1. Introduction

A publication of Goldstein ^[1] marks the beginning of the renewed interest in salt hydrates, i.e. salts that contain a definite number of water molecules in the crystal lattice. Besides water, salts can also include solvents like ammonia, i.e., the so called ammoniates, and methanol, i.e., methanol solvates. The general equation for gas-solid equilibrium reactions will look like ^[2]:

$\label{eq_basic} \text{MX$\cdot$}n\text{L(s)} \rightleftharpoons \text{MX}\cdot m\text{L(s)+}(n-m)\text{L(g)}.$

(1)

where MX$\cdot n$L(s) is a solid salt complex formed from a salt MX$\cdot (m)$L(s) and $(n-m)$ mol solvent, which is present as vapor. The amount of L inside product MX is called the loading of the salt. The decomposition reaction of MX$\cdot n$L is endothermic, i.e. it consumes energy (-$\Delta_r$$H_{m\rightarrow n}$), whereas in the exothermic formation reaction of MX$\cdot n$L energy ($\Delta_r$$H_{m\rightarrow n}$) is produced. Hence, this system is ideal for storing heat loss-free: an ideal "heat battery". The operational parameters for this equilibrium reaction are the vapor pressure of solvate L and the stored chemical energy inside the salt complex. By applying a high vapor pressure complexes with a higher loading of solvate will be formed and heat is generated. In contrast, upon applying energy to the salt complex by increasing the temperature, the salt complex will decompose.

The possibility to control the heat release and storage just by two parameters, i.e., temperature and vapor pressure, makes gas-solid reactions a promising system for heat storage applications. For a particular heat storage system in the build environment, the solvent should be selected based on the vapor pressure at the desired working conditions. This vapor pressure is preferably around 0.1--10 MPa at the temperature range where the system is operational. A high vapor pressure increases the rate of reaction of the solvent with the ammoniates ^[6], but in general at high vapor pressures additional safety precautions are needed. Three main solvents ^[2,7] can be identified as options for heat storage by thermochemical reactions: water, ammonia and methanol. Each solvent has a specific set of working conditions, as decomposition temperature and solvent pressure, in combination with a certain type of salt. Also the toxicity and explosive limits have to be taken into account in choosing a salt and a solvent for a certain application. In Table 1 the main characteristics of the pure solvents are given. It shows that by increasing the working pressure respectively ammonia, methanol and water have to be selected.

Advantages of heat storage based on a solid-gas reaction (Thermochemical materials TCM's) are the relatively high energy density of 0.5--2 GJ/m$^3$, storage without loss of heat and relatively low costs of storage materials ^[8]. The current application of the TCM is foreseen on heat storage for domestic environment. By using materials like ammonia and methanol, heat storage is probably decentralized stored at district level, as the safety regulation with ammonia and methanol are strict. In case the reaction is with water, the heat storage system can be stored in houses. The high energy density and no loss of heat during storage period make this system favorable above a more simplified system like sensible heat storage.

In general, salts in combination with water are well described and information about crystal structures, thermochemical characteristics and densities can be found in extensive compilations of chemical data like the Gmelin (^[9]). In contrast, salt complexes in combination with methanol and ammonia are rarely mentioned in literature. Indeed, about methanol complexes literature is hardly available ^[7]. Ammonia salt complexes have been well studied in the past.

In this paper our goal is to summarize this large set of thermodynamic data of salt complexes with ammonia to be able to identify the most suitable ammoniates for a heat storage system in domestic environment. In the first section, we will give a flavor of the large history in ammonia research and an overview of the ammoniates. The next section we will summarize the observations and these will be discussed afterwards.

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2. Ammoniates

In the second half of the 19th century, the first articles were published about the dissociation pressures of ammoniates at constant temperature. The first articles published dealt with chloride complexes ^[10,11]. After the development of the heat theorem of Nernst ^[12], as first published in 1906, more research was performed on ammoniates. In this research the focus was mainly on the decomposition schemes of the ammoniates by varying the ammonia partial pressure at constant temperature ^{[13,14,15,16]}.

The most detailed investigations were done by two research groups in the beginning of the 20th century. These two groups studied a large number of salt complexes, using similar procedures as mentioned above. Firstly, they grew highly loaded ammoniates, which were decomposed by changing the ammonia pressure at constant temperature. Examples of the isotherms are given in Figure 1, showing the decomposition of MgI$_2\cdot$6NH$_3$ at two temperatures, i.e. 488 K and 503 K. As can be seen, in case the system is equilibrated at a higher temperature, the decomposition starts at a higher vapor pressure. After recording these curves, $\Delta_r$$H^0$ was calculated. This is called the enthalpy of reaction, which is defined by the energy necessary to decompose an ammoniakate into a lower ammoniated salt and ammonia (MX$\cdot n$NH$_3$(s) + $\Delta_r$$H^0_{m\rightarrow n}$ $\rightleftharpoons$ MX$\cdot m$NH$_3$(s)(s) + ($n-m$)NH$_3$(g)). The basic thermodynamic equation for the equilibrium between a condensed phase (solid or liquid) and the vapor phase of a pure substance, under conditions of low pressure, is used for this ^[18]:

