8 Schulman and co-workers investigated the difference in the chemical shifts between the CH3 and OH groups of methanol (∆ν) from 278 to 392 K and to pressures of 1 kbar.9 The conclusions of Schulman et al. regarding the effects of pressure on the hydrogen bond structure in methanol were in direct contrast to the interpretation of the self-diffusion coefficient results presented by Jonas and Akai.8 Even for this simplest of alcohols, the hydrogen bond strength and structure as a function of pressure and temperature remain to be elucidated. In this work, the chemical shifts of the CH3 and OH groups of pure methanol were investigated over an extended temperature range and to greater pressures than those reported earlier. The observed chemical shifts for the CH3 and OH groups are extremely sensitive to changes in their local environments, and the latter can be used to study changes in the hydrogen bond. The use of NMR chemical shifts in conjunction with molecular simulations allows one to establish an appropriate physical model describing the effect of pressure and temperature on the extent of hydrogen bonding for this liquid. Molecular dynamics (MD) simulations were run at densities and temperatures corresponding to the experimental conditions. A phenomenological model of aggregation, accounting for the equilibrium between hydrogen-bonded and free (non-hydrogen-bonded) methanol molecules, is used to interpret * Corresponding author. † Operated by Battelle Memorial Institute. X Abstract published in AdVance ACS Abstracts, February 15, 1996.
0022-3654/96/20100-3959$12.00/0
the experimental results relating hydrogen bond structure as a function of pressure and temperature. In addition to the equilibrium investigations, ∆ν, the difference between the OH and CH3 chemical shifts, is used to correlate changes in the hydrogen bond network of methanol as a function of increasing pressure and temperature with the simulation studies. Experimental Section Anhydrous methanol (Aldrich Chemical Company, Inc.) was used without further purification or drying. All spectra for these studies were acquired on a Varian (VXR-300) 300 MHz pulsed NMR spectrometer with a 7.04 T superconducting magnet. The high-pressure NMR spectra were obtained without sample spinning, and a spectral resolution between 4 and 8 Hz was maintained over the pressure and temperature ranges studied. The high-pressure NMR cell utilized in this investigation has been discussed in recent publications.11,12 In our investigations it has been determined that the 100 µm i.d. capillary material is strong enough to withstand pressures up to 4 kbar. The fused silica capillary tubing (Polymicro Technologies, Inc.) used to construct the NMR cell was 100 µm internal diameter with an external diameter of 360 µm. The spectra were obtained unlocked, which is possible due to the negligible field drift over the course of an experiment. The capillary was connected to the pump, and methanol was purged through the capillary, after which the open end was flame sealed and the capillary pressurized. For these studies, the pressure was measured using a calibrated pressure transducer (Precise Sensors, Inc.) with a precision of (0.7 bar. Temperature was controlled to (0.1 K using the air bath controller on the NMR spectrometer and was calibrated using a reference thermocouple. Results and Discussion High-Pressure NMR. The nuclear shielding constant (σ) is an absolute measure of the electronic contribution to the observed nuclear magnetic moments which are sensitive to a molecule’s local chemical environment and is a second-order molecular property.13 The nuclear shielding constant for a molecule in a liquid has contributions from many sources,14-16
σ(MeOH) ) σB + σA + σW + σE + σEX + σS © 1996 American Chemical Society
(1)
