Abstract
This study examines the effect of a short term rotation on a system of constant volume. Adsorption of CO2 is performed on Activated Carbon (AC) at 281, 293 and 298 K with a special designed device that allows rotation. The adsorption isotherms were conducted up to 10 bar for both No Rotational (NoROT) and Rotational (ROT) cases. The ROT case refers to 60 s of rotation at 5000 rpm. The experimental results were fitted to Langmuir as well as to Dubinin–Astakhov (D–A) models with the latter presenting the best fit. A detailed thermodynamic analysis is performed in order to quantify the overall contribution of the rotation on gas adsorption compared to static case. For the ROT case, the maximum amount adsorbed (q max) is by 12 % higher than the NoROT counterpart, while a decrease in chemical potential as surface loading is increased, indicates that the process after rotation is entropy driven. The outcome of this work suggests that rotation enables gas molecules to access previously inaccessible sites, thus gaining more vacancies due to better rearrangement of the adsorbed CO2 molecules.
1 Introduction
Climate change is the major threat for our planet survival. Human activities increase year by year increasing alongside hazardous emissions such as greenhouse gases. Among greenhouse gases, the most severe contribution to global warming is done by CO2, which has reached 420 ppm in concentration [1]. Adsorption is one of the main methods applied in climate change mitigation technologies including Direct Air Capture (DAC) (e.g. [2, 3]), post combustion CO2 capture (e.g. [4, 5]) and other environmental processes (e.g. [6, 7]).
Activated carbon (AC) is among the most promising materials towards this direction. As adsorbent, AC, exhibits high performance [8], high thermal stability [9], large surface area and good uptake capacity for most of the greenhouse gases such as CO2 and CH4 over low production cost [10, 11]. Specifically, CO2 uptake on activated carbon is mostly due to Van der Waals forces (physisorption) and it is studied at mainly at temperature range from 273 to 303 K and pressure up to 10 MPa. Physisorption has been widely examined and gas uptake is known to be depended on operational temperature and pressure [12].
Adsorption isotherms give an understanding of the adsorption mechanism and thus provide better process design for various adsorption applications. The nature of the process as well as the potentials of a specific system is estimated by the implementation of various theoretical models. The linearization of the isotherm models provide insight on adsorption affinity, mean free energy, whether the adsorption is physisorption or chemisorptions, single layer or multilayer etc. [13, 14]. The best fit of a certain model is determined by the complexity of the system under investigation. Despite its simplicity, Langmuir is one of the most recognized and used isotherm models [15], especially for systems involving microporous materials. Other two parameter models are Temkin, Dubinin–Radushkevich (D–R), modified Langmuir, Dubinin–Astakhov (D–A) etc., as well as models with three or more parameters ([16, 17]).
For systems that operate with physisorption as principle, the knowledge of thermodynamic properties such as the change in enthalpy (ΔH), entropy (ΔS) and Gibbs free energy (ΔG) is mandatory. Specifically, the Gibbs free energy is one of the most important thermodynamic functions for the characterization of a system. In gas adsorption, Gibbs free energy, alongside with the chemical potential, are the basis for system examination at microscopic regime and beyond classical thermodynamics [18, 19]. However, equilibrium studies are more valuable when performed at low pressure regions and room temperatures, giving a better understanding of adsorbate–adsorbent interactions. To this end, there are numerous studies on thermodynamic analysis of adsorption isotherms of different gases on various adsorbents.
Choudhary and Mayadevi [20] analyzed thermodynamically the adsorption of ethane, methane, ethylene and carbon dioxide on silicate-I material. The adsorption isotherms obtained by a gravimetric technique and adsorption models of Dubinin–Polanyi, Freudlich and Langmuir were applied. The different gases fitted better to different models while they demonstrated different behavior regarding surface loading as well. The mobility of the adsorbed gases was also examined by means of entropy calculations finding that the mobility of methane was affected by the surface coverage.
Molecular simulation of CH4 and CO2 was performed by Zhang et al. [21] on two FAU type zeolites. Grand Canonical Monte Carlo simulation conditions were applied for temperatures 288, 298, 308 K and pressure up to 10 MPa while the results were fitted to Langmuir and Toth models. The latter provided better description of the adsorption mechanism. The affinity and the degree of the order of the adsorbed molecules were the outcome of this research.
