Diffusion and Structure in Dilute Aqueous Alcohol Solutions: Evidence

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J. Phys. Chem. B 1998, 102, 8874-8879

Diffusion and Structure in Dilute Aqueous Alcohol Solutions: Evidence for the Effects of Large Apolar Solutes on Water Kenneth R. Harris* and Paula J. Newitt School of Chemistry, UniVersity College, UniVersity of New South Wales, Australian Defence Force Academy, Canberra, ACT 2600, Australia ReceiVed: April 27, 1998; In Final Form: August 6, 1998

By measuring the dependence of molecular motion on pressure, p, using diffusion measurements as a probe, one can obtain information regarding the structure of solutions containing amphiphilic solutes having apolar or hydrophobic groups. We have found that at low temperatures, the intra-diffusion coefficient (D) of water in a dilute solution of aqueous tert-butyl alcohol (mole fraction, x ) 0.025) shows a maximum with increasing p, to a greater relatiVe extent than in pure water under the same conditions. This suggests the water in these solutions is more “structured” than in pure water, though there is a clear distinction from the effects produced by large “structure breaking” ions as solutes where the absolute water diffusion coefficient may show a maximum as concentration or pressure is increased. We have made a survey of a number of other wateralcohol systems; a similar large enhancement occurs in 2-propanol solutions. In solutions of methanol, ethanol, and 2,2,2-trifluoroethanol, the enhancement is similar to that of water with no additional effect. Volumes of activation (∆VD) have been calculated from the diffusion data. From an analysis of the T and p dependence of D and ∆VD, we have concluded that the mechanism for the diffusion of water in these solutions seems likely to be the same as for pure water. The molecules can move around the obstacle solute molecules via the labile hydrogen-bonded network. Where the temperature is low and the solute alcohol molecules are large, the network appears to be distorted such that the effect of pressure on water diffusion is greater with the maximum appearing at higher pressures than in pure water.

Introduction In 1985, Easteal and Woolf1 found that the tracer diffusion coefficients of methanol and ethanol (measured at essentially infinite dilution) in water were enhanced relative to their atmospheric pressure values by high pressure to a greater extent than is the case for the self-diffusion coefficient of pure water. For the majority of liquids, including some hydrogen-bonded liquids such as alcohols,2 high pressure slows their diffusion as the free volume is reduced on compression. For water on the other hand, the rate of its self-diffusion is increased,3-5 and the viscosity decreased, despite a small increase in density. This has been interpreted to be due to the distortion of the labile three-dimensional hydrogen-bonded network of water molecules, with a consequent lowering of translational energy barriers. This effect competes with the reduction in free volume such that below about 30 °C maxima in the p-D curves occur in the region 100-150 MPa. The relative enhancement of D increases as the temperature is lowered5,6 and is larger for pure heavy water.7 Easteal and Woolf interpreted the larger effect of pressure on the tracer diffusion of the two alcohols as being due to distortion of still more structured water caging the alcohol molecules. Easteal and Woolf also made measurements using acetonitrile and formamide as solutes. No maxima were observed in these cases, though one might be expected for acetonitrile due to its similarity to methanol. We are currently examining the pressure dependence of the self-diffusion coefficients of solvent water and solutes in a range of solutions of amphiphilic substances. There are several * Author to whom correspondence should be addressed at School of Chemistry, University College, University of New South Wales, Australian Defence Force Academy, Canberra, ACT 2600, Australia. E-mail: k-harris@ adfa.edu.au.