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TABLE 1: Observed Proton Resonances at 299.95 MHz for CH3 and OH Groups, Chemical Shift Difference (∆ν Hz) between the CH3 and OH Protons as a Function of Pressure, Density, and Temperature for Pure Methanol and Molecular Dynamics Simulation Pressures T, K 297.3
333.7
372.2
413.2
P, kbar
∆ν, Hz
CH3, ppm
OH, ppm
F, g/cm3
sim Pressure, kbar
0.547 1.08 1.67 2.11 2.65 0.548 1.06 1.60 2.09 2.62 0.547 1.08 1.58 2.16 2.50 0.552 1.08 1.62 2.20 2.64
478.7 485.6 492.9 498.1 504.6 369.3 377.8 386.5 394.2 402.0 240.6 255.7 267.7 280.0 286.6 136.0 156.0 172.3 186.3 193.8
3.815 3.747 3.689 3.652 3.612 3.917 3.860 3.807 3.760 3.724 4.111 4.013 3.944 3.879 3.845 4.106 4.011 3.942 3.881 3.843
5.411 5.367 5.332 5.313 5.294 5.149 5.120 5.095 5.074 5.064 4.913 4.865 4.837 4.813 4.800 4.560 4.531 4.516 4.502 4.489
0.828 0.860 0.890 0.908 0.926 0.799 0.835 0.865 0.888 0.906 0.767 0.804 0.834 0.865 0.881 0.739 0.784 0.821 0.850 0.866
3.00
6.86
2.64
8.56
where σB is the contribution from the bulk magnetic susceptibility of methanol, σA represents the contribution from the anisotropy of the magnetic susceptibility of the methanol molecule, σW is due to van der Waals dispersion interactions, σE arises from the polarization of the solvent by the permanent dipole moment of methanol, σEX represents the effect of shortrange exchange interactions, and σS is the contribution from specific interactions such as hydrogen bonding. In the methanol molecule, the CH3 and OH groups will each experience their own nuclear shielding environment as seen in eq 1. The difference in nuclear shielding between the two groups is related to the σS term, caused mainly by the hydrogen bond of the OH group. The use of the difference between the chemical shift for the CH3 and the OH groups, ∆ν (Hz), eliminates the effect of density on the other nonspecific contributions to the nuclear shielding of the two groups. It is assumed that changes in density affect these contributions in a similar manner for both group’s proton resonances. Therefore, changes in ∆ν can be used to study changes in the hydrogen bond network in solution and hydrogen bond strength as a function of pressure and temperature. The experimental data is presented in Table 1. Figure 1 shows a plot of ∆ν versus pressure at various temperatures for methanol. As temperature increases, ∆ν decreases at constant pressure. At constant temperature, ∆ν increases with increasing pressure. The slope ((∂∆ν/∂P)T) also increases with increasing temperature. Similar observations have been reported earlier for methanol and ethanol as a function of pressure.9,17 Since hydrogen bonding removes electron density from the local vicinity of the nucleus, one would expect the nuclei to be more deshielded with respect to the applied magnetic field. An increase in ∆ν reflects an increase in the deshielding of the OH group relative to the CH3 group in methanol. Therefore, the OH group exhibits a change in its hydrogen bond environment. The results in Figure 1 demonstrate that increasing temperature tends to decrease the hydrogen bond network in methanol. One would expect increases in temperature to more readily disrupt the hydrogen bond network, especially on approaching the critical temperature of methanol (512.6 K). Increasing pressure should have a larger effect on the solution’s hydrogen bond structure as more energy is added
Figure 1. Plot of ∆ν (Hz), the difference in the chemical shift between the OH and CH3 group resonances in methanol, as a function of pressure at (b) 24.1, (9) 60.5, (2) 99.0, and (1) 140.0 °C. Solid lines are the least squares fit to the experimental data.
Figure 2. Plot of ∆ν (Hz), the difference in the chemical shift between the OH and CH3 group resonances in methanol, as a function of density at (b) 24.1, (9) 60.5, (2) 99.0, and (1) 140.0 °C. Solid lines are the least squares fit to the experimental data.
