Lithium hydroxide as a high capacity adsorbent for CO2 capture: experimental, modeling and DFT simulation

In this work, the potential of monohydrate Lithium hydroxide (LiOH) as a high capacity adsorbent for CO2 capture was investigated experimentally and theoretically. The effects of operating parameters, including temperature, pressure, LiOH particle size and LiOH loading, on the CO2 capture in a fixed-bed reactor have been experimentally explored using response surface methodology (RSM) based on central composite design. The optimum conditions obtained by the RSM for temperature, pressure, mesh and maximum adsorption capacity were calculated as 333 K, 4.72 bar, 200 micron and 559.39 mg/g, respectively. The experiments were evaluated using isotherm, kinetic and thermodynamic modeling. Isotherm modeling showed that Hill model could deliver a perfect fit to the experimental data, based on the closeness of the R2-value to unity. The kinetics models showed that the process was chemical adsorption and obeyed the second order model. In addition, thermodynamic analysis results showed that the CO2 adsorption was spontaneous and exothermic in nature. In addition, based on the density functional theory, we investigated the chemical stability of LiOH atomic clusters and examined the effects of LiOH nanonization on the physical attraction of carbon dioxide.

The reaction between CO 2 and hydroxides produces pure carbonate by high adsorption capacity, low thermal chemical adsorption, which is able to adsorb CO 2 at ambient temperature and pressure 10 . Lithium hydroxide has been used for CO 2 adsorption due to its high CO 2 storage capacity (30 wt.%), with applications in space life support systems, space shuttle environmental control and submarine scrubbing systems 15 , (theoretically 1 kg of LiOH can absorb up to 0.91 kg of CO 2 10 ). In these applications, air or oxygen laden with CO 2 from human or animal respiration is forced to move through a bed of lithium hydroxide granules. CO 2 is removed and the carrier gas is returned to the environment. The reactions of water and carbon dioxide with lithium hydroxide are as follows 16 : The overall process is exothermic producing 21.4 kcal per mole CO 2 absorbed. Reaction (4) is the classical expression and the sum effect of the intermediate reactions (2) and (3). However, some effort has been made to understand basic factors affecting the adsorption rate without considering the specific application 17 . Williams et al. 17 studied the effect of vapor pressure and moisture percent on the adsorbent for carbon dioxide and lithium hydroxide reaction. Obviously, they proved that the pressure of water vapor in the incoming stream should be equal to or greater than CO 2 partial pressure in order to continue the reaction. Boryta et al. 16 investigated operating variables including the pores factors, adsorbent surface area, the partial pressure of gas, and vapor pressure of water. Wang and Bricker 18 combined the effects of temperature and humidity on carbon dioxide absorption capacity.
Adsorption of CO 2 onto microporous activated carbon powder was investigated in terms of isotherms, kinetic and thermodynamic 19 . It should be noted that activation of carbon in order to sensitize it to the environment should be goal-oriented. Because any type of carbon reduction does not mean effective activation in order to use it as an adsorbent 20  www.nature.com/scientificreports/ its interaction with the environment [21][22][23] . However, there are tricks to adapt activated carbon to adsorb carbon dioxide. Shi et al. 24,25 To make carbon suitable for carbon dioxide adsorption, it was doped with nitrogen in a porous state and then activated it with potassium hydroxide or sodium hydroxide. Cui et al. 26 showed that nitrogen doping more significant effects on enhancing the adsorption heat and selectivity. Recently, less expensive methods have been introduced to activate carbon with biomass-derived for CO 2 uptake 27 . Odin et al. showed that the adsorption of carbon dioxide is done with spherical pheno resins, which is significantly improves by activating with potassium hydroxide 28 . Lee et al. 29 in 2012 investigated adsorption at room temperature onto modified zeolites and activated carbon (AC) by alkali and alkaline earth metals. A fixed-bed adsorption apparatus was used to obtain more information about the effects of impregnated cations. So that, modified zeolites had greater adsorption capacities than ACs, despite their smaller surface areas, because of the electrostatic interfaces between zeolites. The intensity of the electrostatic field, and the charge density in particular, increases in the sequence of K + < Na + < Li + , resulting in enhanced electrostatic fields and greater CO 2 adsorption capacities 29 . Cho et al. in 2015, modified the commercial zeolite of 13X and 5A with lithium hydroxide (LEZ-13X and LEZ-5A) to remove carbon dioxide in the indoor simulated examined. The BET levels of zeolite adsorbents after modification with lithium hydroxide are higher than unmodified zeolite types, as a result, it showed an increase in the adsorption capacity 30 . Krishnan et al. 31 in 2015, proposed a system that made of activated carbon filter consists of a matrix board, lithium hydroxide and calcium hydroxide. The summarized adsorption of carbon dioxide with solid adsorbents and adsorbents modified with LiOH and are presented in Table 1.
