Thermophysical Properties of Lithium Nitrate Trihydrate from (253 to

Apr 10, 2012 - The authors thank the Air Force Research Laboratory, Materials and ... decreases in traditional aircraft heat sinks, and the prevalence...
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Thermophysical Properties of Lithium Nitrate Trihydrate from (253 to 353) K Patrick J. Shamberger*,† and Timothy Reid†,‡ †

Thermal Sciences and Materials Branch, Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433, United States ‡ University of Dayton Research Institute, University of Dayton, Dayton, Ohio 45469, United States ABSTRACT: Lithium nitrate trihydrate is of interest as a thermal energy storage material, due to its large specific and volumetric enthalpy of fusion and its low melting temperature. Here, we report the thermophysical properties of solid and liquid lithium nitrate trihydrate at temperatures from (253 to 353) K and compare this compound to water and octadecane, two other potential thermal energy storage materials. Furthermore, we examine the lithium nitrate− water phase diagram and accurately determine the enthalpies of fusion and melting temperatures for lithium nitrate trihydrate, ΔHfus = (287 ± 7) J·g−1 and Tfus = 303.3 K, and the lithium nitrate trihydrate−lithium nitrate eutectic, ΔHfus = (264 ± 2) J·g−1 and Tfus = 301.4 K.

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offers double the volumetric energy densities (≈400 MJ·m−3) of comparable melting temperature paraffins.2−4 Here, we report the heat capacity, thermal conductivity and diffusivity, density, viscosity, and vapor pressure of LiNO3·3H2O between (253 and 353) K, as determined by a number of analytical techniques. The thermophysical properties of this compound are compared against the properties of water and a paraffin with a similar melting temperature (octadecane, C18H38). Furthermore, we investigate the melting temperature and enthalpy of fusion of LiNO3·3H2O and the LiNO3·3H2O/LiNO3 eutectic.

INTRODUCTION Thermal management of aerospace systems and components is a critical factor in meeting both current and future technological goals for the United States Air Force (USAF).1 This challenge is made more demanding by trends in component miniaturization, increasing power output of components, decreases in traditional aircraft heat sinks, and the prevalence of thermal transients on USAF platforms. For thermal management purposes, thermal energy storage (TES) materials are of great utility, as they absorb transient pulses of heat, averaging heat loads over greater time scales, thereby decreasing the mass and volume of remaining thermal management elements. In practice, materials which undergo a solid−liquid phase transition (commonly referred to as “phase change materials”) are observed to reversibly absorb and release large quantities of heat over very small temperature ranges.2 Belonging to this class of materials, the paraffins have been widely adopted as engineering materials, due to the wide range of melting temperatures observed in different paraffins from (93 to 353) K, their predictable melting and crystallization behaviors, and the workability and nontoxicity of the basic materials. In comparison, a number of salt hydrates have attracted interest which have volumetric storage densities nearly double those of paraffins (due principally to the higher density of the salt hydrates).2−4 However, very few of the thermophysical parameters of these salt hydrate systems are known within a reasonable degree of certainty. This limits comparison with other known TES materials, as well as high-fidelity computational simulations of TES components based on salt hydrates. This paper describes the thermophysical properties of one candidate TES material, lithium nitrate trihydrate (LiNO3·3H2O), recently investigated at the USAF Research Laboratory. LiNO3·3H2O melts at approximately 303 K and © 2012 American Chemical Society

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BRIEF REVIEW OF EXPERIMENTAL DATA FOR LITHIUM NITRATE TRIHYDRATE The equilibrium solubility in the lithium nitrate−water system has been determined as early as 1903,5,6 including the melting temperature of the congruently melting lithium nitrate trihydrate, as well as the melting temperature and composition of the eutectics in the system (Table 1). Recent reviews have critically evaluated solubility in the lithium nitrate−water binary system, as well as in other ternary and multicomponent systems containing lithium nitrate,7 and have extracted the empirical parameters necessary to predict isotherms in these systems.12 The enthalpy of fusion of lithium nitrate trihydrate has been measured by a number of authors using calorimetric techniques; these values are summarized in Table 1.6−10 Reported enthalpies of fusion are within 5 % of each other. As pointed out by Guion et al. (1983), many of the enthalpy of fusion and melting temperature data that exist in the literature are propagated in simple tabular form, and the original experimental details and reference are uncertain.8 Thus, a Received: November 21, 2011 Accepted: March 27, 2012 Published: April 10, 2012 1404

