Thermal Properties and Ionic Conductivities of Confined LiBF4

Article pubs.acs.org/JPCC

Thermal Properties and Ionic Conductivities of Confined LiBF4 Dimethyl Carbonate Solutions Christopher M. Burba,* Eric D. Butson,†,‡ Justin R. Atchley,§,‡ and Mioto Sato Johnson⊥ Department of Natural Sciences, Northeastern State University, Tahlequah, Oklahoma 74464, United States ABSTRACT: Solutions of lithium tetrafluoroborate dissolved in dimethyl carbonate (DMC) are confined within MCM-41, a mesoporous silica matrix. Thermal measurements indicate that the melting points of pure DMC and the DMC solutions are significantly reduced when confined within the pores of MCM41 compared to unconfined samples; this is an observation that is consistent with the Gibbs−Thomson equation. The melting point onsets of confined solutions are slightly lower than that of pure DMC, suggesting the dissolved salts impact the phase-transition temperature of DMC when confined within mesoporous silica. Rotational dynamics of the confined solutions are explored by doping DMC with small quantities of Tempone, an electron paramagnetic resonance (EPR)-active spin probe. Tempone rotational correlation times are an order of magnitude slower for confined liquids compared to unconfined solutions. Temperature-dependent conductivity measurements of the composite materials suggest that the liquid electrolyte solution is distributed among the MCM-41 pores and the intergrain voids between individual MCM-41 particles. Ionic conductivities of confined electrolyte solutions remain above 0.01 mS·cm−1 for temperatures greater than −50 °C. However, the ionic conductivity of the unconfined solutions (i.e., solution occupying the spaces between the MCM-41 particles) rapidly decreases over subzero temperatures. Limitations associated with directly implementing these materials as low-temperature ion conductors are discussed.

1. INTRODUCTION The properties of fluids confined within porous materials are often quite different from the bulk phase because of interfacial energy contributions to the total free energy of the system. Among the affected properties, one of the more widely studied is the reduction of the thermodynamic melting point for the confined liquid. The majority of studies into confinementinduced melting point depression focus on cylindrical pore topologies, where the melting point decrease is inversely proportional to the radius of the nanopore. Thus, small pore diameters lead to lower melting points. In some cases, the melting point of the confined liquid undergoes a substantial decrease relative to the melting point of the unconfined liquid. Liquid water, for instance, freezes at approximately −40 °C when confined within 4 nm diameter pores.1,2 A large fraction of the work on confinement-induced melting point depression focuses on water trapped within various porous media. Nonetheless, several organic solvents have been characterized as well, including acetonitrile,3−5 benzene,6−9 cyclohexane,7 and toluene10 among others.11−14 The underlying physics of confinement-induced melting point depression is generally described through the Gibbs− Thomson equation15 ⎛ 2γ V * T ⎞ s,l m,s unconf ⎟⎛ 1 ⎞ ⎜ ⎟ ΔT = Tconf − Tunconf = −⎜⎜ ⎟⎝ r ⎠ ΔHm ⎝ ⎠ © 2013 American Chemical Society

In this equation, Tconf is the melting point of a solid confined within the pore, Tunconf is the melting point of the unconfined solid, γs,l is the interfacial energy between the solid and liquid phases, Vm,s * is the molar volume of the solid, and r is the radius of the pore. The molar enthalpy of melting, ΔHm, is measured at temperature Tconf. Although a very large number of compounds obey the Gibbs−Thomson equation, there are a few instances where it is believed to be deficient.2,11,16,17 For example, a positron annihilation spectroscopic investigation of benzene revealed a marked deviation from the Gibbs− Thomson equation. This led Dutta and co-workers11,17 to conclude that the parameters within the Gibbs−Thomson equation (viz., density, molar enthalpy change, and solid−liquid interfacial energy) are size dependent, making the equation invalid. In place of the Gibbs−Thomson equation, these researchers propose using molecular cluster theory to describe the pore-size dependence of the solid−liquid phase-transition temperatures. Confinement effects are not restricted to only the phasetransition temperature. In some instances, the crystal structure of the solid phase produced upon freezing a confined liquid is quite different from that observed for the unconfined material. This has been well documented for water, where neutron Received: September 16, 2013 Revised: December 6, 2013 Published: December 6, 2013

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dx.doi.org/10.1021/jp409243b | J. Phys. Chem. C 2014, 118, 366−375