questions of interest. At what concentration does the water stop behaving like pure water? Where do the hydration spheres around the solutes begin to overlap? Is the enhancement for methanol and ethanol observable in other systems? Is it due to the apolar alkyl groups or is it related to the hydrogen-bonding of the hydroxyl to the water lattice? Besides the work of Easteal and Woolf, there have been two other studies of the pressure dependence of diffusion in wateralcohol mixtures, in dilute D2O-2,2-dimethyl-1-propanol (DMP) by Has and Lu¨demann8 and in D2O-2-methyl-2-propanol (tertbutyl alcohol or TBA) by Woznyj9 in the same laboratory. In the DMP system, no enhancement of the DMP intra-diffusion coefficient10 with increasing pressure was observed even at the lowest composition (0.2 wt % or x ) 0.0004) and temperature (5 °C) studied. On the other hand, the pressure derivative (∂D/ ∂p)T,x was positive for D2O in its DMP mixtures at the lowest temperature examined, 1 °C, at up to about 2 wt % (x ) 0.004): the position of the maximum was not established exactly as the upper pressure limit of the experiments was 200 MPa. It must lie above this value. In pure D2O at this temperature it lies between 200 and 300 MPa.7 Only solute diffusion was determined in the D2O-TBA system, and no effects were reported. We have previously reported on correlation lengths (ξ) in water-alcohol systems at atmospheric pressure.11 These are obtained from mutual diffusion (D12) and viscosity (η) data using the relation

ξ ) kT/6πηD12

(1)

where k is Boltzmann’s constant and T is the temperature. The correlation lengths show a trend from water-methanol through

10.1021/jp9820370 CCC: $15.00 © 1998 American Chemical Society Published on Web 10/10/1998

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J. Phys. Chem. B, Vol. 102, No. 44, 1998 8875

TABLE 1: Coefficients for D(H2O) ) D0(1 + a1 p + a2 p2 + a3 p3) for Each System solute MeOH

EtOH 2-PrOH

TBA

TFE

T/°C 0 5 15 25 0 25 -5 0 5 15 25 -5 0 15 25 50 -5 0 25

109 D0/m2 s-1 b

0.965 1.159 1.553 2.081 0.791 1.781 0.569 0.691 0.858 1.189 1.642 0.495 0.616 1.143 1.595 3.017 0.680 0.845 1.912

103 a1/MPa-1

105 a2/MPa-2

108 a3/MPa-3

δ/%a

1.598 1 1.250 2 0.652 51 0.282 09 1.482 24 0.350 01 2.314 9 1.526 2 1.091 9 0.500 54 0.349 35 1.690 3 1.571 4 0.534 01 -0.059 65 -0.452 21 1.809 9 1.253 6 0.071 71

-0.816 68 -0.596 99 -0.218 30 -0.139 43 -0.492 76 -0.249 02 -0.797 14 -0.505 20 -0.342 86 -0.151 67 -0.152 59 -0.300 96 -0.598 69 -0.259 24 -0.056 40 0.0 -0.783 33 -0.525 31 -0.107 38

1.095 9 0.689 36 0.0 0.0 0.385 92 0.263 61 0.755 90 0.453 65 0.201 01 0.0 0.0 -0.156 97 0.747 76 0.253 56 -0.106 82 0.0 0.944 95 0.548 29 0.0

0.9 0.5 0.5 0.3 0.8 0.3 0.2 0.3 0.7 0.3 0.5 1.2 1.7 0.6 0.7 0.3 1.0 0.2 0.2

a δ is the standard deviation of the fit expressed as a percentage of D , the value of D at atmospheric pressure. b D values were fitted rather than 0 rel absolute D values.

