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Mass Transfer Thermodynamics through a Gas-Liquid Interface Alicia Broderick, M. Alejandra Rocha, Yehia Khalifa, Mark B. Shiflett, and John T. Newberg J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.9b00958 • Publication Date (Web): 25 Feb 2019 Downloaded from http://pubs.acs.org on February 26, 2019

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The Journal of Physical Chemistry

Mass Transfer Thermodynamics through a Gas-Liquid Interface Alicia Broderick,1 M. Alejandra Rocha, 2 Yehia Khalifa,1,a Mark B. Shiflett2 and John T. Newberg1,* 1 University

of Delaware, Department of Chemistry and Biochemistry, Newark, DE 19716.

2 University

of Kansas, Department of Chemical and Petroleum Engineering, Lawrence, KS

66045. a

Present address: The Ohio State University, Department of Chemistry and Biochemistry, Columbus, OH 43210.

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Molecular level information about thermodynamic variations (enthalpy, entropy and free energy) of a gas molecule as it crosses a gas-liquid interface is strongly lacking from an experimental perspective under equilibrium conditions. Herein we perform in situ measurements of water interacting with the ionic liquid (IL) 1-butyl-3-methylimidazolium acetate, [C4mim][Ace], using ambient pressure X-ray photoelectron spectroscopy in order to assess the interfacial uptake of water quantitatively as a function of temperature, pressure and water mole fraction (xw). The surface spectroscopy results are compared to existing bulk water absorption experiments, showing that the amount of water in the interfacial region is consistently greater than the bulk. The enthalpy and entropy of water sorption vary significantly between the gas-liquid interface and bulk as a function of xw, with a crossover that occurs near xw = 0.6 where the waterIL mixture converts from being homogeneous (xw < 0.6) to nanostructured (xw > 0.6). Free energy results reveal that water at the gas-IL interface is thermodynamically more favorable than in the bulk, consistent with the enhanced water concentration in the interfacial region. The results herein show that the efficacy for an ionic liquid to absorb a gas phase molecule is not merely a function of bulk solvation parameters, but also significantly influenced by the thermodynamics occurring across the gas-IL interface during the mass transfer process.


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1. Introduction The mass transfer of gas phase molecules into a bulk liquid must cross a gas-liquid interface, a process that is ubiquitous in environmental, biological and engineered liquids1. The free energy profile during mass transfer across a gas-liquid interface has been fairly well characterized by molecular dynamics simulations of liquid water2-15 and ionic liquids16-23. Experimentally measuring the thermodynamic profile across the gas-liquid interface requires the ability to deconvolute the gas-bulk and gas-interface thermodynamics. While measuring gas-bulk liquid thermodynamics is common, the ability to measure directly the surface thermodynamics of gas phase species interacting with a liquid interface under in situ conditions is technologically very challenging24. There is currently a lack of direct measurements of a gas-liquid interface using molecular level surface science techniques25,26 to determine the surface enthalpy, entropy and free energy under equilibrium conditions. This is due, in part, to the technological challenges of probing a gas-liquid surface directly under equilibrium conditions with atomic and chemical specificity, while varying both temperature and gas phase pressure. Herein we utilize ambient pressure X-ray photoelectron spectroscopy (AP-XPS)27-30 to determine the enthalpy, entropy and free energy of gas phase water at the gas-liquid interface of an ionic liquid. Ionic liquids (ILs) are low temperature molten salts (melting point < 100 °C) with a negligible vapor pressure, where different cations and anions can be combined to tune the IL physical properties. For this reason, ILs have sparked interest as a gas absorbent medium31. The gas-IL and vacuum-IL interface in the presence of water has been investigated by a number of surface analytical techniques32. Water adsorption energetics with IL interfaces under vacuum conditions have been assessed by line of sight mass spectrometry (LOSMS)33 and X-ray photoelectron spectroscopy (XPS)34. Using flowing jet sheet beam King Wells the initial dissolution probability