The Journal of Physical Chemistry C

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scattering18 and X-ray diffraction19,20 studies confirm the formation of the cubic Ic phase when water is frozen inside small pores. The hexagonal crystal structure (Ih) is obtained when water is housed within larger diameter pores. There is also evidence that crystallization may be completely suppressed for some materials when the pore diameter falls below some critical value.7,12 For example, Dosseh et al.7 used differential scanning calorimetry (DSC) data to establish vitrification of cyclohexane and benzene in 5 nm diameter pores, whereas those liquids formed small crystallites in larger-sized cylindrical pores. Although thermal properties of confined liquids have been heavily investigated, there is ample evidence in the literature indicating a confinement effect on the molecular dynamics of liquids. The general consensus is that confined liquids exhibit a combination of bulklike properties, which originate from the center of the pores, and a surface contribution that arises from molecules in the vicinity of the pore wall. Molecular-level interactions between the surface and the solvent molecules lead to longer translational and rotational correlation times for the solvent molecules. This is obviously more pronounced in the interfacial region, but molecular dynamics simulations of confined benzene show that the effects may propagate somewhat into the center of the pore.21 Raman22 and NMR23 spectroscopic studies provide additional evidence for the pore-size dependence on the molecular dynamics of benzene. In both sets of experiments, dynamics of confined benzene molecules are slower compared to the bulk. Other confined solvent systems likely experience reduced molecular dynamics; however, the interactions between the pore wall and the solvent molecules will almost certainly define the magnitude of any confinement-induced changes. While there have been advances in our understanding of confined, single-component systems, similar studies of confined organic electrolyte solutions are relatively scarce. Confined electrolyte solutions lie at the heart of many important fields, including nanofluidics, biological ion-conducting channels, and solution−substrate interactions in subsurface geological formations, to name a few. Furthermore, the ability to significantly reduce the thermodynamic melting point of a solution by confining the solution within a nanoporous matrix may open new approaches to designing low-temperature ion conductors for battery and electrochemical capacitor applications. In all of these examples, the ionic conductivity of the electrolyte solution is a key system property that often defines the suitability of the material for a particular application. The general lack of experimental studies for confined organic electrolyte solutions represents a significant knowledge gap that may hinder development in these fields. In our previous work, we demonstrated that LiPF6-dimethyl carbonate (DMC) electrolyte solutions confined within the pores of MCM-41 experience significant confinement-induced melting-point depression.24 The overall ionic conductivity of the composite materials decreased sharply when the temperature fell below 0 °C. The central goal of this investigation is to expand upon these initial studies and to better understand the thermal, molecular dynamics and ion transport properties of confined solutions by exploring confinement effects for a series of LiBF4-DMC electrolytes. Organic electrolytic solutions, such as those based on DMC, are essential parts of many electrochemical devices. Thus, there is ample experimental data available for these systems to compare against.

Composite gel electrolytes represent one approach to confining electrolyte solutions within a pore network. Traditional composite gel electrolytes are prepared by mixing fumed silica with low molecular weight solvents and lithium salts.25,26 The resulting composite materials exhibit high ionic conductivities and favorable mechanical properties.27,28 Fumed silica is an amorphous, nonporous silica that forms fractal-like networks with large open pores (∼0.5 μm) when mixed with electrolyte solutions. The pore diameters present in those systems are too large to impart significant melting-point depression. Therefore, we have chosen to focus most of our experiments on composite gel electrolytes prepared with MCM-41. Flooding the narrow pores of MCM-41 will enable us to characterize confinement effects on the thermal properties and the ion transport behavior of the electrolyte solutions.