to water-1- propanol and water-TBA, with those for the lower alcohols varying little with composition but those for 1-propanol and TBA rising to a maximum at low mole fractions, beginning at about x ) 0.06 (at 25 °C). This behavior is suggestive of long-range correlation of molecular motion or pseudo-critical behavior in these latter systems. As a first step, we have chosen to survey a number of wateralcohol mixtures at a lower composition, x ) 0.025, over a range of temperatures, at pressures up to 400 MPa. At this composition, the atmospheric pressure correlation lengths are all of the order of the distance between neighboring water molecules and each solute molecule is surrounded by a complete hydration sphere. We have measured the pressure enhancement of the water intra-diffusion coefficient to see whether there is an effect attributable to increased water structure around the alcohol solute molecules, and these results are reported here. Experimental Section The high-pressure NMR spin-echo apparatus has been described previously.12 The steady-gradient method was employed. At each state point, diffusion coefficients obtained from two runs using constant magnetic field gradients (one positive, one negative) over a range of rf-pulse separations and a third run using constant rf-pulse separation over a range of gradients were averaged. The rf and quadrupole gradient coils are both mounted in grooves cut in the same Macor glass (Corning) former and held in place by epoxy cement (Araldite K138). The former is contained within the Be-Cu pressure vessel. The sample cell used was of the Teflon bellows type13 and is always placed in the same position within the combined fields of the rf and gradient coils. This is a particular advantage in this type of work. Pressures (accuracy, (0.5 MPa) were measured with a Heise-Bourdon gauge calibrated against a Budenberg 283 deadweight piston gauge. The hydraulic fluid was 3M FC-75, a fully fluorinated material. Temperatures (accuracy, (0.02 K) were measured with a calibrated four-lead Pt resistance (Leeds and Northrup) inserted in the bottom closure of the pressure vessel; this is sensitive enough to detect the adiabatic changes induced when the pressure is pumped up or let down. The pressure vessel is immersed in a Dewar flask containing ethanol as the thermostat liquid. The temperature is controlled by

circulating liquid from a Julabo HP50 bath through a copper coil wrapped around the pressure vessel. A second sample holder was used for some atmospheric pressure measurements to provide a check on the high-pressure system. The gradient coils were calibrated using the reference values for the self-diffusion coefficient of water established at 0.1 MPa by Mills.14 During the course of this work the epoxy cement holding the gradient coils in position on both highpressure coil formers used became swollen, causing one former (#6) to crack and the calibration constant of the gradient coil of the other (#9, used in our pure water study5) to change slightly (by -1.6%). Experiments showed that alcohols (unlike the FC75 used as the hydraulic fluid) are absorbed by the epoxy, so it is possible that the swelling was caused by exposure either to the ethanol from the Dewar or to sample solutions leaking from the Teflon cell. Such leakage does occur occasionally after repeated p-T cycling. Nevertheless, though the absolute values obtained from the two coils differed in some instances for a given system at a given temperature, the values relative to the atmospheric pressure diffusion coefficients matched within experimental error. In other words, temperature change sometimes affected the damaged coils, but pressure did not. Where necessary, therefore, values for a given high-pressure isotherm were normalized relative to the value obtained at 0.1 MPa with the atmospheric pressure probe. Further check measurements with former #9 following recalibration (see Table 1S) confirmed that the relative D values were the same before and after the coils were damaged. The precision of the diffusion coefficients obtained is estimated at (1% and the accuracy at (2%. Solutions were made up by weight using deionized water. As the NMR frequency is low, 20 MHz, the apparatus is unable to resolve different proton resonances. Therefore, deuterated alcohols were used as solutes. These were obtained from CENSaclay, France (methanol-d4, 99.5%), Cambridge Isotope Laboratories (ethanol-d6, 99%) and the Aldrich Chemical Co. (2,2,2trifluoroethanol-d3, 99.5%; 2-propanol-d8, 99%; 2-methyl-2propanol-d10, 99%). At x ) 0.025, the effect of isotope exchange at the alcohol hydroxy group on the self-diffusion coefficient of water is likely to be small. The effect of replacing the hydrogen atoms on the alcohols by deuterium is more difficult to quantify. The difference between the tracer diffusion coefficient of ethanol (EtOH) in mixtures with water15 and that

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Harris and Newitt

Figure 1. Relative intra-diffusion coefficients for water in watermethanol (x ) 0.025).

Figure 3. Relative intra-diffusion coefficients for water in water-2propanol (2PrOH) (x ) 0.025).

Figure 2. Relative intra-diffusion coefficients for water in waterethanol (x ) 0.025).

