Desorption characteristics and kinetic parameters determination of molecular sieve by thermogravimetric analysis/differential thermogravimetric analysis technique

Abstract

The kinetics of the thermal desorption of CO₂ adsorbed on zeolite 13X were obtained using a differential thermogravimetric analyser under two different carrier gas conditions. The varying heating rates were set as 8, 12, 16, and 20 K min⁻¹, respectively. The desorption activation energy of the physisorption sites for this experiment evaluated by an integral method without prediction of the reaction order ranged from 12.15 to 14.12 kJ mol⁻¹ (CO₂ as the carrier gas) and 43.32 to 50.42 kJ mol⁻¹ (Ar as the carrier gas), respectively. The desorption activation energy of the chemisorption sites ranged from 57.95 to 58.53 kJ mol⁻¹ (CO₂ as the carrier gas) and 74.02 to 79.92 kJ mol⁻¹ (Ar as the carrier gas), respectively.

Keywords

Thermal kinetics differential thermogravimetric analysis adsorption carbon dioxide zeolites

Introduction

CO₂ is considered to be the main greenhouse gas responsible for global warming, formed primarily through combustion processes in power plants and through burning of flammable gases, such as methane, in gas flares in crude oil extractions sites (Cavenati et al., 2005a, 2005b; Chen et al., 2014). Carbon capture and storage (CCS) technologies are increasingly viewed as a potential solution for carbon sequestration (Ordorica-Garcia et al., 2010). Liquid amine sorption of CO₂ is one of the main sequestration methods but has drawbacks, such as high equipment corrosion rate, high energy consumption in regeneration, and a large absorber volume required. Adsorption processes with solid sorbents, such as zeolites, have been suggested and studied to overcome many of these drawbacks through their greater stability over a wide range of temperatures and pressures, lower energy requirements, and lower costs. Consequently, these types of materials are being increasingly reported and investigated as practical methods for CO₂ capture (Cavenati et al., 2004; Huang et al., 2007; Ko et al., 2002; Liang et al., 2009; Walton et al., 2006). Present studies of physical adsorbents are listed in Table 1.

Table 1.

Present studies of physical adsorbents.

Adsorbents	Merits	Research concerns	References
Carbonaceous adsorbents	a) Wide availability b) Low cost c) High thermal stability d) Low sensitivity to moisture	a) Improve surface area and pore structure b) Amine-loaded carbonaceous adsorbents	Cinke et al. (2003), Hsu et al. (2010), Saha and Deng (2010), and Su et al. (2009)
Carbonaceous adsorbents			Wang et al. (2011)
Zeolites	a) Low cost b) High thermal stability c) Characteristics of exchange cations	a) Altering their composition in terms of Si/Al ratio b) Exchange with alkali and alkaline earth cations	Palomino et al. (2010) and Remy et al. (2014)
Zeolites			Yang et al. (2012)
Ordered mesoporous silica	a) High surface area b) High pore volume c) Tunable pore size d) Good thermal and mechanical stability	a) Studies on new families of material, such as M41S, SBA-n, and ABS. b) Amine-loaded mesoporous silica	Chew et al. (2010), Liu et al. (2005), and Sun et al. (2007)
Ordered mesoporous silica			Kamarudin and Alias (2013) and Xue and Liu (2011)
Metal-organic frameworks (MOFs)	a) Remarkably high surface area b) Controllable pore structures c) Tuneable pore surface properties	a) Studies on new types of MOFs b) Verify their practical applications	Banerjee et al. (2008, 2009) and Millward and Yaghi (2005)

Studies on the adsorption of CO₂ on zeolite 13X have been reported regarding the influence of sorbent characteristics (Shen et al., 2013), gas composition (Mulgundmath et al., 2012; Siriwardane et al., 2003), pressure (Siriwardane et al., 2003), and temperature (Siriwardane et al., 2005). However, the existing literature on the desorption of CO₂ from 13X is scarce and limited. Desorption characteristics play a significant role in the selection of appropriate adsorbents for the CCS process and also provide guidance for the exploration of adsorption and desorption mechanisms. An adequate understanding of desorption kinetics is useful for further investigations of zeolites as practical CO₂ adsorbents, offering reference for the CCS process at a low regeneration energy cost. Thermogravimetric analysis (TGA) and differential thermogravimetric analysis (DTG) have been widely used to study thermal desorption in a molecular sieve. The key kinetic parameters, such as desorption activation energy, reaction order, and pre-exponential factor, could be obtained by mathematical calculations under a non-isothermal condition (Pérez-Maqueda et al., 2002). Several authors have studied the activation energy by the integral method (El-Sayed and Mostafa, 2014) and differential method (Yang et al., 2001) (or ‘DTG curve fitting method’).