The low heat of reaction for the reaction between carbon dioxide and LiOH compared to other hydroxides, as well as the lower risks of keeping the lithium hydroxide adsorbent in a closed environment to adsorb carbon dioxide, greater compatibility with the environment and human living environment, the ability to adsorb in temperature and the ambient pressure is more justified than sodium hydroxide, potassium hydroxide and other physical and chemical adsorbents.
In this work, the kinetic, thermodynamic and isotherm of CO 2 adsorption by LiOH was investigated experimentally and theoretically. In the design and statistical evaluation of experiments, response surface methodology (RSM) can be exploited for process modeling and optimization. RSM based on the central composite design was applied in order to design the experiments, build models and measure the optimum modification conditions to achieve desirable responses 32 . The main objective of this work is to explore the influence of modification parameters on the CO 2 adsorption performance of the solid adsorbents in a fixed-bed reactor. In addition, the adsorption process of carbon dioxide by lithium hydroxide atomic cluster has been simulated. The simulations were performed based on the density functional theory. The simulation results are about the type of interaction between CO 2 and lithium hydroxide at room temperature, and the effect of the size of grains on the adsorption of carbon dioxide gas.

Materials and producers
Materials. Lithium Hydroxide (LiOH) was purchased from Merck chemical Co., and purified carbon dioxide gas (99.98%) was supplied by Sabalan Gas Co. (Tehran, Iran). LiOH is a solid powder and density, melting point, and solubility of LiOH sorbent in water are 2540 kg/m 3 , 20 °C and 12.8 g/100 g, respectively.
Characterization of adsorbents. The solids and liquids were analyzed to identify the links and chemical structure. Laboratory FTIR spectrometer system, is able to pass and adsorption spectra of liquid, solid and Table 1. Review of carbon dioxide adsorption using solid adsorbents.

Researchers
Year Adsorbent type Gas composition Q (mg/g) T (K) P (bar) Lee  powder. The FTIR spectroscopy analysis was performed using a spectrometer (Perkin Elmer, Model 2000 FTIR, USA) to identify surface functional groups in LiOH. X-ray diffraction is used to identify the chemical composition and properties of crystalline crystals, ceramics, metals, alloys and synthetic materials widely used in chemical engineering.