of D2O with an IL was used to determine the initial dissolution enthalpy and entropy35. These aforementioned studies33-35 examined the surface energetics under non-equilibrium conditions. Example surface analytical techniques that have examined the gas-IL interface under elevated pressures include neutron reflectometry36, X-ray reflectivity37 and sum frequency generation38-45. While these techniques have provided valuable information on the influence of water on IL interfacial structure under in situ elevated pressure conditions, the ability to determine the thermodynamics of water in the interfacial region requires the capability of quantitatively assessing the amount of interfacial water as a function of both temperature and pressure which to our knowledge has not been accomplished to date. Recently we have shown the ability to quantitatively assess the amount of water at the gas-IL interface as a function of variable pressure (at room temperature) using AP-XPS46,47. Herein we extend these studies by assessing water as a function of both pressure and temperature using APXPS to extract surface thermodynamics. The standard state surface enthalpy, entropy and free energy are compared to bulk thermodynamics modeled from existing bulk absorption measurements48,49 in order to assess the mass transfer thermodynamics across the gas-liquid interface.

2. Methods The ionic liquid 1-butyl-3-methylimidazolium acetate [C4mim][Ace] (Iolitec, 98%) has a melting point of –20 °C and density50 (ρ) of 1.06 g cm-3, and was used without further purification. The IL was stored in a vacuum desiccator prior to use. The sample was prepared by applying a thin film of IL ( 0.990 for all empirical fits). Results from Figures 3a and 3b show that the lnp versus 1/T fits are very linear with strong correlation coefficients (R2



Figure 3. Interface versus bulk water sorption enthalpy for [C4mim][Ace] from 0.4 < xw < 0.75. (a) lnp versus 1/T for AP-XPS results of 0, 10, 22, 32 and 42 C isotherms. (b) lnp versus 1/T for gravimetric results of 22, 30 and 42 C isotherms. (c) Using the slopes from (a) and (b) and Eqn. (3), the calculated interfacial and bulk enthalpy are displayed as a function of xw. Error bars represent one standard deviation in the slopes. Dashed line is the enthalpy of condensation for bulk water at 25 °C. > 0.992 for all fits), confirming that the derived thermodynamic model is well described by the simple interaction of Eqn. (2) for gas phase water forming a WIL complex with [C4mim][Ace] at the interface and within the bulk. The strong linearity also indicates that the values for ∆𝐻°s and ∆𝐻°b do not vary strongly with temperature within the range of our experiments. We have restricted our thermodynamic analyses to 0.4 < xw < 0.75 in order to keep the range within both AP-XPS and gravimetric experimental data sets (see Figures 2a,b), allowing for a confident comparison of the enthalpies. Using the slopes and Eqn. (3), Figure 3c plots ∆𝐻°s (black) and ∆𝐻°b (grey) as a function of xw. Error bars represent one standard deviation in the slopes. Negative values of enthalpy indicate that heat is released upon gas phase water interacting with IL ions. The enthalpy values determined herein are an indicator of the strength of interaction between water and IL ions in the interfacial region (∆𝐻°s) compared to water interacting with IL ions in the bulk (∆𝐻°b). For comparison, the dashed line represents the enthalpy of condensation for bulk water (∆𝐻°w = –44 kJ mol–1)60. For lower water mole fractions (0.40 < xw < 0.60) the enthalpies derived from AP-XPS and gravimetric


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analysis are more negative than ∆𝐻°w. These results are consistent with the strength of interaction between water and IL ions (dipole-ion) being greater than water-water (dipole-dipole) interactions. When comparing the interfacial region to the bulk for 0.40 < xw < 0.60, ∆𝐻°s is more favorable than ∆𝐻°b. This suggests that the strength of interaction between water and IL ions is greater in the interfacial region versus the bulk in the range of 0.40 < xw < 0.60. As xw increases to ~0.65 (corresponding to ~2 waters per IL pair) the water-IL interaction is similar to the water-water interaction for both the interfacial region and within the bulk. For xw > 0.65 there is an interesting crossover where ∆𝐻°b becomes more negative than ∆𝐻°s, suggesting that the strength of interaction is greater in the bulk from 0.65 < xw < 0.75. To assess the entropy of water sorption at the gas-IL interface (∆𝑆°s) relative to the IL bulk (∆𝑆°b ), the AP-XPS and gravimetric isothermal data are plotted as Tlnp versus T at constant xw in Figures 4a and 4b, respectively. Results are very linear with strong correlation coefficients (R2 > 0.990 for all fits). Using the experimentally determined slopes and Eqn. (4), Figure 4c plots ∆𝑆°s (black) and ∆𝑆°b (grey) as a function of xw. Error bars represent one standard deviation in the slopes.