Commercial activated carbon Norit® SX2 was examined for CO2 capture after combustion by Rashidi et al. [22]. Authors implemented four different two parametric adsorption models including Langmuir, Temkin, D–R and Freundlich. The last one gave the best fit to the experimental data. The process was designated as exothermic and it was determined by the fact that with increase in temperature, the amount adsorbed decreased.
Singh and Kumar [23] investigated both subcritical and supercritical CO2 thermodynamic properties on three different activated carbons for cooling system application. Calculation of Gibbs free energy, entropy and isosteric heat of adsorption were provided from experimental data by volumetric adsorption techniques. The isothermal adsorption model used was Dubinin–Astakhov (D–A), while isosteric heat of adsorption was evaluated from Clausius–Clapeyron equation. The results indicate that the system is highly temperature dependent.
Accordingly, Saha et al. [24] conducted volumetric CO2 adsorption measurements on two types of activated carbon. For the particular experiments, the temperature range used was from −18 to 80 °C and up to 10 MPa. The results were fitted to a number of adsorption models, such as Langmuir, D–A, Toth and modified D–A with the last two presenting the best fit. The specific study showcase the sensitivity of the proposed models, where temperature is neglected and the parameters are analogous to surface loading.
In the case of Rotating Packed Beds (RPB), which is an industrially promising system applying high gravitational forces [25, 26], there is a lack of fundamental studies on the gas behavior; only tangential gas velocities have been studied. For instance, Gao investigated the characteristics of the gas within a RPB system [27]. The conducted study visualized gas velocity across the bed by implementing Particle Image Velocimetry (PIV). The finding indicated that gas is eventually synchronized with the packing while mean tangential slip velocity decreased radially. To this direction another study, this time of Wang et al., implemented Computational Fluid Dynamic (CFD) model to investigate further the effect of rotational speed and other properties on the tangential kinetic energy of the gas [28]. However, a direct thermodynamic comparison between physisorption and the performance of rotation is important for the design optimization of RPBs.
In the present study, the effect of rotation on the gas adsorption mechanism is examined for the first time. A system of constant volume is subjected to the effect of rotation and a detailed thermodynamic analysis is presented in order to qualify and quantify the overall contribution of this extra variable.
2 Experimental procedure
2.1 Routine characterization methods
Commercial activated carbon in fine powder, with particle size of ∼100 μm, was used. The morphology of the sample’s surface was investigated by Scanning Electron Microscopy-SEM (JEOL, 6390LV, Akashima, Japan). The material’s structural properties were characterized with N2 adsorption measurements by NOVA 4200e Quantachrome porosimeter. Table 1 presents the results including total pore volume (V tot) and the specific surface area according to Brunauer–Emmett–Teller (BET) theory; (SABET).
Activated carbon properties derived from N2 adsorption measurements.
| Sample | SABET (m2/g) | SAext (m2/g) | SAmic (m2/g) | V mic (cm3/g) | V tot (cm3/g) |
|---|---|---|---|---|---|
| Activated carbon | 1141 | 163 | 978 | 0.434 | 0.632 |
In order to validate the in-house special designed rotational device, the adsorption isotherms of CO2 were also measured by the Intelligent Gravimetric Analyzer (Hiden Isochema, IGA01, Warrington, United Kingdom), at three different temperatures: 281, 293 and 298 K. For this particular set of experiments, 43 mg of the AC were placed into the reactor and system evacuation was conducted for a period of 14 h. Temperature control was achieved by a water bath circulator. Sequence mode was chosen in order to set the exact pressure steps and waiting time (60 min) as in the volumetric experiments.
2.2 Rotational device
Isothermal experiments are conducted with the use of an ad hoc volumetric (manometric) device similar to Sievert’s type, specially designed for the purpose of the present research. The device allows the rotation of the sample cell at high rotational speed and under constant volume conditions. Figure 1 shows the device which consists of a sample cell, a vertical rotary motor, a pressure transducer coupled with a thermometer, two valves, and a slip ring. The device is supported on a three-leg fixed table, while the slip ring is fixed on a hollow cylinder where a pressure transducer is housed in. The bottom part of the sample cell is mounted on the vertical rotary motor, while the top part can be moved upwards and downwards in order to place the adsorbent inside the cell. On the top part of the cell, there are two valves placed symmetrically that serve as gas inlet–outlet ports. In the center of the top part, the pressure/temperature transducer (PV8003, ifm electronics, Essen, Germany) is connected, which is capable of recording relative pressure at prescribed time intervals (down to 1 ms). A more detailed description is given elsewhere [29]. For the specific work, the rotational speed was 5000 rpm and experiments were conducted at three different temperatures, namely 281, 293 and 298 K.