to disrupt the hydrogen bond network of the solvent through temperature increases. Thus, one would expect a larger slope ((∂∆ν/∂P)T) with increasing pressure at higher temperatures. Figure 2 is a plot of ∆ν as a function of methanol density at constant temperature. The methanol densities were interpolated from the literature8,18 and the estimated accuracy of the methanol densities under experimental conditions is approximately 10%. Similar trends are seen in this figure as in Figure 1, that is, at constant density ∆ν decreases with increasing temperature. The slopes also increase as temperature increases. With increasing density at all temperatures the OH group resonance shifts further downfield compared to the CH3 resonance. The increasing slope at higher temperatures demonstrates that increasing density, as
Hydrogen Bond Structure of Liquid Methanol with increasing pressure, has a greater effect on the hydrogen bond network at higher temperatures. One can separate the volume and temperature effects on ∆ν for the experimental conditions studied. During a constant pressure experiment ∆ν will be affected by both changes in density and temperature. At a constant pressure of 0.5 kbar, ∆ν changes by 1.14 ppm over the temperature range from 297.3 to 413.2 K. The density at 0.5 kbar and 297.3 K is 0.828 g/cm3. At this constant density over the same temperature range, ∆ν is 1.00 ppm. Thus, 0.14 ppm is due to the volume change (packing effects) in this temperature interval. This small density effect (∼12%) relative to the larger kinetic effect is comparable to that reported for ethanol.17 The large thermal effect reflects the fact that for methanol the hydrogen bond network is more sensitive to kinetic effects as compared to volume effects. Therefore, ∆ν appears to follow changes in both the strength of the hydrogen bond and the extent of hydrogen bonding in methanol. The volume change resulting from increasing density (packing effects) would contribute to a shortening of the intermolecular distance between hydrogen-bonded neighbors, but this is a small contribution to the overall ∆ν value. Highpressure Raman investigations of methanol have shown a shortening of the hydrogen bond length, and this was interpreted as an increase in hydrogen bond strength with increasing pressure.4,19 The predominant kinetic effect on ∆ν reflects changes in the extent of hydrogen bonding in the methanol network. Molecular Dynamic Simulations and Equilibrium Cluster Model. Simulations were performed on liquid methanol using Jorgensen’s transferable intermolecular potential (TIP) model.7 Each simulation contained 216 methanol molecules and was run under constant volume-constant temperature conditions. A Nose´ thermostat was used to maintain the temperature.20 The interatomic pair potentials were truncated at 8.5 Å using a shifted-force truncation scheme.21 Each simulation was run for a period of 50 ps using a 2.5 fs time step. Simulations were performed at the temperatures and densities indicated in Table 1. These correspond to the extremes in pressure and temperature investigated experimentally using NMR. The TIP model does a very poor job of reproducing the experimental pressures of methanol, although the pressures calculated in these simulations are compatible with results reported by Jorgensen.7 Because the model has such poor pressure characteristics, all the simulations reported here were based on the densities of the experimental systems. During each simulation, the distribution of hydrogen-bonded clusters was calculated. Two molecules were considered to be in the same cluster if they were connected by a hydrogen bond. A hydrogen bond was defined, in turn, to occur whenever the hydrogen on the methanol’s OH group fell within 2.5 Å of the oxygen on another methanol molecule (2.5 Å corresponds to the location of the first minimum after the hydrogen-bonding peak in the OH pair distribution function). The average number of nonbonded hydrogens per cluster was also accumulated along with the cluster distributions. The hydrogen-bonded cluster distributions for 297.3 and 413.2 K at 0.55 and 2.65 kbar are plotted in Figure 3. The mole fraction of clusters of size N, xN, is plotted as a function of cluster size. All four simulations show a broad distribution of cluster sizes. The distributions at 413.2 K are peaked around the smaller cluster sizes while the distributions at 297.3 K are noticeably shifted out toward larger clusters. The distributions also show a significant dependence on pressure (density). As the pressure is increased, the distributions shift toward higher clusters.
J. Phys. Chem., Vol. 100, No. 10, 1996 3961
Figure 3. Molecular dynamic simulations determining the mole fraction of cluster size (xN) versus cluster size (N).
Figure 4. Molecular dynamic simulations determining the number of free OH groups per cluster as a function of cluster size (N).
