Thermodynamics of irreversible adsorption of water vapours by montmorillonite

Abstract

The adsorption–desorption of water vapours on swelling layer silicate is considered in the framework of the Brunauer-Emmett-Teller (BET) and Frenkel-Halsey-Hill (FHH) formalisms. The theoretical dependencies calculated with reasonable and consistent values of model parameters are shown to agree quite satisfactorily with the experimental data. Based on these equations, the description of the adsorption hysteresis related to Type III adsorption isotherms is proposed, which also yields a good reproduction of the experimentally observed values.

Introduction

Clay minerals, due to their unique adsorption and physicochemical properties, are long since and widely used as a valuable natural resource in various areas of human activity. They find diverse application in petroleum, chemical, textile, food, pharmaceutical and other industries. It is essential that clay minerals are used mostly in the form of water suspensions; therefore, the studies of hydrophilic properties of these minerals are of large theoretical and practical importance.

Of particular interest in this regard is the adsorption hysteresis effect, which is closely related to the mineral swelling, and is observed, in particular, in the montmorillonite, the clay mineral with lamellar (slit-like) pores. To the best of the authors’ knowledge, the first detailed studies of this phenomenon were made in the mid-20th century, see e.g. Mooney et al. (1952a, 1952b) and Norrish (1954). Since then, various aspects of swelling and adsorption hysteresis were discussed in a number of publications, of which the most relevant, to the authors’ opinion, are Prins (1967), Barrer (1978), Tarasevich and Ovcharenko (1980), Giese and van Oss (2002), Lagaly (2006) and Smalley (2006). However, up to now, theoretical models for the isotherms of water adsorption–desorption by hydrophilic clay minerals are quite scarce. In particular, no theoretical treatment was proposed for the calculation of adsorption hysteresis related to Type III adsorption isotherms (Brunauer et al., 1967; Gregg and Sing, 1982; Adamson and Gast, 1997).

In the proposed publication, we present an experimental study of water adsorption–desorption isotherms measured at the typical hydrophilic layered clay mineral, the Oglanlyn montmorillonite, and an attempt of a theoretical description of these isotherms to derive a model for the hysteresis loop.

Materials and methods

Montmorillonite belongs to the class of lamellar (layered) silicates with expanding structural cells and possesses a porous structure. The primary porosity of the mineral is formed by the thin slit-like micropores (Barrer, 1978; Tarasevich and Ovcharenko, 1980), which during the adsorption can accommodate up to four layers of water molecules. The hysteresis related to the adsorption–desorption of polar molecules in montmorillonite occurs mainly due to the intercrystalline swelling; the X-ray data show that the interplanar distance of natural calcium montmorillonite increases up to 1.67–1.77 nm, while the thickness of an elementary package (sheet) is 0.94 nm. The mineral also possesses intermediate pores of 4.5 to 5.0 nm in effective radius and secondary pores; these contribute negligibly to the adsorption of polar substances.

The chemical composition, crystal-chemical data and physicochemical properties of the montmorillonite from the Oglanlyn deposit (Turkmenistan) used in the present study were the same as described in Tarasevich and Ovcharenko (1980). The adsorption of water vapours by the samples of montmorillonite was studied using an vacuumised setup equipped with a McBain-Bakr quartz spring balance and thermostabilised at 293.0 ± 0.2 K. The samples with a mass of 0.1–0.2 g were pre-dried at 388 K during 2 hours. The evacuation using the forepump and oil diffusion pump was performed until the stabilisation of the sample mass was reached. The residual pressure (0.013 Pa) was monitored by a thermocouple vacuum ionisation gauge. The partial pressure of the gaseous sorbate was measured using a U-shaped mercury manometer. The equilibration time was 24 hours. The change in the mass of the samples and difference in the manometer levels were measured by a cathetometer; the total measurements error did not exceed ±2%.

