Dehydration Pathways of Gypsum and the Rehydration Mechanism of Soluble Anhydrite γ-CaSO4.

The dehydration products of gypsum under different temperature and water vapor pressure were investigated by thermodynamic theory. Additionally, the rehydration mechanism of soluble anhydrite was also studied by Monte Carlo (MC) simulations. The thermodynamic calculation results reveal that the dehydration mechanism of gypsum significantly depended on ambient temperature and water vapor pressure. In the high-temperature and low water vapor pressure region, gypsum dehydrates to form γ-CaSO4 in a single-step process (CaSO4·2H2O → γ-CaSO4); with increasing water vapor pressure, gypsum undergoes the CaSO4·2H2O → γ-CaSO4 → β-CaSO4·0.5H2O reaction path and as water vapor pressure increases further, the occurrence of a two-step conversion path CaSO4·2H2O → β-CaSO4·0.5H2O → γ-CaSO4 was observed. It was also found that gypsum is stable in the low-temperature and high water vapor pressure region and does not dehydrate to form any calcium sulfate hemihydrate. Finally, the rehydration mechanism of soluble anhydrite was studied by MC simulations. The simulation results are in agreement with the experimental data and support the finding that γ-CaSO4 rehydration forms CaSO4·0.67H2O in high relative humidity. Another important result revealed by the MC simulation is that γ-CaSO4 has an extraordinary ability to capture water molecules from an extremely dry atmosphere, which is very useful in some fields, such as in drying processes and even for extracting liquid water from extremely dry atmosphere.

Introduction

Gypsum is one of the most important minerals on earth, and its dehydration product, plaster of paris, is mainly used as a building material. Furthermore, there are abundant deposits of gypsum mineral in nature; moreover, recent studies have indicated that Mars also has an abundance of gypsum mineral as well as other mineral calcium sulfate phases (β-CaSO4·0.5H2O).[1−6] Furthermore, both the phosphate industry and thermal power plants generate large amounts of byproduct gypsum (phosphogypsum, flue gas desulfurization gypsum, etc.). Extensive efforts have been made to studying the process of gypsum dehydration. However, the dehydration mechanisms of gypsum that have been reported in previous studies still remain confusing and even contradictory. Some researchers have argued that gypsum undergoes a two-stage dehydration process, where β-CaSO4·0.5H2O is formed first and then γ-CaSO4 is obtained by further dehydration of β-CaSO4·0.5H2O.[7−10] McAdie[11] studied the gypsum dehydration process at 124.3 °C under different water vapor partial pressures. Their experimental results reveal that gypsum dehydration proceeds through only a single CaSO4·2H2O → γ-CaSO4 step when the ambient water vapor pressure is less than 26664 Pa; however, a two-step process of CaSO4·2H2O → β-CaSO4·0.5H2O → γ-CaSO4 is observed if the practical water vapor pressure is greater than 40 130 Pa. Badens et al.[12] investigated the dehydration process of gypsum using a combination of controlled transformation rate thermal analysis and Laue diffraction, concluding that there is only one dehydration step from gypsum to γ-CaSO4 at 500 Pa or below; whereas β-CaSO4·0.5H2O is an intermediate product when the practical water vapor pressure reaches 900 Pa. Ball and Norwood[13] have argued that γ-CaSO4 is directly obtained during gypsum dehydration at a water vapor partial pressure range of 1.33 × 10–2 to 6000 Pa and at a temperature below 115 °C. Lou et al.[14] studied the dehydration mechanisms of flue gas desulfurization gypsums and pointed out that gypsum dehydration proceeds through a one-step process at a negligible partial water vapor pressure and below 100 °C, while two-step processes are observed at an autogenous water vapor pressure and a temperature of approximately 100 °C. Abriel et al.[15] studied the dehydration mechanism of gypsum using neutron and X-ray diffraction (XRD) and proposed a novel gypsum dehydration pathway of CaSO4·2H2O → CaSO4·0.75H2O → γ-CaSO4. Prasad et al.[16] and Carbone et al.[17] investigated the dehydration mechanism of gypsum using in situ micro-Raman and energy-dispersive XRD, respectively, and concluded that γ-CaSO4 was first obtained in the gypsum dehydration process, and then the formed γ-CaSO4 was transformed into β-CaSO4·0.5H2O by a rehydration reaction in which 0.5H2O water molecules reentered into the crystal structure of γ-CaSO4.

To date, much effort has been made to researching the dehydration pathways of gypsum; however, it is still not well understood. In this study, a theoretical thermodynamics approach was employed to elucidate the dehydration pathways of gypsum.