An important indication about the structure of the clusters can be found by examining the average number of nonbonded hydrogens per cluster. A plot of the number of free hydrogens per cluster as a function of cluster size is shown in Figure 4. It is immediately apparent that the number of free hydrogens per cluster is close to 1 for almost all cluster sizes for which significant statistics are available (less than 10 methanol molecules per cluster). One free hydrogen per cluster suggests that the clusters are forming linear chains, with a free hydrogen at one end of the chain. A monomer/tetramer equilibrium model has been used to analyze hydrogen bonding in methanol.9,22-25 This equilibrium premise is inconsistent with the results of the MD simulations that show a distribution of cluster sizes. Although it is interesting that the distributions from the MD simulations do show features for cluster sizes of 4, the distributions show significant clusters of sizes above 20 at 297.3 K and above 10 at 413.2 K. Another model in which the total chemical shift, δOH, is assumed to be a linear combination of the chemical shift of a free (nonhydrogen-bonded) OH group, δF, and the chemical shift of a hydrogen-bonded OH group, δHB, was used to explain the experimental data as a function of temperature and pressure (density). If the mole fraction of the free OH groups is xF, then δOH is given by
δOH ) xFδF + (1 - xF)δHB
(2)
3962 J. Phys. Chem., Vol. 100, No. 10, 1996
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This predicts that as the distribution of hydrogen-bonded chains, and hence xF, shifts with changes in temperature and pressure (density), the total chemical shift δOH changes. A phenomenological method describing aggregation in simple systems was used to describe the equilibrium thermodynamic formulation for association of molecules in solution.26 In this equilibrium picture, the chemical potential of all methanol molecules in different aggregates is assumed to be the same. With this assumption, the mole fraction of methanol molecules in a cluster of size N, xN, is given by
xN ) N {x1 exp[(µ1 - µn)/kBT]}N
(3)
where µN is the mean interaction free energy per molecule in a cluster of size N, kB is the Boltzmann constant, and T is the temperature. For methanol, we assume that the clusters are linear, formed by hydrogen bonding with an average free energy for a hydrogen bond, independent of the cluster size, of ∆GHB. On the basis of the MD simulations we assume that each cluster has one OH group without a hydrogen bond. The total interaction free energy of a cluster of size N is then given by
NµN ) (N - 1)∆GHB
(4)
Substituting eq 4 into eq 3 gives
xN ) N (x1eR)N e-R
(5)
where we define the unitless parameter R by ∆GHB ) -RkBT. Since we are treating a pure liquid, the mole fractions for each cluster size must sum to unity. This provides a normalization condition that allows solution for x1
x1 )
1 + 2eR - x1 + 4eR 2eR
(6)
The mole fraction of free OH groups is easily expressed in this model by ∞
xF )
xN
∑ N)1 N
(7)
Using eqs 5 and 6, eq 7 reduces to
xF )
x1 + 4eR - 1 2eR
(8)
Thus, the mole fraction of free OH groups is given in terms of the single dimensionless parameter R, which is directly proportional to the free energy of hydrogen bonding. The OH chemical shift in eq 2 is determined in this model by the shifts of the free and hydrogen-bonded OH group, δF and δHB, and the free energy of hydrogen bonding, ∆GHB. The mole fractions of monomers x1 and free hydrogens xF both behave similarly in the limits R f (∞. As R f ∞, corresponding to an infinite negative free energy for forming a hydrogen bond or zero temperature, the system condenses to a single infinite cluster, and both the mole fractions x1 and xF vanish. As R f -∞, corresponding to an infinitely positive free energy for forming a hydrogen bond, no hydrogen bonds are formed and both x1 and xF become unity. In the infinite temperature limit, R f 0, x1 and xF go to two different values. Because of the finite concentration of monomers, clusters still form even at infinite temperature, leading to a value less than 1 for x1, and hence, from eqs 5 and 7, to a different value of xF.