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Table 1. Tfus and ΔHfus of LiNO3·3H2O and wLiNO3 and Teut of the LiNO3·3H2O/LiNO3 Eutectic as Reported in the Literature ΔHfus

Tfus K 302.8 ± 303.6a 303.1 ± 303.03a 303.3 ± 303.1 ± a

J·g

−1

0.1 0.1 0.1 0.1

liquid lithium nitrate−water solutions of varying concentrations (mass fraction of water, 0.65 > w > 0.40).24 Both viscosity and vapor pressure measurements for lithium nitrate−water solutions will be compared to new measurements taken specifically for stoichiometric LiNO3·3H2O.

Teut wLiNO3

K

ref

0.61 ± 0.01 0.608a

301.1 ± 0.1 302.00a

6 7b 8b 9b 10 11

296 ± 30 296a 290 ± 10 283 ± 3

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EXPERIMENTAL METHODS Lithium nitrate trihydrate (LiNO3·3H2O) samples were synthesized by adding stoichiometric quantities of deionized water to as-received anhydrous lithium nitrate (w > 0.99, Alfa Aesar). A second batch of LiNO3·3H2O was synthesized from deionized water and as-received high purity anhydrous lithium nitrate (w > 0.9998, metals basis, Alfa Aesar) to characterize the effect of purity on undercooling. Anhydrous lithium nitrate was weighed in a sealed vial to minimize water absorption, after which a calculated amount of water was added. Mass fractions of samples were determined by mass measurements using a digital balance, and the estimated uncertainty is u(w) = 0.002. A TA Instruments Q2000 differential scanning calorimeter (DSC) was used to determine melting temperatures and enthalpies of fusion, as well as heat capacities. The enthalpy of fusion was measured from melting peaks that were obtained at a heating rate of 2 K·min−1, after calibrating the DSC cell with a pure indium standard (w = 0.999, supplied by TA Instruments) to a reference value of ΔHfus = 28.66 J·g−1.25 Reported melting temperatures are the intercept of the baseline with the tangent of the DSC trace with the maximum slope. The uncertainty of temperature measurements was verified by the melting temperature of indium (429.75 K)25 and is u(T) = 0.2 K. The relative uncertainty of individual enthalpy of fusion measurements is ur(ΔHfus) = 0.05, based on repeated analysis of indium and pure water standards. Reported melting temperatures and enthalpies of fusion are averages of six different samples. Heat capacities were determined using the modulated DSC technique, after calibrating the cell with a sapphire standard. The relative uncertainty of heat capacity measurements is ur(Cp) = 0.05, based on repeated analysis of sapphire and water reference standards.26 Reported DSC heat capacities are averages of three different samples. All DSC samples were (10 to 15) mg and were hermetically sealed in aluminum test pans during testing. Thermal properties of the liquid (diffusivity, conductivity, and heat capacity) were analyzed by the transient hot wire technique (PSL Systemtechnik Lambda 01/L) following ASTM D2717.27 Prior to analysis, the instrument was calibrated with water at 288.15 K, and the temperature scale was calibrated using a high precision digital thermometer (GMH 3710), with a manufacturer specified uncertainty of u(T) = 0.01 K. Uncertainties of thermal diffusivity, thermal conductivity, and heat capacity are all estimated to be ur(α, k, Cp) = 0.05 based on repeated analysis of ultrapure water (18.2 MΩ·cm, ASTM/ CAP/NCCLS type I) and toluene standards. 28 Liquid LiNO3·3H2O was poured into the hot wire sampling cup under an argon atmosphere. Porous cork stoppers were placed in the sample assembly's vent ports, allowing for gas expansion while minimizing the introduction of moisture. Reported thermal properties are averages of 10 measurements at each temperature. Thermal transport properties of the solid (diffusivity, conductivity) were analyzed by the transient plane source technique (ThermTest Hot Disk TPS 2500S thermal constant analyzer). Heat capacities of the solid measured by DSC were utilized in the calculation of diffusivity and conductivity.

