Table 1.Average thermodynamic entities (ΔH°f, ΔG°f, S°, Cp and V) of liquid water and ice.
1. Introduction
Many papers have suggested that several specific “types” of H2O exist. These have been labelled variously as “ zeolitic”, “ loosely held”, “structural”, “crystal”, “tightly bound” and “external” [1-3]. These labels suggest both the differing apparent energies of H2O as well as their differing apparent structural roles. Three useful distinctions can be made about H2O in compounds:
H2O that varies in content as a continuous function of temperature and pressure
H2O that changes discontinuously at a unique temperature for a given pressure
H2O that is sorbed to external surfaces
The first type (continuously varying H2O) is characteristic of the zeolites and clay minerals and considers that most of the zeolites and clay minerals lose or gain H2O in response to small changes in temperature and pressure over an extended temperature, relative humidity or the nature of cations in exchanged sites.
The second type of H2O is similar in nature to that found in hydrates of salts and considers that dehydration occurs over narrow temperature intervals in some compounds. Some zeolites, like analcime and laumontite, do not exchange water at room temperature. This type can be called “hydrate” H2O and has a specific position in the crystal structure. Hydroxides are excluded from this chapter because the H2O molecule is not identified but is only virtually present as a hydroxyl OH.
The third type of H2O is externally sorbed to the crystal and may be referred to as external. This type is present in quantities much smaller than the H2O present within the structure of any zeolite grain size. In the clay minerals, whose specific surfaces are greater than those of zeolites, the water located in inter-particle spaces, in inter-aggregate spaces and at the surface of uncharged clays minerals indicates that a special status of H2O may be different in the regimes of adsorption or of capillary condensation, and this is not considered in this chapter.
2. Definition of thermodynamic entities of hydration
In evaluating the thermodynamic quantities, it is important to define the standard state chosen for a given constituent. In the present study, the standard state for water is chosen as pure water at a temperature of 25°C with a vapour pressure of Po, and for the minerals, the dry compound is at a temperature of 25°C with a vapour pressure of P=0.
The reaction of hydration may be expressed by the following reaction:
If we consider any standard thermodynamic entity of hydration
where
The standard thermodynamic parameters of the hydration water can be calculated if the thermodynamic entities of formation (enthalpy
where H2O(hyd) represents the hydration water. The thermodynamics of the intra-crystalline reaction can be written as follows:
By assuming that the standard thermodynamic entities of the intra-crystalline reaction are equal to zero,
The aim of this chapter is to determine how the thermodynamic entity
3. Measurements of thermodynamics of hydration in minerals
Different methods of measurements of thermodynamic entities of hydration are presented in this section:
Hydrofluoric acid solution calorimetry. The calorimetric measurements of the heat of dissolution of anhydrous and hydrated compounds provide the enthalpy of formation to form elements. The enthalpies of hydration are obtained by measuring the difference in the enthalpy of the solution in HF acid at approximately 70°C, of a hydrated and a dehydrated zeolite [4-6] or at 25°C in a HF - HNO3 solution for clay minerals [7].
Transposed-temperature drop calorimetry. The enthalpy of hydration data are obtained by measurements of the heat evolved from a sample dropped at room temperature into a calorimeter maintained at 700–800°C [8], [9-12]. One of the difficulties associated with this measurement includes the enthalpy effects because of the irreversible structural changes at 700–800°C.
Adiabatic low temperature calorimetry. This is performed on the anhydrous and hydrated compounds to determine the third law of entropy for the zeolites [4-6] and clay minerals [7, 13].
Heat of adsorption combined with adsorption-desorption isotherms. This method provides measurements of integral enthalpies of hydration as a function of the degree of hydration. Some of the difficult parameters to control include the amount of H2O adsorbed by the sample (requires knowledge of the amount of H2O in the sample while immersed in water), the accurate measurement of the initial state of dehydration and the potential for irreversible change in the zeolite structure during dehydration such that the sample does not re-adsorb its full capacity of H2O during immersion [14]. For clays, the measurements of heat of adsorption were performed on eight homoionic SWy-1 montmorillonites[15-17] [18] [19] [20] and on vermiculites[21]. One advantage of the method is that it is a direct measurement of the enthalpy of hydration.
Phase equilibriums. The enthalpy of hydration can be determined from the phase equilibrium measurements of the isoteric method, which are plotted as Ln P (or Ln K) versus 1/T at a constant hydration state. The slopes of these lines give the enthalpy of hydration for zeolites [22], [23] and for montmorillonites[24-26].
Gas-adsorption calorimetry. The enthalpies of hydration data are obtained by exposing a bed of zeolite to differing vapour pressures within a calorimeter [27]. One of the difficulties of this method is the kinetic limitations on attainment of equilibrium (slow kinetics requires a very sensitive and stable calorimeter). An advantage of the method is the capacity to measure partial molar enthalpies of hydration directly.
Adsorption-desorption isotherms measured at different temperatures. With the Clausius-Clapeyron relationships, the ability to extract the integral and partial thermodynamic entities of hydration from isotherms at any two temperatures was developed by [28, 29] and applied on montmorillonite in [30] and [31]
Thermochemistry and Raman spectroscopy. A combined study of thermochemistry and raman spectroscopy has been tested on zeolites [32] and clays [33][34].
4. Inventory of different values from prediction methods of thermodynamic entities of hydration water
The thermodynamic data of liquid water and ice are displayed in Table 1. The formation properties of the hydration water may vary depending on the nature of the physical-chemical properties of the anhydrous compound [35]. In any case, when the minerals exist as hydrated phases, the presence of water molecules stabilises them. Thermodynamically, this corresponds to ΔG0hyd< 0 kJ mol-1 or ΔG0f,(H2OHyd) < -237.14 kJ mol-1, the value for bulk water at 250C and 1 bar [36]. Additionally, the maximum entropy is for bulk water and implies that S0(H2OHyd) < 69.95 J K-1 mol-1 [36]. The minimum entropy may be assessed by considering the entropy of Ih ice, as refined by Tardy et al. [37] (44.77 J K-1 mol-1). To give a minimum value for ΔG0f(H2OHyd) is more complicated. Ice cannot be of use, for example, because it is not stable at room temperature, and on the contrary, ΔG0f(Ice Ih) >ΔG0f (bulk water), with –236.59 kJ mol-1. For the enthalpy term ΔH0f(H2OHyd), because ΔG0hyd< 0 kJ.mol-1 and S0(H2OHyd) < S0(bulk H2O) for hydrated minerals, then ΔH0hyd must be negative or ΔH0f(H2OHyd) <ΔH0f(bulk H2O) with -285.83 kJ mol-1 [36]. For the heat capacity of hydration water, very few measurements have been actually performed so far.