TABLE 2: Three-Parameter Regression at Constant Density of the OH Chemical Shifts. See Text for Description of Parameters F, g/cm3
δHB, ppm
∆HHB (F), kJ/mol
∆SHB (F), J/mol‚K
χ
0.828 0.866
5.946 5.946
-18.92 -17.84
-27.26 -24.89
0.009 0.005
Using eqs 2 and 8, we extract information about ∆GHB and δHB by fitting to the experimental data. The chemical shift of the free OH, δF, has been determined to be from 0.5 to 0.9 ppm from dilution studies.23-25 For this study, we assume a value of 0.8 ppm for δF.9 Three parametrization procedures for the hydrogen-bonded chemical shift, δHB, and the free energy, ∆GHB, are used in this study. In all three cases, δHB is assumed to be independent of both the temperature and the density or pressure. In the first case, the variation of the degree of hydrogen bonding with temperature will have a component associated with the change in density as well as the direct effect of the change in temperature. To better decouple the effect of temperature from the second variable, we chose to do the parametrization as a function of temperature for fixed values of density rather than fixed values of pressure. The free energy is regressed to a linear function of temperature for fixed values of the density, F,
∆GHB(T,F) ) ∆HHB(F) - T∆SHB(F)
(9)
where we have used the interpretation of the constant and linear terms as temperature-independent enthalpy and entropy terms, respectively, that are also functions of the density. We determine a single value of δHB by performing a least squares fit of δHB, ∆HHB(F), and ∆SHB(F) to reproduce the variations of δOH with temperature for a single, fixed value of the density, 0.828 g/cm3. Four data points corresponding to the four temperatures in Table 1 are used in each least squares fit. Values of the OH chemical shifts at the same density for all four temperatures are obtained by linear interpolation of δOH as a function of density at constant temperature. Using the value of δHB obtained from the fit at the density 0.828 g/cm3, a second least squares regression at the density 0.866 g/cm3 is performed to obtain ∆HHB(F) and ∆SHB(F). Values of the parameters δHB, ∆HHB(F), and ∆SHB(F) are listed in Table 2. The average deviation χ for the fits (defined as the square root of the average squared deviations) is also shown. In the second case, we perform a simultaneous regression in both temperature and density. From the first case, we see that both ∆HHB(F) and ∆SHB(F) have a substantial dependence on F. We use the same form as in eq 9, but instead of using ∆HHB(F) and ∆SHB(F) as parameters at different densities, we fit them to linear functions of density
∆HHB(F) ) ∆EHB + C1F 0 + C2F ∆SHB(F) ) ∆SHB
(10)
0 , C1, where ∆EHB is the energy for hydrogen bonding and ∆SHB and C2 are parameters. All five parameters, δHB, ∆EHB, ∆SHB, C1, and C2, are obtained by a least squares fit to the 20 data points in Table 1. The results of this procedure are shown in Table 3. The average deviation χ for the regression is also shown. In the third case, we perform a regression in temperature and pressure (instead of density). On the basis of the form used for the free energy as a function of temperature and density (eqs 9 and 10), the free energy is fit to the following form
Hydrogen Bond Structure of Liquid Methanol
J. Phys. Chem., Vol. 100, No. 10, 1996 3963
∆GHB(T,P) ) ∆HHB(P) - T∆SHB(P)
TABLE 3: Five-Parameter Regression of the OH Chemical Shifts as a Function of Temperature and Density. See Text for Description of Parameters
0 P ∆HHB(P) ) ∆EHB + ∆VHB
∆SHB(P) )
0 ∆SHB
+
1 ∆VHB P
(11)
where ∆EHB, ∆HHB(P), and ∆SHB(P) are the energy, enthalpy, and entropy for hydrogen bonding. One can define the molar volume change for the association of a monomer with a cluster:
∆VHB(T) )
∂(∆GHB(T,P)) ∂(P)T
0 1 ) ∆VHB - T∆VHB
(12)
δHB, ppm
∆EHB, kJ/mol
0 ∆SHB , J/mol K
C1 kJ/mol‚ (g/cm3)