Theoretical and Simulation Methods

Monte Carlo Simulations

The number of sorbates is allowed to vary in the grand canonical ensemble (μVT). In view of this, adsorption isotherms were calculated using grand canonical Monte Carlo (GCMC) simulations with the Metropolis algorithm.[18] The GCMC simulations were carried out using periodic boundary conditions of 3 × 3 × 3 unit cells of γ-CaSO4.

The water molecules used in the simulation calculations are rigid molecules. The force field plays a key role in MC simulations. In this work, the DREIDING force field[19] was employed to model all interactions between water molecules and the γ-CaSO4 lattice. The theoretical formulae of the nonbonded interactions in the DREIDING force field are represented by the 12-6 LJ potential and Coulombic termswhere r and σ are the actual and reference distances between atoms i and j, respectively; εo is the permittivity of free space (εo = 8.8543 × 10–12 C2 J–1 m–1); ε is the potential well-depth; and q and q are the value of the charge on atoms i and j. The LJ interactions between unlike atoms are treated with the sixth-order mixing rule.[20]

The atom-based summation method with a cutoff distance of 0.15 nm was employed to compute both the Coulombic interactions and the van der Waals interactions between the water molecules, the calcium sulfate framework, and the hydrogen bond terms in the system (spline width: 0.1 nm; buffer width: 0.05 nm). The MC simulations were performed at 215 and 298 K. The coupling to the heating bath was carried out using a Nose thermostat.

Thermodynamic Data for CaSO4·2H2O, β-CaSO4·0.5H2O, and H2O(g)

Thermodynamics is a rigorous theory and is widely used in chemistry, materials science, metallurgy, and other fields. The large number of thermodynamic calculations used in this work is very helpful for determining the gypsum dehydration pathways.

The standard Gibbs energy of formation values of CaSO4·2H2O, β-CaSO4·0.5H2O, γ-CaSO4, and H2O(g) can be obtained from the literature;[21,22] these thermodynamic data are crucial for calculating the phase equilibrium of the CaSO4–H2O system. Thermodynamic data are generally tabulated in the literature at the interval of 100 K, which is inconvenient for thermodynamic calculations. Therefore, it was necessary to fit the values of the standard Gibbs energy of formation of CaSO4·2H2O, β-CaSO4·0.5H2O, and H2O(g) using polynomial functions of the temperature; the numerical calculations were performed by MATLAB, T represents the numerical value of Kelvin temperature, and it was found that the results could be represented by the following equations

Correction of the Gibbs Free Energy of Formation of γ-CaSO4

The water molecules in the air can easily enter into the γ-CaSO4 lattice because of its honeycomb structure. Because of this, pure γ-CaSO4 without a trace of crystal water is difficult to obtain. Therefore, the value of the Gibbs free energy of formation of γ-CaSO4 tabulated in the literature is not sufficiently accurate. To obtain exact thermodynamic data, it is necessary to make a correction for the Gibbs free energy of formation of γ-CaSO4. Kevin[23] studied the effect of relative humidity on the number of combined water molecules in the calcium sulfate subhydrate unit cell at a temperature of 298 K, and the experimental result indicates that the total number of combined water is strictly equal to 0.5 when the relative humidity is maintained at 0.1%. Additionally, CaSO4·2H2O began to dehydrate when it was heated to 459 K under a water vapor partial pressure of 1 atm. On the basis of these experimental results, the numerical values of the Gibbs free energy of formation of γ-CaSO4 at 298 and 459 K can be calculated using eq , obtaining −1311.74 and −1250.19 kJ·mol–1, respectively.

The process of γ-CaSO4 transformation into β-CaSO4·0.5H2O by absorbing the water vapor in the air can be expressed by the following reaction

To calculate the standard Gibbs energy of formation of γ-CaSO4, we write

To obtain the accurate expression of the Gibbs free energy of formation of γ-CaSO4 at the temperature of interest, eq can be transformed into the following formwhere the symbol a and the symbol b in eq are the two undetermined parameters. By substituting the values of the standard Gibbs energy of formation of γ-CaSO4 at 298 and 459 K for parameters a and b successively, a matrix equation was derived.

The numerical values of parameters a and b were obtained by solving the above matrix equation, and the calculation reads

By inserting the numerical values of a and b into eq , the accurate expression for the Gibbs free energy of formation of γ-CaSO4 was rewritten as follows

Gibbs Free Energy of Formation of CaSO4·nH2O

The framework of γ-CaSO4 has a honeycomb structure;[24] therefore, γ-CaSO4 quite easily rehydrates to form calcium sulfate subhydrate (CaSO4·nH2O)

Karni argued that the number of combined water in CaSO4·nH2O can range from 0 to 0.67.[25]

The Gibbs free energies of CaSO4·2H2O, β-CaSO4·0.5H2O, and γ-CaSO4 at different temperatures can be calculated using eqs , 6 and 13, and the calculation results are tabulated in Table .