$\ln{\frac{p}{p^0}} = \frac{\Delta H^0_{m\rightarrow n}}{RT}-\frac{\Delta S^0_{m\rightarrow n}}{R}\label{eq_DG},$

(2)

where $p$ is the decomposition vapor pressure in Pa, $p^0$ is the reference vapor pressure of 10$^5$ Pa, $\Delta_r$$H^0_{m\rightarrow n}$ is the standard enthalpy of a salt in J/mol, $T$ is the temperature in Kelvin. For the reaction of MgI$_2\cdot$6NH$_3$ into MgI$_2\cdot$2NH$_3$ the $\Delta_r$$H^0_{m\rightarrow n}$ $=$ (74$\pm$3)$\cdot$10$^1$ kJ/mol $\Delta_r$$H^0$ at a vapor pressure of 0.9 MPa and a temperature of 613 K ^[17].

This equation allows to calculate with know decomposition temperatures and pressures the corresponding enthalpy and entropy of reaction $\Delta_r$$H^0_{m\rightarrow n}$ of a salt.

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2.1. Literature of ammoniates

We can group the literature about ammoniates:

• General literature: ^{[19,20,21,22,23,24,25,26,27,28]}.

• Halogenides: Cl^{[20,15,29,10,30,31,32,33,34,35,36,11,27,1,37,38,39,40,40,41,42,43,44,45,46,47,48,49,17,50,51,52,13,2,16,53,54,55,56,57,58]}, Br^{[20,33,29,32,35,36,27,37,38,59,39,40,41,42,43,44,45,46,47,48,49,17,50,51,52,14,54,55,57,60,58]}, I ^{[20,33,29,34,32,35,36,27,37,59,39,40,41,42,43,44,45,46,47,48,49,17,50,51,52,54,55,57,58]} and F ^[61,14].

• Alkali metals: Li ^{[49,20,13,16,57,27]}; Na^{[49,20,27,34]}; K ^[49,20,34]; Rb ^[49,20,34] and Cs ^[49,20].

• Alkaline earth metals: ^{[20,50,51,62,30]}; Mg ^{[20,17,50,54]}; Ca ^{[20,63,2,1,27,35,10,31]}; Sr ^{[20,63,50,64,33]} and Ba ^{[20,63,50,1,27,36]}.

• Transition metals (3d): Cr ^[38,37,15]; Mn ^{[20,45,50,54,62,39,27]}; Fe ^{[20,45,50,54,62,39,37,27]}; Co ^{[20,45,50,14,54,62,39,59]}; Ni ^{[20,47,50,54,55,62,40,39,59,27]}; Cu^{[20,50,54,57,58,62,43,40,64,27,65,29]} and Zn ^{[20,54,44,62,42,40,39,64,10]}.

• Other metals: Pt ^[37]; Ag ^{[20,52,56,62,64,11,10]}; Au ^[46,60]; Cd ^{[50,54,62,40,64]}; Hg^[50,61,62]; Al ^[53,37,32]; In ^[32]; Tl ^[20,37,29]; Sb ^[61]; Sn ^[20,48,62] and Pb ^[20].

• Sulphates ^{[62,43,42,59,37,65]};

• NiXO$_4$ (X=S; Se; Cr; W or Mo) ^[66];

• Double salts ^{[48,60,67,65]}

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2.2. Thermodynamic overview of ammoniates

The $pT$ data from the literature gives the possibility to determine the enthalpy of reaction of various ammoniates, ($\Delta_r$$H^+$=$\Delta_r$$H^0\cdot (m-n)$), as a function of the decomposition temperature, $T$, which is plotted in Figures 2. As can be seen for various loadings of the ammoniates an approximately linear relationship between enthalpy of reaction and dissociation temperature is found for each specific loading and charge combination. Also, a higher loading corresponds to a higher enthalpy of reaction and a lower dissociation temperature. In this graph some reactions have a reaction temperature below the 294 K, the equilibrium temperature of NH$_3$ at 0.9 MPa. These reactions seems unrealistic and will be indicated as such in Appendix 1.

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2.2.1. Selection of salts

Selection of the most suitable salt complex for heat storage from the point of view of energy density, is based on the amount of heat that is stored in the system by removing one ammonia molecule from the salt crystal. In Figure 3, we plotted the enthalpy of reaction stored in a complex divided by the amount of ammonia molecules from a structure $\Delta_r$$H^0$) plotted against the decomposition temperature for the ammonia pressures at 0.9 MPa (equal to an equilibrium vapor pressure of ammonia at 294 K). The symbols of the data points refer to specific loading and release of ammonia during the reaction. As can be seen a linear trend exists at constant pressure. In the inset, the average enthalpy of reaction is plotted for the four groups, indicating that the alkali metals have the lowest energy stored per added mole ammonia and the transition metals (3d) have the highest amount of energy stored per added mole ammonia. As the difference in average enthalpy of reaction between the metals is smaller than the error bars, no conclusions can be drawn.