Uncertainty not stated. bNot a primary experimental reference.

redetermination of these values was strictly necessary for this work. Substantial data on the density of liquid and solid LiNO3·3H2O have been previously determined by volume displacement methods (e.g., pycnometry)13−16 and by the flotation method.17 Reported densities are within 0.5 % of each other. Furthermore, the concentration dependence of density for lithium nitrate−water solutions has been studied at lower concentrations of LiNO 3 than the stoichiometric LiNO3·3H2O.18−20 Extrapolation of these data trends provides good agreement with density data for liquids from other sources.13,14 Solid densities of single crystals, determined by the flotation method,17 are up to 0.5 % larger than densities of powdered solids determined by volume displacement methods.13,14 The thermal properties of LiNO3·3H2O have not been wellcharacterized in the literature. The heat capacity of both solid and liquid LiNO3·3H2O was measured by adiabatic calorimetry and reported in the literature.11 However, the concentration of water in the sample was not known with certainty, the uncertainty of the measurement technique was not reported, and duplicate experiments varied significantly (up to 30 %).17 The heat capacity for lithium nitrate−water solutions up to ≈14 mol·kg−1 has been measured by the transient hot wire technique at (323 and 363) K, but it is difficult to extrapolate these limited data to LiNO3·3H2O (18.50 mol·kg−1).18 Thermal transport measurements for LiNO3·3H2O are equally lacking. Again, the thermal conductivity for lithium nitrate− water solutions has been measured by the transient hot wire technique at (313, 333, and 363) K, but only up to concentrations of ≈14 mol·kg−1.18 The thermal diffusivity was also measured for LiNO3·3H2O using a custom transient measurement apparatus, but the uncertainty of this approach was not quantified and is likely large, and the phase of LiNO3·3H2O during the measurement was not specified.9 Finally, thermal conductivity of the solution can be calculated using a simple linear model and empirically determined parameters correlating the effect of various cation and anion species on thermal conductivity.21 However, this model is most appropriate for dilute concentrations, and it should only be used as an approximation of the thermal conductivity of liquid LiNO3·3H2O. Consistent concentration-dependent viscosities for lithium nitrate−water solutions have been measured by capillary flow techniques at (298, 323, and 348) K by multiple authors.22,23 The viscosity for liquid LiNO3·3H2O may be interpolated from data measured at higher concentrations of LiNO3.22 Finally, equilibrium vapor pressure has been measured directly for 1405

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Relative uncertainties of thermal conductivity and diffusivity measured by this system are estimated to be ur(α, k, Cp) = 0.10, based on the repeated analysis of Vespel and Pyrex standards. This uncertainty is likely large in part due to the role of contact resistance in the transient plane source technique. Liquid LiNO3·3H2O was loaded into a 12 mm diameter Teflon liquid cell with a 2 mm diameter sensor suspended in the center. The cell was sealed with a paraffin film to minimize the absorption of moisture and was allowed to cool and solidify. Reported values are averages of five measurements at each temperature. Upon opening the cell, good contact between the in situ solidified salt hydrate and the sensor was confirmed. Liquid density was measured using an oscillating u-tube with viscosity correction and a reference oscillator (Rudolph Research Analytical DDM 2911 densitometer). The DDM 2911 was calibrated using pure water. The relative uncertainty of individual liquid density measurements is estimated to be ur(ρ) = 0.005, based on repeated analysis of air and of a pure water standard. Liquid LiNO3·3H2O was drawn into a syringe and capped under an argon atmosphere. The densitometer's utube was purged with N2, and the outlet was protected with a drying tube. The sample was introduced into the u-tube via the syringe. A fresh sample was used at each 10 K temperature step from (303 to 363) K. Solid densities were calculated from the crystal structure data for LiNO3·3H2O as determined by X-ray and neutron diffraction.29,30 Relative uncertainties of solid densities are ur(ρ) = 0.002, based on the reported uncertainty of the lattice parameters. Kinematic viscosity was measured by flow rate through a glass capillary tube following ASTM D445.31 The capillary tube calibration was verified using Cannon viscosity standard S2000 at 373.15 K and was within 0.07 % of the specified standard value (within the tolerance band of ± 0.30 % defined by ASTM D445). The relative uncertainty of viscosity measurements using this technique is estimated to be ur(ν) = 0.01, based on a comparison of interlaboratory results of fluids with kinematic viscosities < 10 mm2·s−1.31 Liquid LiNO3·3H2O was drawn into a glass capillary under an argon atmosphere, and the viscosity tube was fitted with molecular sieve drying tubes to minimize the exposure of the sample to atmospheric moisture. Reported viscosities are averages of three measurements. Vapor pressure was measured directly by evacuating a glass vial containing a few grams of LiNO3·3H2O to below 0.1 kPa. The vial was immersed completely in a water bath and was allowed to thermally equilibrate. Pressure was measured using a digital diaphragm pressure gauge (Vacuubrand GMBH VSK 3000) with an uncertainty of u(p) = 0.02 kPa. The relative uncertainty of vapor pressure measurements using this method was ur(p) = 0.15, based on the analysis of a pure water reference material. Accuracy was likely limited due to thermal gradients existing within the pressure gauge.