Families | Ref. | ΔH°f | ΔG°f | S° | Cp | V |
(kJ mol-1) | (kJ mol-1) | (J K-1 mol-1) | (J K-1 mol-1) | cm3 mol-1 | ||
Liquid water | 1 | -285.84±0.04 | -237.18±0.05 | 69.923±0.03 | 75.576 | 18.064 |
Ice | 2,3 | -292.75±0.1 | -236.59±0.1 | 44.771±0.05 | 42.008 | 19.228 |
Among the numerous methods of prediction of thermodynamics entities of compounds (salts, and minerals), only twelve are retained and exhibit different values of the thermodynamic entities of ice-like water obtained from the statistical results from the anhydrous and hydrated compounds (Table 2).
Families | Ref. | Nb. | ΔH°f | ΔG°f | S° | Cp | V |
comp | (kJ/mole) | (kJ/mole) | (J/K/mole) | (J/K/mole) | cm3/mole | ||
Sulphates & sulphites | 1 | 41 | -301.4±7.7 | -244.4±7.9 | 41.5±6.0 | 39±5.2 | 14.5±1.2 |
Chlorates & Chlorides | 1 | 34 | -308.3±8.6 | -251.8±8.5 | 43.7±5.9 | 42±2.7 | 14.1±2.3 |
Zeolites | 2 | 15 | 59.1 | ||||
Hydrates | 3 | 342 | -298.6±20.5 | -242.4 | 40.9 | 42.8 | 14.75 |
Silicates | 4 | ? | 39.3±4.2 | 13.7±0.5 | |||
Silicates | 5 | 3 | 54.123 | ||||
Hydrates | 6 | ? | -297.06 | ||||
RE chlorides | 7 | 8 | -297 | 46.4 | |||
Binary comp. of Na | 8 | 42 | -297±8.3 | ||||
Silicates | 9 | 7 | 43.5 | 14 | |||
Silicates | 10 | 7 | -306.99±12.8 | 44.1±2.0 | 14.6±0.09 | ||
Silicates | 11 | 6 | -292.37±4.6 | -239.91±5.7 | |||
Borates | 12 | 23 | -290.42 | -237.28 | 54.86 | ||
U bearing minerals | 13 | 14 | -295.58 | -241.1 |
All of these models of predictions are built on a simple additive scheme and require knowledge of the thermodynamic entity of the anhydrous compound, the number of water molecules and the thermodynamic entity of formation of “ice-like” water or of hydration water obtained by statistical regressions. For each thermodynamic entity (enthalpy, free energy, entropy, heat capacity and molar volume), the values are significantly different within the nature of the compounds or minerals. For each prediction model, the nature of family, number of compounds and statistical errors are provided to check the extent and the validity of the model. There appear to be few models of prediction of free energies of hydration, which is the most useful parameter in geochemical modelling. The best way to reach this target is to combine the enthalpy and entropy of hydration. Despite the great diversity of the enthalpy of formation of the hydration water and its great error within different families of compounds, some recent and accurate models of prediction of the enthalpy of hydration are important to introduce for compounds such as salts, zeolites and clays minerals.
To improve the accuracy of prediction, the next section develops several models of prediction based on different kinds of minerals displaying recent measurements of the thermodynamic entities of the hydration water closely related either to the environmental conditions and or to the nature and chemical formulas of the anhydrous compounds.
5. Recommended models of prediction of thermodynamic entities
5.1. Enthalpy of formation
the enthalpy of hydration of the reaction (6) becomes
where n is the number of molecules of crystalline water contained in the hydrate under consideration and
This parameter is analogous to the enthalpy of dissolution of an anhydrous salt per equivalent (characterised by the product of charges of the cation and anion). The relationships of the enthalpy of hydration of a salt to the number of the molecules of water and to the nature of the salt is:
where
The enthalpy of the formation of ice used in Eq. (7) [50-52] comes from Robie&Waldbaum[53] and is equal to -279.8 kJ mol-1. As this value is very different from those given in table 1, the values of coefficients (
The values of
An example is given by considering the data of all of the sodium salts displayed in Figure 1A and shows the great variation of the enthalpy of hydration having the same number as the crystalline water. The different straight lines are obtained from Eq. (10) with values of
Cations | β | Nb. of data | % error1 | Std dev. | |
(kJ/mol H2O) | |||||
Li+ | -0.277 | -0.341 | 19 | 0.34 | ± 3.58 |
Na+ | -0.294 | 1.759 | 61 | 0.29 | ± 3.44 |
K+ | -0.115 | -9.168 | 15 | 0.66 | ± 10.70 |
Rb+ | -0.360 | -6.769 | 6 | 0.29 | ± 3.38 |
Cs+ | -0.577 | 18.954 | 4 | 0.48 | ± 6.35 |
Be+2 | -0.485 | -3.068 | 7 | 0.25 | ± 3.48 |
Mg+2 | -0.312 | -10.708 | 21 | 0.43 | ± 5.39 |
Ca+2 | -0.270 | -3.892 | 25 | 0.44 | ± 4.64 |
Sr+2 | -0.349 | -1.894 | 20 | 0.32 | ± 5.93 |
Ba+2 | -0.327 | -4.637 | 19 | 0.80 | ± 5.31 |
Zn2+ | -0.211 | -16.461 | 12 | 0.44 | ± 6.57 |
Cd2+ | -0.322 | 2.266 | 8 | 0.33 | ± 4.29 |
Cu+2 | -0.433 | -1.791 | 11 | 0.65 | ± 4.22 |
Ni2+ | -0.176 | -18.056 | 10 | 0.46 | ± 2.81 |
Co2+ | -0.260 | -2.296 | 11 | 0.36 | ± 3.60 |
Fe2+ | -0.136 | -17.806 | 6 | 0.18 | ± 1.58 |
Mn2+ | -0.238 | -5.144 | 15 | 0.25 | ± 6.14 |
Cr+2 | -0.478 | 31.459 | 3 | 0.28 | ± 1.77 |
UO2+2 | -0.247 | -7.945 | 18 | 0.35 | ± 4.80 |
From the selected average enthalpies of hydration of the different zeolites with their chemical formulas (145 data points), a regression equation for the enthalpy of hydration per mole of water is proposed [54]:
where coefficients a and b are
Coefficients of Eqs. (11) (12) and (13), such as the ratio Al/Si, Al/(Al+Si), FDanh.,
The framework density (FD) [55, 56] represents the number of tetrahedral atoms per 1000 Å3 and are obtained as:
The electronegativity of site Az+, defined by ΔHO=(site A), represents the weighed average of ΔHO=Mz+(aq) of nc different cations in the exchanged site A:
The number of oxygens balancing site Mz+ (in extra-framework sites) is then:
The parameter ΔHO= Mz+ (aq) characterises the electronegativity for a given cationMz+ and is defined as the difference between the enthalpy of formation of the corresponding oxides
where z is the charge of the cationMz+ and x is the number of oxygen atoms combined with one atom of M in the oxide (x = z/2), such that the difference in Eq. (17) refers to one oxygen atom. A set of internally consistent values was presented by Vieillard& Mathieu [54] and is given in Table 4.