2. EXPERIMENTAL METHODS 2.1. Sample Preparation. MCM-41 mesoporous silica was used as the porous compound for most of the confinement studies. The synthetic protocols adopted in this work most closely mirror those of Beck et al.29 The synthesis of MCM-41 began by dissolving 16.77 g of cetyltrimethylammonium bromide in 50 mL of water; the solution was heated to 42.8 °C to aid in dissolving the surfactant. In addition, 18.63 g of sodium silicate (∼27 wt % SiO2 and ∼14 wt % NaOH) was added to 40 mL of water. The pH of the sodium silicate solution was reduced from 11.8 to 10.8 with concentrated sulfuric acid (∼1.5 g). The two solutions were mixed together under magnetic stirring (pH = 10.89, T = 30 °C). After 30 min, an additional 21 mL of water was added to the mixture. The solution was transferred to a static, poly(tetrafluoroethylene)lined Parr high-pressure reactor and was heated at 100 °C for 144 h. The as-synthesized mesoporous material was filtered, was washed with copious amounts of water, and was dried overnight in air. The recovered material was calcined at 500 °C for ∼4 h to remove the templating molecules. The synthesized MCM-41 was dried in a vacuum oven before use, and manipulations with the compound were performed in a dry environment. SBA-15 silicas were prepared from a 4 wt % aqueous solution of a triblock ethylene oxide−propylene oxide−ethylene oxide polymer (Pluronic P123), which has a nominal chemical formula of OH(CH 2 CH 2 O) 20 −(CH 2 CH(CH 3 )O) 7 0 − (CH2CH2O)20H).30 The solution was heated to approximately 40 °C, and HCl was added to obtain a pH of 1.5. While stirring, 10 g of tetraethoxysilane was added to the solution. The mixture was then placed in the Parr high-pressure reactor, and the temperature was maintained at 35 °C for 24 h. Subsequently, the temperature of the reaction mixture was increased to a temperature between 60 and 100 °C. The pore diameter of the resulting porous silica depends on the temperature of this final thermal treatment.30 The resulting mesoporous silica was filtered and was washed with copious amounts of deionized water. The product was calcined at 550 °C under air for 5 h, and infrared spectroscopy was used to confirm that all of the templating surfactant molecules were removed from the product. The SBA-15 compounds were dried with a vacuum oven, and any further use of the compounds was performed under a dry atmosphere. Stoichiometric quantities of lithium tetrafluoroborate (LiBF4, Aldrich) were mixed with dimethyl carbonate (DMC, Aldrich) under an argon atmosphere (VAC glovebox, ca. 0.5 ppm H2O) to form 0.5, 1.0, and 1.5 m electrolyte solutions. Solution 367



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confinement was achieved by mixing weighed amounts of the LiBF4 in DMC solution or in pure DMC with MCM-41 under a dry argon atmosphere. 2.2. Differential Scanning Calorimetry. The thermal properties of the confined solutions were determined by differential scanning calorimetry (DSC) using a Mettler-Toledo DSC 1. Composite samples containing pure DMC or LiBF4DMC solutions were packed in 40 μL aluminum crucibles and were hermetically sealed. All sample preparation and manipulation for DSC analysis was performed under an argon atmosphere. Each sample was cooled from 25 to −100 °C and then was heated to 50 °C at a rate of 10 °C min−1. The thermal tests were performed under a flow of dry nitrogen gas. 2.3. Electron Paramagnetic Resonance (EPR) Spectroscopy. X-band EPR spectra of confined and unconfined DMC were measured with a Bruker EMX spectrometer operating at room temperature. A small quantity of 4-oxo2,2,6,6-tetramethyl-1-piperidinyloxy (Tempone, 0.25 mM) was used as the spin probe. Samples were placed within sealed quartz NMR tubes, and the microwave power was set to 20.07 mW. Collected spectra were the average of four individual scans, and each scan consisted of 2048 data points using a magnetic field modulation of 0.2 G at 100 kHz with the time constant and the conversion time both set to 20.48 ms. Diphenylpicrylhydrazyl (DPPH), which has a known g value of 2.0036, was used as a standard to calibrate the EPR spectrometer. Rotational correlation times for the nitroxide spin probe were determined from the EPR spectra. For fast rotational times (τc ≲ 3 ns), the rotational correlation times may be estimated through line shape analysis of the hyperfine lines using motional narrowing theory.31,32 According to the theory, the spectral line widths for the hyperfine lines, δmI, were related to the nuclear spin quantum number, mI, by δmI = A + BmI + Cm2I . Goldman et al.33 derived general relationships between the B and C parameters and the anisotropic rotational correlation times, τl,ml for l = 2 and ml = ±2; the integers l and ml correspond to quantum numbers for the symmetric rotor wave functions. Although Tempone is an approximate prolate rotor, several studies suggest that the molecule undergoes isotropic rotational motion in a variety of solvents.34,35 Rotational correlation times may be directly evaluated from the B coefficient for composite DMC-MCM-41 samples. For isotropic rotational motion (τ2,0 = τ2,±2 = τc) with fast rotational correlation times (ω2e τ2c ≪ 1)33 B=