Schematic representation of the experimental setup; the dashed line frame represents the insulated container, while V (1–5) stands for existing valves. A vacuum pump can be connected interchangeably to any part of the system.
2.2.1 Static adsorption isotherms
In order to perform CO2 adsorption isotherms, 3.6 g of the AC were placed into the sample cell and after the cell was sealed, the system was evacuated for overnight (14 h). Carbon dioxide was first introduced to a vessel of known volume, the so called reservoir, and then to the sample cell by opening the connected valves.
As soon as pressure in the reservoir equilibrated with that of the sample cell (a few seconds), inlet valve closed and pressure was recorded. Throughout the experiment, pressure ranged from 10−2 bar–10 bar with ∼1 bar as a dosing step. Pressure and temperature of the system were recorded every second throughout the measurement with a relative pressure transducer coupled with a thermocouple. As equilibration time, 60 min were estimated to be satisfactory following the work of Saha et al. [24].
2.2.2 Rotational adsorption isotherms
The effect of the rotation on the adsorption isotherms was investigated with the introduction of 60 s rotation at a predefined pressure step. The rotational time was investigated from 10 to 120 s. It can be shown that rotation gives rise to a well as it is described in [29] which is correlated with the extra amount of adsorbate molecules colliding on the pore walls. However, the time of rotation does not affect the depth of this well; it is the rotational frequency that affects this depth at a given initial pressure. Therefore, the selected rotational time is considered to be sufficient to enhance adsorption without changing the isothermal temperature, due to mechanical friction, and thus maintaining the adiabaticity of the process. In contrary, prolonged rotation would cause a temperature increase complicating the analysis of the results.
More specifically, adsorption isotherms curves with the introduction of the rotational force were obtained following the same procedure as the static whereas rotation took place at the fifth pressure step (introduction of ∼5 bar). After 60 s, the rotational motor was turned off and the system was left to complete the 60 min period. Next, the rest of the pressure steps were conducted as in the static measurements up to 10 bar.
2.2.3 Adsorbed amount calculation
The pressure recorded by the transducer refers to bulk gas pressure. For estimating the amount adsorbed at each equilibrium pressure of the isotherm, the number of molecules involved was calculated by subtracting the pressure value at equilibrium (P e ) from the introduced pressure. The resulted ΔP then was solved for n moles at each pressure step from universal gas equation:
where z is the compressibility factor and it was taken into account for each equilibrium pressure at the respective temperature. The volume, V void, was estimated by firstly calculating the geometrical volume of the cell (V gcell) corresponding to 6.36 cm3. Knowing the bulk density of the AC (0.882 g/cm3) and the placed mass (3.6 g) the volume occupied by the AC grains is V AC = 4.08 cm3. Finally, V void is 2.28 cm3. The amount adsorbed is then calculated by adding the number of moles of the previous step to the next gas dosage.
3 Modeling of the adsorption isotherms
The experimental adsorption isotherms data, for both NoROT and ROT modes, were modeled by fitting them both to Langmuir and to D–A adsorption models.
Langmuir adsorption isotherm is a two-parametric model that describes the adsorption rate as result of surface coverage at a given time. In other words, Langmuir model quantify the adsorption capacity of a material by implementing dynamic equilibrium of the adsorption and desorption relative rates in respect to the vacant sites of the adsorbent material. The Langmuir equation is given as [15]:
where, q e (kg/kg) is the amount adsorbed at equilibrium point of each step and q max is the maximum amount that can be adsorbed at given conditions (kg/kg), b is the Langmuir adsorption constant and P e (bar) is the pressure at equilibrium. The linear form can be written as follows:
The maximum amount adsorbed (q max) as well as b can be obtained from the plot of P e /q e versus P e . The slope gives the b value, while q max is derived from the intercept.