In this study, we conducted experiments under two different carrier gases, i.e. argon and CO₂, respectively. The parameters of non-isothermal desorption of CO₂ from zeolite 13X under two types of carrier gases were examined. Furthermore, the mechanism of adsorption and desorption performances over 13X, as affected by the pore size distribution (PSD) and adsorption sites of the sorbents, is discussed.

Materials and methods

Experimental materials

Adsorption experiments were carried out with a TA Q-500 chemisorption instrument. The commercial zeolite 13X-APG adsorbent used in this study was purchased from Shanghai Jiuzhou Chemicals Co., Ltd. The CO₂ adsorbate (99.999%) was obtained from Beijing Qianxi Gas Co. Ltd, and the Ar shielding gas (99.999%) was acquired from Praxair (China) Investment Co. Ltd. The specific surface and porosity analyser Autosorb-1 manufactured by Quantachrome Inc. was used to obtain the PSD of zeolite 13X. Liquid nitrogen was used to maintain the temperature of the adsorption environment at 77.3 K.

Experimental method

Characterization of zeolite 13X

The characterization of the 13X sorbents was obtained by Autosorb-1. Prior to the determination, the samples were maintained at 393 K and 10⁻⁵Torr for 12 h for complete desorption. The specific surface areas were determined by the Brunauer–Emmett–Teller (BET) method based on the adsorption isotherms of N₂ at 77 K. The non-local density functional theory was used to obtain the PSD.

Thermogravimetric experiment

An isothermal process was set for 30 min, in which 45 ± 2 mg of the 13X sample was placed on a platinum pan and loaded with CO₂ for saturation adsorption. After that step, for the purge stage, the sample was treated, respectively, with CO₂ (condition1) or Ar (condition2) at a flow rate of 40 ml·min⁻¹ at the adsorption temperature (293 K) for at least half an hour. Next, the thermogravimetric non-isothermal experiments were performed from 293 to 700 K at four heating rates (β = 8, 12, 16, and 20 K·min⁻¹) purged with the same gas as the previous stage. The curves of mass loss versus temperature (TG) were subsequently recorded.

Summit-differential method

Generally, the desorption rate under non-isothermal conditions could be expressed by the following equation

\frac{d α}{d t} = - A \exp (- \frac{E}{R T}) f (α)

(1)

where A, T, R, E, and t are the pre-exponential factor (s⁻¹), temperature (K), universal gas constant (kJ·mol⁻¹·K), activation energy (kJ·mol⁻¹), and time (s) respectively.

f (α)

is a function, the type of which depends on the reaction mechanism. α is the degree of desorption and is the normalized form of the weight loss data of decomposed sample and is defined by the following expression

α = \frac{m_{i} - m_{t}}{m_{i} - m_{f}}

(2)

where

m_{i}

is the initial weight,

m_{t}

is the weight at temperature T, and

m_{f}

is the final weight of each zone.

The uniform kinetic reaction is obtained according to the Polanyi–Wigner equation (Cvetanović and Amenomiya, 1972), widely used in the temperature-programmed desorption process, and could be written as follows

f (α) = {(1 - α)}^{n} = θ^{n}

(3)

where n is the order of reaction and θ is the surface coverage.

In this experiment, the temperature T is a function of time t since heating occurs in a linear fashion (T₀ = initial temperature)

T = T_{0} + β t

(4)

Hence, t = (T − T₀)/β, and combining equations (1) to (3), the desorption rate equation becomes

- \frac{d θ}{d T} = \frac{A}{β} \exp (- \frac{E}{R T}) \cdot θ^{n}

(5)

As the DTG curve is a differential of the TG curve, for any point on the curve in this experiment, θ can be expressed as follows

θ_{i} = \frac{1}{100} S_{i} = \frac{1}{100} \int_{T_{i}}^{T_{f}} h_{i} d T

(6)

As Figure 1 shows, S_i is the area of the partial integral of the desorption curve (T ≥ T_i), T_f is the end temperature of desorption, and h_i corresponds to the intensity observed at T_i. Combining equations (5) and (6), the equation could be shown as

h_{i} = - \frac{d S_{i}}{d T} = \frac{{0.01}^{n - 1} A}{β} e^{(- E / R T_{i})}

(7)