56πωe (g A 0 + 2g2A 2 )τc 30 3 γe 0

This analysis assumed a Lorentzian peak shape for the hyperfine lines with Iml representing the intensity of a particular hyperfine line in the EPR spectrum and with δo representing the width of the mI = 0 line. 2.4. Impedance Spectroscopy. Samples for impedance analysis were prepared by mixing MCM-41 with a small quantity of shredded poly(tetrafluoroethylene), typically 5−7 wt %, and were pressed into free-standing films. Circular disks were cut from the film, and individual layers were laminated with a pellet press (69.5 MPa). The final dimensions of the pellets were 0.150−0.200 cm thick with a cross-sectional area of 1.60 cm2. Appropriate quantities of the solutions were then added to the pressed pellets to confine the solutions within the MCM-41 pore network. Composite samples containing the DMC solutions were rapidly placed between stainless steel blocking electrodes and were sealed in CR2032 coin cells to prevent evaporation of the DMC solvent. Temperaturedependent conductivities of the composite solutions were evaluated with a PAR Parstat 2263 frequency response analyzer. The oscillating voltage was set to 10 mV, and the frequency was scanned from 1 MHz to 100 mHz. Temperature control was achieved with a Teney T2RC environmental chamber (−50 °C < T < 30 °C) with a resolution of 1 °C.

3. RESULTS AND DISCUSSION 3.1. Thermal Properties of DMC Confined within Nanoporous SiO2. DSC thermographs of composite samples containing 15 wt % nanoporous SiO2 with pure DMC are provided in Figure 1. Three endothermic thermal transitions are observed for each of the samples. Two of the thermal transitions (−55 and 3.9 °C) are assigned to unconfined, bulk DMC that is present in the composite samples. These phasetransition temperatures are not affected when the pore radius of the silica is increased from 1.64 to 4.18 nm. The large endothermic peak with a melting point onset of 3.9 °C is assigned to melting of unconfined DMC, while the weak endothermic transition near −55 °C is believed to be a solid− solid phase transition of crystalline DMC. The third endothermic peak in each DSC trace strongly depends on the pore radius of the silica, and this peak is attributed to the melting of solid DMC confined within the pores. The validity of the Gibbs−Thomson formalism is tested for DMC confined within a series of mesoporous silicas. A linear correlation is obtained when melting point depression values derived from Figure 1 are plotted against the inverse of the corresponding pore radius (Figure 2). The best-fit linear regression is obtained when a nonfreezable layer of DMC equal to 0.37 nm in thickness is subtracted from the total length of the pore radius. This corresponds to a layer of DMC molecules along the silica surface that is between two to three DMC molecules thick. Thus, DMC obeys the Gibbs−Thomson equation when confined within nanoporous silica possessing a cylindrical pore topology, such as MCM-41. 3.2. Thermal Properties of Confined Electrolyte Solutions. Thermal properties of LiBF4-DMC solutions containing ca. 0 wt % and 50 wt % MCM-41 are determined from DSC scans and are summarized in Table 1. Representative DSC data for the 1.0 m LiBF4-DMC solution is depicted in Figure 3; similar data are observed for the 0.5 and 1.5 m samples. Unconfined solutions have melting points that are at or slightly below 0 °C. Thermal transitions that may be assigned to confined solutions are observed near −90 °C. This

(2)

The Larmor frequency for the electron spin is ωe, while γe is the magnetogyric ratio. Anisotropy in the hyperfine coupling tensor, A, and in the g tensor is represented by Ai and gi for i = 0 and 2, respectively. Principal values of the g and A tensors were estimated from the data provided by Snipes et al.36 Spectral line widths for the three hyperfine lines of the 0 wt % sample were almost identical, which precludes directly using eq 2 to determine B. In this case, the B coefficient was calculated from slight differences among the relative intensities of the hyperfine lines37 B=

1 ⎛ I0 δ0⎜⎜ − 2 ⎝ I −1

I0 ⎞ ⎟⎟ I+1 ⎠

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Table 1. Onset Temperatures for Confined and Unconfined LiBF4-DMC Solutions unconfined

confined

LiBF4 concentration (m)

cooling (°C)

heating (°C)

cooling (°C)

heating (°C)

0.00 0.50 1.00 1.50

3.03 0.00 −1.23 −6.47

4.91 0.51 −0.29 −6.75

−86.95 −84.00a −88.90 −88.80

−86.59 −87.55 −89.07 −92.62

a

The freezing point onset was difficult to measure because of an uneven baseline.

Figure 1. DSC traces for dimethyl carbonate (DMC) confined in a series of nanoporous silica. Endothermic transitions for DMC confined within the nanopores are denoted with red asterisks, while transitions for unconfined, bulk DMC are enclosed in a blue box. Unconfined DMC undergoes a solid−solid phase transition near −55 °C, which is marked with a green dotted line. Pore radii for each nanoporous silica sample are determined from DSC analysis of confined water and from the empirical relationship found in ref 1.

Figure 3. DSC data for 1.0 m LiBF4 solution mixed with 0 wt % (A) and 50 wt % (B) MCM-41.