The total intracrystalline pore volume, WP, was introduced by Barrer [57] for determining the volume of liquid water that can be recovered thorough the outgassing of the fully hydrated zeolite. Assuming that the unit cell volume of zeolitic water is the same as that of liquid water (
where Vu.c. hyd. represents the unit cell volume of a hydrated zeolite containingnH2O water molecules. Assuming that the number of water molecules nH2O varies from 0 to nH2O max, the unit cell volume of a zeolite can be directly related to the number of water molecules. Although such variations in the unit -cell volume do occur, let us assume a linear variation in the unit-cell volume as a function of the number of water molecules:
where Vu.c. anh. represents the unit-cell volume of the anhydrous zeolite. Parameter k weights the variation in the unit-cell volume between an anhydrous zeolite and a fully hydrated zeolite per one water molecule. This parameter can be calculated from the available unit-cell volumes of anhydrous and fully hydrated zeolites. Thus, knowledge of the number of water molecules and the unit-cell volume of anhydrous and hydrated zeolites is required for the calculation of the water porosity:
Ions | ΔHO=Mz+(aq) | Ions | ΔHO=Mz+(aq) |
(kJ mol-1) | (kJ mol-1) | ||
Li+(aq) | -40.90 | Ca+2(aq) | -92.1 |
Na+(aq) | 65.80 | Mg+2(aq) | -134.6 |
K+(aq) | 141.00 | Fe+2(aq) | -181.58 |
Rb+(aq) | 163.24 | Mn+2(aq) | -164.4 |
Cs+(aq) | 170.0 | Zn+2(aq) | -197.07 |
Ba+2(aq) | -15.6 | La+3(aq) | -124.8 |
Sr+2(aq) | -40.4 | H+(aq) | -285.83 |
By eliminating 9 erroneous data points [54], the regression coefficient for 136 data is R2= 0.880, with a standard error of ± 3.46 kJ mol-1 for all data, regardless of the nature of the experimental data. Figure 2 displays the predicted enthalpy of hydration of zeolitic water calculated from Eqs. (11) (12) and (13) versus the experimental enthalpy of hydration coming from the different technical measurements. Regression coefficients and standard errors are different within the two main groups: R2= 0.88 and std. err. = ± 3.41 kJ mol-1 for TTDC data (67 data points), R2= 0.658 and std err. = ± 2.66 kJ mol-1 for the “IC” data (57 data points).
When Al/Si and Al/(Al+Si) = 0, the hypothetical integral enthalpy of water in zeolites obtained by the extrapolation of Eq. (11) is 0, which corresponds to the enthalpy of hydration of water in cordierite (2.2 ± 1.6 kJ mol-1 from Carey [58]). Unlike zeolites, the water in cordierite is not coordinated by cations, so the molecular environment of H2O in cordierite is similar to that of H2O in water.
A detailed computation of the enthalpy of hydration is given as an example for three natural clinoptilolites (-Ca, -Na and –K)with the following chemical formula given by [22]:
Clinoptilolite-Na: (Ca0.12Mg0.29K0.75Na5.21)(Al6.78Fe0.06Si29.2)O72.05-21.3H2O
Clinoptilolite-K: (Ca0.13Mg0.25K5.84Na0.27)(Al6.85Fe0.1Si29)O71..9-18.5H2O
Clinoptilolite-Ca: (Ca2.34Mg0.57K0.9Na0.18)(Al6.7Fe0.017Si29)O71..8-21.9H2O
The values of the ratio Al/Si yield a constant value of 0.235. The electronegativity of the exchangeable site Az+ for clinoptilolite-Na is, for example, the average electronegativity of four cations (Na+, K+, Ca2+ and Mg2+ (table 4)) as follows:
i.e.,
The unit-cell volume of the anhydrous clinoptilolite–K (V u.c.) is 2019.51 Å3[59]. This means that there are 35.95 tetrahedral atoms (6.95+0.1+29) in 2019.51 Å3; which indicates that FDanh.= 17.8 tetrahedral atoms in 1000Å3. The unit-cell volume of the hydrated clinoptilolite-K (at saturation or fully hydrated) with 18.5 moles of zeolitic waters is 2089.50 Å3[54], which is slightly greater than the anhydrous form and allows the setting of the relationship of water porosity versus the number of hydration water moles:
From these previous examples, the parameters requested for the prediction of the enthalpy of hydration are displayed in table 5 for the three clinoptilolites (-Na, -K and –Ca).
Zeolite minerals | V u.c.anh. | Vu.c. hydr. | k | ΔHO= | FD. | WP | Al/Si |
(Å3) | (Å3) | Site A | Anh. | ||||
kJmol-1 | |||||||
Clinoptilolite -Na | 2000.00 1 | 2140.00 1 | 6.35 | 51.39 | 18.02 | 0.31 | 0.23 |
Clinoptilolite-K | 2019.51 2 | 2089.50 2 | 3.78 | 109.16 | 17.80 | 0.26 | 0.24 |
Clinoptilolite -Ca | 2019.51 2 | 2089.50 2 | 3.20 | -64.60 | 17.78 | 0.31 | 0.23 |
From the values given in table 5, the enthalpy of hydration of the zeolitic water,
The model of the computation of the enthalpy of hydration of the hydration water represents a very useful tool and contributes to the knowledge of enthalpies of formation of hydrated zeolites from anhydrous ones [61].
A useful method for avoiding complications at the outset of a thermodynamic analysis is to emphasise the H2O rather than the zeolite structure. Using such an approach, the equilibriums can be consideredas the equilibrium between the H2O in the fluid-vapour phase and the H2O in the zeolite. According to the definition of equilibrium, the chemical potential of H2O in the vapour phase must equal thechemical potential of the H2O component in the zeolite. Any series of measurements of the amount ofH2O in zeolite at a known fugacity (or partial pressure of H2O under ideal gas conditions) providesthe basis for the thermodynamic description of the system. The most elegant approach to develop athermodynamic formulation is to know the partial molar enthalpy of hydration,
Zeolite minerals | |||
predicted(kJ mol-1 H2O) | measured(kJmol-1 H2O) | References | |
Clinoptilolite.-Na | -22.20 -22.20 | -30.17 | [22] |
Clinoptilolite -K | -20.24 | -23.97 | [22] |
Clinoptilolite-Ca | -29.03 | -32.87 | [22] |
The bulk enthalpy of hydration or the integral enthalpy of hydration can be used as the product of the enthalpy of hydration of the water times the number of zeolitic water:
As the integral hydration enthalpy
The fractional water content can be obtained if the maximum number of zeolitic waters is known at the saturation state and is equal to:
From values of table 5, the partial molar enthalpy of clinoptilolites K, Na and Ca can be calculated versus the fractional water content and plotted in Figure 3 with the experimental partial molar enthalpies measured from immersion calorimetry [62] and from thermogravimetry [22]. The modelled values of the partial molar enthalpy for the three clinoptilolites appear to be closer to the data from the immersion calorimetry than from thermogravimetry. The second important point is the fact that the calculated and experimental partial molar enthalpy of hydration has a similar behaviour.