C2 J/mol‚K‚ (g/cm3)
χ
5.947
-40.01
-71.84
25.59
54.18
0.008
TABLE 4: Five-Parameter Regression of the OH Chemical Shifts as a Function of Temperature and Pressure. See Text for Description of Parameters δHB, ppm
∆EHB, kJ/mol
0 ∆SHB J/mol‚K
0 ∆VHB kJ/mol‚kbara
1 ∆VHB J/mol‚K‚kbar
χ
5.790
-22.42
-33.05
1.473
3.038
0.012
a
0 , δHB, ∆EHB, ∆SHB
0 ∆VHB ,
1 ∆VHB ,
and are All five parameters, obtained by a least squares regression to the 20 data points in Table 1. The results of this fitting procedure are shown in Table 4. The average deviation χ is also shown. The values for the total chemical shift of the hydrogen-bonded OH groups range from 5.79 to 5.95 ppm. These are slightly larger than the chemical shift predicted for hydrogen-bonded OH groups from dilution studies using a monomer/tetramer model.23-25 It is reassuring that the values for δHB from the two regressions to density (cases 1 and 2) are nearly identical. By construction, the enthalpies for hydrogen bonding show no temperature dependence, but they do exhibit a dependence on density and pressure within experimental error. The two regressions to density predict very similar values for ∆HHB(F) (for example, case 2sthe five-parameter fitsgives a value of -18.83 kJ/mol at 0.828 g/cm3 compared to -18.92 kJ/mol for the three-parameter fit at the same density). Both cases 1 and 2 predict an increase in ∆HHB(F) with increasing density. The model also predicts a negative value for the entropy, which is consistent for an association process. The entropy penalty for association is seen to decrease with increasing density in both cases 1 and 2. The third case, regressed as a function of temperature and pressure, shows a higher average deviation χ than cases 1 and 2 that were regressed as a function of temperature and density, but the average deviation is sufficiently smaller than variations in the experimental data that we can still draw qualitative conclusions. The enthalpies are about 1-2 kJ/mol smaller than for the five-parameter fit to density (case 2). Consistent with the trends for case 2, the enthalpy and entropy are seen to increase with increasing pressure. Using eq 12, the molar volume change for the association of a monomer with a cluster is 5.7 and 2.2 cm3/mol at 297.3 and 413.2 K, respectively. A positive molar volume change is consistent with the increase in free energy that is observed with increasing density as well as with increasing pressure, thereby favoring smaller clusters with increasing pressure. Schulman et al.9 reported a constant value of -51 kJ/mol for the enthalpy of forming a tetramer from monomers for pressures up to 1 kbar. Similarly, Feeney and Walker23 reported a value of -47.7 kJ/mol for this enthalpy at room temperature and pressure. Assuming that there are 3 hydrogen bonds in a linear tetramer, our results of -17.8 to -21 kJ/mol for the enthalpy of association of a monomer with a cluster lead to values of -53 to -63 kJ/mol for forming a linear tetramer from monomers. Schulman et al. reported a negative value for ∆VHB, in contrast to the results reported here.9 On the basis of the analysis of the self-diffusion data for methanol, Jonas and Akai8 have presented an argument for decreased clustering with increasing pressure that is consistent with a positive value for ∆VHB as reported here.
Note that kJ/mol‚kbar ) 10 cm3/mol.
TABLE 5: Comparison of Predicted Values of Free OH Groups, xF, from Fits of the Model to Experimental Data and from MD Simulations xF T, K
P, kbar
F, g/cm
297.3 297.3 413.2 413.2
0.55 2.65 0.55 2.64
0.828 0.926 0.739 0.866
3
case 1
case 2
case 3
MD
0.11
0.11 0.13 0.27 0.28
0.08 0.10 0.25 0.26
0.22 0.19 0.39 0.31
0.28
Figure 5. Comparison of molecular dynamic simulations to equilibrium cluster model cases 2 and 3 for the two temperatures (297.3 and 413.2 K) and two pressures (0.55 and 2.65 kbar).