Adsorption setup. All CO 2 adsorption experiments were performed by Lithium hydroxide with mesh of No70. The laboratory set up includes three parts: (1) gas infusion device, (2) CO 2 reactor device, (3) investigation of CO 2 pressure changed in the reactor during uptake process. The reactor length, inner radius and the internal volume were 9 cm, 3 cm and 255 cm 3 , respectively. At the beginning of the test, CO 2 transferred from the cylinder to the reactor encasement via pressure current supervisors. As well as, the required temperature for each experimental run was provided by thermocouple linked to the reactor body and controlled via regulating the set point for the system. Changing in the temperature and pressure for 1 h of the reactor comprising solid adsorbent were analysis and control online during the process. All data were stored in separate Excel files in a reference computer with the temperature, pressure, time and the date. The pressure, temperature and amount of the adsorbent ranged between 1 and 9 bar, 298-363 K and 2.4 g, respectively. When pure CO 2 was injected to the reactor containing solid adsorbent, adsorption process was began and CO 2 was captured through the solid adsorbent. During the CO 2 adsorption process, the pressure in the reactor was decreased. The CO 2 adsorption rate as the difference between initial and final of CO 2 pressure by the gas sensor was measured. The adsorption capacity of the adsorbent was calculated through the following equation: K d is the distribution coefficient (cm 3 /g). The distribution coefficient was calculated through the following equation: where w is the weight of adsorbent. q e is the adsorption capacity (mg/g), P i is the initial pressure (bar), P e is the equilibrium pressure (bar), m is the dosage of adsorbent used (g) and v is the volume of the gas (L -1 ). The adsorption percentage of CO 2 was calculated as follows: where P i and P f are the initial and final pressure, respectively. Also, the correlation coefficient (R 2 ), which represents the variability percentage in the dependent variable (the variance about the mean) is employed to analyze the fitting degree of isotherm and kinetic models with the experimental data (Eq. 8) 33 . Its value may vary from 0 to 1 34 .
where q e,meas and q e,calc are the measured and calculated adsorption capacity (mg/g), respectively.

LiOH atomic clusters
The density functional theory (DFT) was applied for analysis of carbon dioxide adsorption by LiOH atomic clusters. Previously, using the density functional theory, extensive research has been done on the interaction of carbon dioxide and lithium compounds [35][36][37][38][39][40][41] . The nanonization effects of LiOH salt on carbon dioxide adsorption was investigated. To investigate the effect of carbon impregnated with lithium hydroxide on carbon dioxide capturing, we performed modeling based on density functional theory (DFT). The calculations are based on the B3LYP functional [42][43][44][45][46] , and the electron density is modelled with the LANL2DZ basis set 47,48 . Our DFT simulations are performed using the Gaussian software package 49 .

Response surface methodology
The effects of the three independent variables, including temperature, pressure and LiOH particle size (mesh size), on the CO 2 adsorption capacity was explored using the central composite design. These variables, along with their respective regions of interest, were selected based on the literature and preliminary investigations 50 . Table 2 presents the range and levels of the independent numerical variables in terms of actual and coded values.  Response surface methodology results. In the present work, response surface methodology (RSM) explores the relationships between input variables including temperature, pressure and LiOH particle size (mesh size) and CO 2 adsorption capacity as a response variable. The RSM method was applied to design the experiments and investigate the optimization of the process. In the RSM, A-temperature, C-mesh size, B-pressure, AB, and C 2 affect the response variable significantly; all these outcomes have been taken from the information given in the p-value column ( Table S1 in the supplementary). The P-value model is lower than 0.001, which shows that the model terms are highly significant. P-values less than 0.05 and 0.001 indicate that the model terms are significant and highly significant, respectively. While P-values greater than 0.1 indicates that the model terms are not significant. The same way, f-value substantial range is 1-40 53,54 .

Results and discussion
In order to industrialize the alkali metal-based sorbent, the effects of the operation conditions on CO 2 capture performance should be determined in details (Table S2 in the supplementary). There are 8 factorial points, 6 axial points and 6 replicates at the center points, indicated by a total of 20 experiments, as calculated from N = 2 n + 2n + n = 20.
In addition, the experimental values for responses are in good agreement with the amounts predicted by the RSM model. The predicted values, were more close to the experimental values, due to possessing high R 2 (Fig. S3 is in the supplementary).