Dubinin–Astakhov (D–A) isotherm model is applied taking into account the heterogeneity of the material while the calculated maximum adsorption is restricted by the micropore filling theory [30]. The specific model relates the equilibrium pressure, temperature and the amount adsorbed for an adsorbate–adsorbent system. Dubinin–Astakhov equation is given as:
where q e is again the amount adsorbed at equilibrium while q o is the amount filling the micropore volume (cm3/g). In the nominator, V a is the adsorbed specific volume estimated using triple point properties of CO2 and thermal expansion co-efficient, which is given from Eq. (5) while A being the adsorption potential, E is the characteristic energy of the adsorption and ν is the heterogeneity index. The latter can take values that comply with 1<ν < 2. When ν = 2 the adsorbent’s structure is considered homogeneous while ν = 1 for non-porous materials [31]. In the formula for calculating A, P s is the saturation pressure for the given temperature. The equation for the estimation of V α is:
where V t and T t are the specific volume of the liquid adsorbate and the temperature at the triple point (V t = 0.8486 × 10−6 m3/g and T t = 216.6 K) respectively and α is the thermal expansion coefficient (1/T) [32].
The heterogeneity index is used empirically to achieve the overall best fitting, while the rest important parameters, namely E and q o are withdrawn from the plot of lnq e versus A ν calculated from the linear form:
The obtained parameters for both models (Langmuir and D–A) are tabulated in Table 2.
Adsorption isotherm parameters for Langmuir and D–A models.
| Temperature (K) | Langmuir | ||||||
|---|---|---|---|---|---|---|---|
| q max (kg/kg) | Δq max (%) | b | r 2 | ||||
| NoROT | ROT | NoROT | ROT | NoROT | ROT | ||
| 281 | 0.450 | 0.500 | 11.11 | 0.22 | 0.19 | 0.9987 | 0.9912 |
| 293 | 0.418 | 0.470 | 12.44 | 0.21 | 0.17 | 0.9992 | 0.9956 |
| 298 | 0.380 | 0.390 | 2.63 | 0.20 | 0.16 | 0.9981 | 0.9985 |
| Dubinin–Astakhov | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| q o (cm3/g) | Δq o (%) | E (kJ/mol) | ν | r 2 | |||||
| NoROT | ROT | NoROT | ROT | NoROT | ROT | NoROT | ROT | ||
| 281 | 0.418 | 0.447 | 6.94 | 6.94 | 7.44 | 1.85 | 2.00 | 0.9999 | 0.9995 |
| 293 | 0.388 | 0.427 | 10.05 | 6.67 | 7.15 | 1.94 | 1.87 | 0.9998 | 0.9996 |
| 298 | 0.370 | 0.395 | 6.76 | 6.46 | 7.07 | 1.98 | 1.97 | 0.9995 | 0.9967 |
3.1 Adsorption thermodynamics
Thermodynamic analysis of adsorption isotherm gives an insight in the adsorption mechanism. The standard Gibbs free energy (ΔG°) shows the spontaneity of a reaction. Other key role parameters are standard entropy and enthalpy changes, ΔS° and ΔH° respectively. To obtain those values, Van’t Hoff equation [Eq. (9)] is used. This equation relates the change in equilibrium due to temperature and it is derived from Gibbs free energy, so it is [18]:
By plotting lnb (obtained from Langmuir model) versus 1/T, ΔH° and ΔS° are derived from the slope and intercept respectively. The standard change in Gibbs free energy can be calculated from any of Eqs. (7) or (8). In the present work it is calculated from Eq. (7).
To have an estimation of the strength of adsorbate–adsorbent binding, isosteric heat of adsorption is calculated from Clausius–Clapeyron equation which is given as [33]:
Essentially Q st is the heat released during the exothermic reaction of the physisorption. The equilibrium pressure (P e ) used must correspond to the same amount adsorbed for all temperatures. For the specific calculus, the logarithmic P e value was obtained by solving the Langmuir equation for the pressure using the calculated q max and the theoretical amount adsorbed q e at each equilibrium point. By plotting lnP e over 1/T, Q st is obtained from the slope multiplied by the gas constant. The calculated value then can be presented as the change in enthalpy (ΔH st ) which is the energy required to reverse the process (desorption) [34].
For calculation of ΔG, ΔH and ΔS under isothermal conditions, the following equations were used [20]:
where P is the standard pressure (1 bar), S g and S ad are the entropy of the bulk gas and adsorbed film respectively. The entropy of the bulk gas at operation conditions was obtained according to NIST webook [35].
