Shock Hugoniot Equations of State for Binary Ideal - American

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Shock Hugoniot Equations of State for Binary Ideal (Toluene/ Fluorobenzene) and Nonideal (Ethanol/Water) Liquid Mixtures Peter A. Schulze, Nhan. C. Dang, Cynthia A. Bolme, Kathryn E. Brown, Shawn D. McGrane, and David S. Moore* Shock and Detonation Physics Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States S Supporting Information *

ABSTRACT: Laser shock Hugoniot data were obtained using ultrafast dynamic ellipsometry (UDE) for both nonideal (ethanol/water solutions with mole percent χethanol = 0%, 3.4%, 5.4%, 7.5%, 9.7%, 11%, 18%, 33%, 56%, 100%) and ideal liquid mixtures (toluene/fluorobenzene solutions with mole percent χtoluene = 0%, 26.0%, 49.1%, 74.9%, 100%). The shock and particle velocities obtained from the UDE data were compared to the universal liquid Hugoniot (ULH) and to literature shock (plate impact) data where available. It was found that the water UDE data fit to a ULH-form equation suggests an intercept of 1.32 km/s, lower than the literature ambient sound speed in water of 1.495 km/s (Mijakovic et al. J. Mol. Liq. 2011, 164, 66−73). Similarly, the ethanol UDE data fit to a ULH-form equation suggests an intercept of 1.45 km/s, which lies above the literature ambient sound speed in ethanol of 1.14 km/s. Both the literature plate impact and UDE Hugoniot data lie below the ULH for water. Likewise, the literature plate impact and UDE Hugoniot data lie above the ULH for ethanol. The UDE Hugoniot data for the mixtures of water and ethanol cross the predictions of the ULH near the same concentration where the sound speed reaches a maximum. In contrast, the UDE data from the ideal liquids and their mixtures are well behaved and agree with ULH predictions across the concentration range. The deviations of the nonideal ethanol/water data from the ULH suggest that complex hydrogen bonding networks in ethanol/ water mixtures alter the compressibility of the mixture.

I. INTRODUCTION Shock waves are characterized by a nearly discontinuous change in the thermodynamic properties of a material and create states of high pressure and temperature behind the shock front. Shock propagation velocities through many materials are on the order of kilometers/second, so the very short transition times from unshocked to shocked states make observing thermodynamic properties and the dynamic responses of materials to shocks very difficult. Due to the lack of microstructure in liquids and the associated complications arising from heterogeneities and defects, liquids under shock compression are a common model system that can provide a homogeneous sample for focused study of intermolecular bonding. Further, efforts to predict explosives’ product equations of state (EOS) require not only understanding of the behavior of pure fluids under shock loading but also understanding of the behavior of fluid mixtures. As a first effort toward understanding the behavior of nonideal liquid mixtures under shock loading, Hugoniot EOS data were obtained for a series of binary mixtures of water and ethanol. Hugoniot EOS data from an ideal liquid mixture (toluene and fluorobenzene) were obtained for comparison. The Hugoniot (traditional shock data obtained from refs 2−13 can also be found on the worldwide Web shock database at http://www.ficp.ac.ru/rusbank/catsearch.php) EOS for pure water and pure ethanol were first measured in 1956 by Walsh and Rice and have been well documented and studied since then.2−13 However, Hugoniot EOS data for binary mixtures of © XXXX American Chemical Society

water and ethanol do not exist in the literature. Unshocked mixtures of water and ethanol have been extensively studied, due to the nonideality and anomalous thermodynamic properties of the mixture.14−16 Of particular interest is the nonmonotonic trend in sound speed through the mixtures from pure water to pure ethanol; there is a maximum sound speed at ethanol mole fraction χethanol = 15%,1 as seen in Figure 1. Moreover, the molecular structures of water and water and ethanol mixtures have been studied spectroscopically in an effort to explain such irregular thermodynamic behavior.17−19 Fluorobenzene and toluene were chosen as an “ideal” binary liquid mixture primarily because of the absence of hydrogen bonding in the neat and binary mixtures. Other properties of fluorobenzene and toluene were considered, including sufficiently different sound speeds so their shock EOS are distinguishable, similar molar masses and molecular shapes to minimize other intermolecular forces, as well as miscibility with one another. In addition, Hugoniot data (plate impact) exist for toluene.2,4,11,20 The universal liquid Hugoniot (ULH)21,22 is given in eq 1 Special Issue: Prof. John C. Wright Festschrift Received: January 10, 2013 Revised: May 7, 2013