\frac{d h_{i}}{d T} = \frac{{0.01}^{n - 1} A}{β} e^{(- E / R T_{i})} [n S_{i}^{n - 1} \frac{d S_{i}}{d T_{i}} + E / R T_{i}^{2} \cdot (S_{i}^{n})]

when T = T_max

{(\frac{d h_{i}}{d T})}_{T = T_{\max}} = \frac{{0.01}^{n - 1} A}{β} e^{(- E / R T_{\max})} [n S_{\max}^{n - 1} {(\frac{d S_{i}}{d T_{i}})}_{T = T_{\max}} + E / R T_{\max}^{2} \cdot (S_{\max}^{n})] = 0

which means that

n S_{\max}^{n - 1} {(\frac{d S_{i}}{d T_{i}})}_{T = T_{\max}} + E / R T_{\max}^{2} \cdot (S_{\max}^{n}) = 0

(8)

Rewriting equation (8) as

n {(\frac{d S_{i}}{d T_{i}})}_{T = T_{\max}} + \frac{E}{R T_{\max}^{2}} \cdot S_{\max} = 0

(9)

Combining equations (7) and (9), the reaction order is shown as

n = \frac{E S_{m a x}}{h_{\max} R T_{\max}^{2}}

(10)

Taking the logarithm of equation (7), it can be expressed as follows

\ln h_{i} = \ln (\frac{{0.01}^{n - 1} \cdot A}{β}) - (\frac{E}{R T_{i}}) + n \ln S_{i}

(11)

Equation (10) gives the expression of n, so equation (11) could be rewritten as

\ln h_{i} = \ln (\frac{{0.01}^{n - 1} \cdot A}{β}) - \frac{E}{R} (\frac{1}{T_{i}} - \frac{S_{\max} \ln S_{i}}{h_{\max} T_{\max}^{2}})

(12)

Results and discussion

Texture properties of 13X

The PSD of zeolite 13X, which was obtained by the BET method, is illustrated in Figure 2 and includes micropores (0.7–2 nm) that consist of 52% of the total pore volume, and mesopores (2–50 nm) that consist of 48% of the total pore volume. This finding confirmed that 13X is a microporous molecular sieve (Lillo, 2005; Rege et al., 2000). The adsorption capacity of CO₂ on zeolite 13X is large as a result of the strong adsorption capacity of micropores and capillary condensation in the mesopores.

Desorption characteristic

Adsorption could be divided into physisorption and chemisorption on the basis of different forces between adsorbents and adsorbates, which have different thermal behaviours during the desorption process (Groß, 2009). Physisorption, based on Van der Waals’ (VDW) force, reaches adsorption equilibrium extremely quickly and desorbs at a lower temperature. Chemisorption, i.e. ‘activated adsorption’, is the result of chemical bond force and the adsorbates are difficult to escape. From the perspective of heat, the adsorption heat released by physisorption is usually similar to the liquefaction heat of gaseous adsorbate, while the adsorption heat of chemisorption, reaching the order of chemical reaction heat, is considerably larger than the former.

Figures 3 and 4 are the combined TG and DTG profiles showing the thermal desorption characteristics of CO₂ on zeolite 13X at a heating rate of 8 K·min⁻¹ under CO₂ and Ar as carrier gases, respectively. The weight loss process of the CO₂-loaded sample can be divided into two main regions (Klepel and Hunger, 2005): escape at low temperature (293–450K); outgas at high temperature (>450 K). As shown in Figures 3 and 4, the removal of very light components is followed by the first region of weight loss at ∼400 K. Much of the desorption occurred in the first region of weight loss, a result of the thermal breaking of weak bonds formed by VDW and the unstable adsorption equilibrium.

Meanwhile, although the amount of desorption of the first zone is significantly different under the two carrier gas conditions, the amount of the second zone remains essentially unchanged. In the DTG curve, the summit position of the curve describes the temperature at which the maximum weight loss rate occurs. The DTG curve of the samples during the desorption stage shows two distinct peaks (which are represented by a noticeable change in the slope of the TG curve). Based on the temperature range at which CO₂ has been previously observed to escape, the DTG peaks can be assigned as follows: one between 293 and 450 K and one between 450 and 600 K, written as P_L and P_R. The highest desorption rate of P_L is significantly greater than that of P_R. Since the temperature range for the two peaks is comparable, this means that under the same β the total desorption taking place in the temperature range of P_L is always greater than that of P_R. Figure 3 shows that in the case of CO₂ as the carrier gas, the separation of the two desorption peaks is not obvious, since the carrier gas introduced is the same as the loaded gas and is equal to an indirect partial pressure applied on the sample. Meanwhile, as seen from Figure 4, the demarcation of the two zones is trenchant.