Table 1

Standard Molar Gibbs Free Energy of Formation of γ-CaSO4, β-CaSO4·0.5H2O, and CaSO4·2H2O at Temperatures Ranging from 300 to 400 K; Herein T Is the Unit of Kelvin Temperature

	the standard molar Gibbs free energy of formation (kJ·mol–1)
T (K)	CaSO4(γ)	CaSO4·0.5H2O(β)	CaSO4·2H2O
300	–1310.98	–1435.10	–1795.72
320	–1303.45	–1425.77	–1780.59
340	–1295.87	–1416.44	–1765.45
360	–1288.26	–1407.12	–1750.32
380	–1280.61	–1397.80	–1735.19
400	–1272.94	–1388.42	–1720.01
420	–1265.24	–1379.02	–1704.80
440	–1257.52	–1369.63	–1689.60
460	–1249.79	–1360.25	–1674.42
480	–1242.03	–1350.87	–1659.25
500	–1234.27	–1341.51	–1644.10
520	–1226.50	–1332.18	–1628.98
540	–1218.72	–1322.86	–1613.89
560	–1210.95	–1313.58	–1598.83
580	–1203.17	–1304.32	–1583.81
600	–1195.40	–1295.09	–1568.82

The standard molar Gibbs free energy of formation of CaSO4·nH2O is not available in literature studies. Valero[26] proposed an approximation method and provided a mathematic expression to calculate the thermodynamic properties of the hydrated substance, as in eq .where and are the standard molar Gibbs free energies of formation of γ-CaSO4 and H2O, respectively; ΔGhydr,Ao is the standard molar hydration Gibbs free energy of CaSO4; and n is the total number of the water molecules in the CaSO4·nH2O phase.

While the above formula is accurate and its associated deviation rarely exceeds ±2%, it still does not meet the requirements for the exact thermodynamic calculation in this work. Expression (15) is only a first-order linear function of the independent variable n, and consequently, its precision is limited. The values presented in Table indicate that the standard molar Gibbs free energy of formation of the CaSO4·nH2O phase depends on the two independent variables, namely, the temperature (K) and total water content (n). This implies that nonlinear multiple regression is suitable for evaluating the standard molar hydration Gibbs free energy of the CaSO4·nH2O phase. Therefore, the following polynomial for the CaSO4·nH2O phase was employed (Figure )where a, b, c, d, e, f, and g are all underdetermined parameters. MATLAB was used to fit the nonlinear function, given by eq , to the data presented in Table , and the calculation results indicate that the values of coefficients a, b, c, d, e, f, and n are −1426.73, 3.8422 × 10–1, 1.6603 × 10–6, −292.72, 2.1002 × 10–1, 1.4389 × 10–1, 5.0550 × 10–5, and −1.9774 × 10–8, respectively. Inserting these values into eq yields

Figure 1

Standard Gibbs energy of formation of CaSO4·nH2O as a function of temperature (T) and combined water content (n).

Results and Discussion

Thermodynamic Analysis of the Pathway of Gypsum Dehydration

Each of the below three chemical reactions may be spontaneous when gypsum is heated in ambient condition. However, the question of which dehydration reaction of gypsum will occur in practice requires further analysis of the thermodynamic calculations and the experimental results.

The standard Gibbs energy for a chemical reaction is the difference in standard molar Gibbs energies of the products and reactants in their standard states; it is easy to obtain the standard Gibbs energy of reaction by using the appropriate combination

When a system is in equilibrium, its standard Gibbs energy of reaction is equal to zero, that is,

Substituting eqs into 21 yields

By applying the above-mentioned formula 23 to reactions 18–20 successively, we obtain

By inserting the polynomials 4, 6, 7, and 9 into eqs –26 separately and by simplifying the result, we obtain the following three expressionswhere PH is the equilibrium water vapor pressure of the reaction for the transformation of CaSO4·2H2O into β-CaSO4·0.5H2O, PH represents the dissociation pressure of β-CaSO4·0.5H2O dehydrated to form γ-CaSO4, and PH naturally denotes the equilibrium water vapor pressure of the transformation of β-CaSO4·0.5H2O into γ-CaSO4.

To show the results of thermodynamic calculations more clearly, expressions 27–29 are simultaneously plotted in Figure .