Figure 4. Relative intra-diffusion coefficients for water in water-2methylpropanol (TBA) (x ) 0.025).

in mixtures with D2O16 is about 20% at x(EtOH) ∼ 0.1 and 4% at x ∼ 1, but this is mainly due to the different properties of water and D2O; their self-diffusion coefficients, for example, differ by 19%.14 The effect here is likely to be very much smaller. The ranges of temperatures and pressures for which data are reported were limited by the freezing surfaces (pTx). (This surface has been determined only for water-TBA.9) Consequently no measurements were taken for the methanol and ethanol systems below 0 °C or for the TBA system above 320 MPa at 0 and -5 °C. Sample freezing sometimes caused inhomogeneous solutions to be formed on melting, and new solutions were prepared when this happened. Results and Discussion The results for each of the systems studied are presented in detail in Table 1S of the Supporting Information and summarized in Table 1. Relative diffusion coefficients (Drel ) D(p)/ D(0.1 MPa)) are plotted against pressure, p, in Figures 1 to 5 with the corresponding values for pure water4,5 given in Figure 6. Figures 7 to 11 allow comparison of the results for the different mixtures and water at common temperatures. In constructing these graphs, values of D(0.1 MPa) for water at -20, -10, and -5 °C of 0.430, 0.721 and 0.892 10-9 m2 s-1, respectively, were estimated from the data of Gillen et al.,17 adjusted upward by 3% to agree with the results of Mills in their overlapping temperature range. For water-TBA at the same temperature, D(0.1 MPa) was obtained by extrapolation of the high-pressure data (10 MPa was the lowest pressure measurable), giving a value of 0.511 10-9 m2 s-1.

Figure 5. Relative intra-diffusion coefficients for water in water-2,2,2trifluoroethanol (TFE) (x ) 0.025).

The maximum in the self-diffusion coefficient at low temperatures is one of the anomalous properties of water that distinguishes it from other liquids. For the lower alcohols (methanol (MeOH), ethanol, and 2,2,2-trifluoroethanol (TFE)), at temperatures of 0 °C and above, the p-Drel isotherms are essentially the same as those for pure water within experimental error. The same is true for all the systems we have measured at 25 °C and above. At -5 °C, the enhancement in the waterTFE mixture is less than that in pure water. This could be for several reasons; there are too few data to permit comment. For the mixtures containing the two larger alcohols, 2-propanol (2-PrOH) and TBA, however, the maxima are larger at 0 and -5 °C and are displaced to higher pressures than for pure water (Table 2). This suggests greater structure around the

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J. Phys. Chem. B, Vol. 102, No. 44, 1998 8877

Figure 7. Relative intra-diffusion coefficients for water in wateralcohol (x ) 0.025) solutions at -5 °C compared with those for pure water. Symbols: O, water; 2, 2-PrOH; 1, TBA; [, TFE. Figure 6. Relative intra-diffusion coefficients for pure water.4,5 Experimental points are shown below 0 °C to indicate the liquid region. The ice I-ice III-liquid triple point occurs at -22 °C, 209 MPa.

TABLE 2: Positions of Maxima in Water Intra-Diffusion Coefficient Isotherms system water water-2-PrOH water-TBA

T/°C

pmax/MPa

0 -5 0 -5 0 -5

100-200 125-175 150-250 150-250 200-250 200-250

solute molecules than in pure water under the same conditions, which requires greater pressure to distort and hence facilitate molecular motion. However, there is no absolute enhancement of the water diffusion coefficient like that occurring in certain electrolyte solutions. Solutions containing structure-breaking ions such as Rb+, Cs+, Br-, I-, NO3-, etc., can show maxima in the water diffusion coefficient as the electrolyte concentration is increased,18,19 and this effect is stronger at lower temperatures.20 As with pure water, the enhancement itself can show a maximum when pressure is applied, though only one example seems to have been studied to date (CsCl).20 In the systems studied here, the presence of the alcohol solute lowers the absolute diffusion coefficients, presumably due to obstruction; the water structure seems to be modified in a different way to that in an electrolyte containing large ions. A more quantitative examination of these changes can be made using the pressure derivative (∂D/∂p)T,x in the form of the volume of activation, ∆VD:

Figure 8. Relative intra-diffusion coefficients for water in wateralcohol (x ) 0.025) solutions at 0 °C compared with those for pure water. Symbols: as Figure 7 plus b, MeOH; 9, EtOH.