Figure 1. Representative DSC profiles of LiNO3−H2O solutions (endothermic is down) illustrating: ---, a eutectic point Teut = 301.4 K; ···, the melting temperature of LiNO3·3H2O, Tfus = 303.3 K. The mass fraction of LiNO3, w, is indicated on the figure.

(corresponding to the LiNO3·3H2O/LiNO3 eutectic temperature) and the higher temperature Tfus ≈ 303 K. As the concentration of LiNO3 approaches the LiNO3·3H2O/LiNO3 eutectic composition, the higher temperature peak disappears (Figure 1). At lower concentrations of LiNO3, a significant fraction of melting still occurs at or just below 303 K, but melting no longer starts at a well-defined temperature. Additionally, a second melting peak is observed at T ≈ 250 K, corresponding to the H2O/LiNO3·3H2O eutectic temperature. This melting peak is not observed in all cases, as subcooling prevents crystallization in some runs. Melting temperatures (both Tfus, the onset of the melting peak and Tpk, the temperature of the maximum of the melting peak) are illustrated in Figure 2, alongside data originally reported by

Figure 2. Phase diagram of the LiNO3·3H2O system: △, onset of melting Tfus, this work; ×, maximum of melting peak Tpk, this work; ○, equilibrium solubility, Campbell and Bailey;6 (eu1, eu2), eutectic points.

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RESULTS AND DISCUSSION Melting temperatures were measured by DSC for compositions along the LiNO3−H2O binary between LiNO3 mass fractions of w = 0.497 and 0.646. This compositional range includes stoichiometric LiNO 3 ·3H 2 O (w = 0.561) and the LiNO3·3H2O/LiNO3 eutectic composition (w ≈ 0.61).6 Example melting curves are illustrated in Figure 1. Stoichiometric LiNO3·3H2O (w = 0.561) indicates a sharp melting peak with an onset melting temperature (Tfus) at 303.3 K. Compositions enriched in LiNO3 display a superposition of two melting peaks, with the lower temperature Tfus = 301.4 K

Campbell and Bailey (1958).6 In all cases, the observations reported here are consistent with those previously reported results. The enthalpy of fusion (ΔHfus) and entropy of fusion (ΔSfus) of LiNO3·3H2O (mass fraction of LiNO3 w = 0.561) and of the approximate composition of the LiNO3·3H2O/LiNO3 eutectic (w = 0.616) were both determined by DSC (Table 2). The latter composition involves the melting of two distinct phases: LiNO3·3H2O and LiNO3.6 Reported melting temperatures and 1406

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Table 2. Tfus, ΔHfus, and ΔSfus of LiNO3·3H2O and the LiNO3·3H2O/LiNO3 Eutectic ΔHfusb

Tma wLiNO3 LiNO3·3H2O LiNO3·2.39H2O a

a

0.561 0.616

K

J·g

−1

287 ± 7 264 ± 2

303.3 301.4

ΔHfusb −1

kJ·mol

35.3 ± 0.8 32.5 ± 0.3

ΔSfusb −1

J·K ·kg

−1

946 ± 23 876 ± 7

ΔSfusb J·K−1·mol−1 116 ± 3 108 ± 1

u(w) = 0.002, u(T) = 0.2 K. bThe reported uncertainty is ± 2σx̅ of six different samples.