The degree of melting point shift is calculated by subtracting the melting point onset of pure, unconfined DMC from the melting point of the confined solution (i.e., ΔT = Tconf − Tunconf * , where the asterisk denotes the pure solvent). The magnitude of the melting point depression decreases as the salt concentration increases (see Figure 4), demonstrating that the concentration of the dissolved solute does affect the phasetransition temperature of DMC when confined within MCM41. 3.3. EPR Spectroscopy. Although the melting points of the LiBF4 solutions are significantly reduced through confinement, it is not clear how confining the solutions affects the molecular dynamics of the solutions. EPR spectroscopy has a long history of providing molecular-level information in regions of samples that are hard to access with traditional techniques. EPR-active spin probe molecules are very sensitive to their immediate molecular neighborhood. Thus, it is possible to gather information about the surrounding solvent through the rotational dynamics of the spin probe itself. Such studies are attempted for unconfined, bulk DMC and DMC confined within MCM-41 to better understand how confinement affects the solvent molecules. Figure 5 contains EPR spectra of Tempone in 0 and 40 wt % MCM-41/DMC samples recorded at room temperature. Both spectra contain triplet hyperfine structure because of the

Figure 2. A linear correlation between melting point depression of dimethyl carbonate and the inverse of the pore radius for various mesoporous silicas. The definition of the temperature change is ΔT = * . The best-fit linear regression was found for t = 0.37 nm. Tconf − Tunconf

represents a substantial decrease in the thermodynamic melting point of the solvent and suggests that the melting point of the solutions may be significantly reduced if the nanopore radius is made sufficiently small. Increasing the relative amount of MCM-41 suppresses the thermal transitions of the unconfined solutions. Indeed, the thermal signatures of unconfined LiBF4 solutions are virtually eliminated from the DSC traces when the amount of MCM-41 reaches 50 wt %. Consequently, nearly all of the solution volume is contained within the pore network of MCM-41. Melting point onsets for confined LiBF4-DMC solutions are all lower than the melting point onset for pure DMC (−86.6 °C). 369



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samples were evaluated from the experimental data using eqs 2 and 3, respectively. The calculated rotational correlation time for the confined solution is 4.0 × 10−11 s, whereas the rotational correlation time for the unconfined DMC solution is 5.7 × 10−12 s. Our thermal data presented in section 3.1 suggests the presence of a 0.37 nm thick layer of nonfreezable DMC along the pore wall. For MCM-41, this nonfreezable layer accounts for approximately 40% of the total DMC volume occupying the pore. Molecules in the vicinity of the pore wall are known to experience reduced molecular dynamics, while molecules occupying the center of the pores tend to possess molecular dynamics that are reminiscent of the bulk phase. According to the Stokes−Einstein equation for rotational diffusion, the rotational correlation time of a molecule, such as Tempone, is proportional to the microviscosity of the solvent. Thus, the slower rotational correlation times for Tempone in the confined system may imply higher microviscosities for DMC within the pores of MCM-41; this observation is consistent with interfacial interactions between DMC molecules and the SiO2 framework resulting in slower dynamics for the DMC molecules. We do want to emphasize, however, that the rotational correlation times calculated from the EPR spectra require knowledge of the principal values of the g and A tensors for Tempone. As discussed above, these values depend on the local polarity of the Tempone molecule. It is possible that the local polarity about the spin probe may be altered for molecules located near the pore wall where the Tempone molecules may directly interact with both DMC and the SiO2 wall. Given this uncertainty, explaining the EPR spectra through changes in the microviscosity of the DMC solvent should be taken with some degree of caution. 3.4. Ionic Conductivity of Confined Electrolyte Solutions. The ionic conductivity of an electrolyte solution is an important parameter that often defines the functionality of the solution. Impedance spectroscopy affords a convenient means to experimentally probe various conductive regions within a composite sample. In brief, a typical impedance spectroscopic experiment consists of placing the composite sample between blocking electrodes and applying a sinusoidal potential to the sample. The impedance is then measured as a function of the oscillating potential’s frequency. Resulting impedance data are typically resolved into real and imaginary components and are plotted with the imaginary part of the impedance along the ordinate and with the real part of the impedance on the abscissa (i.e., the so-called Nyquist plot). The resulting data are then interpreted by constructing equivalent circuits to model the electrical response of the sample. Many equivalent circuits have characteristic signatures that appear in the impedance data, and there are several excellent reference texts on impedance spectroscopy that discuss the electrical response of the common circuit elements (e.g., see ref 38 or 39). Representative impedance data of a LiBF4-DMC composite sample containing 50 wt % MCM-41 is presented as a Nyquist plot in Figure 6 along with proposed equivalent circuits (Figure 7). For the 50 wt % compositions investigated here, the majority of the electrolyte solution is confined within the pores of MCM-41. Although it is likely that residual amounts of the solutions exist along the surface of the MCM-41 particles themselves and are possibly filling voids between individual particles in the composite material, the quantity of this solution