Figure 2

Dehydration boundaries of the gypsum–H2O system in the range of 300–460 K. The symbols represent the experimental data of Kelley:[27] open circles and diamond denote the water vapor partial pressure of gypsum–hemihydrate and hemihydrate–soluble anhydrite equilibrium, respectively. Symbol A is the intersection of red, green, and blue curves and the axis of ordinates, B, C, and D, are the intersections of red, green, and blue curves and the horizontal line in Figure , respectively.

Three curves of the equilibrium water vapor pressure plotted versus the changes in temperature divide Figure into four parts. It is easy to conclude that CaSO4·2H2O is stable and does not dehydrate to form β-CaSO4·0.5H2O or γ-CaSO4 when the temperature and water vapor partial pressure are located in the zone above curve AB. With the increase of temperature, CaSO4·2H2O will partially lose its combined water and produce β-CaSO4·0.5H2O. If the temperature and water vapor pressure increase further, that is, if the coordinate point defined by the two values of both the temperature and water vapor pressure is in the ACD zone, CaSO4·2H2O first dehydrates to form γ-CaSO4 and then the formed γ-CaSO4 absorbs the water molecules in the autogenous or ambient atmosphere. Consequently, the water molecules reenter the γ-CaSO4 framework to generate β-CaSO4·0.5H2O. In the region below curve AD, both β-CaSO4·0.5H2O and γ-CaSO4 are thermodynamically unfavorable; hence, gypsum dehydrates to directly form γ-CaSO4 in a single-step process (CaSO4·2H2O → γ-CaSO4).

The open circles and diamond denote the experimental water vapor partial pressure of gypsum–hemihydrate and hemihydrate–soluble anhydrite equilibrium, respectively. It is clear that the experimental results agree well with the result of the thermodynamic calculations.

Thermodynamic Analysis for the Transformation of Gypsum into the CaSO4·nH2O Phase

Over the past decades, many studies have proposed the existence of various subhydrates with a general chemical formula of CaSO4·nH2O, where the numerical value of n ranges from 0 to 0.67.[25,28] If the dehydration product CaSO4·nH2O occurs upon the heating of gypsum, then the dehydration reaction of gypsum can be expressed as the following reaction

Considering that reaction (30) is at equilibrium if the total difference in the Gibbs free energy is equal to zero, that is,

By inserting (4), (7), and (17) into (31), the expression is simplified to

Figure shows an overview of the effect of the temperature and water vapor pressure on the combined water number n in the CaSO4·nH2O phase formed by the dehydration of gypsum. In the higher relative humidity and lower temperature zone, the thermodynamic calculation results favor the occurrence of the CaSO4·nH2O (n > 0.5) phase and the combined water number n can approach its maximum of 0.67 because of the effect of the steric hindrances associated with the H2O–H2O bond distance in the channel of the γ-CaSO4 lattice.[29] In fact, the occurrence of the CaSO4·0.67H2O phase has been confirmed by the in situ XRD, and the initial dehydration product of gypsum was the CaSO4·0.67H2O phase.[1]

Figure 3

(a) Surfaces of the equilibrium water vapor pressure calculated by eq and of the saturated vapor pressure of water. (b) Projections of the intersection of different relative humidity water vapor surfaces and the equilibrium water vapor surface obtained from eq .

If the ambient temperature is low and the relative humidity is high, gypsum is stable and does not decompose to form any calcium sulfate hemihydrate. Furthermore, gypsum is thermodynamically unstable when the ambient temperature and relative humidity are high.

MC Simulation of Adsorption Water Vapor in the γ-CaSO4 Lattice

The γ-CaSO4 lattice consists of Ca2+ ions and a SO42– tetrahedron, and the alternating Ca2+ and SO42– ions in chains −Ca–SO4–Ca–SO4– form straight chains running along the [001] direction[30,31] such that these chains present a periodic arrangement and show a honeycomb structure. The faveolate voids appear to give the γ-CaSO4 framework the ability to absorb water molecules from the air, forming a CaSO4·nH2O phase. In fact, the study of the adsorption phenomenon has a significant benefit for the manufacturing of plaster of paris and for obtaining the water vapor content in very dry areas, such as the desert or even Mars (Figure ).

Figure 4

Projection of the γ-CaSO4 lattice along the [001] vector, illustrating that the channels consist of six chains of alternating Ca2+ and SO42– perpendicular to the plane of the paper.