Adsorption thermodynamics shows the relationship between the adsorption–desorption process and pressure, as well as temperature. As shown in Figure 5, the curve is the critical state of adsorption and desorption which is generally written as the adsorption–desorption equilibrium state. When the pressure and temperature are P_e and T_e, respectively, point e is on the equilibrium curve. Point e′ is in the adsorption zone along the pressure rise to P′ without variation of temperature and cannot escape from the adsorbent. The temperature should be set slightly higher than T′ for the desorption of adsorbates.

The equilibrium adsorption amount has an enhancement as a result of the partial pressure increase of the component. By comparing Figures 3 and 4, a conclusion can be obtained in that elevating the pressure is a non-positive factor for desorption and leads to an increase of the peak height and end temperature of P_L; meanwhile, it has an undetectable effect on P_R. The surface science tells us that the adsorbates captured by chemisorption could only escape under a sufficiently high temperature and are particularly unaffected by pressure change (Groß, 2009).

The desorption rates versus temperature under different heating rates are shown in Figures 6 and 7. The desorption amounts of the first zone under CO₂ atmosphere were higher than those of Ar, corresponding to larger mass losses. The desorption process on a heterogeneous surface during a TPD experiment has been described according to the multiadsorption centre model (Dumesic et al., 1993), which could be used to explain the formation of two peaks in the desorption DTG curves. Two hypotheses have been proposed which explain the presence of the two desorption peaks in this experiment (Yang, 2002): (1) there are two separate active sites for CO₂ adsorption on the surface of zeolite 13X, with one clearly exhibiting a stronger adsorption than the other; (2) diffusion towards the positive and negative directions occurred between the surface-adsorbed molecules and sub-layer molecules. It has been found that both adsorption peaks remain when β is varied, so it is safe to ignore any possible diffusion between the adsorbed CO₂ multilayers. We propose that the first hypothesis is more likely to occur under the aforementioned conditions. Therefore, for physisorption, we believe it occurs primarily in the micropores along with the amount of capillary condensation in the mesopores. In summary, it could be concluded that P_R is chemisorbed and P_L is physically adsorbed from another point of view (Siriwardane et al., 2005).

Kinetic parameters study

Summit-differential method

As Figure 8 shows, the slope of the fitted straight line of the plot represents –E/R, which can be used to evaluate the activation energy. Adding this E to equation (10) will derive the reaction order n. The pre-exponential factor A can be determined from the intercept of the line with the vertical axis.

Figure 1.

Schematic diagram of S_i.

Figure 2.

PSD for the sorbent of 13X.

Equation (12) shows that E, n, and A can be obtained by plotting $\ln h_{i}$ as a function of $\frac{1}{T_{i}} - \frac{S_{\max} \ln S_{i}}{h_{\max} T_{\max}^{2}}$ . Equation (6) shows that under conditions of constant β, the size of area S_i depends on the degree of desorption α, while E is influenced by S_max, h_max, and T_max. In summary, α, S_max, h_max, and T_max which could be directly obtained from the TG or DTG curves are the influential parameters.

Table 2 shows the key influential parameters for different desorption conditions. With the same adsorption carrier gas, the α value of P_L or P_R has a regular variation with increasing heating rate whereas the α value of the total desorption process remains almost unchanged.

Table 2.

Key influential parameters.

Carrier gas		β	100α	S_max	h_max	T_max	T_f
Carrier gas		(K min⁻¹)	100α	S_max	(K⁻¹)	(K)	(K)
CO₂	First zone	8	15.01	1038	13.16	321	495
		12	14.75	1054	13.00	322	497
		16	14.31	1069	13.10	324	480
		20	14.25	1031	12.92	326	481
	Second zone	8	2.28	117	1.473	538	700
		12	2.40	126	1.475	540	700
		16	3.02	168	2.020	541	700
		20	3.13	172	2.094	542	700
Ar	First zone	8	3.85	189	6.767	322	405
		12	4.58	254	7.336	323	433
		16	4.32	226	6.722	327	427
		20	4.92	272	7.196	329	454
	Second zone	8	2.47	129	2.305	518	727
		12	1.67	88	1.460	543	728
		16	1.98	111	1.699	544	728
		20	1.37	64	1.152	566	727

From Table 2 and Figure 3, P_L and P_R will overlap when CO₂ is the carrier gas. Yang (1983) presented the following points in the desorption spectrum analysis: (1) the contributions of the two peaks to the overlapping parts are generally unequal; (2) the non-overlapped side of the peak is less affected or even negligible by the other one. Therefore, the desorption activation energy should be calculated from the range close to the summit of each peak, which is distant from the overlapping region.