Figure 4. Concentration dependence of the melting point shift for LiBF4-DMC solutions confined within MCM-41. The definition of the * . temperature change is ΔT = Tconf − Tunconf

Figure 5. EPR spectra of (A) unconfined DMC and (B) DMC confined within MCM-41.

nuclear spin of the 14N atom for the nitroxide spin probe (I = 1, S = 1/2). The hyperfine lines undergo asymmetric peak broadening when the Tempone-DMC solution is confined within MCM-41. Asymmetric peak broadening is a well-known phenomenon in EPR spectroscopy that is related to the rotational correlation time of the spin probe. The rotational correlation times for the 40 wt % and 0 wt % MCM-41/DMC 370



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along the electrolyte−electrode interface for the two stainless steel blocking electrodes. The composite samples investigated here consist of a reasonably high degree of silica filler. Therefore, the distribution of the solution within the composite materials is not expected to be uniform, requiring the use of a constant phase element in the equivalent circuit. A common expression for the impedance of a constant phase element arising from a two-dimensional distribution of time constants is38

Ze =

1 (iω)α Q

(4)

The adjustable parameters Q and α are independent of the frequency, ω. This expression for a constant phase element reduces to an ideal capacitor when α = 1 and to an ideal inductor for α = −1. The phase angle associated with this expression for a constant phase element is independent of frequency, and intermediate values of α produce sloping lines in a Nyquist presentation of impedance data at low frequency, similar to what is observed in Figure 6A. A more complicated equivalent circuit (Figure 7B) is required to interpret the impedance data at subzero temperatures. Thermal data presented in Figure 3 and Table 1 clearly demonstrates that the portions of the solution confined within the pores of MCM-41 remain in the liquid state at subzero temperatures. However, any electrolyte solution that is outside the pores would solidify between 0 and −10 °C. The appearance and subsequent growth of a semicircle in the impedance data at subzero temperatures indicates the formation of nonconducting domains within the composite samples. These regions are most likely due to portions of the electrolyte solutions that are not confined within the MCM-41 pores. We have chosen to model these domains as a resistor, Runconfined, and as a constant phase element, CPEunconfined, connected in parallel. The resistance of the confined solution is defined as Rconfined to distinguish it from the resistance of the unconfined solution. The values of Rconfined and Runconfined are obtained from the high and low frequency intercepts of the impedance data, respectively. The definition of CPEconfined and CPEunconfined in Figure 7B is the same as that for CPEelectrode in Figure 7A. Different labels are used to distinguish between the two domains present in the samples over subzero temperatures. Temperature-dependent ionic conductivities of confined and unconfined LiBF4-DMC electrolyte solutions are estimated from the impedance data and are provided in Figure 8. The composite materials have ionic conductivities of ∼10 mS·cm−1 between 0 and 30 °C. Over this temperature range, the solutions are in the liquid phase and exhibit ionic conductivities typical of liquid electrolyte solutions. Conductivity data for LiBF4-DMC composite materials measured at −30 °C as a function of salt concentration are provided in Table 2. In all three samples, the conductivity of the unconfined solution is substantially lower than that of the confined solution. Solutions that are outside the pores freeze at much higher temperatures, producing poorly conducting solid regions along the outside of the MCM-41 particles. This appears as a dramatic decrease in the conductivity of the unconfined solution. In contrast, ionic conductivities of the confined solutions decline monotonically over the temperature range investigated, ranging from ∼0.01 to ∼0.1 mS·cm−1. 3.5. Implications for Potential Applications of Confined Electrolyte Solutions. The thermal and ionic conductivity data demonstrate that LiBF4-DMC confined

Figure 6. Representative impedance data for 1.0 m LiBF4-DMC composite materials at (A) 30 °C and (B) −40 °C. The samples contain 50 wt % MCM-41.