enthalpies of fusion are averages of 6 independent samples; uncertainties are ± 2σx̅ (where σx̅ is the standard deviation of the mean) and define an interval with a confidence level of 95 %. These enthalpies of fusion both exceed that of octadecane (244 J·g−1) but are less than the enthalpy of fusion of pure water (334 J·g−1).32 Enthalpy of fusion of LiNO3/H2O mixtures decrease nearly linearly away from stoichiometric LiNO3·3H2O composition. Enthalpies of fusion of LiNO3·3H2O are consistent with previously reported results (Table 1). The density of liquid LiNO3·3H2O was measured with a commercial densitometer at temperatures between (308 and 353) K. Solid densities are calculated from X-ray and neutron diffraction data collected at (120 and 295) K (Table 3, Figure Table 3. Density, ρ, of LiNO3·3H2O

a

Ta

ρa

K

g·cm−3

technique

phase

ref

120 295 308.2 313.2 318.2 323.2 328.2 333.2 338.2 343.2 348.2 353.2

1.610 1.575 1.425 1.420 1.413 1.408 1.402 1.395 1.390 1.384 1.378 1.372

diffraction diffraction densitometer densitometer densitometer densitometer densitometer densitometer densitometer densitometer densitometer densitometer

solid solid liquid liquid liquid liquid liquid liquid liquid liquid liquid liquid

30 30

Figure 3. (a) Density ρ, (b) deviation from the linear fit (ρexp − ρfit/ ρfit), and (c) volumetric thermal expansion αV of LiNO3·3H2O: □, density presented in this work; ×, Mashovets et al., Zavodnaya and Vorob'ev;13,14 +, Grodzka and Hoover;15 ○, Lane et al.;16 ●, Alimova and Ryskin;17 ◊, Puchkov and Matashkin.19,20 Lines represent: ···, linear fits to density and thermal expansion presented in this work; , density of H2O;28 ---, density of C18H38.3 Volume contraction or expansion ΔV/V upon melting is calculated by extrapolating densities to Tfus.

temperature−density trends to the transition temperature. During crystallization, LiNO3·3H2O contraction is ΔV/V = 0.100. Thus, LiNO3·3H2O differs from pure water which expands during freezing and is comparable to the volumetric expansion of octadecane upon melting (ΔV/V = 0.098). Densities of LiNO3·3H2O are within 0.5 % of previously reported results. The volumetric enthalpy of fusion of LiNO3 ·3H2O, calculated from calorimetric and density data, is 452 MJ·m−3 for the solid phase (just below Tfus) and 409 MJ·m−3 for the liquid phase (just above Tfus). Assuming that the eutectic has approximately the same density as stoichiometric LiNO3·3H2O, the volumetric enthalpy of fusion of the LiNO3·3H2O/LiNO3 eutectic is approximately 415 MJ·m−3 for the solid phase (just below Tfus) and 375 MJ·m−3 for the liquid phase (just above Tfus). These values are approximately twice the volumetric enthalpy of fusion of octadecane (Figure 4) and even exceed the volumetric enthalpy of fusion of water (307 MJ·m−3 for the solid, 332 MJ·m −3 for the liquid). 3,28,32 Thus, both compositions of interest represent some of the largest known values for volumetric enthalpy of fusion in the low temperature range (273 to 373 K). This higher density of LiNO3·3H2O relative to that of water or paraffins is largely responsible for the high volumetric latent enthalpy of fusion LiNO3·3H2O relative to those materials.

u(T) = 0.1 K, ur(ρ)sol = 0.002; ur(ρ)liq = 0.005.

3).29,30 Experimental data are all well-described by a simple linear dependence on T over this temperature range. ρ/g·cm−3 = A + B ·T /K

(1)

Here, ρ is the density, T is the temperature, and A and B are parameters fit to the data. For the solid, A = 1.6336 and B = −0.000199; for the liquid, A = 1.7896 and B = −0.001183. The fractional deviation of experimental data in this study from the linear fit (|ρexp − ρfit|/ρfit) is < 0.001; the deviation of experimental data from other previous studies from the fit is < 0.04.13−17 The density of LiNO3·3H2O exceeds that of both octadecane (ρLiNO3·3H/ρoctadecane) = 1.7 to 1.9) and water (ρLiNO3·3H2O/ρH2O)(= 1.4 to 1.8). The volumetric thermal expansion (αV) of LiNO3·3H2O is calculated numerically from the density data and is also illustrated in Figure 3. The average αV of solid LiNO3·3H2O is 1.3·10−4 K−1 between (120 and 295) K. In liquid LiNO3·3H2O, αV increases from 8·10−4 K−1 at 308 K to 9·10−4 K−1 at 353 K. The thermal expansion of liquid LiNO3·3H2O is comparable to that of pure water over the same temperature range (3.5·10−4 K−1 at 308 K to 6.5·10−4 K−1 at 353 K). Volumetric expansion and contraction during melting/crystallizing were calculated by linearly extrapolating 1407