The partial molar enthalpy of hydration per mole of H2O increases smoothly from low water content to high θ and indicates that the H2O in clinoptilolites occupies a continuum of energetic states. This is not the case for chabazite-Ca [23], which exhibits three energetically distinct types of H2O.
This shows that, within different zeolites with the same exchangeable cation, the partial molar enthalpy as a function of the hydration degree may display different functions. This is the reason why the fundamental relationship verifying the enthalpy of hydration by means of the chemical composition and the accurate knowledge of the unit-cell parameters of anhydrous and hydrated zeolites needs to be improved with new data of hydration enthalpy of the partially hydrated zeolites on the one hand and a better fit of the effective water porosity as a function of the hydration degree on the other hand. Then, the thermodynamic description of the hydration-dehydration process can be modelled as a function of pressure and temperature with the contribution of predicted enthalpies of hydration and entropies of hydration.
Unlike zeolites, smectites are clearly not inert phases, as the particles size increases with the relative humidity [15]. Adsorbed water is distributed throughout the interlayer space, the outer surfaces of particles and the open pores space in the sample. [15-17] provided measured values of the surface covering waters for both the hydration and dehydration reactions of a set of eight homo-ionic SWy-1 montmorillonites saturated by alkali and alkaline-earth cations from their BET specific surface area (Table 1) and their basal spacing variations with relative humidity. To quantify the effective amount of water involved in the hydration reaction, the amount of poral H2O must be quantified and subtracted from the total amount of H2O taken up by the clay sample. The number of external surface water molecules (expressed in mmol/g dry clay) can be expressed as a function of relative humidity [63]. There are numerous papers about the adsorption-desorption isotherms performed on various clays minerals, but few are devoted to the acquisition of enthalpy of hydration-dehydration on SWy-1 [15-17, 64] [18, 19, 30] [20] [34] [24, 26, 65] [25] and on vermiculites [21].
All recent predictive models of the hydration of smectites are based on an approach that uses the solid solution initiated by Ransom &Helgeson[66]. The hydration of a smectite is considered through the following reaction between hydrated and dehydrated end-members:
where nm represents the maximal number of moles of water that can be included in the smectite on the basis of a half-cell (i.e., O10(OH)2). One considers the interlayer water H2O(i) (where subscript i stands for interlayer) as a variable weighing the hydration ratio. The amount of interlayer water in a smectite is proportional to the mole fraction of hydrated end-member: x*H2O= nm*xhs=(1-nm)*xas;to the mole fraction of the hydrous end-member, xhs or to the anhydrous end-members xas. Ransom &Helgeson[66] considered the system hydrated smectite – anhydrous smectite + bulk water as a strictly regular binary solid solution by considering the free energy only. Thus, the excess free energy of mixing can be expressed as follows:
where WG is an excess mixing constant. The integral Gibbs free energy of hydration is:
in which
Vidal et al. [68-69] have assumed that a smectite could be considered strictly regular solid solutions between four end-members with 0.7 H2O, 2 H2O, 4 H2O, and 7 H2O. Those compositions correspond to four different hydrated states (with 0, 1, 2, and 3 water sheets, respectively).For any strictly regular solid solution, the integral enthalpy of hydration is expressed as the following:
with
The hydration enthalpy is retrievedfrom data of [24] for montmorillonite –Na and –K and derived from differential heats of adsorption obtained from the measurements of the heat of immersion [18, 20] for Na-, Ca- and Mg- montmorillonite. Thus, an integral enthalpy of hydration
Units (kJ mol-1) | H2O | Cs | Rb | K | Na | Ba | Sr | Ca | Mg |
4.5 | -289.93 | -290.23 | -290.45 | -291.25 | -294.14 | -294.57 | -294.86 | -295.71 | |
0-0.7 | -295.50 | -299.71 | -301.43 | -302.86 | |||||
WH2 | 0. | 0. | 0. | 0. | |||||
0-2 | -293.58 | -295.90 | -298.60 | -300.05 | |||||
WH2 | -10. | -10. | -10. | -10. | |||||
0-4 | -291.96 | -293.83 | -296.25 | -297.62 | |||||
WH 2 | -10. | -10. | -10. | -10. | |||||
0-7 | -291.05 | -292.33 | -293.86 | -294.69 | |||||
WH2 | -10. | -10. | -10. | -10. | |||||
5.5 | -287.47 | -288.01 | -288.16 | -290.01 | -292.10 | -292.65 | -294.72 | -296.56 | |
16.0 | 19.0 | 15.0 | 8.0 | -60.0 | -55.0 | -60.0 | -49.0 | ||
-90.0 | -95.0 | -68.0 | -33.0 | -75.0 | -90.0 | -100.0 | -129.0 |
The integral hydration enthalpy is obtained by the following relationships:
in which
The curve 1 in Figure 4A (yellow dotted line) comes from model of Ransom &Helgeson [66], is linear and is obtained from the following equation of integral enthalpy of hydration:
where the coefficient -24.39 is computed from
The curve 3 (black line) in Figure 4A comes from the model of Vieillard et al. [63] and is represented by the following equation:
It appears that integral enthalpy of hydration modelled by Vieillard et al. [63] (black line) based on experimental measurements of heat of adsorption from [15-17] encompasses nearly all experimental data. As the standard entropy of hydration is assumed constant in [66] and [68] models, the integral hydration enthalpies provided by these two previous models are nearly linear. Those obtained by [68] exhibit three sections of curves corresponding to the three states of hydration (1, 2 and 3 water layers).