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provide meaningful insight into the dynamic effects of intermolecular forces. The use of laser-generated shocks and ultrafast dynamic ellipsometry (UDE) mitigates many of the obstacles presented by traditional plate impact shock experiments by incorporating high temporal (ps) resolution interferometric diagnostics into a small-scale experiment that can rapidly produce data from hundreds to thousands of shock events. This methodology enables a practical, accurate, and time-efficient means to establish the role of concentration dependence on the Hugoniot EOS for systems of mixtures. Herein, we present the measured Hugoniot EOS for water, ethanol, and eight of their binary mixtures: χethanol = 3.4%, 5.4%, 7.5%, 9.7%, 11%, 18%, 33%, 56%, as well as for toluene, fluorobenzene, and three of their binary mixtures: χtoluene = 26.0%, 49.1%, 74.9%. EOS data for these 15 liquids and liquid mixtures were compiled from UDE data from ca. 1600 shock events, which were analyzed to obtain the shock velocity, particle velocity, and shocked refractive index at a large range of shock input stresses (see Tables S1 and S2 in the Supporting Information). The UDE data for the liquids and liquid mixtures were then compared to the predicted ULH and plate impact data where available.

II. EXPERIMENTAL METHODS A. Brillouin Scattering Measurements for Obtaining Sound Speeds in Mixtures. Although the sound speeds of water, ethanol, and their mixtures are available in the literature,1 we used Brillouin scattering to determine the acoustic velocities in all the liquids and liquid mixtures used in the UDE experiments, including the toluene/fluorobenzene mixtures, for which ambient sound speed data are unavailable in the literature. The Brillouin instrument has been described in detail previously.23 Brillouin spectra were obtained using a tandem Fabry−Pérot interferometer (TFP-1, JRS Scientific Instruments). Both backscattering and equal-angle scattering geometries were used to measure the Brillouin shift, which enabled determination of both the sound velocity and the refractive index at 532 nm for each sample.23 In addition, the refractive index at 589.3 nm for each sample was obtained using a refractometer (J357, Rudolph Research Analytical). The measured refractive index at 532 or 589.3 nm was used as the unshocked refractive index at 800 nm for UDE analysis. This is an approximation justified by being far from any electronic resonances, which are in the ultraviolet for these materials. Further, the refractive index was used to verify ethanol concentration using water/ethanol concentration/refractive index tables. B. Shock Generation. The laser shock drive utilized in these experiments has been discussed in detail previously.24−27 A 10 Hz Ti:sapphire chirped pulse amplified laser was used to generate both the laser shock drive and the interferometric probe. To generate the shock waves in the liquids, the chirped pulse was spectrally shaped by cutting off the long wavelength portions resulting in a sharp rise time (∼5 ps) on the leading edge of the pulse. The total chirped pulse duration was 300 ps fwhm so that a supported shock wave of approximately the same duration could be driven through the sample. The chirped pulse was split into two separate beams: the pump beam, which was focused onto the back of the sample cell for shock generation (at 65 μm diameter spot size), and the probe beam, which was used for UDE measurements. Progressively

Figure 1. (a) Sound speed data versus concentration for water and ethanol mixtures as obtained using Brillouin scattering spectroscopy are shown (red squares/dashed line). Also shown are literature sound speeds1 (black triangles/dotted dashed line). The sound speed in mixtures of water and ethanol reaches a maximum at χethanol ≈ 15%. ULH best fit sound speeds for water and ethanol mixtures (blue rhombi/solid line) are plotted versus concentration. The ULH best fit sound speed for plate impact Hugoniot data (where available) is plotted (green circles). (b) Sound speed data versus concentration as obtained using Brillouin scattering spectroscopy are shown for toluene and fluorobenzene mixtures (red squares/dashed line). ULH best fit sound speeds for toluene and fluorobenzene mixtures (blue rhombi/ solid line) are plotted versus concentration. The ULH best fit sound speed for plate impact Hugoniot data is plotted for toluene (green circle). Error bars represent plus/minus one standard deviation of the absolute error of the Hugoniot data from the best fit ULH.