In Figure 4, the enthalpy of reaction stored in a complex divided by the number of ammonia molecules is plotted against the number of moles ammonia in a complex. The pressure used for this graph is 0.9 MPa. The averaged $\Delta_r$$H^0$ decreases from 70 kJ/mol (mono ammoniate) to 30 kJ/mol (octa ammoniate). It is harder to release the last ammonia molecule of a complex than to release one ammonia molecule at higher loadings. We can understand this by the fact that, relatively, the crystal structure is changing more in case of smaller loadings. At the higher loadings (above six NH$_3$ molecules per mole salt) the enthalpy of reaction falls down to almost the level of the enthalpy of reactions of decomposition of ammonia. In general, from the point of view of heat storage, therefore, it will be of interest to select a complex, which totally decomposes at the applied temperature and pressure, with a maximum loading of six ammonia molecules per complex, based on Figure 4.

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2.3. Discussion

The operation conditions are a first criteria for selection an ammoniate as TCM. For example in the case of a heating system in houses, the turnover temperature should be between 343 K and 393 K for sufficient charging power with help of solar collectors ^[68]. In addition, secondly the amount of ammonia per mol salt refines the selection. With a larger loading number, less salt is needed to store all heat, but as already mentioned, a loading above six is not favorable. The final selection criteria is the amount of ammonia, which is lost at the applied temperature. Moreover, thirdly, the equilibrium ammonia pressure of the reaction at temperature of 343--393 K should be in the order of 0.6--1 MPa, what are the equilibrium vapor pressures of ammonia between 283--298 K. This is necessary as the TCM is connected with a storage vessel of ammonia. In case the equilibrium pressure of ammonia of the storage vessel is higher than of the equilibrium pressure of the reaction, the salt will not deammoniate. Or the other way around, in case the equilibrium pressure of the storage vessel is lower that the equilibrium pressure of the reaction, the salt will not ammoniate. As the storage vessel can be kept at a temperature of 283 K in the winter and 298 K in the summer the working pressures are chosen between 0.6--1 MPa.

As in the literature not all decomposition reactions are fully given, only the enthalpy per released mole NH$_3$ is plotted against the equilibrium temperature between 330--410 K in figure 5. As can be seen a large range of materials fits the demands. As currently not sufficient data is available a single choice of material can not be made. Based on prices of the future heat storage systems, materials like silver, copper, cesium and lithium are not considered. Based on this data sheet, the most common materials are indicated with a solid sphere (MgCl$_2\cdot$6NH$_3$, CaCl$_2\cdot$8-4NH$_3$, and ZnCl$_2\cdot$6NH$_3$). In further research other material properties like melting points, densities, deliquescence points and costs should be considered as well. These parameters should be considered before a heat storage system for domestic households based on ammoniates can be designed.

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2.4. Concluding remarks

We analyzed a large set of thermodynamic data of ammoniates. For various loadings of ammoniates, the dissociation temperature shows an approximate linear relationship with the enthalpy of reaction. Indeed, by dividing the enthalpy of reaction by the loading, all data points fall on one master curve, which can be divided by the periodic groups. Lower loadings have a large heat storage capacity per molecule of complex, implying that complexes with loading of six or lower are more favorable for heat storage application. With the help of this data set, appropriate ammoniates can be selected as heat storage material for a given temperature and ammonia partial pressure. In the future, before heat storage in domestic environment is feasible, additional research should be performed on melting temperature of certain complexes, deliquescence of the complex, density of the complexes and combined transitions.

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2.5. Appendix 1

Salt is the basic salt in the reaction; Initial is the highest loading in the reaction; Final the lowest loading in the reaction; $\Delta H^0$ is the enthalpy of the reaction; $\Delta S$ the entropy of the reaction; T$_{p=9 bar}$ is the maximum ammoniation temperature by 9 bar ammonia vapor pressure. The used type of thermodynamic data and source is given in column pT/H and in case of $pT$ data is used the minimum and maximum temperature of the used $pT$ data is given in columns $T_{min}$ and $T_{max}$ and the number of data points used in the next column. If the final loading is unknown, this is indicated with a question mark(?). In case doubts about the reliability of the data is raised, they are indicated with an asterisk $^*$.

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Acknowledgements

This research was carried out under project number M75.7.11421 in the framework of the Research Program of the Materials innovation institute (M2i) (www.m2i.nl)

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Conflict of Interest

All authors declare no conflict of interest in this paper.

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