In Figure 4B, a relationship between the standard state enthalpy of interlayer water with the nature of the interlayer cation located in the SWy-1 montmorillonite with a constant layer charge of 0.38, characterised by its electronegativity (ΔHO=Mz+ (aq), Table 4) is proposed [63] and given as follows:
Lowering the electronegativity of cation in the interlayer sites stabilises the enthalpy of formation of the interlayer water. It should be kept in mind that Eq. (39) has been settled for the same support,
5.2. Entropy
where
J/K/mole | J/K/mole | J/K/mole | J/K/mole | |
Cs+ | 64.6 | 163.5 | -348.0 | -78. |
Rb+ | 63.8 | 142.0 | -355.0 | -84. |
K+ | 63.7 | 104.0 | -267.5 | -93. |
Na+ | 59.8 | 49.1 | -94.0 | -130. |
Ba2+ | 55.7 | -116.0 | -211.5 | -224. |
Sr2+ | 54.3 | -117.8 | -244.5 | -261. |
Ca2+ | 51.5 | -93.5 | -270.5 | -271. |
Mg2+ | 45.4 | -42.8 | -380.0 | -350. |
Figure 5A displays the comparison of the integral entropy of hydration of a smectite- Na computed from the three models [67] [68] and [63] developed previously with different experimental values.
As indicated in the enthalpy section, integral hydration entropies modelled by [66] (yellow dotted line, N°1) and [68] (green dotted line, N°2a, 2b and 2c corresponding to 1st, 2nd and 3rd layer) are linear and merge together. In the model proposed byVieillard et al. [63], three calculated integral entropies of SWy1-Na –water system were plotted in Figure 5Aand correspond to the adsorption (red line), the desorption (blue line) and the theoretical equilibrium water – Swy1-Na (black line, N° 3), whose equation is given:
The comparison of hydration-dehydration curves calculated by [63] with those provided by Fu et al. [34] show an opposite interpretation. The data from [34] show that integral entropies during adsorption are less negative than those during desorption. Data from our model show the opposite. This difference is explained by the fact that from experimental works of [34], adsorption follows desorption, while with our data, desorption follows adsorption. Thus, a maximum entropy difference between hydration and dehydration functions can be depicted and is equal to 18 J/K/mole. These observations show the importance of movement of exchangeable cations from ditrigonal cavities and the rotation of tetrahedrals in the tetrahedral sheets when dry collapsed layers are progressively exposed to water vapour.
A correlation between the entropy of interlayer cation
Negative values of the hydration entropy of the hydrated ion lower the hydration entropy of the interlayer water.
5.3. Heat capacity
Heat capacity function (298.15- 500 K) | ||
Eq. A | [41] | |
Eq. B | [74] | |
Eq. C | [45] | |
Eq. D | [72] |
Heat capacities of the hydration in zeolites have been performed by Neuhoff& Wang [75] on three zeolites (analcime, natrolite and wairakite) and exhibit marked variations in the heat capacity of hydration with temperature. Four zeolites (mordenite, wairakite and two different values from different sources for analcime and natrolite) for which the heat capacity of zeolitic water can be obtained by a difference between the heat capacities measured on both the anhydrous and the hydrated phases [72] are representedin Figure 6A. Also displayed are the heat capacity values of water in all its states (ice, liquid and vapour) for comparison [35]. The heat capacity values of zeolitic water obtained by minimisation techniques (Eq. D of table 9, turquish line) matches with the heat capacity function equations of [74] and [45].
Eq. D of table 9 provides a statistical error of 4.51%, 2.35% and 4.18% for hydrated zeolites at 298.15 K, 400 K and 500 K, respectively. To improve the accuracy of the prediction of the heat capacity of hydrated zeolites, one considers the normalised hydration volume, which is the difference of unit-cell volume (Vu.c.) between the hydrated and dehydrated forms for any zeolite per zeolitic water molecule [72]:
The heat capacities of hydration water given in Figure 6B have been calculated for the four hydrated zeolites (mordenite, analcime, wairakite and natrolite) from the unit-cell volumes of their dehydrated and hydrated forms[72]. It can be observed that the heat capacities of hydration water calculated in this way are much better than those obtained by Eq. D of table 9 (indicated in Fig. 6B as a turquishfull line). With this improvement, the errors made on hydrated zeolites decrease to 3.5%, 2.35% and 3.89% at 298.15 K, 400 K and 500 K, respectively.
This heat capacity equation has also been used by [68] and by [63] in the behaviour of thermodynamic entities versus temperature.
5.4. Molar volume
6. Discussion of the Gibbs free energy of the formation behaviourof the hydration water in environmental conditions
The relationships among the free energy change, enthalpy of reaction and entropy for an isothermal process is:
where ΔG stands for free energy change, ΔH for enthalpy of reaction, ΔS for the change in entropy and T for the absolute temperature. This relationship holds true for both the integral entities that are represented by
The predicted values contribute to the variations of solubility products and the cation selectivity constants among the series of salts. An example is given in [78] for two series of hydrated salts of MgCl2 and SrCl2.
For zeolites and clays, the adsorbent (a single smectite or zeolite phase) is supposed to be inert so that the derived enthalpy and entropy functions formally represent the energy variations between the adsorbed and the bulk water.
The integral free energy of hydration
where R = 8.314 J.mol-1K-1 is the ideal gas constant, n is the amount of adsorbed water, P is the partial water vapour pressure, and P0 is the saturated water vapour pressure at temperature T (P/P0 = Relative Humidity/100). This value can be determined by plotting R*T*Ln(P/Po)versus the water content n (adsorbed or desorbed) and determining the area under the curve from 0 to nw. When nw approaches 0, R*T*Ln(P/Po) approaches infinity, making integration somewhat difficult.
In each figure, the data of the free energy of hydration (Eq. 50) from the experimental isotherms [15, 16] (blue square for adsorption and red square for desorption) and the free energy of hydration are computed and are reported for comparison of three different works: the Vieillard et al. model [63] (blue, red and black lines for adsorption, desorption and theoretical equilibrium, respectively), the Ransom &Helgesonmodel [66] (dotted yellow line), and the Vidal &Dubacq model [68] (dotted green line). For the adsorption and desorption reactions, the modelled isotherm calculated by the Vieillard et al.model[63] (blue and red lines, respectively) agrees well with the experimental data acquired by [15, 16] in high relative humidity.
At low relative humidity, the uncertainty appears very important between the experimental desorption data and the desorption curve from the model in [63] (3 kJ/mol for integral free energy, Fig C) due to the analytical limits and mathematical constraints.