us = 1.37c0 − 0.37c0 exp( −2u p/c0) + 1.62u p

(1)

where us is the shock velocity; up is the particle velocity; and c0 is the ambient condition sound speed. The ULH was determined empirically using liquids with low intermolecular forces and is often utilized as a model for the dynamic shock response of a wide variety of pure liquids. However, the predictions of the ULH do not account for the influences of intermolecular forces, such as hydrogen bonding, which play a dominant role in mixing. Thus, for certain liquids, such as water, and for nonideal liquid mixtures, deviations from the ULH are commonly observed.2−13 Nevertheless, deviations from the ULH have yet to be fully understood, but the magnitude and direction of the deviation are expected to B

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our measured sound speeds. Brillouin measured sound speeds for toluene/fluorobenzene (blue squares/dashed line) are shown in Figure 1b and exhibit linear, monotonic dependence on concentration. Raw UDE Hugoniot data for the liquids and liquid mixtures are shown for ethanol and water in Figure 2a

increasing the laser drive energy resulted in shock stresses ranging from ∼1 to 20 GPa. C. Liquid Film Samples. The liquids were confined to a cell mounted into a 1 in. diameter holder, as is described in Dang et al.28 The cell was comprised of a series of stacked materials (in order from the laser shock drive entry side of the sample toward the direction of propagation of the shock): 0.5 mm thick sapphire (Esco, not oriented), 2 μm of aluminum (physical vapor deposited on UV/ozone cleaned sapphire), 6 μm of liquid (Harrick Scientific Mylar spacer), and 2 mm of calcium fluoride (International Crystal Laboratories, not oriented). D. Ultrafast Dynamic Ellipsometry (UDE). Ultrafast dynamic ellipsometry was performed as described in Dang et al.28 Briefly, the probe beam that was split off from the chirped spectrally shaped main beam was used for UDE measurements. The probe was further split into two individual interferometers, each with the sample in one path of the interferometer, at low and high angles from normal incidence (29° and 65°, respectively), to resolve both material motion as well as changes in the optical properties of the material. The reference and probe beams of each interferometer were recombined spatially and temporally on a slit and imaged onto the face of a CCD after passing through a spectrometer. The spectrometer dispersed the wavelength chirp of the laser spatially across the front of the CCD. Knowing the chirp of the laser allowed us to map position on the CCD to time. Wollaston prisms were used to obtain images at s- and p-polarizations in each interferometer, providing four data sets for the determination of the three unknowns (up, us, and ns). UDE data were recorded for each laser shock event. These data were fit to simulations of shock propagation through liquid samples. Fourier analysis provided spatially resolved phase maps as a function of time that followed the Gaussian profile of the shock generation pulse. The UDE data from the central 5 μm diameter of each shock profile were averaged to obtain plots of phase shift vs time in the region of highest pressure and lowest curvature.27 The derivatives of these plots were fit to obtain initial parameters using the method described by Armstrong et al.29 Best fits of the data were determined using a Levenberg−Marquardt algorithm as described in detail elsewhere24,28 to obtain the shock velocity, us, the particle velocity, up, and the shocked refractive index of the sample, ns. Two to four separate full runs of data were taken for each liquid and liquid mixture to ensure consistency. A full run consisted of placing a liquid sample into the UDE sample cell and shocking and recording UDE data for progressively higher shock stresses by iteratively increasing laser input energy from 0.2 to 2.5 mJ in 0.1 mJ steps. Three to five shock events were recorded at each laser input energy.

Figure 2. (a) Shock and particle velocity of the ethanol/water mixtures determined from UDE (open circles) along with predictions made by the ULH (solid lines) with each curve offset vertically by 2 km/s. The liquids from bottom to top are (1) pure water, (2) χethanol = 3.4%, (3) χethanol = 5.4%, (4) χethanol = 7.5%, (5) χethanol = 9.7%, (6) χethanol = 11%, (7) χethanol = 18%, (8) χethanol = 33%, (9) χethanol = 56%, and (10) pure ethanol. (b) Shock and particle velocity of the toluene/fluorobenzene mixtures determined from UDE (open circles) along with predictions made by the ULH (solid lines) with each curve offset vertically by 2 km/s. The liquids from bottom to top are (1) toluene, (2) χtoluene = 26.0%, (3) χtoluene = 49.1%, (4) χtoluene = 74.9%, and (5) fluorobenzene.