We can also compare the results of the simple cluster model for the cluster distributions and number of free OH groups, xF, with those obtained directly from the MD simulations. Figure 5 compares the cluster distributions for the fits extracted from the experimental data with those for the MD simulations. Note that the MD simulations were actually run at densities corresponding to the experimental pressures shown in Figure 5 and that the computed pressures were not in good agreement with the experimental ones. We only show the results from case 2 (5-parameter fit to temperature and density) and case 3 (5parameter fit to temperature and pressure), since the results of case 1 are almost identical to those from case 2. For the lowtemperature systems, the regression to experiment shows much broader distributions than the MD simulations. The MD simulations do show a shift toward smaller clusters with increasing temperature, as is seen in the experimental fits. At the higher temperature the agreement between the MD distributions and experimental fits is quite good. In Table 5 we compare the predicted number of free OH groups for the three model cases and for the MD simulations. Consistent with the findings for the cluster distributions, the MD simulations show a significant reduction in free OH groups (more clustering) at the
3964 J. Phys. Chem., Vol. 100, No. 10, 1996 lower temperature. We also note that the MD simulations predict more clustering (xF decreases) as the pressure increases, contrary to what is observed for the fits to experiment. However, as stated before, the MD simulations do not reproduce the pressure for fixed densities (see Table 1), so it may be too much to expect them to reproduce the more subtle changes with pressure. These comparisons do indicate that the interaction potential used in the MD simulations may not be sufficiently accurate to reproduce the clustering behavior in methanol over the temperature and pressure ranges studied here. Further investigations are clearly needed to determine the accuracy of the potential. The investigation of the methanol equilibrium as a function of pressure and temperature describes changes in the number of hydrogen bonds under varying thermodynamic conditions and provides complementary information to the measured chemical shift differences (∆ν) of the OH and CH3 groups. Conclusions The results of this high-pressure NMR study of liquid methanol show that ∆ν is dominated by kinetic effects, reflecting changes in the extent of the hydrogen bond network, while packing considerations (strength) plays a minor role. Cluster equilibrium is shifted toward the free monomer as a function of increasing pressure at constant temperature. This shift in cluster population is supported by the earlier investigation of deuterated methanol by Jonas and Akai.8 These authors reported a change in the slip/stick boundary limits to the Stokes-Einstein diffusion equation for both temperature and pressure. At constant density the boundary limit value decreased slightly with increasing temperature, which was interpreted as a disruption in the hydrogen bond network with increasing thermal energy. As density increased at constant temperature the boundary limiting value decreased toward the slip limit, which was interpreted as the disruption of the hydrogen bond network due to repulsive interactions in the solvent as it was compressed. In the present study, the positive volume of association and entropy values obtained from the fit to the experimental data also supports an equilibrium shift toward more free OH groups as a function of increasing pressure at constant temperature. The linear chain model and the experiments are in good agreement with the molecular dynamics simulations on the effect of temperature on the hydrogen-bonding networks but disagree as to the effect of pressure. The simulations indicate that increasing pressure results in more extensive hydrogen bonding whereas the linear chain model suggests that increasing pressure disrupts hydrogen-bonding. There are several possible origins for this discrepancy. One possibility is that the molecular dynamics potential may not be capable of correctly reproducing the behavior of the hydrogen-bonding network under these conditions. The large differences between the simulation pressure and the experimental pressure suggest that the potential function can be improved. A second problem involves the large number of approximations in the linear chain model. The model assumes that only the σs term in eq 1 contributes to the chemical shift, but temperature and density may affect the other shielding contributions differently for the two resonances. An alternative to looking at the chemical shift δOH would be to fit the behavior of ∆ν, but this would involve additional assumptions about eq 1. A more sophisticated approach to modeling the NMR chemical shifts in methanol would be to develop a chemical shift function σ(R) where R is a generalized coordinate vector that describes the location and orientation of all molecules in the system. This function would be similar to the molecular potential energy function used in conventional MD simulations.