(2)

Figure 9. Relative intra-diffusion coefficients for water in wateralcohol (x ) 0.025) solutions at 5 °C compared with those for pure water. Symbols: as Figures 7 and 8.

The derivative was obtained from the polynomial fits in Table 1. The polynomial orders were chosen to give reasonably smooth derivatives, consistent with a fit within experimental error, though there is some spread at the high pressures due to the effect of the higher order terms. Figure 12 shows ∆VD values for water at various temperatures. ∆VD is negative at low pressures and becomes more so at low temperatures. It is interesting that this property at high pressures converges on a common value in the experimental temperature range -15-60 °C and that this convergence occurs at about 250 MPa. Analysis of existing self-diffusion data for D2O,6,7,22 and tracer diffusion data for HTO in H2O3 and for

DTO in D2O23 give very similar values of ∆VD within the experimental uncertainties. There is no clear distinction between the behavior in the different systems, though there is perhaps a tendency for values in the last system to be more negative at 7 and 15 °C and at low pressures than for the others under the same conditions. Figures 13-15 show ∆VD for water in the alcohol solutions at -5, 0, and 25 °C. At 0 °C and above, the values are essentially equal to those for pure water. At -5 °C, the lowpressure values for 2-PrOH, TBA, and TFE are somewhat less negative than for pure water. As Figure 7 shows, the maxima lie at higher pressures than for pure water, so even though the

∆VD ) - RT (∂D/∂p)T,x/D

8878 J. Phys. Chem. B, Vol. 102, No. 44, 1998

Figure 10. Relative intra-diffusion coefficients for water in wateralcohol (x ) 0.025) solutions at 15 °C compared with those for pure water. Symbols: as Figures 7 and 8.

Figure 11. Relative intra-diffusion coefficients for water in wateralcohol (x ) 0.025) solutions at 25 °C compared with those for pure water. Symbols: as Figures 7 and 8.

Figure 12. ∆VD for water. Solid and dashed lines refer to alternate isotherms in the series - 15, -10, -5, 0, 10, 25, 45, and 60 °C.

enhancement is larger, the slope, which governs the magnitude of ∆VD, is less. Therefore it seems that the mechanism for the diffusion of water in these solutions is the same as for pure water, and the molecules move around the solute molecule obstacles via the labile hydrogen-bonded network. Where the temperature is low and the solute alcohol molecules are large, the network appears to be distorted such that the effect of pressure on water diffusion is greater, with the maximum appearing at higher pressures than in pure water. This may well be due to the hydrophobic interaction; if so, the effect on the solute alcohol tracer diffusion coefficients should be larger than Easteal and Woolf have observed for MeOH and EtOH.1 It would be of particular interest if (neutron) scattering measurements could be performed on water-TBA and water-

Harris and Newitt

Figure 13. ∆VD for water in water-alcohol (x ) 0.025) solutions at -5 °C compared with those for pure water (O).

Figure 14. ∆VD for water in water-alcohol (x ) 0.025) solutions at 0 °C compared with those for pure water (O).

Figure 15. ∆VD for water in water-alcohol (x ) 0.025) solutions at 25 °C compared with those for pure water (O). The latter are not distinguishable from the mixture curves.

2-PrOH at low temperatures in order to examine solution structure from a different experimental perspective. In addition, viscosity measurements should also show a pressure enhancement of the fluidity at low temperatures and low alcohol concentrations. We hope to report the results of such viscosity measurements in future work. We are also currently conducting diffusion measurements across the whole composition range in these systems to determine answers to some of the other questions raised in the Introduction. Acknowledgment. We are grateful to Ken Piper, Kerry Richens, and Steve Cheney for workshop support services and to Dr. Lawrie Woolf for criticism of the manuscript. This work was supported in part by a grant from the Australian Research Council (A29600620).