The interaction of operating parameters in CO 2 adsorption was obtained by RSM. Figures 1 and 2 illustrate the dimensional response surfaces, which show the effects of the significant variables. Figures 1a,b and c illustrate the dimensional response surfaces, which show the effects of the significant variables including pressure, temperature and adsorbent mesh on CO 2 adsorption percentage. The Figures show that increasing pressure and temperature resulted in an increase in the adsorption percentage, while increasing the adsorbent mesh size led to a decrease in the adsorption percentage. Figures 2a,b and c show the dimensional response surfaces, which show the effects of the significant variables including pressure, temperature and adsorbent mesh on CO 2 adsorption capacity. It is clear that pressure and temperature have positive effects on CO 2 adsorption capacity whereas increasing the mesh size of the adsorbent has negative effects on CO 2 adsorption capacity. Surface area of the adsorbent increased by decreasing the mesh size, and consequently, adsorption resistance of the adsorbent decreased.
Isotherm modeling. To optimize the design of CO 2 adsorption system, it is important to determine the appropriate mechanisms and describe the thermodynamic equilibrium quantitatively. Hence, it is necessary to understand the equilibrium to predict the adsorbent behavior. Therefore, the equilibrium experimental data for CO 2 adsorbed in the lithium hydroxide adsorbent were investigated using Langmuir isotherm, Freundlich, Dubinin-Radushkevich (D-R) and Hill. The constant values of Langmuir, K L and q m of the K and n constants for the Freundlich, the q m and E constants for Dubinin-Radushkevich, and so on, the constants for the Hill, models at 303 K, are given in Table 3. The Langmuir equation is given by Eq. (9) below: where q e is the amount of CO 2 adsorbed at equilibrium (mg/g), q m is the maximum adsorption capacity of the adsorbent (mg/g), P CO 2 is the equilibrium pressure of the gas adsorbed (bar), and K L is the Langmuir adsorption constant that relates to the free adsorption energy (1/bar) 55 . The Freundlich isotherm model is the earliest known relationship that presents a non-ideal and reversible adsorption process 56 . Freundlich is applicable to the multilayer adsorption, and it is based on an assumption that the adsorption energy will exponentially decrease with an extent of the adsorption process 57 . The model can be expressed by Eq. (10) 50 : where k 1 is the distribution coefficient and n is related to a correction factor. As the k 1 value increases, the adsorption capacity of adsorbent for a given adsorbate will also increase. The adsorption capacity or surface heterogeneity is determined from the slope value of 1/n, in which n is between 0 to 1, and by shifting the value towards zero, where R is the gas constant (8.314 J/mol K) and T is the absolute temperature. Dubinin-Radushkevich isotherm is an experimental model initially conceived for the adsorption of subcritical vapors onto micropore solids, following a pore filling mechanism, which is generally applied to express the adsorption mechanism with a Gaussian energy distribution onto a heterogeneous surface 59 . Following the introduction of the isotherms, the Hill isotherm model, originated from the NICA model 58-60 , was postulated. The model describes binding of different species onto homogeneous substrates. The model assumes that the adsorption is a cooperative event, and the binding ability of the ligands at one site on the macromolecule are similar with other macromolecule binding sites. This Hill isotherm model is defined by Eq. (12) 59 : where n H is the constant incorporating both Langmuir and Freundlich isotherm models for representing the equilibrium adsorption data. In Fig. 3, the experimental comparison of data with Langmuir, Freundlich and D-R models is well represented at 303 K. The desirability of the adsorption process is shown by correlation coefficient (R 2 ).