Figure 3.

TG and DTG curves with CO₂ as the carrier gas.

Figure 4.

TG and DTG curves with Ar as the carrier gas.

Figure 5.

Adsorption–desorption process.

Figure 6.

Desorption rates with CO₂ as the carrier gas under different β.

Results and reaction mechanism

The three-dimensional structure of zeolite 13X, a faujasite-type zeolite, is shown in Figure 9(a). It is composed of alumina tetrahedra and silicon oxygen tetrahedron consisting of oxygen bridge according to a certain spatial structure to form a uniform aperture crystal. The basic structural unit of 13X is a beta cage, and adjacent beta cages form the molecular sieve by the six-angle prism connection. The alumina tetrahedra show electronegativity, and Na⁺ neutralizes the negative charge. The Na⁺ in 13X occupies three positions (Feuerstein and Engelhardt, 1998) as shown in Figure 9(b). The SI and SI′ positions are not exposed and cannot be used to interact with the adsorbed molecules after the dehydration. The SII and SIII positions are exposed and can participate in adsorption.

Figure 7.

Desorption rates with Ar as the carrier gas under different β.

Figure 8.

Schematic diagram of the calculation method of kinetic parameters.

Siriwardane found that the adsorption mode of CO₂ on 13X can be categorized into two types: (a) physisorption of CO₂ occurs with CO₂ in linear orientation by ion–dipole interaction

{(Al}^{3 +} / S i^{4 +}) \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot^{δ -} O = C = O^{δ +}

(13)

(b) chemisorption of CO₂ by Na⁺ as shown in Figure 10 (Siriwardane et al., 2005). Figure 10(a) and (b) shows the adsorption positions SII and SIII, respectively. As CO₂ is a linear triatomic molecule, position SII is Na⁺–O and position SIII is Na⁺–C. SII is located in the concave surface, wherein CO₂ molecules are adsorbed both by Na⁺ and tetrahedrally coordinated lattice Al or Si atoms to form a carboxylate species. Position SIII has CO₂ molecules adsorbed by Na⁺ to form a true carbonate structure that requires specific lattice O atoms adjacent to it. This structure makes the bond stronger than the former.

Figure 9.

Structure diagram of zeolite 13X.

Figure 10.

Chemisorption of CO₂ on 13X.

Table 3 shows the key kinetic triplets obtained from the summit-differential method. E_ave is the average value of calculated values of E at different heating rates. As the sample size (the number of experiments is 4, and therefore the degree of freedom is 4–1 = 3) is small, T distribution should be used to avoid the inaccuracies caused by the size of the sample in the error analysis. The significance level is selected as 0.05 (confidence probability is 95%) to calculate confidence intervals. Referring to the T distribution list, $t_{0.05 / 2} (3) = 3.182$ , and the standard error of E_ave should be $S_{E_{ave}} = \pm \sqrt{\frac{\sum_{i = 1}^{4} {(E_{i} - E_{a v e})}^{2}}{4 \times (4 - 1)}}$ , where E_i is the calculated value of the activation energy at each heating rate. Hence, the confidence interval should be ( $E_{ave} - t_{0.05 / 2} (3) S_{E_{a v e}}$ , $E_{ave} + t_{0.05 / 2} (3) S_{E_{a v e}}$ ) and is listed in Table 3.

Table 3.

Key kinetic triplets by the summit-differential method.

Carrier gas		β	E	E_ave	ln A
Carrier gas		(K min⁻¹)	(kJ mol⁻¹)	(kJ mol⁻¹)	(min⁻¹)	n
CO₂	First zone	8	14.12	13.35 (13.35 − 1.49, 13.35 + 1.49)	4.87	1.2
		12	14.07		5.31	1.1
		16	13.04		5.60	1.2
		20	12.15		5.80	1.2
	Second zone	8	58.53	58.24 (58.24 − 0.45, 58.24 + 0.45)	7.25	2.0
		12	58.42		7.44	2.0
		16	57.95		8.26	2.0
		20	58.05		8.37	1.6
Ar	First zone	8	50.42	46.39 (46.39 − 4.90, 46.39 + 4.90)	4.24	1.2
		12	46.97		4.57	1.3
		16	44.84		4.78	1.3
		20	43.32		4.96	1.4
	Secondzone	8	77.22	76.87 (76.87 − 3.88, 76.87 + 3.88)	7.60	1.7
		12	76.32		7.59	2.1
		16	79.92		8.08	1.6
		20	74.02		7.91	2.2