The theoretical equilibrium (black line) suggests that the hydration of a Na-SWy-1 begins at only R.H.= 0.15 (Figure 7A), which correlates well with the experimental adsorption but not with the desorption. The integral Gibbs free energy of hydration (figure 7B and 7C) and the Gibbs free energy of the interlayer water (Figure 7D) of the theoretical equilibrium between the water and Na-Smectite (black line) are plotted and correspond to the average values of calculated adsorption-desorption isotherms. The theoretical curve of equilibrium between the water and Na-smectite provided by Ransom &Helgeson [66] displays a small number of moles of the interlayer water close to saturation, while those of Vidal &Dubacq[68] reproduce this stepwise behaviour fairly well because it assumes three solid solutions with 3 end-members (0.7 H2O, 2 H2O, 4.5 H2O). However, it does not match the behaviour of water adsorption versus relative humidity, which is not a step function. The advantage of this approach is that it allows reproducing the observed stepwise evolution of the smectite volume and water content with varying T and relative humidity. At low relative humidity, as the hydration of a Na-SWy-1 begins at only R.H.= 0.15, the computations from [68] and [66] (green and yellow dotted lines) do not match the observed isotherms because there is a strong hydration in the RH= 0.0- 0.18 range. During the interval of R.H.=0.0-0.2, the adsorption of water molecules occurs predominantly on the external surface of tactoids (basal external faces and edges of tactoids). This explains why we observe a very negative integral free energy in the low relative humidity domain for these two models (green dotted line and in a less extent, yellow dotted lines). The necessity to take into account only the hydration water, sensu-stricto, is justified. This procedure has been incompletely performed by Ransom &Helgeson [66] with the external surface of a kaolinite to estimate the amount of surface covering water, while Vidal &Dubacq [68] made no correction on the gravimetric waters. At high relative humidity, Vidal &Dubacq [68] proposed a third step of hydration, with the number of water molecules increasing up to 7 moles per O10(OH)2. All of the experimental isotherms performed by [15, 16] exhibit an increase in the water contents beyond RH = 0.9, identified as osmotic water. The osmotic swelling of the sodium montmorillonite corresponds to an iso-enthalpic effect, with the heat of adsorption being constant. The theoretical equilibrium between water and Na-SWy-1 (black line) matches the experimental dehydration near saturation.
The cationic exchange and hydration reactions are intimately related, and the cationic exchange reactions not only modify the interlayer composition but also imply changes in the interlayer water content. These changes can be quite significant and can be evaluated using the Vieillard et al. model [63], which provides a theoretical number of moles of interlayer water and integral thermodynamic properties (H, S and G) for the SWy-1 montmorillonites. Thus, the cationic exchange reactions may depend on an external parameter, such as the relative humidity.
7. Conclusions and perspectives
This chapter demonstrated some useful relationships in the prediction of thermodynamic entities. Some important areas are still lacking and deserve further study.
Among the anhydrous and hydrated salts, the relationships between the entropy and molar volume may exist and will improve the prediction of the entropy of hydration. The function of the average heat capacities for the hydration water is lacking and will help in characterising the behaviour of the crystalline water versus temperature.
In the zeolite field, the relationships among the molar volume, water content and relative humidity may exist within zeolites families with a reversibility in the hydration-dehydration processes. These relationships will contribute to a better understanding of the behaviour of partial molar enthalpy versus the degree of saturation or versus the relative humidity.
In the clay Minerals, three following recommendations are needed: 1) to dissociate the hydration water from the gravimetric water; 2) to measure the heat of hydration among the dioctahedral and trioctahedral clays; and 3) to find a relationship between the hysteresis and the entropy of the hydration-dehydration by the molecular modellings. With these three aims, the knowledge of mechanisms of the hydration within clay minerals will advance our understanding of cationic exchange in soils under various physical and chemical constraints.
Acknowledgement
Financial support from the French National Radioactive Waste Management Agency (ANDRA), from the French Geological Survey(BRGM) and from the national council for scientific Research (CNRS) is gratefully acknowledged. Special thanks to Ph. Blanc, H. Gailhanou and Cl. Fialips for their effective and decisive contribution to this document.
References
- 1.
Reeuwijk van LP 1974 The thermal dehydration of natural zeolites In: H. V, B.V. Z, editors. Wageningen1 88 - 2.
Tardy Y. Mercury L. Roquin C. Vieillard P. 1999 Le concept d’eau ice-like: hydratation-deshydratation des sels, hydroxydes, zéolites, argiles et matières organiques vivantes ou inertes Compt. Rendus Académie Science Paris329 377 388 - 3.
Mercury L. Vieillard P. Tardy Y. 2001 Thermodynamics of Icepolymorphs and "Ice-like" water in hydrates and hydroxides. Appl. Geochem.16 161 181 - 4.
Johnson GK, Flotow HE, O’Hare PAG, Wise WS 1982 Thermodynamic studies of zeolites : analcime and dehydrated analcim e. Amer. Mineral.67 736 748 - 5.
Johnson GK, Flotow HE, O’Hare PAG 1983 Thermodynamic studies of zeolites:natrolite mesolite and scolecite. Amer. Mineral.68 1137 1145 - 6.
Johnson GK, Tasker IR, Flotow HE, O’Hare PAG 1992 Thermodynamic studies of mordenite, dehydrated mordenite and gibbsite. Am. Mineral.77 85 93 - 7.
Gailhanou H. Blanc P. Rogez J. Mikaelian G. Kawaji H. Olives J. et al. 2012 Thermodynamic properties of illite IMt-2, smectite MX-80 and beidellite SBld-1 by calorimetric methods: Enthalpies of formation, heat capacities, entropies and Gibbs free energies of formation.. Am Mineral. (submitted). - 8.
Kiseleva I. Navrotsky A. Belitskii I. A. BA Fursenko 1996 Thermochemistry and phase equilibria in calcium zeolites Am. Mineral.81 658 667 - 9.
Sun P. Deore S. Navrotsky A. 2007 Enthalpy of formation and dehydration of lithium and sodium zeolite beta Microporous Mesoporous Mat.98 29 40 - 10.
Sun P. Navrotsky A. 2008 Enthalpy of formation and dehydration of alkaline earth cation exchanged zeolite beta Microporous Mesoporous Mat.109 147 155 - 11.
Yang S. Y. Navrotsky A. 2000 Energetics of formation and hydration of ion-exchanged zeolite Y Microporous Mesoporous Materials37 175 186 - 12.
Shim S. H. Navrotsky A. Gaffney T. R. Macdougall J. E. 1999 Chabazite: Energetics of hydration, enthalpy of formation, and effect of cations on stability. Amer. Mineral.84 1870 1882 - 13.
Gailhanou H. van Miltenburg J. C. Rogez J. Olives J. Amouric M. Gaucher E. C. et al. 2007 Thermodynamic properties of anhydrous smectite MX-80, illite IMt-2 and mixed-layer illite-smectite ISCz-1 as determined by calorimetric methods. Part I: Heat capacities, heat contents and entropi es. Geochim.Cosmochim. Acta71 5463 5473 - 14.
Barrer RM, Cram PJ 1971 Heats of immersion of outgassed and ion-exchanged zeolites. In: L.B. FEMS, editor. Molecular sieves zeolites. Washington D.C.: American Chemical Society.105 131 - 15.