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Table 5. Thermal Conductivity, k, Thermal Diffusivity, α, and Heat Capacity, Cp, of LiNO3·3H2O, as Measured by the Transient Hot Wire Technique

a

Ta

ka

αa

Cpa

K

W·m−1·K−1

m2·s−1

J·K−1·g−1

phase

308.2 313.2 318.2 323.2 328.2 333.2 338.2 343.2 348.2 353.2

0.584 0.581 0.587 0.583 0.585 0.588 0.588 0.588 0.595 0.611

14.1 14.0 14.1 14.1 14.1 14.2 14.2 14.2 14.3 14.5

2.91 2.91 2.94 2.94 2.96 2.98 2.99 3.00 3.03 3.07

liquid liquid liquid liquid liquid liquid liquid liquid liquid liquid

u(T) = 0.1 K, ur(k, α, Cp) = 0.05.

Figure 4. Specific and volumetric enthalpy of fusion, ΔHfus for: ●, solid and ○, liquid LiNO3·3H2O, this work; ■, solid and □, liquid LiNO3·3H2O/LiNO3 eutectic, this work; ⧫, solid and ◊, liquid H2O;28 ▲, solid and △, liquid simple paraffins with even numbers of carbon atoms.3,32

The constant pressure heat capacity Cp of LiNO3·3H2O is measured by DSC (Table 4) and by the transient hot wire Table 4. Heat Capacity, Cp, of LiNO3·3H2O at Selected Temperatures, as Measured by DSC

a

Ta

Cpa

K

J·K−1·g−1

phase

253.2 263.2 273.2 283.2 288.2 313.2 323.2 333.2 343.2 353.2

1.59 1.63 1.67 1.71 1.73 2.76 2.77 2.76 2.77 2.76

solid solid solid solid solid liquid liquid liquid liquid liquid

Figure 5. Constant pressure heat capacity Cp of LiNO3·3H2O: □, Cp measured by the hot wire technique, this work; ···, Cp measured by DSC, this work; ●, solid and ○, liquid Cp from Koski et al.;10 +, liquid Cp extrapolated from Gierszewski et al.18 Lines represent: , H2O;26 ---, C18H38.3

u(T) = 0.2 K, ur(Cp) = 0.05.

technique (Table 5) and is illustrated as a function of temperature in Figure 5. The heat capacity of liquid LiNO3·3H2O at temperatures just above the phase transition is 2.8 J·g−1·K−1, while the heat capacity of solid LiNO3·3H2O at temperatures just below the phase transition is 1.8 J·g−1·K−1. The liquid heat capacity is measured by both DSC and hot wire techniques; both measurements are within experimental uncertainty of each other. Liquid heat capacity is nearly constant across the temperatures investigated ((308 to 358) K) and is larger than the heat capacity of octadecane over the same temperature range (Figure 5). The solid heat capacity increases linearly from (248 to 288) K (at 0.0041 J·g−1·K−2, at approximately the same slope as water) but is less than both water and octadecane over this temperature range. The thermal conductivity (Figure 6) and thermal diffusivity (Figure 7) of solid and liquid LiNO3·3H2O were measured between (253 and 353) K using the transient hot wire (liquid, Table 5) and transient plane source (solid, Table 6) methods.