Figure 7. Equivalent circuits for (A) conductivity data above 0 °C and (B) conductivity data below 0 °C.

must be small since DSC data do not show substantial endothermic transitions for the freezing or melting of these regions. All samples exhibit a single sloping line for temperatures higher than 0 °C, but a semicircle appears in the Nyquist plots at subzero temperatures. The size of the semicircle increases as the temperature is decreased until it becomes the dominant feature (cf. the −40 °C data in Figure 6). The impedance data recorded for T > 0 °C displays typical behavior for a conductive electrolyte solution sandwiched between two blocking electrodes. Therefore, an appropriate equivalent circuit for the impedance data collected at these temperatures is a resistor, Relectrolyte, and a constant phase element, CPEelectrode, connected in series (Figure 7A).38 The resistance of the empty cell is negligible; hence, Relectrolyte is assigned solely to the resistance of electrolyte solution within the composite materials. Although it is likely that there is both confined and unconfined solution present in these samples, the ionic conductivities of the two are expected to be similar given that the confined solutions are in the liquid state above 0 °C. Thus, the resistances of the solutions are represented by a single resistor in the equivalent circuit. The constant phase element is associated with double layer capacitance arising 371



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nonbridging oxygen atoms along the pore wall and generate negative surface charges. Electrostatic interactions then cause cations to preferentially bind to the silica surface, leaving anions to accumulate in the center of the pores. In contrast, solutions with pH values below the isoelectric point contain an abundance of Si−OH groups that facilitate anion adsorption along the surface. The concentration profile of the Li+ and BF− ions within the pore will be controlled by the presence of surface charges along the pore walls, which impart a radial concentration dependence for the ions. The Poisson−Boltzmann equation provides an elegant framework for predicting ion concentration profiles for solutions confined within mesoporous compounds. In its general form, the Poisson−Boltzmann equation equates the charge density in Poisson’s equation for the electrostatic potential, ψ, to the ion concentrations in the surrounding solvent. The ion concentrations are assumed to follow the Boltzmann distribution, and the solvent has a permittivity of εrεo:

Figure 8. Temperature-dependent ionic conductivities of 1.0 m LiBF4DMC solution. The samples contain 50 wt % MCM-41. Unconfined and confined solution conductivities overlap above the freezing temperature of the unconfined solutions.

Table 2. Conductivities for LiBF4-DMC Solutions Mixed with 40 wt % MCM-41a

a

concentration (m)

0.5

1.0

1.5

σconfined (mS·cm−1) σunconfined (mS·cm−1)

4.6 × 10−2 4.1 × 10−5

6.3 × 10−2 3.8 × 10−5

7.4 × 10−2 7.3 × 10−5

∇2 ψ = −

1 εr ε0

⎛ zieψ ⎞ ⎟ kT ⎠

∑ zieNo,iexp⎜⎝− i

(5)

In this formula, the total number concentration is given as No,i for the ith ion having charge zie. For simple 1:1 electrolytes within a cylindrical pore of radius r, the Poisson−Boltzmann equation becomes

The temperature is −30 °C.

solutions experience substantial reduction in their melting points while maintaining relatively high ionic conductivities. The combination of high ionic conductivities with favorable thermal properties suggests that confined solutions may be useful as low-temperature ion conductors for applications such as lithium ion batteries. In that case, the ion mobility and transference number for the lithium ions is of paramount importance since battery performance hinges on the efficient transport of lithium ions through the electrolyte solution. Experimental and computational studies on confined ionic liquid systems may provide some insight into how confinement will affect ion transport in these systems. As with most conventional solvents, the thermal properties of ionic liquids are reduced when the materials are constricted within small nanopores.40−42 Furthermore, the molecular dynamics of confined ionic liquids follows the same general trend as found in most traditional solvents. That is, ionic liquid located near the pore wall interacts with the silica and exhibits slower molecular dynamics. In contrast, the molecular dynamics of the ionic liquid in the center of the pore is similar to what is found in the bulk.43 Coasne et al.44 modeled the molecular dynamics of an ionic liquid within nanoporous silica. They determined that the ionic conductivity of ionic liquid located along the pore wall was approximately one-fourth lower than the ionic conductivity found in the pore center. Thus, the location of ions within the pore may be an important parameter in the overall ion transport mechanism of the confined LiBF4-DMC electrolyte solutions investigated here. Molecular dynamics simulations of dissolved salts in water highlight the important role of silica−ion interactions in defining the locations ions occupy within the nanopore.45−47 When aqueous electrolyte solutions are confined within porous silica, the water molecules adopt a layered structure parallel to the pore axis.45−47 The location of the ions within the pore channels, however, is highly dependent on the surface charge density of the silica walls. Solutions with pH values higher than the isoelectric point of silica promote deprotonatation of

⎛ zeψ ⎞ 1 d ⎛ dψ ⎞ 2zeNo ⎟ ⎜r ⎟ = sinh⎜ ⎝ kT ⎠ εr εo r dr ⎝ dr ⎠

(6)