Cases J. M. Bérend I. Besson G. François M. Uriot J. P. Thomas F. et al. 1992 Mechanism of adsorptionand desorption of water vapor by homoionic montmorillonite. I.The sodium-exchanged form. Langmuir8 2730 2739 - 16.
Bérend I. Cases J. M. François M. Uriot J. P. Michot L. Masion A. et al. 1995 Mechanism of adsorption and desorptionof water vaporby homoionic montmorillonites:2. The Li+, Na+, K+, Rb+ and Cs+ exchanged forms. Clays Clay Minerals43 324 336 - 17.
Cases J. M. Bérend I. François M. Uriot J. P. Michot L. Thomas F. 1997 Mechanism of adsorption and desorption of water vapor by homoionic montmorillonite: 3. the Mg2+, Ca2+,Sr2+ and Ba2+ exchanged forms. Clays Clay Minerals45 8 22 - 18.
Keren R. Shainberg I. 1975 Water vapor isotherms and heat of immersion of Na/Ca-Montmorillonite systems. I Homoionic clay. Clays Clay Minerals23 193 - 19.
Keren R. Shainberg I. 1979 Water vapor isotherms and heat of immersion of Na/Ca-Montmorillonite systems- 2. Mixed systems. Clays Clay Minerals27 145 - 20.
Dios Cancela. G. Huertas F. J. Romero Taboada. E. Sánchez-Rasero F. Hernández Laguna. A. 1997 Adsorption of Water Vapor by Homoionic Montmorillonites. Heats of Adsorption and Desorption J. Colloid Interface Sci.185 343 354 - 21.
van Olphen H. 1965 Thermodynamics of interlayer adsorption of water in clays. I.--Sodium vermiculite. J. Coll. Sci.20 822 837 - 22.
Carey JW, Bish DL 1996 Equilibrium in the clinoptilolite- H2O system. Ame r. Mineral.81 952 962 - 23.
Fialips CI, Carey JW, Bish DL 2005 Hydration-dehydration behavior and thermodynamics of chabazite Geochim. Cosmochim. Acta69 2293 2308 - 24.
Koster van Groos. A. F. Guggenheim S. 1984 The effect of pressure on the dehydration reaction of interlayer water in Na-montmorillonite (SWy-1). Amer. Mineral.69 872 879 - 25.
Wu-C T. Bassett W. A. Huang-L W. Guggenheim S. Koster van Groos. A. F. 1997 Montmorillonite under high H 2 O pressures; stability of hydrate phases, rehydration hysteresis, and the effect of interlayer cations. Amer. Mineral.82 69 78 - 26.
Koster v. Groos A. F. Guggenheim S. 1986 Dehydration of K exchanged montmorillonite at elevated temperatures and pressures Clays Clay Minerals34 281 286 - 27.
Petrova N. Mizota T. Fujiwara K. 2001 Hydration heats of zeolites for evaluation of heat exchangers J. Therm. Anal. Calorim.64 157 166 - 28.
Hill TL 1949 Statistical mechanics of adsorption V. Thermodynamics and heat of adsorption. J. Chem. Phys.17 520 535 - 29.
Hill TL 1950 Statistical Mechanics of Adsorption. IX. Adsorption Thermodynamics and Solution Thermodynamics. J. Chem. Phys.s18 246 256 - 30.
Keren R. Shainberg I. 1980 Water vapor isotherms and heat of immersion of Na/Ca-Montmorillonite systems- 3. Thermodynamics. Clays Clay Minerals28 204 210 - 31.
Hall PL, Astill DM 1989 Adsorption of water by homoionic exchange forms of Wyoming montmorillonite (SWy-1) Clays Clay Minerals37 355 363 - 32.
Valueva GP, Goryainov SV 1992 Chabazite during dehydration: thermochemical and Raman spectroscopy study. Russian Geologica Geophys.33 68 75 - 33.
Xu W. Johnston C. T. Parker P. Agnew S. F. 2000 Infrared study of water sorption on Na-, Li-, Ca- and Mg-exchanged(SWy-1 AND SAz-1) montmorillonite. Clays Clay Minerals48 120 131 - 34.
Fu MH, Zhang ZZ, Low PF 1990 Changes in the properties of a montmorillonite-water system during the adsorption and desorption of water: hysteresis. Clays Clay Minerals38 485 492 - 35.
Mercury L. Vieillard P. Tardy Y. 2001 Thermodynamics of Icepolymorphs and "Ice-like" water in hydrates and hydroxides. Appl. Geochem.16 161 181 - 36.
Cox JD, Wagman DD, Medvedev VA 1989 CODATA Key values for thermodynamics New York: Hemisphere Publishing Corporation. 271 p. - 37.
Tardy Y. Mercury L. Roquin C. Vieillard P. 1999 Le concept d’eau ice-like: hydratation-deshydratation des sels, hydroxydes, zéolites, argiles et matières organiques vivantes ou inertes Compt. Rendus Académie Science Paris329 377 388 - 38.
Chipera SJ, Apps JA 2001 Geochemical stability ofnatural zeolites. In: Bish DLM, D.W., editor. Natural Z eolites:Occurence, properties Applications. Blacksburg (Va)117 161 - 39.
Glasser L. Jenkins H. D. B. 2007 The thermodynamic solvate difference rule: Solvation parameters and their use in interpretation of the role of bound solvent in condensed-phase solvates. Inorg. Chem.46 9768 9778 - 40.
Sidorov YI 1988 Estimating silicate standard entropies. Geochem. Intern.80 85 - 41.
Robinson GR, Haas JL 1983 Heat capacity, relative enthalpy and calorimetric entropy of silicate minerals : an empirical method of prediction. Amer. Mineral.68 541 443 - 42.
Moiseev G. K. Sestak J. 1995 Some calculations methods for estimation of thermodynamical and thermochemical properties of inorganic compounds Prog Cryst Growth Charact.30 23 81 - 43.
Burylev BP 1988 Thermodynamics of crystal hydrates of rare-earth metal chlorides Sov. Radiochem. 29):653 EOF 655 EOF - 44.
Burylev BP, Kritskaya EB, Moisov LP, Kostenko NB 1995 Calculation of the standard enthalpies of formation of hydrous sodium salts Inorg. Mater.31 727 729 - 45.
Van Hinsberg VJ, Vriend SP, Schumacher JC 2005 A new method to calculate end-member thermodynamic properties of minerals from their constituent polyhedra II: heat capacity, compressibility and thermal expansion. J. Metamorph Geol.23 681 - 46.
Van Hinsberg VJ, Vriend SP, Schumacher JC 2005 A new method to calculate end-member thermodynamic properties of minerals from their constituent polyhedra I: enthalpy, entropy and molar volum e. J. Metamorph. Geol.23 165 179 - 47.