Wallen et al. The shifts could then be calculated as part of a simulation to get the average chemical shift for each type of proton. The resulting shift could then be compared directly to experiment. High-pressure NMR studies have demonstrated the ability to determine the effect of pressure on the hydrogen bond network in liquid methanol. The chemical shift difference in liquid methanol as a function of temperature and pressure can be used to provide insight into the solution dynamics for this molecule. This work extends the pressure range of earlier chemical shift difference studies in methanol. The equilibrium association model investigated demonstrates a decrease in the hydrogen-bonding network as a function of increasing pressure, which supports the earlier self-diffusion coefficient measurements based on relaxation times in methanol by Jonas and Akai8 and is contrary to the work of Schulman et al.9 The chemical shift difference for liquid methanol was dominated by kinetic constraints over the temperature and pressure ranges studied. Changes in the chemical shift with pressure were larger at higher temperatures but were generally smaller than the changes seen as a function of temperature. The measurement of the chemical shift difference could prove to be an interesting technique to study intra- versus intermolecular hydrogen bonding as a function of both increasing pressure and temperature using highpressure NMR. Acknowledgment. Work at the Pacific Northwest National Laboratory (PNNL) was supported by the Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U. S. Department of Energy, under Contract DE-AC076RLO 1830. References and Notes (1) Magini, M.; Paschina, G.; Piccaluga, G. J. Chem. Phys. 1982, 77, 2051. (2) Haughney, M.; Ferrario, M.; McDonald, I. R. Mol. Phys. 1986, 58, 849. (3) Pettitt, B. M.; Rossky, P. J. J. Chem. Phys. 1983, 78, 7296. (4) Mammone, J. F.; Sharma, S. K.; Nicol, M. J. Phys. Chem. 1980, 84, 3130. (5) Narten, A. H.; Habenschuss, A. J. Chem. Phys. 1984, 80, 1984. (6) Montague, D. G.; Gibson, I. P.; Dore, J. C. Mol. Phys. 1981, 44, 1355. (7) Jorgensen, W. L.; Ibrahim, M. J. Am. Chem. Soc. 1982, 104, 373. (8) Jonas, J.; Akai, J. A. J. Chem. Phys. 1977, 66, 4946. (9) Schulman, E. M.; Dwyer, D. W.; Doetschman, D. C. J. Phys. Chem. 1990, 94, 7308. (10) Oldenziel, J. G.; Trappeniers, N. J. Physica A 1976, 83, 161. (11) Pfund, D. M.; Zemanian, T. S.; Linehan, J. C.; Fulton, J. L.; Yonker, C. R. J. Phys. Chem. 1994, 98, 11846. (12) Yonker, C. R.; Zemanian, T. S.; Wallen, S. L.; Linehan, J. C.; Franz, J. A. J. Magn. Reson., Ser. A 1995, 113, 102. (13) Jameson, C. J. Chem. ReV. 1991, 91, 1375. (14) Raynes, W. T.; Buckingham, A. D.; Bernstein, H. J. J. Chem. Phys. 1961, 34, 1084. (15) Rummens, F. H. A.; Bernstein, H. J. J. Chem. Phys. 1965, 43, 2971. (16) Buckingham, A. D. Can. J. Chem. 1960, 38, 300. (17) Linowski, J. W.; Liu, N-I.; Jonas, J. J. Magn. Reson. 1976, 23, 455. (18) Agaev, N. A.; Pashaev, A. A.; Kerimov, A. M. Zh. Fiz. Khim. 1975, 49, 3021. (19) Zerda, T. W.; Thomas, H. D.; Bradley, M.; Jonas, J. J. Chem. Phys. 1987, 86, 3219. (20) Nose´, S. J. Chem. Phys. 1984, 81, 511. (21) Brooks, C. L.; Pettitt, B. M.; Karplus, M. J. Chem. Phys. 1985, 83, 5897. (22) Liddel, U.; Becker, E. D. Spectrochim. Acta 1957, 10, 70. (23) Feeney, J.; Walker, S. M. J. Chem. Soc. A 1966, 1148. (24) Davis, J. C.; Pitzer, K. S.; Rao, C. N. R. J. Phys. Chem. 1960, 64, 1744. (25) Saunders, M.; Hyne, J. B. J. Chem. Phys. 1958, 29, 1319. (26) Israelachvili, J. Intermolecular and Surface Forces, 2nd ed.; Academic Press: San Diego, CA, 1992.
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