Figure shows the adsorption isotherms of water in the γ-CaSO4 framework, along with the experimental data. It is clear that the MC simulation calculations agree well with the experimental results;[28,29] therefore, the relevant parameter setting employed in the simulation calculation processes is a suitable and powerful tool for investigating and predicting the adsorption isotherms of water vapor on the γ-CaSO4 lattice at different ambient temperatures and relative humidities, especially in a very low temperature and humidity environment that is very difficult to be achieved in the laboratory.

Figure 5

(a) Cumulative H2O occupancy for the CaSO4·nH2O (0 < n < 0.67) phase from 0 to 100 RH % derived from Rietveld refinements[1] and simulation at 298 K. (b) Density maps for water vapor molecules in a γ-CaSO4 framework.

The experimental and calculated results presented in Figures and 6 indicated that γ-CaSO4 has an excellent ability to adsorb water vapor at fairly low relative humidities in the temperature range of 215–298 K. γ-CaSO4 can rehydrate to form CaSO4·0.5H2O by adsorbing water vapor from the air when the relative humidity is as low as approximately 1% at 298 K; however, the number of combined water in the γ-CaSO4 lattice approaches 0.67 when the relative humidity is more than 80% at 298 K. Additionally, the MC simulation results also reveal the conformation of the water molecules distributed in the channel of the γ-CaSO4 framework.

Figure 6

Cumulative H2O occupancy for the CaSO4·nH2O (0 < n < 0.67) phase from 0 to 0.07 kPa derived from the simulation at 215 K.

It is obvious that γ-CaSO4 has a strong adsorption ability under low water vapor pressure and at low temperature, although the amount of water adsorbed of γ-CaSO4 is less than MOF-801 (a porous metal–organic framework, Zr6O4(OH)4 (fumarate)6).[32] With further decreases in the ambient temperature, γ-CaSO4 can still capture 0.5 combined water molecules per CaSO4 unit cell at about 0.04 Pa water vapor pressure and 215 K; these numbers show clearly that it may be utilized to harvest water from the extremely dry Martian atmosphere. Because the water vapor mixing ratio and atmospheric pressure on the surface of Mars are circa 600 ppm[33] and 610 Pa, respectively,[34] it is easy to draw the conclusion that the water vapor pressure on the Martian surface is approximately equal to 0.366 Pa. The MC simulation result (Figure ) indicates that γ-CaSO4 has the ability to absorb water molecules to form CaSO4·nH2O phases from the extremely dry Martian atmosphere; the numerical value of crystal water n increases from 0 to 0.5 when the water vapor pressure ranges from 0 to 0.04 Pa at the average surface temperature of 215 K on Mars. Obviously, the water vapor pressure on Mars is far higher than the equilibrium water vapor pressure for γ-CaSO4 rehydration to transform CaSO4·0.5H2O. Thus, γ-CaSO4 has a great potential to be used as a key material to indigenously obtain water on Mars. Additionally, the structures of γ-CaSO4 and CaSO4·0.5H2O are highly similar as both crystal lattices provide honeycomb channels of 0.4 nm diameter.[35,36] As a result, the faveolate framework of γ-CaSO4 can remain almost unchanged throughout many cycles of the dehydration and water absorption processes of γ-CaSO4.

Conclusions

In this work, the dehydration pathways of gypsum and the rehydration mechanism of soluble anhydrite were mainly investigated by thermodynamic modeling and MC simulations. The dehydration pathways of gypsum are largely determined by ambient temperature and water vapor pressure. In the low-temperature and high water vapor zone above curve AB in Figure , gypsum is thermodynamically stable; in the ABC zone, CaSO4·2H2O will partially dehydrate its crystal water to form β-CaSO4·0.5H2O, and as the temperature is increased, gypsum undergoes a two-step dehydration process (CaSO4·2H2O → γ-CaSO4 → β-CaSO4·0.5H2O). In the region below curve AD, both β-CaSO4·0.5H2O and γ-CaSO4 are all thermodynamically unfavorable; therefore, gypsum dehydrates to directly form γ-CaSO4 in a single-step process (CaSO4·2H2O → γ-CaSO4). Additionally, in the processes of gypsum dehydration and γ-CaSO4 rehydration, the maximum n, which is the number of crystal water of the formed CaSO4·nH2O, approaches 0.67; furthermore, MC simulations have successfully predicted the occupation of water molecules in the γ-CaSO4 framework.

γ-CaSO4 has an extraordinary ability to capture water molecules from extremely dry atmosphere, endowing γ-CaSO4 a great potential to become a key material used to extract liquid water from very dry air. Moreover, it could also be used to industrial drying processes at room temperature in many fields because of its remarkable ability to absorb water vapor.