III. RESULTS Sound speed data for the mixtures of water and ethanol (red squares/dashed line) obtained from Brillouin spectroscopy are shown in Figure 1a, which shows the nonmonotonic trend in sound speed with ethanol concentration. Because the mixtures χethanol = 18%, 33%, and 56% were prepared by volume at a known temperature and pressure and later converted to mole fraction, the concentration error bars for those mixtures are roughly represented by the size of the marker. We find the maximum sound speed in ethanol/water mixtures at χethanol = 15%, in good agreement with Mijakovic et al.;1 the Mijakovic data are plotted (black triangles/dotted dashed line) alongside

and for toluene and fluorobenzene in Figure 2b alongside the ULH line for each. Data are offset 2 km/s for clarity. All data in these figures are available in Tables S1 and S2 in the Supporting Information for this paper. Since we are looking for small changes in the Hugoniot as the concentration of ethanol in water varies, we need to establish the bounds on the accuracy of our method. We utilized an equation with the form of the ULH, but with the intercept c0 being a fitted parameter, to compare plate impact and UDE data. The fitted intercepts provide a basis to discuss deviations from the ULH observed in the UDE data, as well as plate impact data where available, and to decide whether those C

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deviations are significant. The fitted intercepts are given in Table 1 along with their precision. The precisions were determined by the standard deviation of the absolute errors for each data point from the ULH-form equation fit to the data. Table 1. Fitted Intercepts, Their Precisions, and Sound Speeds for Water, Ethanol, and Toluene

water ethanol toluene

sound speed (km/s)

plate impact (km/s)

plate impact precision (km/s)

UDE (km/s)

UDE precision (km/s)

1.496 1.166 1.384

1.399 1.254 1.340

0.057 0.075 0.070

1.323 1.452 1.409

0.096 0.145 0.096

The fitted intercepts for pure water and ethanol (both UDE and plate impact) as well as all of their studied mixtures (UDE only) are given in Figure 1a along with the measured ambient sound speeds of the materials. The fitted intercepts for the pure toluene (both UDE and plate impact) and fluorobenzene as well as all of their studied mixtures (UDE only) are given in Figure 1b along with their measured ambient sound speeds. Error bars are determined from the standard deviation of the absolute error of the data to the best fit ULH-form equation.

IV. DISCUSSION We find that both the UDE Hugoniot data for water exemplified by the best fit ULH and the literature plate impact Hugoniot data for water2,4,6−13 exemplified by the best fit ULH deviate below the ULH, as can be seen in Figure 3a. Likewise, we find that UDE Hugoniot data for ethanol as well as literature plate impact Hugoniot data for ethanol2−5,8 deviate above the ULH. Figure 1a shows that the best fit intercepts for the water/ethanol mixtures do not lie on a straight line connecting the pure water and pure ethanol values, nor do they lie on the curve defined by the ambient condition sound speeds of the mixtures. In contrast, UDE and plate impact Hugoniot data for toluene2,4,20,30 both agree well with the prediction made by the ULH, as do the UDE data for fluorobenzene and the toluene/fluorobenzene mixtures, as seen in Figure 3b. These correlations can be seen in Figure 1a and 1b as well as the data in Table 1. Both water and ethanol are nonideal liquids in that strong intermolecular interactions, such as hydrogen bonding, govern the physical properties of the liquids. Neither toluene nor fluorobenzene is expected to exhibit strong hydrogen bonding. Hydrogen bond networks in both pure ethanol and pure water have been studied extensively, and many irregular, albeit welldocumented, thermodynamic properties have been attributed to them (i.e., higher boiling and melting points in water relative to similar molecules).31 It is possible that the hydrogen bonding networks in these liquids cause the Hugoniot to be shifted from the prediction made by the ULH. Water features an open tetrahedral-like hydrogen bond network. It is proposed that the open structure of the H-bond network allows the network to collapse under shock loading which raises the compressibility of the medium sufficiently to cause the Hugoniot data to deviate below the ULH. Ethanol, like other monohydric alcohols, may only form two hydrogen bonds per molecule, and thus features a linear or zigzag H-bond network.32 Here, we suggest that because ethanol does not feature an open H-bond structure the network cannot collapse under shock loading, and hence, the compressibility of ethanol is lowered sufficiently so that the