Results and discussion

The adsorption–desorption isotherm for water vapour on the studied adsorbent is shown in Figure 1, where x is the relative adsorptive pressure, a is the adsorbed amount. It is seen that the experimental isotherms are clearly different with regard to their classification (Brunauer et al., 1967; Gregg and Sing, 1982).

Figure 1.

Adsorption (○) and desorption (•) experimental isotherms of water on Oglanlyn montmorillonite; curves, the adsorption (dashed curves A_l, A_h) and desorption (solid curves D_l, D_h) isotherms in the low (A_l, D_l) and high (A_h, D_h) relative pressure range (for details see text), and adsorbed amount values on the adsorption (▪, ♦) and desorption (□, ⋄) branches in the low (▪,□) and high (♦,⋄) relative pressure range recalculated via the adsorption hysteresis equations.

The adsorption isotherm (open circles) is a clearly expressed type III isotherm, which is characteristic for the adsorption of gases (vapours) on non-porous and macroporous solids. In the low relative pressure range, due to weak adsorbent–adsorbate interactions, the adsorbed amount is low. With the increase of the adsorptive relative pressure, the cooperative adsorption mechanism plays an increasingly significant role: the molecules already adsorbed on the surface stimulate further adsorption of molecules from the adsorptive bulk. As water molecules are capable for the formation of hydrogen bonds, the water adsorption isotherm is ‘sensitive’ to the polarisation of the adsorbent surface. In adsorption systems which exhibit type III isotherms, it is impossible to clearly distinguish between the stages of a monolayer and polylayers formation, because in this case the rigorous model which assumes the formation of close packed monolayer is inapplicable.

The desorption isotherm is shown in Figure 1 by filled circles. The desorption process in these systems requires the breakage of strong hydrogen bonds formed by the adsorbed water molecules with the active centres at the adsorbent surface during the adsorption process. Strong localisation of adsorbed molecules leads to the formation of a stable polylayer phase. In this case, the isotherm corresponds to the type II.

In this study, the attempt is made to analyse (in the first approximation) the adsorption and desorption isotherms using the BET (Brunauer et al., 1967) and FHH (Steele, 1967) formalisms.

In what follows, the subscripts a and d refer to the adsorption and desorption branch, respectively, the subscript m refers to the monolayer capacity value, and x is the relative adsorptive pressure.

It is seen from Figure 1 (dashed curve labelled A_l) that in the low relative pressure range (0.05 ≤ x < 0.6), the adsorption isotherm obeys the BET equation with C_a = 1 and a_{m, a}  = 5.7 mmol/g

$${\theta }_a^{(l)}=\frac{C_a}{(1-x+{\mathrm{xC}}_a)}\frac{x}{1-x}\equiv \frac{x}{1-x}$$

(1) where the superscript (l) refers to the low pressure range, ${\theta }_a^{(l)}=a_a/a_{m,a}$ , a and a_m,a are the adsorbed amount and monolayer capacity values, respectively, at the adsorption branch of the isotherm. The fact that C_a = 1 indicates that the adsorption isotherm in the low relative pressure range is of type III. In this range, equation (1) fits the experimental values to within the relative deviation of $\mp \sigma =9.2\%$ .

In the initial state, the adsorbent possesses a lamellar porous structure, and in the higher adsorptive pressure range, the formation of molecular associates occurs in the slit-like pores to the adsorption amount value of 1.6 × a_{m, a} (Brunauer et al., 1967; Gregg and Sing, 1982). The equation of state of molecular associates proposed by the authors earlier (Kutarov et al., 2013) reads

$${\theta }_a^{(h)}=(\frac{1}{\phi }+\frac{A_0}{A})=(\frac{1}{\phi }+\frac{\ln (1/x_0)}{\ln (1/x)})$$

(2) where the superscript (h) refers to the higher relative pressure range, ϕ is a measure of the increase of adsorption energy in the pores as compared to that at the open surface, and $A=\mathrm{RT}\ln (1/x)$ is the adsorption potential. The value A₀ of the adsorption potential corresponds to the relative pressure x₀ at which the adsorbed phase transforms from the molecular associates to a condensed film (polylayer adsorption). As shown in Figure 1 (dashed curve labelled A_h), with the values x₀ = 0.82 and ϕ = 1.54 the equation (2) fits the adsorption isotherm in the range 0.6 ≤ x < 0.9 to within the relative deviation of $\mp \sigma =8.5\%$ .