In a component isotherm study, determining the best-fitting model is the key analysis to mathematically describe the adsorption system. With respect to the R 2 values, the suitability of these models in predicting the sorption behavior follows the order of Hill > D-R > Freundlich > Langmuir. Furthermore, the computed value of n F < 1 implies that the CO 2 adsorption onto the LiOH is a chemisorption process, whereas if the value is larger than 1, it suggests a physisorption process 61 . In Table 3, the value of R 2 is in the range of 0-1, which shows that CO 2 adsorption is desirable or not. According to R 2 , the most suitable models for predicting adsorption behavior are Hill > D-R > Freundlich > Langmuir. Perez et al. suggested that Langmuir's model is the best one for describing the chemical reactions due to its limitation to one layer. While Freundlich primarily represents the process of (11) q e = q s × exp K ad × R × T × log 1 + 1 P CO 2 2 (12) q e = q s × P nH www.nature.com/scientificreports/ physical adsorption because it allows adsorbent molecules to form a continuous layer on the adsorbent surface. The CO 2 adsorption is shown in the range of 0-2 by a 1/n constant Freundlich. The value of 1/n < 1 shows that the CO 2 adsorption onto the adsorbent is chemical adsorption. While for the value of 1/n > 1, the adsorption would be a physical process. The D-R isotherm provides useful information about energy parameters. E is defined as the energy of free adsorption. Accordingly, the value of E < 8 kJ/mole corresponds to a physical adsorption, the value in the range of 8 < E < 16 indicates that the adsorption is controlled by the ion exchange mechanism, and the value of E > 16 kJ/mol shows that the adsorption is due to the influence of particle penetration [62][63][64] and it is a chemical adsorption.  involves matching empirical data to a set of fixed models and choosing the best one. Among all the existing kinetic models presented, the first-order and second-order models are the easiest to describe the kinetics of CO 2 adsorption (Table S3 in the supplementary). The another applicable kinetics models are Elovich, Ritchie second order and Rate control. The results of the models are presented in Fig. 4. Specifications and parameters of each model are presented separately at temperature in range of 303 to 363 K. As the results of the correlation coefficient R 2 in the Table 4, the first-order model is weak, while the second-order models are suitable for all experimental results. In this model, the parameter R 2 is very close to the unit value. In particular, the first-order model can indicate the reciprocal interaction between adsorbent and adsorption, which is suitable for predicting the behavior of CO 2 adsorption in physical adsorbents, such as activated carbon and zeolite. On the contrary, the second-order model assumes that the interaction between adsorbent and adsorption is caused by a strong gas connection to the adsorbent surface, which is more suitable for chemical moieties and CO 2 -adsorption processes involving chemical interactions and chemical bonding. The CO 2 adsorption on the lithium hydroxide is well suited for chemical adsorption. In Table 4, the value of R 2 is in the range of 0-1, which shows that CO 2 adsorption is desirable for second-order model. In Fig. 5, the experimental comparison of data with first order, second order, Elovich and Rate controlling models is well represented at 303 K.

Adsorption thermodynamics. In the adsorption processes, thermodynamic factors including entropy
and Gibbs free energy should be considered in order to determine which adsorption process will occur spontaneously. Enthalpy change (ΔH°), Gibbs free energy change (ΔG°) and entropy change (ΔS°) can be estimated using equilibrium constants changing with temperature. The distribution coefficient at constant temperature was calculated using Eq. (17). www.nature.com/scientificreports/ where K d is the distribution coefficient (cm 3 /g), ΔS° is entropy change, ΔH° is enthalpy change, T is the absolute temperature (K), R is gas constant (kJ/mol K). The standard free energy values was calculated using Eq. (18).
The values of the enthalpy change and entropy change are calculated from the slope and intercept of the plot of Ln(K d ) versus (1/T) as presented in Fig. 5. The values of ΔH°, ΔS° and ΔG° are listed in Table 5. It is clear that the adsorption reaction of CO 2 on LiOH is endothermic. The free energy value for all the temperatures is negative, and the decrease in the value of ΔG° with increase in temperature shows that the reaction can be done easier at high temperatures.
The experiments were carried out at 303-363 K and pressure of 6 bar of CO 2 . The values of ΔH° and ΔS° were calculated from the slopes and intercepts of linear regression of Ln k d versus 1/T. The results in Table 5 indicates that the process is exothermic and the adsorption capacity of the adsorbent increases with increase in temperature. The results shows that the adsorption percentage has increased with increasing the adsorption temperature (Fig. S4 in the supplementary). The negative value of ΔH indicates that the adsorption process is exothermic and shows the chemical reaction between the gas and adsorbent. As the temperature rises, the reaction progresses   www.nature.com/scientificreports/ and the adsorption capacity increases, resulting in irreversibility of the reaction between CO 2 -lithium hydroxide in the reactor and the production of lithium carbonate. The negative value of ΔS represents the tendency to the adsorbent material and some structural changes in the adsorbent and the absorbent. On the other hand, negative entropy indicates an increase in irregularities during adsorption and a slight change in the absorbent and adsorbent structural changes, and thus, indicating a spontaneous reaction. significant enthalpy changes indicate that the process is sensitive to temperature, and conversely, slight enthalpy changes indicate that the adsorption process is not sensitive to temperature 65,66 .