4 Results and discussion
4.1 Material characterization
Activated carbon was characterized structurally by means of N2 adsorption measurements at 77 K. Table 1 presents the structural properties of the AC as obtained from N2 adsorption measurements. The specific AC is characterized by good specific surface area according to BET model (SABET) equals to 1141 m2/g while the external surface area (SAext) is almost ten times less (163 m2/g). The surface area of the micropores (SAmic) is equal to 978 m2/g, which is rational because AC is a microporous dominant material. Subsequently, the micropore volume (V mic) is the ∼70 % of the total pore volume (V tot) calculated at P/P 0 = 0.99. In order to exclude structural alterations, such as fragmentation due to rotation, AC was also characterized after each ROT set measurement; the results show no differences, nor in volume or in surface area properties.
Figure 2 presents the surface morphology of the AC adsorbent obtained by SEM. From the micrograph, the pores opening can be seen on the outer surface of the AC grain indicating that the intra-particle space of the material is mainly composed of open-end pores.
SEM micrograph of the AC surface.
4.2 Rotational device
The rotational device measures volumetrically the amount adsorbed by measuring the pressure drop within a known and constant volume system. To validate the results, a commercially available adsorption instrument based on gravimetric measurements is used. Figure 3 shows adsorption isotherm curves generated by IGA (Intelligent Gravimetric Analyzer) and the rotational device for temperatures of 281, 293 and 298 K.
Experimental results comparison; dashed lines correspond to IGA isotherm and circles to the rotational device (green for 281 K, blue for 293 K and yellow for 298 K).
Although the two instruments are working on different principles, the obtained values of CO2 uptake from the bespoke device is in accordance with the commercial one. This result highlights the validity of the rotational device allowing to proceed with the thermodynamic analysis of the experimental data. Experimental results of NoROT and ROT isotherms are fitted by both Langmuir and D–A isotherm models. The first is chosen as a well known and versatile adsorption model describing satisfactory adsorption occurred on microporous materials [16]. However, Langmuir model implementation is based on the assumption that the surface of the adsorbent is homogeneous and there are no lateral adsorbate–adsorbate interactions. For reasons of a more detailed comparison between static and rotational conditions, D–A model is applied. The specific model accounts for possible interactions between adsorbed molecules while it employs a parameter (ν) accounting for material heterogeneity [36].
Figure 4 presents the fitting on both models for all three temperatures (281 K, 293 K and 298 K); left column is for Langmuir model while the right is for D–A. The first top two subfigures are for NoROT and the bottom two for ROT experimental data. Although graphical representation shows that experimental results have good fit on both models, a quantitative analysis gives a better perception of the differences as they are outlined in Table 2.
Fit of experimental isotherm adsorption data to (a) Langmuir and (b) D–A models; green for 281 K, blue for 293 K and yellow circles for 298 K.
From the correlation coefficient r 2 of the Table 2, it can be seen quantitatively that experimental data are fitted better by the D–A model. In addition, D–A model provides insight regarding the characteristic energies (E) of the system which for ROT case are about 7 % larger compared to NoROT one. Furthermore, both q max (Langmuir) and q o (D–A), are greater for the ROT case at all temperatures. Specifically, for 293 K, the percentage difference between ROT and NoROT is the highest for both models; room temperature is considered the optimal condition where the effect of rotation is not hidden neither by the adsorption dynamics at low temperature nor by the weaker adsorption as the temperature reaches its critical value (304 K) for CO2.
This result is in accordance to the suggested phenomena of enhanced adsorption after rotation takes place. The reason to this is the increased “accessibility” of the gas molecules during but also after rotation ceases. From the Langmuir analysis we obtain the adsorption constant (b) that shows in both cases the expected trend; as temperature increases the value decreases. However, for NoROT this value is higher than it is for ROT counterpart at the same temperature. The amount adsorbed in the NoROT case approaches the corresponding q max faster than in the ROT case because in the latter more sites which were previously inaccessible became accessible; hence b ROT < b NoROT.
Figure 5 shows Van’t Hoff plot of lnb over 1/T, employed to obtain important thermodynamic properties at zero surface loading, such as ΔS° and ΔH° from the slope and intercept of the linear function. Gibbs free energy at standard state is calculated from Eq. (9).
Van’t Hoff plot of lnb over 1/T for NoROT (empty squares) and ROT (yellow squares).