Figure 4. Interface versus bulk water sorption entropy for [C4mim][Ace] from 0.4 < xw < 0.75. (a) Tlnp versus T for AP-XPS results of 0, 10, 22, 32 and 42 C isotherms. (b) Tlnp versus T for gravimetric results of 22, 30 and 42 C isotherms. (c) Using the slopes from (a) and (b) and Eqn. (4), the calculated interfacial and bulk entropy are displayed as a function of xw. Error bars represent one standard deviation in the slopes.



The strong linearity of the Tlnp versus T plots are a further indication of the validity of the simple Eqn (2) model, and further indicate that the values for ∆𝑆°s and ∆𝑆°b are independent of temperature within the range of our experiments. With ∆𝑆° defined as the entropy of the products minus reactants in Eqn. (2), the negative values for ∆𝑆°s and ∆𝑆°b are indicative of the large entropy of gas phase water (Wg) compared to the condensed phase IL and WIL. Given ΔG° = ΔH° – TΔS°, the less negative the entropy (going down the y-axis in Figure 4c), the more negative the free energy and therefore the more favorable (entropically) the water-IL interaction via Eqn (2). Similar to the enthalpy results for Figure 3c, there is an interesting crossover in entropy near xw = 0.60. In the low xw range from 0.40 < xw < 0.60 values of ∆𝑆°b are less negative (more favorable entropically) than of ∆𝑆°s. These results indicate that the water-IL interaction in the interfacial region is more ordered than in the bulk for the range of 0.40 < xw < 0.60. The opposite is true for higher xw values, where the water-IL interaction in the interfacial region is more disordered than within the bulk from 0.6 < xw < 0.75. Molecular dynamics (MD) simulations for [Cnmim][Ace]-water mixtures (n = 2, 4, 6) indicate that there is a turnover in bulk density for xw in the range of 0.5 to 0.7 depending on the size of the alkyl chain (n) for the imidazolium cation61. Under low xw conditions the bulk IL-water mixture is homogeneous, whereas at high xw values the mixture converts to a nanostructured system with separated hydrophilic and hydrophobic regions. This same phenomenon has been observed experimentally for [C4mim][BF4] with neutron scattering62, where the addition of water resulted in nanometer-sized clusters at xw  0.6. We have shown previously with our room temperature [C4mim][Ace]-water AP-XPS study that there is a sudden change in the shape of the C 1s spectra near xw  0.6, which we attributed to a change in nanostructuring in the interfacial region46. For these reasons, we believe the crossover in enthalpy (Figure 3c) and entropy (Figure 4c) between


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interfacial and bulk values near xw  0.6 is attributed to an IL-water system conversion from a homogeneous mixture to a nanostructured mixture. The significant variations in interfacial versus bulk enthalpy and entropy suggest that the overall mechanism for the absorption-evaporation process is separated into an interfacial region water-IL mixture (WILs) and bulk water-IL mixture (WILb) as depicted in Figure 5a. Corresponding energy level diagrams for this sorption process are shown in Figure 5b (enthalpy) and Figure 5c (entropy). The experimental values of ∆𝐻°s and ∆𝐻°b are taken from Figure 3c while values for ∆𝑆°s and ∆𝑆°b from Figure 4c, and comparing xw = 0.4 (green, homogeneous mixture) and xw = 0.75 (red, nanostructured mixture). The overall process of bulk water sorption is enthalpically favorable (going left to right in Figure 5b). However, the influence of the interfacial region on the enthalpy of bulk absorption and evaporation depends on xw. For xw = 0.40, ∆𝐻°s is