For the first zone, there is a perfect linearity of $\ln h_{i}$ versus $\frac{1}{T_{i}} - \frac{S_{\max} \ln S_{i}}{h_{\max} T_{\max}^{2}}$ . As shown in Table 3, the increasing heating rates have slight impact on E, while they have a role in promoting A, which indicates the desorption rate under the same θ. The distinction in the desorption activation energy of different conditions, in which different gases are used as the carrier gas after the adsorption stage, is due to the different adsorption status of CO₂. When CO₂ is used as the carrier gas (written as condition 1), the value of E ranges from 12.15 to 14.12 kJ mol⁻¹ and is comparable to the estimated activation energy calculated by Kamiuto et al. (2006) (11.7 kJ mol⁻¹), which is frequently used in the characterization of the mass transfer rate of the adsorbate on the open surface of the adsorbent. Compared to the case of Ar as the carrier gas (written as condition 2), a certain amount of partial pressure of adsorbate exists; therefore, some weaker adsorption sites can also capture CO₂ molecules, even though these equilibria are relatively unstable for the adsorption of these sites. During the desorption process, the main factor that restricts the escape of molecules from the adsorbent surface is not the binding of VDW forces but the mass transfer velocity in the channels of zeolites, resulting in the calculated value of E being similar to the estimated activation energy, which means that the desorption is controlled by pore diffusion limitation. Under this condition, even a number of non-adhesive pores are inhabited by CO₂ molecules in a ‘pseudo-adsorption’ state which can be disrupted as a result of small temperature fluctuations as the ‘pseudo-adsorption’ state is extremely volatile. It can be seen from Figure 3 that a sharp increment emerges in the initial heating stage. Nevertheless, this part of data is not used in the calculation of E and will not affect the value of E. The value of E under condition 2 ranges from 43.32 to 50.42 kJ mol⁻¹ in the range of physisorption heat, and the physical interaction is shown as constitutional formula (13). As the number of desorption molecules under condition 2 is relatively smaller than that of condition 1, the pore diffusion limitation is not considered.

For the second zone, the value of E under condition 1 is significantly lower than the value under condition 2. One of the possible reasons is that the demarcation of the first zone and the second zone is indistinct, causing difficulty in determining the exact starting point of the calculation and the result is presented as an average of desorption activation energies of both physisorption and chemisorption. Meanwhile, regardless of which gas is used as the carrier gas, the calculation results of E in the second region fluctuate within a certain range. The reaction order n can be considered as 2 in the second zone and 1 in the first zone, which means that the desorption mechanisms corresponding to the two zones are different. Although the value of A in the second zone is higher than that in the first zone, the desorption rate in the second zone being faster than the first zone cannot be explained due to the different desorption amount between the two zones, and the value of A used to determine the value of the desorption rate assumes the same desorption amount. Taking the heating rate as the only variable, the value of A increases along with the growing heating rate which represents an increase in the desorption rate. This is because the same number of CO₂ molecules needs to escape from the surface of molecular sieves.

It can be seen that the unconsidered selection of the existing data of E in other articles is not advisable because the atmosphere conditions in actual engineering are not completely consistent with the experimental conditions. For different engineering applications, there are great discrepancies between the atmosphere and adsorption sites where the main adsorption occurs.

Conclusions

A pressure difference can be formed between the adsorption–desorption process by the method using two different gases as the carrier gas (one gas should be the adsorbate), which plays a supplementary role in the determination of adsorption and desorption mechanisms. A conclusion could be drawn that the physisorption and chemisorption of CO₂ on zeolite 13X exist simultaneously.

The summit-differential method without a need of estimating n could be used to obtain the key kinetic triplet, i.e. activation energy, pre-exponential factor, and reaction order, accurately. For the calculations of the desorption activation energy of different engineering applications, it is necessary to adjust the carrier gas atmosphere on the basis of various actual conditions and adsorption mechanisms to obtain the proper desorption activation energies.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The project was supported by the Fundamental Research Funds for the Central Universities (FRF-BD-16-009A).

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