Table 3 presents the calculated thermodynamic parameters both for zero and various surface loadings. The tabulated values for zero loading showcase that the spontaneity indicated by ΔG° is increased after rotation. The same result is also observed for ΔH° and ΔS°. As mentioned above, for zero surface loading, the values were obtained from the linear form of Van’t Hoff equation and they are dependent on the obtained Langmuir adsorption constant b. The same thermodynamic parameters were also calculated for surface loadings of 0.100, 0.150, 0.200, 0.250 and 0.300 kg of CO2 per kg of AC. Interestingly, here the case is different; those values have been calculated based on the ΔH st from Clausius–Clapeyron equation (Eq. (10)) derived from the slope of each linear plot (Figure 6).
Thermodynamic properties at zero loading.
| Thermodynamic properties at zero loading | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| ΔH° (kJ/mol) | ΔS° (kJ/mol K) | ΔG° (kJ/mol) | |||||||
| NoROT | ROT | NoROT | ROT | Temperature (K) | |||||
| 1.98 | 4.42 | 0.02 | 0.03 | 281 | 293 | 298 | |||
| NoROT | ROT | NoROT | ROT | NoROT | ROT | ||||
| −3.55 | −3.93 | −3.78 | −4.28 | −3.88 | −4.46 | ||||
| Thermodynamic properties at surface loading | |||||||||
| ΔS (kJ/mol K) | |||||||||
| Amount adsorbed | Temperature (K) | ||||||||
| ΔH st (kJ/mol) | (kg/kg) | 281 | 293 | 298 | |||||
| NoROT | ROT | NoROT | ROT | NoROT | ROT | NoROT | ROT | ||
| 11.56 | 10.13 | 0.100 | 0.039 | 0.038 | 0.036 | 0.031 | 0.035 | 0.030 | |
| 13.35 | 12.00 | 0.150 | 0.041 | 0.050 | 0.037 | 0.032 | 0.036 | 0.031 | |
| 15.97 | 14.64 | 0.200 | 0.046 | 0.063 | 0.042 | 0.037 | 0.040 | 0.036 | |
| 20.19 | 18.65 | 0.250 | 0.058 | 0.080 | 0.052 | 0.047 | 0.050 | 0.045 | |
| 28.22 | 25.56 | 0.300 | 0.083 | 0.108 | 0.075 | 0.067 | 0.071 | 0.064 | |
| ΔG (kJ/mol) | |||||||||
| 0.100 | −0.543 | −0.674 | −0.963 | −1.111 | −1.346 | −1.336 | |||
| 0.150 | −1.834 | −1.930 | −2.367 | −2.455 | −2.840 | −2.796 | |||
| 0.200 | −2.913 | −2.957 | −3.569 | −3.573 | −4.165 | −4.069 | |||
| 0.250 | −3.922 | −3.898 | −4.745 | −4.620 | −5.531 | −5.346 | |||
| 0.300 | −4.957 | −4.836 | −6.045 | −5.700 | −7.202 | −6.825 | |||
Clausius–Clapeyron plot of the logarithm of equilibrium pressure (P e ) in bar and the reverse of the experimental temperature in K at various surface loadings (0.100, 0.150, 0.200, 0.250 and 0.300) in unit mass of CO2 per unit mass of AC (kg/kg).
From the Table 3, it can be stated that the effect of rotation alters the adsorption mechanism in a quite complex manner, whereas the mechanism itself depends on the temperature. The latter can be observed from the different trend of ΔS that NoROT/ROT comparison at 281 K showcases compared to the other two, higher temperatures; at 281 K the ΔS for the ROT case is greater than the NoROT case attributed to the increase of the kinetic energy of the gas molecules in the bulk phase. For the 293 and 298 K, the change in entropy is lower for the ROT cases implying that adsorbed molecules increased their entropy, hence the difference between S g and S ad is smaller. Another point of interest is that the absolute value of ΔG decreases after the rotation point (at around 0.200 kg/kg surface loading); it gets less spontaneous that is translated into a more thermodynamically stable system [37, 38].
For a more clear understanding we recall the Everett analysis of chemical potential of the adsorbed phase. In his series of work [39–41], Everett examines the change in chemical potential in respect to surface coverage, given as:
where, μ Γ and P Γ are chemical potential and pressure at a specific surface loading, respectively. The relationship of chemical potential change and surface loading for all temperatures and for both cases is given in Figure 7(a). The adsorption isotherms of NoROT and ROT are compared in Figure 7(b), where is obvious that until the rotation point, both curves are identical and only after rotation step they diverge resulting in a “fork” shape difference.