The electrostatic potential, and in turn the concentration profiles of the ions, is thus determined by solving eq 6 with the normal boundary conditions for solutions confined within a cylindrical geometry, (dψ/dr)|r=0 = 0 and (dψ/dr)|r=R = [σs/ (εrεo)][(R + (a/2))/R].48 Here, σs is the surface charge density along the pore wall and a is the ionic radius. Several workers have examined the validity of the Poisson−Boltzmann equation for solutions within nanoporous compounds,49−56 and the overall consensus is that the equation gives satisfactory results for monovalent cations and anions;53,57 however, the model begins to fail for divalent ions.53,55−57 In a nanopore, such as MCM-41, the surface charge density along the silica surface produces an electrical double layer that can extend across the entire pore. Although the surface charge density of MCM-41 in contact with DMC is not known, experimental surface charge densities for SBA-15 mesoporous silica in aqueous solutions range from 0.0 to −0.1 C m−2, depending on the pH of the solution and the solute type.58 Thus, MCM-41 filled with LiBF4-DMC likely possesses a negative surface charge density, and Li+ counterions are predicted to accumulate along the pore wall in response to the negative surface charge density. Concomitantly, electrostatic repulsion between the pore wall and the BF4− co-ions are expected to result in depleted BF4− ion concentrations near the pore wall. In the context of lithium ion conductors, the concentration profiles of the Li+ and BF4− ions as a function of the pore radius are expected to have an influence on ion mobility and transference numbers because the lithium ion concentration will be highest near the pore wall where molecular dynamics is typically slower. This could obviously have important implications in the overall ion transport mechanism of a confined electrolyte solution. 372



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through the composite sample, and (3) the important role of silica−ion interactions within the pore. All of these are important issues to consider and overcome before implementing these materials as ion conductors for low-temperature applications.

Although the ionic conductivity and thermal properties of the confined LiBF4-DMC solution are attractive, there are many other potential issues that may inhibit the direct use of these materials. First, it is not enough to maintain high ionic conductivities for the solutions only within the pores at subzero temperatures. Ion conduction in these materials will require ions to migrate down the MCM-41 channels and then to transport across intergrain boundaries from one MCM-41 pore to another pore on a separate MCM-41 particle; the resistance of ion transport across these boundaries is an important component in the overall ion transport mechanism. The resistance for ion transport between individual MCM-41 particles will be controlled by the conductivity of unconfined solutions trapped in the space between individual MCM-41 grains. As shown in Figure 8, the ionic conductivity of the unconfined solutions decreases substantially at subzero temperatures, severely limiting the ability of ions to migrate between particles under the influence of an external electric field. A second concern centers on the orientation of MCM-41 pores. The composite materials investigated in this study contain silica particles that are randomly oriented with respect to each other. Thus, nanopores of the MCM-41 particles do not form continuous channels through the sample, and ions will have to navigate a tortuous pathway through the composite material. The increased time required for ions to migrate through the composite electrolyte will likely have a deleterious impact on the performance of these materials. Last, a third potential complication lies with constricting ion transport within very narrow channels. The melting point depression of the confined electrolyte solution is inversely proportional to the pore radius. Also, the desire for a low melting point may prompt researchers to select a narrow pore diameter. Although pore size does not appear to impact water structure, it is possible that ions strongly bound to the pore wall may obstruct axial diffusion along the pore channel if the diameter is made sufficiently small. The possibility for axial obstruction by ions bound to the pore wall, particularly for porous hosts with very narrow pore diameters, should be considered when designing low-temperature ion conductors from confined electrolyte solutions.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +1 918 444 3835; fax: +1 918 458 2325; e-mail: burba@ nsuok.edu. Present Addresses †

Oklahoma State University, Department of Chemistry, 501 Athletic Ave., Stillwater, OK 74078. § University of Oklahoma, College of Pharmacy, 4502 East 41st Street, Suite 1H13, Tulsa, OK 74135. ⊥ Outreach Laboratory, 311 North Aspen, Broken Arrow, OK 74012. Author Contributions ‡

These authors contributed equally.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors wish to thank Dr. Susan L. Nimmo (Department of Chemistry and Biochemistry) at the University of Oklahoma for providing access to an EPR spectrometer. This work was supported by awards from Research Corporation and Northeastern State University to C. M. Burba. E. D. Butson was partially supported through a grant from the Oklahoma Louis Stokes Alliance for Minority Participation.

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REFERENCES

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Thermal Properties and Ionic Conductivities of Confined LiBF4

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