Let us consider now the desorption isotherm. It is seen from Figure 1 (solid curve labelled D_l) that within the range of 0.05 ≤ x < 0.5, the BET equation provides a good fit to the experimental desorption isotherm

$${\theta }_d^{(l)}=\frac{C_{d}x}{(1-x)(1-x+C_{d}x)}$$

(3) where ${\theta }_d^{(l)}=a_d/a_{m,d}$ , a_m,d = 3.2 mmol/g, C_d = 15. It should be noted that $C_a<<C_d$ , which indicates that during the adsorption on the pore walls the adsorbed molecules become localised due to strong hydrogen bonds. It could be supposed that in the higher relative adsorptive pressure range 0.5 ≤ x < 0.9, a stable condensate film exists on the pore walls. For this range, the experimental desorption values are fitted by the FHH equation (see solid curve labelled D_h in Figure 1)

$${\theta }_d^{(h)}=(\frac{b_d}{-\ln x}{)}^{{\alpha }_d}$$

(4) with b_d = 2.73 and ${\alpha }_d$  = 0.46. Equation (4) approximates the desorption isotherm in the range 0.6 ≤ x < 0.9 to within the relative deviation $\mp \sigma =7.8\%$ .

To describe the adsorption hysteresis loop one has to express the values of adsorbed amount on the desorption branch via the values on the adsorption branch, and vice versa. Let us consider first the low relative pressure range. Eliminating x between equations (1) and (3) one obtains

$${\theta }_d^{(l)}=C_d\frac{{\theta }_a^{(l)}(1+{\theta }_a^{(l)})}{1+C_d{\theta }_a^{(l)}}$$

(5)

The values of adsorbed amount in the low relative pressure range of the desorption branch calculated from equation (5) for the experimental points at the adsorption branch are shown by open squares (□) in Figure 1. The good fit of the experimental data on the desorption branch is obvious. Next, inverting equation (5) to express ${\theta }_a^{(l)}$ via ${\theta }_d^{(l)}$ , one obtains a quadratic equation which yields the values of adsorbed amount on the adsorption branch shown in Figure 1 by filled squares (▪), which also exhibit a good fit to the experimental values.

Similarly, eliminating x between equations (2) and (4) one obtains

$${\theta }_d^{(h)}=[\frac{({\theta }_a^{(h)}-1/\varphi )b_d}{-\text{ln}{x}_0}{]}^{{\alpha }_d}$$

(6) which yields the values of adsorbed amount in the high relative pressure range of the desorption branch shown by open diamonds (⋄) in Figure 1. Finally, the inversion of equation (6) to express ${\theta }_a^h$ via ${\theta }_d^{(h)}$ yields the values shown by the filled diamonds (♦). These values are also in a quite good agreement with the experimental data for the adsorbed amount on the desorption and adsorption branch, respectively.

Conclusions

An approach is presented to describe the experimental isotherm of water adsorption–desorption on the swelling layer silicate montmorillonite. The approach is based on the analytical expressions: the BET equation in the lower relative pressure range for both adsorption and desorption branches; an equation proposed by the authors earlier for the adsorption branch in the high relative pressure range where the formation of associates occurs in the slit-like micropores and the FHH equation for the desorption branch in the high relative pressure range, where the condensate film exists on the pore walls. This approach is shown to be capable to reproduce the experimental dependencies with quite reasonable accuracy, and to describe quite satisfactory the adsorption hysteresis loop.