Chermak JA, Rimstidt JD (1989 ) Estimating the thermodynamic properties (and) of silicate minerals at 298 K from the sum of polyhedral contributions. Amer. Mineral.74 1023 1031 . - 48.
Li J. Li B. Gao S. 2000 Calculation of thermodynamic properties of hydrated borates by group contribution method 27 342 346 - 49.
Chen FR, Ewing RC, Clark SB 1999 The Gibbs free energies and enthalpies of formation of U6+ phases: An empirical method of prediction Amer. Mineral.84 650 664 - 50.
Vieillard P. Jenkins H. D. B. 1986 Empirical relationships for estimation of enthalpies of formation of simples hydrates. Part I Hydrates of alkali- metal cations, of hydrogen and of monovalent cations. J. Chem. Res.:444 445 - 51.
Vieillard P. Jenkins H. D. B. 1986 Empirical relationships for estimation of enthalpies of formation of simples hydrates. Part 2.Hydrates of alkaline-earth metalcations. J. Chem. Res.:446 447 - 52.
Vieillard P. Jenkins H. D. B. 1986 Empirical relationships for estimation of enthalpies of formation of simples hydrates. Part 3.Hydrates of transition metalcations (Cr2+,Fe2+,Co2+,Ni2+,Cu2+,Zn2+,Cd2+and UO22+). J. Chem. Res.:448 449 - 53.
Robie RA, Waldbaum DR 1968 Thermodynamic properties of minerals and related substances at 298.15°K (25°C) and one atmosphere (1.O13 bars) pressure and at higher temperatures. U. S. Geol. Surv. Bull., 1259, 256 p. - 54.
Vieillard P. Mathieu R. 2009 A predictive model for the enthalpies of hydration of zeolites Amer. Mineral.94 565 577 - 55.
Meier W. M. Olson D. H. Baerlocher C. 1996 Atlas of Zeolite Structure types: 4th revised Edn. Zeolites17 1 230 - 56.
Meier WM, Olson DH 1971 Zeolites Frameworks In: Flanigen EM, Sand LB, editors. Molecular Sieve Zeolites155 170 - 57.
Barrer RM 1982 Hydrothermal chemistry of Zeolites Press A, editor. London New York: Harcurt Brace Jovanovich.1 360 p. - 58.
Carey JW 1995 A thermodynamic formulation of hydrous cordierite Contrib. Miner. Petrol.119 155 165 - 59.
Armbruster T. 1993 Dehydration mechanism of clinoptilolite and heulandite: Single-crystal X-ray-study of Na-poor and K-Mg-richclinoptilolite at 100K. Amer. Mineral.78 260 264 - 60.
Bish DL, Carey JW 2001 Thermal behavior ofnatural zeolites. In: D.W. BDLM, editor. Natural zeolit es:occurrence, properties Applications. Blacksburg: Mineralogical Society of America.403 452 - 61.
Mathieu R. Vieillard P. 2010 A predictive model for the enthalpies of formation ofzeolites.. Microporous Mesoporous Mat.132 335 351 - 62.
Carey JW, Bish DL 1997 Calorimetric measurement of the enthalpy of hydration of clinoptilolite Clays Clay Minerals45 826 833 - 63.
Vieillard P. Blanc P. Fialips C. I. Gailhanou H. Gaboreau S. 2011 Hydration thermodynamics of the SWy-1 montmorillonite saturated with alkali and alkaline-earth cations: a predictive model Geochim.Cosmochim. Acta75 5664 5685 - 64.
Fripiat J. Cases J. Francois M. Letellier M. 1982 Thermodynamic and microdynamic behavior of water in clay suspensions and gels.J. Colloid Interface Sci.89 378 400 - 65.
Koster van Groos. A. F. Guggenheim S. 1987 Dehydration of a Ca- and a Mg-exchanged montmorillonite (SWy-1) at elevated pressures Amer. Mineral.72 292 298 - 66.
Ransom B. Helgeson H. C. 1994 A Chemical and Thermodynamic Model of Aluminous Dioctahedral-2/1 Layer Clay Minerals in Diagenetic Processes- Regular Solution Representation of Interlayer Dehydration in Smectite. Amer. J. Sci.294 449 484 - 67.
Ransom B. H. H. C. 1994 Estimation of the standard molal heat capacities, entropies, and volumes of 2:1 clay mineral s. Geochim. Cosmochim. Acta58 4537 4547 - 68.
Vidal O. Dubacq B. 2009 Thermodynamic modelling of clay dehydration, stability and compositional evolution with temperature, pressure and H2O activity Geochim.Cosmochim. Acta73 6544 6564 - 69.
Dubacq B. Vidal O. De Andrade V. 2010 Dehydration of dioctahedral aluminous phyllosilicates: thermodynamic modelling and implications for thermobarometric estimates Contri. Miner. Petrol. 159: 159. - 70.
Helgeson HC, Delany JM, Nesbitt HW, Bird DK 1978 Summary and critique of the thermodynamic properties of the rock-forming mine rals. Am. J. Sci.278 A: 1-229. - 71.
Johnson G. K. Tasker I. R. Jurgens R. O’Hare P. A. G. 1991 Thermodynamic studies of Zeolites-Clinoptilolite. J.Chem. Thermodyn.23 475 484 - 72.
Vieillard P. 2010 A predictive model for the entropies and heat capacities ofzeolites. Eur. J. Mineral.22 823 836 - 73.
Marcus Y. 1994 A simple empirical model describing the thermodynamics of hydration of ions of widely varying charges, sizes, and shape s. Biophys. Chem.51 111 127 - 74.
Berman RG, Brown TH 1985 Heat capacity of minerals in the system Na2O-K2O-CaO-MgO-FeO-Fe2O3-Al2O3-SiO2-TiO2-H2O-CO2, representation, estimation and high temperature extrapolation. Contrib. Miner. Petrol.89 168 183 - 75.
Neuhoff P. S. Wang J. 2007 Heat capacity of hydration. Amer. Mine ral.92 1358 1367 - 76.
Fyfe W. S. Turner F. J. Verhoogen J. Metamorphic reactions and metamorphic facies. In: Memoirs GSoA, editor.1958 253 p. - 77.
Cruciani G. 2006 Zeolites uponheating: Factors governing their thermal stability and structural changes. J. Phys. Chem. Solids67 1973 1994 - 78.
Lassin A. Duplay J. Touret O. Tardy Y. 2000 Thermodynamic treatment of hydrates. Comptes Rendus Acad. Sci. Paris SER II A330 533 540 - 79.
Barshad I. 1960 Thermodynamics of water adsorption and desorption on montmorillonite Clays Clay Minerals:84 101