Figure 3. (a) The best fit ULH to the water UDE Hugoniot data is shown (solid blue line) along with the best fit ULH to water plate impact Hugoniot data2,4,6−13 (dashed green line) and the ULH using the measured ambient sound speed in water, c0 = 1.496 km/s (red dotted-dashed line). (b) The best fit ULH to the toluene UDE Hugoniot data2,4,20,30 is shown (solid blue line) along with the best fit ULH to toluene plate impact Hugoniot data (dashed green line) and the ULH using the measured ambient sound speed in toluene, c0 = 1.384 km/s (red dotted-dashed line).

Hugoniot data deviate primarily above the ULH. Figure 4 features UDE data and the ULH for ethanol and water plotted in pressure/specific volume space. For a given pressure in pressure/specific volume space, water was compressed to a smaller volume than predicted by the ULH. This suggests that water is more compressible than predicted by the ULH. For ethanol, UDE data exhibit larger volume for a given pressure than predicted by the ULH, suggesting that ethanol is less compressible then predicted by the ULH. Both of these liquids are in sharp contrast with toluene, which does not feature hydrogen bonding, and both UDE Hugoniot data and literature plate impact data for toluene find excellent agreement with one another as well as the prediction made by the ULH. The use of the ULH as a reliable model for the shock response of liquids is often justified, as the ULH has been shown to make highly accurate predictions for many simple organic liquids with weak intermolecular interactions.22,28 However, the ULH fails to make accurate predictions for some pure liquids with strong intermolecular forces in both UDE and plate impact shock experiments. D

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of studies, where large sets of data from many materials and mixtures are involved.

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ASSOCIATED CONTENT

S Supporting Information *

All of the UDE Hugoniot data in the Tables S1 and S2. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: (505) 665-6089. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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Figure 4. UDE data and ULH for neat water (blue circles/solid blue line) and neat ethanol (red squares/dashed red line) are plotted in pressure volume space. For a given pressure, UDE data for water exhibit a smaller volume than its ULH as well as UDE data for ethanol, suggesting water is more compressible than both ethanol and the ULH for water. Likewise, for a given pressure, ethanol UDE exhibits greater volumes than the prediction made by its ULH, suggesting ethanol is less compressible.

ACKNOWLEDGMENTS The Los Alamos National Laboratory is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the US Department of Energy under contract DE-AC52-06NA25396. The authors gratefully acknowledge the support of this study by Rick Martineau through Science Campaign 2: HE Science. The authors also thank Dr. Joshua Coe and Dr. Charles Kiyanda in providing theoretical advice and consultations and Dr. Bryce Tappan and Maxwell Schulze for graciously assisting us in the use of their refractometer.

The region χethanol = 0% to χethanol = 20% correlates with the maximum in the sound speed vs concentration plot of ethanol/ water mixtures and has long been associated with other anomalous changes in the thermodynamic properties of binary mixtures of monohydric alcohols and water. Theoretical studies of the hydrogen bonding networks in binary mixtures of tertbutyl alcohol and water show certain concentrations in which the hydroxyl group from an alcohol molecule participates in the hydrogen bond network of surrounding water molecules, creating a clathrate cage effect.32 Further, the nonpolar alkyl tails in the alcohol create clusters of alcohol molecules through hydrophobic interactions.33 Both of these factors are thought to substantially alter the quality of the H-bond network and change the compressibility of the medium.1,34 We hypothesize that the anomalous behavior of these shocked liquid mixtures is due to the complex and ever-changing H-bond networks and cluster formation in the medium. Molecular dynamics simulations of ethanol/water mixtures under shock pressures and temperatures could help elucidate the structural origins of the unusual effects observed in shocked water, ethanol, and their binary mixtures.

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REFERENCES

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