Figure 5. Water vapor mass transfer thermodynamics for [C4mim][Ace]. (a) Mechanism of water sorption across the gas-IL interface and associated energy diagrams for (b) enthalpy and (c) entropy at xw = 0.40 (green) and xw = 0.75 (red).



more favorable than ∆𝐻°b showing that it is enthalpically unfavorable to remove water from the interfacial region via the sorption process (WILs  WILb) and desorption process (WILs  Wg). The situation is different for xw = 0.75, where ∆𝐻°b is more favorable than ∆𝐻°s, revealing that it is enthalpically favorable to take water from the interfacial region into the bulk. The overall process of bulk water sorption is entropically unfavorable (going left to right in Figure 5c) no matter the value of xw, which is consistent with taking gas phase water and condensing it into the IL. For xw = 0.40, ∆𝑆°s is entropically less favorable than ∆𝑆°b, indicating that there is an entropic barrier to take water from the gas phase through the interfacial region and into the bulk. Likewise, to evaporate water from the bulk there is an entropic barrier for water to go through the interfacial region. For xw = 0.75, ∆𝑆°s is entropically more favorable than ∆𝑆°b and there is no longer an entropic barrier to evaporate water from the IL bulk. Combining results from enthalpy and entropy, Figure 6a shows the Gibbs free energy at 25 °C (standard state temperature) as a function of xw. Error bars represent the propagated error in ∆ 𝐻° and ∆𝑆° determined from their corresponding slopes. Values of ∆𝐺° < 0 indicate that the

Figure 6. Free energy for water vapor mass transfer with [C4mim][Ace]. (a) Interface versus bulk water sorption Gibbs free energy for [C4mim][Ace] from 0.4 < xw < 0.75 at 25 °C. Error bars represent propagated error from ∆𝐻° and ∆𝑆°. (b) Gibbs free energy diagram data in (a) at xw = 0.40 (green) and xw = 0.75 (red). (c) Equilibrium constants associated with proposed mechanism.


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interaction of water vapor with [C4mim][Ace] is thermodynamically favorable. The free energy for both the gas-IL interface (∆𝐺°s) and bulk (∆𝐺°b) becomes more thermodynamically favorable as xw decreases. Over the entire xw range for which the thermodynamics was determined experimentally (0.40 < xw < 0.75), ∆𝐺°s is thermodynamically more favorable than ∆𝐺°b. These results indicate that there is a free energy minimum for water to reside in the interfacial region at 25 °C (Figure 6b) independent of the value of xw. Similar trends are seen over the entire temperature range examined (see Figure S3). Thus, over the entire range of experimental temperatures, pressures and xw examined herein, there is a free energy minimum for water to reside in the interfacial region relative to the bulk. These results suggest that the overall bulk absorption of water vapor into [C4mim][Ace] is influenced by surface thermodynamics. Equations (10) to (12) are the equilibrium constants associated with the proposed mechanism of water crossing the gas-IL interface (see Figure 6c). 𝑥sw

(10)

𝐾s = 𝐾°𝑝(1 ― 𝑥s ) s

w

𝑥bw

(11)

𝐾sb = 𝑥s

w

𝑥bw

(12)

𝐾b = 𝐾°𝑝(1 ― 𝑥s ) s

w

where 𝑥sw and 𝑥bw are the water mole fractions at the gas-IL interface and bulk, respectively, Ks is measured by AP-XPS, Kb is measured by gravimetric analysis and Ksb is the equilibrium between WILs and WILb. Substituting Eqns. (10) and (11) into Eqn. (12) gives: (13)

𝐾𝑏 = 𝐾s𝐾sb

Equation (13) shows that the measured bulk absorption constant is a function of the equilibrium constants established across the interfacial region. From a free energy perspective (K = e–G/RT) Eqn (13) becomes:



∆𝐺°b = ∆𝐺°s + ∆𝐺°sb

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(14)

For ∆𝐺°sb > 0, which is the case for the study herein, the free energy is more favorable for the gas phase species to be at the interface relative to the bulk leading to a surface concentration enhancement. MD simulations have provided potential of mean force (PMF) profiles for gas phase water across IL interfaces of [C4mim][X] (X = BF4, Tf2N and PF6)18,19. Using polarizable forcefields, the free energy decreased (i.e., became more negative) monotonically from the gas phase into the liquid phase for all three of these ILs and no free energy minimum was observed at the interface. This contrasts with the experimentally observed free energy minimum for [C4mim][Ace] herein. It is worth noting that all three of the aforementioned ILs simulated by MD are less hydrophilic than [C4mim][Ace], which may be a cause for the contrasting observations. Moreover, the experiments herein observed a free energy minimum for [C4mim][Ace] with water present within the IL (0.4 < xw < 0.75), whereas the MD PMF studies18,19 examined water going through a pure IL. Complementary MD PMF studies for [C4mim][Ace] are strongly needed as a function of xw. While MD PMF studies of gas phase interactions with liquid water have successfully decomposed the enthalpy and entropy contributions as a function of liquid depth9-12,15, this is not the case for ionic liquid MD PMF studies to date16-23. Future IL MD PMF studies that decompose enthalpy and entropy contributions may provide further insight into the structural dynamics driving the thermodynamic variations across the gas-IL interface.

4. Conclusions The uptake of water vapor at the gas-IL interface was examined for the first time under equilibrium conditions as a function of temperature (0 - 42 C) and pressure (high vacuum to 5.0


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Torr) using ambient pressure XPS. The water mole fraction as a function of relative humidity at the gas-IL interface of [C4mim][Ace] was measured via AP-XPS and compared to published bulk absorption measurements determined by gravimetric analysis. Results showed that under the entire RH range measured, the gas-IL interface contained a larger xw compared to the bulk. Thermodynamic analyses of the AP-XPS and gravimetric data were performed in order to extract the standard state enthalpy and entropy as a function of xw between the gas-IL interface and the IL bulk. Results reveal that the surface and bulk thermodynamics vary significantly as a function of xw. For xw < 0.6 the enthalpy is more favorable and entropy less favorable at the gas-IL interface relative to the bulk. For xw > 0.6 the opposite occurs, where the enthalpy is less favorable and entropy is more favorable at the gas-IL interface relative to the bulk. This crossover in thermodynamics at xw = 0.6 is attributed to a phase change in the IL where it goes from a homogeneous water-IL mixture (xw < 0.6) to a heterogeneous mixture of isolated nanostructures of hydrophilic and hydrophobic regions for xw > 0.6. Results of free energy analyses reveal that it is energetically more favorable for water to reside at the gas-IL interface relative to the bulk over the entire range of experimental temperature, pressure and xw examined. In summary, we have shown using molecular level surface spectroscopy under equilibrium conditions that the mass transfer process of water interacting with [C4mim][Ace] is significantly influenced by the interfacial region. The overall process of bulk absorption and evaporation is not merely a function of three-dimensional solvation within the bulk, but also a function of the surface thermodynamics as evidenced by a free energy minimum and enhanced water concentration at the gas-IL interface relative to the bulk. Complementary molecular dynamic simulations and potential of mean force calculations are strongly needed in order to assess the structural and dynamical



influences on the experimentally determined interfacial versus bulk thermodynamics revealed herein.

Associated Content Supporting Information Initial XPS spectra under vacuum, N 1s spectral characterization at 0 C, thermodynamic model derivation, and free energy versus xw at highest and lowest temperatures.

Corresponding Author * [email protected]

ACKNOWLEDGMENTS J.T.N. acknowledges support from an ACS PRF New Doctoral Investigator award 56249-DNI5.

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TOC Figure


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Mass Transfer Thermodynamics through a Gas-Liquid Interface - The

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