Figure 6. Thermal conductivity k of LiNO3·3H2O: □, measured by the hot wire technique, this work; ◊, measured by the hot disk technique, this work; ○, extrapolated from Gierszewski et al.;18 ●, calculated k from Tsederberg.21 Lines represent: , H2O;28 ---, C18H38.3 1408

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Table 7. Kinematic, ν, and Absolute Viscosity, η, of LiNO3·3H2O Ta K 308.2 313.2 318.2 323.2 328.2 333.2 338.2 343.2 348.2 353.2

Figure 7. Thermal diffusivity α of LiNO3·3H2O: □, measured by the hot wire technique, this work; ◊, measured by the hot disk technique, this work; ○, Grodzka.9 Lines represent: , H2O;28 ---, C18H38.3

a

νa 2 −1

m ·s

3.75·10−6 3.38·10−6 3.09·10−6 2.81·10−6 2.57·10−6 2.37·10−6 2.20·10−6 2.05·10−6 1.91·10−6 1.79·10−6

ηa mPa·s

phase

5.34 4.80 4.37 3.96 3.60 3.31 3.06 2.84 2.63 2.46

liquid liquid liquid liquid liquid liquid liquid liquid liquid liquid

u(T) = 0.1 K, ur(ν,η) = 0.01.

Table 6. Thermal Conductivity, k, and Thermal Diffusivity, α, of Solid LiNO3·3H2O, as Measured by the Transient Plane Source Technique Ta K 294.2 293.2 283.2 273.2 263.2 253.2 a

αa

ka −1

−1

W·m ·K 0.82 0.75 0.76 0.77 0.74 0.76

m2·s−1

phase

30·10−8 27·10−8 28·10−8 29·10−8 29·10−8 30·10−8

solid solid solid solid solid solid

u(T) = 0.5 K, ur(k, α) = 0.10.

Figure 8. Absolute viscosity η of LiNO3·3H2O: □, this work; ○, Puchkov et al.9 Lines represent: ···, fit to η presented in this work; , H2O;28 ---, C18H38.3

Liquid thermal conductivity (0.59 W·m−1·K−1) and thermal diffusivity (14.1·10−8 m2·s−1) remain constant within experimental uncertainty between (308 and 353) K and are both very near the values for pure water ((0.62 to 0.67) W·m−1·K−1, (14.9 to 15.7)·10−8 m2·s−1). In agreement with the linear model for thermal conductivity in aqueous solutions presented by Tsederberg, the addition of lithium nitrate to water depresses the thermal conductivity of the liquid.21 However, liquid thermal conductivities presented here are over 10 % greater than previously reported values.18,21 The solid thermal conductivity (0.75 W·m−1·K−1 ) and thermal diffusivity (29·10−8 m2·s−1) also remain constant within experimental uncertainty between (253 and 293) K but are only a small fraction of the values for pure water (Figures 6 and 7). In contrast, the ratio kLiNO3·3H2O/koctadecane is 4 for the liquid and 2 for the solid, and the ratio αLiNO3·3H/αoctadecane is 2 for the liquid, 1.2 for the solid. Given an identical temperature gradient, the local heat flux density is proportional to the thermal conductivity. Thus, TES components based on LiNO3·3H2O may be expected to have higher cooling power densities than those based on paraffins. The kinematic viscosity of liquid LiNO3·3H2O was measured by the capillary flow technique at temperatures between (308 and 353) K (Table 7). The absolute (dynamic) viscosity was calculated from kinematic viscosity and from density measurements taken at the same temperatures (Figure 8). Experimental data were fit with a polynomial equation as a function of temperature, following a form previously used for hydrous LiNO3 solutions.33

η /Pa·s = A + B /(T /K) + C /(T /K)2

(2)

Here, η is absolute viscosity (in Pa·s), T is the temperature (in K), and A = 5.7606·10−2, B = −42.478, and C = 8125.3 are parameters fit to the data. The deviation of experimental data from the polynomial fit to the linear fit (|ηexp − ηfit|/ηfit) is < 0.005. The absolute viscosity of LiNO3·3H2O is greater than that of octadecane, although the kinematic viscosity of LiNO3·3H2O is less, due to the density difference between the two materials (Figure 8). The absolute viscosity as measured in this study is in excellent agreement with previously presented results.22 The equilibrium vapor pressure of LiNO3·3H2O was measured directly at temperatures between (288 and 313) K (Table 8). All vapor pressure data are fit with the August equation, assuming a temperature-independent heat of vaporization (Figure 9). log10(p /kPa) = A − B /(T /K)

(3)