Effect of operational conditions on adsorption capacity. The effect of different LiOH loadings on CO 2 adsorption capacity is illustrated in Fig. 6. It is clear that increasing the adsorbent loading results in an increase in the adsorption of CO 2 . The lowest adsorption capacity of 180.196 mg/g was exhibited by the lowest LiOH dosage of 1.2 g, and further dosage from 2.4 to 4.8 g did not substantially increase the CO 2 adsorption capacity (277.99 and 290.127 mg/g). Due to this, the adsorption capacity of CO 2 was determined at an optimal adsorbent of 2.4 g. Since the CO 2 adsorption reaction with lithium hydroxide is associated with the production of water, the production of water during the reaction requires heat, and the overall reaction is a thermal one. Hence, by increasing the amount of the adsorbent, the heat required for the second reaction is provided. Similarly, Fig. 7 shows a schematic representation of increasing the amount of adsorption by increasing the amount of the adsorbent.
The results show the effect of particle size of lithium hydroxide on CO 2 adsorption capacity. The solid lithium hydroxide was crushed using a mortar and passed through a mesh strainer. The particle size was determined in meshes of 200, 300, 500 and 800 microns. Reducing the particle size of the Lithium Hydroxide powder leads to an increase in the CO 2 adsorption capacity (Fig. S5 in the supplementary).
The adsorption experiments were carried out using various particle sizes of the adsorbent (diameter of the LiOH particles 200 to 800 µm) at 6 bar and 303 K. The analysis of CO 2 adsorption at different particle sizes showed that the CO 2 removal rate increased with a decrease in the particle diameter (Fig. 8). In this temperature and pressure, that smaller particles possess large surface areas, the required time to reach equilibrium for fine particles is less of the time required for the coarse particles. The reduction of particle diameter caused to raise the gas-solid contact surface resulting in a faster equilibrium achievement 67 .   Fig. 9.The amounts of adsorption at higher temperatures show that the adsorption capacity increases at higher temperatures. This trend of higher adsorption capacity with high temperatures indicate that the adsorption of CO 2 on LiOH is chemical adsorption. The catalytic effect of water on the adsorption of CO 2 has been proved by Miller and Piatt 69 to have a substantial effect on the reaction, as exhibited in the Eq. (3). Boryta and Maas 16 suggested that in order to absorb CO 2 effectively, a reactive intermediate lithium hydroxide monohydrate, LiOH·H 2 O, should be first formed (reaction Eq. (2)). Moreover, according to the FTIR analysis, the surface of LiOH contained some -OH, which may be responsible for the CO 2 adsorption at low temperatures. The reaction of lithium hydroxide with CO 2 is an exothermic reaction due to the acid strength and power of lithium hydroxide. Similarly, Fig. 10 shows a schematic representation of increasing the amount of adsorption by increasing the temperature.
Pressure is one of the most important parameters in the adsorption processes. The effect of pressure and time on adsorption capacity are presented in Figs. 11 and 12 at temperature of 303 K. In Figs. 11 and 12, it is clear that the highest CO 2 adsorption capacity was achieved at pressure of 9 bar, demonstrating that pressure had a   www.nature.com/scientificreports/ positive effect on the adsorption capacity. This trend is on a higher upward pressure level so that at high pressures, the equilibrium is not noticeably visible and adsorption is still ongoing. This leads to an increase in adsorption capacity by increasing pressure. The equilibrium constant increases with increasing pressure, and therefore, the amount of molecules filled on the surface increases. The effect of pressure on increasing the position of molecules in adsorbent vacant sites and unreacted adsorbent portions leads to increased gas adsorption capacity. In this way, air can simulate in high pressure and low pressure environments. It is noteworthy that these consequences imply that the final CO 2 pressure is controlled by the chemical equilibrium of the carbonation reaction. As the pressure increases, the adsorption capacity increases.