Comparison of NoROT and ROT; (a) chemical potential for NoROT (empty circles) and R (filled circles) for the three temperatures, (b) all three isotherms for both cases (circles for NoROT and triangles for ROT; yellow at 298 K, blue at 293 K and green at 281 K). The same color coding is valid for chemical potential graph as well. The insert in (b) shows ±2 % error bars of 293 K adsorption curve of both NoROT and ROT cases.
The rotation makes the system to have a lower chemical potential than NoROT case at the same surface loading, hence for the same P e , the amount adsorbed will be greater for ROT case. The root-mean-square deviation of the data was calculated according to the following equation [24]:
where, q exp and q th are experimental and theoretical amount adsorbed respectively, while N is the number of points. In both cases, NoROT and ROT, each experimental point is found to be within ±2 % deviation with Langmuir model.
Figure 7(b) shows the result while the insert presents the error bars for the isotherms at 293 K. From the results, a situation of adsorbed molecules rearrangement can be stated, the proposed mechanism is depicted in Figure 8. In fact, the phenomenon indicates entropy driven adsorption after the rotation happens.
Isosteric heat of adsorption from Clausius–Clapeyron equation with respect to surface loading; empty squares representing NoROT and yellow ROT case at different surface loading.
The isosteric heat of adsorption is the measure of the heat released during exothermic reactions such as physisorption. Figure 8 shows the trend of both examined cases with an increase in ΔH st as adsorption proceeds. This upwards curve is indicative for microporous materials when adsorbate–adsorbate interactions are pronounced [42–44]. The curve for ROT solely is in parallel but lower compared to that of NoROT case. This fact is attributed to differentiation of energetic sites distribution due to rotation by enhancing the adsorbate/adsorbent interaction, as it is supported also by the increase in E from D–A model (Table 2).
As mentioned previously, rotation enables molecules to access sites within pores that were previously inaccessible, resulting in increased molecule population inside a single pore. According to literature, the number of molecules inside a pore, alters the structural transformation of the adsorbate [45, 46].
Figure 9 shows the mechanism of the effect of the rotation on the adsorbed CO2 molecules. To exemplify, let us use the case of a gas molecule deposited on the opening of a narrow pore, the initial orientation of this molecule prevents it from being inserted deeper inside the pore. We can interpret rotation as this force that allows as to rearrange the already adsorbed molecules and thus altering their configuration on the surface. The same result was observed from Small Angle X-ray Scattering (SAXS) measurements of CH2Br2 on Vycor porous glass [47], where after rotation the adsorbed film was minimized in thickness indicating a more close and thermodynamically stable packing after rotation.
Schematic representation of the effect of rotation on the sites accessibility.
5 Conclusions
The present study investigates the effect of rotation on gas adsorption. Rotation is introduced to a constant volume adsorbate/adsorbent system allowing a detailed analysis of the mechanism involved. The system was examined for static (non rotational-NoROT) and under rotation adsorption (ROT) of CO2 on activated carbon. The conducted thermodynamic analysis shows that even a short time rotation impacts the overall adsorption in an entropy driven process.
The effect of the rotation is more pronounced at room temperatures (293 and 298 K) where, from ΔG calculations, it is seen that rotation increases adsorbate/adsorbent interactions resulting in a less spontaneous process and thus more thermodynamically stable system compared to NoROT case for all three temperatures.
Chemical potential change Δμ interpretation points to this direction as well, where the ROT case shows a minimized Δμ at higher surface loading compared to the same loading for the NoROT case. In parallel, the amount adsorbed at the same equilibrium pressure is greater for the ROT case as was shown from the adsorption isotherms. Combining the results, it is obtained that rotation: (i) makes the adsorbed molecules to rearrange, (ii) increase the gas molecules population inside the pores and (iii) alters the energy distribution by enhancing adsorbate–adsorbent interactions due to different orientation leading to a more stable adsorbed film. The proposed mechanism is well exemplified as an energy “shake” that makes the already adsorbed molecules more ordered.
Finally, this study aims to introduce a new measurement technique by the implementation of the rotational device for thermodynamic properties determination in various intensification processes involving rotation. However, in order to understand better the mechanism, further systematic research is considered important.
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Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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