Dilute Aqueous Alcohol Solutions Supporting Information Available: Table 1S contains all the diffusion data (5 pages). Ordering information is given on any current masthead page. References and Notes (1) Easteal, A. J.; Woolf, L. A. J. Phys. Chem. 1985, 89, 1066. (2) Hurle, R. L.; Easteal, A. J.; Woolf, L. A. J. Chem. Soc., Faraday Trans. 1 1985, 81, 769. (3) Woolf, L. A. J. Chem. Soc., Faraday Trans. 1 1975, 71, 784. (4) Harris, K. R.; Woolf, L. A. J. Chem. Soc., Faraday Trans. 1 1980, 76, 377. (5) Harris, K. R.; Newitt, P. J. J. Chem. Eng. Data 1997, 42, 346. (6) Prielmeier, F. X.; Lang, E. W.; Speedy, R. J.; Lu¨demann, H.-D. Ber. Bunsen-Ges. Phys. Chem. 1988, 92, 1111. (7) DeFries, T. H.; Jonas, J. J. Chem. Phys. 1977, 66, 5393. (8) Has, M.; Lu¨demann, H.-D. Z. Naturforsch. A 1993, 48, 793. (9) Woznyj, M. Thesis, University of Regensburg, Germany, 1985. See also Lang, E. W.; Lu¨demann, H.-D. in High-Pressure NMR; Jonas, J., Ed.; Springer-Verlag: Berlin, 1991; p 129. (10) Intra-diffusion refers to the thermal motion of a component of a mixture and is differentiated from inter-diffusion due to mixing caused by a concentration difference; self-diffusion refers to the special case of intradiffusion for a pure substance. See Albright, J. G.; Mills, R. J. Phys. Chem.

J. Phys. Chem. B, Vol. 102, No. 44, 1998 8879 1965, 69, 3120 and Tyrrell, H. J. V; Harris, K. R. Diffusion in Liquids; Butterworth: London, 1984; pp 4, 279 ff, and 318 ff. Both intra- and selfdiffusion coefficients are obtained from experimental tracer diffusion coefficients using either isotopic (often radioisotopic) or nuclear spin labeling (in NMR spin-echo measurements). Sometimes corrections for mass or moment of inertia effects are needed to obtain intra-diffusion coefficients from tracer data. As we are interested in the relative effect of pressure, no such corrections have been applied in this study. (11) Harris, K. R.; Lam, H. N. J. Chem. Soc., Faraday Trans. 1995, 91, 4071. (12) Harris, K. R.; Lam, H. N.; Raedt, E.; Easteal, A. J.; Price, W. E.; Woolf, L. A. Mol. Phys. 1990, 71, 1205. (13) Easteal, A. J.; Woolf, L. A.; Wilson, F. L. J. Magn. Reson. 1983, 54, 158. (14) Mills, R. J. Phys. Chem. 1973, 77, 685. (15) Harris, K. R.; Newitt, P. J.; Derlacki, Z. J. J. Chem. Soc., Faraday Trans. 1998, 94, 1963. (16) Sacco, A.; Holz, M. J. Chem. Soc., Faraday Trans. 1997, 93, 1101. (17) Gillen, K. T.; Douglass, D. C.; Hoch, M. J. R. J. Chem. Phys. 1972, 57, 5117. (18) McCall, D. W.; Douglass, D. C. J. Phys. Chem. 1965, 69, 2001. (19) Hertz, H.-G.; Mills, R. J. Chim. Phys. 1976, 73, 499. (20) Akai, J. A.; Jonas, J. J. Solution Chem. 1976, 5, 563. (21) Prielmeier, F. X. Thesis, University of Regensburg, Germany, 1988. (22) Woolf, L. A. J. Chem. Soc., Faraday Trans. 1 1976, 72, 1267.