Here, p is the pressure, T is the temperature, and A = 8.990 and B = 2711 are parameters fit to the data. This model is adequate to describe the vapor pressure−temperature relationship, given the relatively large uncertainty of the data reported here. The equilibrium vapor pressure of LiNO3·3H2O is only a fraction of the equilibrium vapor pressure of pure liquid water (peqLiNO3·3H2O ≈ 0.25 peqH2O), representing a significant negative deviation from Raoult's law (which would predict a vapor pressure of peqLiNO3·3H2O ≈ 0.6peqH2O, assuming Li+ and NO3− 1409

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Table 8. Vapor Pressure, p, of LiNO3·3H2O a

a

Table 9. Undercooling, ΔT, of LiNO3·3H2O as a Function of Starting Material

a

T

p

K

kPa

phase

288.2 293.2 298.2 303.2 308.2 313.2 308.2 303.2 298.2 293.2 288.2

0.4 0.5 0.7 1.0 1.3 2.2 1.7 1.4 0.7 0.5 0.4

solid solid solid liquid liquid liquid liquid liquid solid solid solid

ΔTa/K lithium nitrate, anhyd. w = 0.9998 lithium nitrate, anhyd. w = 0.99 lithium nitrate, anhyd. w = 0.99, aged for 7 to 14 days at T = 323 K

avg.

2σ

Nb

39.3 12.5 45.5

14.3 2.3 8.7

19 15 6

a u(T) = 0.2 K. bReported values are averages of N independent measurements.

that impurities either dissolve or react with the liquid salt solution, decreasing their effectiveness as nucleation sites. Research into stable nucleation agents to promote heterogeneous nucleation is ongoing in the authors' research group.36

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u(T) = 0.1 K, ur(p) = 0.15.

CONCLUSIONS The thermophysical properties of LiNO3·3H2O are measured at temperatures between (253 and 353) K. These are compared against the properties of water and octadecane, two other potential thermal energy storage materials. Both LiNO3·3H2O (287 J·g−1, 409 MJ·m−3) and the LiNO3·3H2O/LiNO3 eutectic (264 J·g−1, ≈ 375 MJ·m−3) have a very high volumetric energy storage density, which even exceeds that of water. Furthermore, these two compositions have a higher specific energy density, thermal conductivity, and thermal diffusivity than that of comparable paraffins (octadecane). Thus, LiNO3-based salt hydrates are very competitive as thermal energy storage materials and excel in applications where volume is at a premium. Further studies of other salt hydrate systems are needed to evaluate their potential as TES materials and to establish compositional trends in material properties.

Figure 9. Vapor pressure p of □, LiNO3·3H2O, this work; ○, solutions with varying mass fractions of LiNO3, w, as indicated, Campbell et al.24 Lines represent: ···, fit to p presented in this work; , H2O.28

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AUTHOR INFORMATION

Corresponding Author

*Phone: +1 (937) 255-6809. Fax: +1 (937) 255-2176. E-mail: [email protected].

are nonvolatile solutes). Vapor pressures presented here are in general agreement with vapor pressures measured for other concentrations of lithium nitrate−water solutions.24 The equilibrium vapor pressure of LiNO3·3H2O is much lower than the ambient relative humidity in laboratory environments (typically from 0.4 to 0.6 peqH2O). Thus, the low equilibrium vapor pressure of LiNO3·3H2O is responsible for its hygroscopic behavior. In fact, crystalline LiNO3·3H2O left exposed to ambient air was observed to absorb moisture and to deliquesce, as the melting temperature of the material decreases with an increase in water content (Figure 2). Certain salt hydrates are known to exhibit a large temperature difference (ΔT) between the equilibrium crystallization temperature and the temperature at which crystallization actually takes place. This undercooling is related to the large energy barrier required for homogeneous nucleation and can cause potential problems for TES components by limiting their ability to regenerate without active cooling.2,34,35 In small volumes of LiNO3·3H2O (on the order of 10 μL), ΔT is relatively large (>10 K) and is even larger with a higher purity starting material (Table 9). This observation is consistent with the hypothesis that impurities in the starting material serve as potential nucleation sites for crystalline LiNO3·3H2O, proposed based on observations of undercooling in a variety of materials systems.35 Aging lower purity samples at temperatures above their melting temperature (>323 K) for a period of 7 to 14 days leads to ΔT comparable with higher purity samples, suggesting

Funding

The authors thank the Air Force Research Laboratory, Materials and Manufacturing Directorate for providing necessary financial support to carry out the present work. Notes

The authors declare no competing financial interest.

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REFERENCES

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