DFT simulation results. The simplest model that can be considered for the adsorption of CO 2 by lithium hydroxide is that lithium hydroxide adsorbs carbon dioxide and turns into lithium bicarbonate. Now, we use the Gibbs free energy equation to have a view of how lithium hydroxide reacts with carbon dioxide and forms lithium bicarbonate at room temperature 22 : For this purpose, we calculate the enthalpy and entropy changes for the desired chemical reaction at room temperature, i.e. 298.15 K. Table 6 shows the data related to enthalpy and entropy of the reaction components   www.nature.com/scientificreports/ of carbon dioxide adsorption by lithium hydroxide and the changes in the related thermodynamic parameters are given. Gibbs free energy changes indicate that the process of chemical adsorption of carbon dioxide by lithium hydroxide cannot be spontaneous at room temperature, for this process to be spontaneous; the ambient temperature needs to be less than 55 K. Now we will check whether there is physical adsorption between lithium hydroxide and carbon dioxide at room temperature or not. We first modeled a single layer of lithium hydroxide crystal structure; you can see its model in Fig. 13.
To estimate the amount of attraction or repulsion between lithium hydroxide and CO 2 , we calculate the binding energy between several atomic clusters of lithium hydroxide and CO 2 in the optimal state relative to each other. We calculate the size of the desired dependence energy from the following equation 68 .
In Fig. 14, the lithium hydroxide atomic clusters investigated in this research, which are LiOH, Li 2 (OH) 2 , Li 3 (OH) 3 , Li 4 (OH) 4 and Li 4 (OH) 5 , are shown in the optimal structures obtained by density functional theory calculations. Note that the Li 4 (OH) 5 cluster is the smallest salt crystal that can be seen repeatedly in the lithium hydroxide crystal structure.
By examining the chemical hardness of the above atomic clusters, we can conclude that the above structures have acceptable chemical stability. The chemical hardness can be obtained for each atomic cluster of lithium hydroxide using the following relationship.
For each of the introduced atomic clusters, the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO) and the HOMO-LUMO gap and finally the chemical hardness were obtained ( Table S4 in the supplementary).
By observing the chemical hardness of lithium hydroxide atomic clusters, we conclude that these structures are chemically stable. Usually, with the nanonization of materials their chemical reactivity increases; but with the nanonization of lithium hydroxide, it turns from a salt structure into covalent atomic clusters. For the above structures, there are no imaginary vibrations (For example, the IR frequency spectrum for Li 4 (OH) 5 is shown in Fig. S6 in the supplementary). Now, after determining the chemical stability of lithium hydroxide atomic clusters, we consider a compound system between the atomic clusters introduced with carbon dioxide, and concluded that there will be physical attraction between lithium hydroxide and carbon dioxide clusters in the optimal state. In Table 7, there is www.nature.com/scientificreports/ information about the size of the clusters, the optimal distance between the clusters and carbon dioxide, and finally the binding energy between each of the clusters and carbon dioxide in the optimal state. The first result that can be obtained from the data in the above table is that as the clusters get bigger, their optimal distance with the carbon dioxide molecule tends to a limit value, which is around 2.1 angstroms here. This distance is the same value that the carbon dioxide molecule can have in the optimal state with the lithium hydroxide salt crystal. The second point that can be noticed is that the smaller the size of the clusters, the greater its attraction to carbon dioxide, or in other words, the attraction of small clusters is closer to chemical adsorption. And finally, there is a third point about the Li 4 (OH) 5 cluster, which, as mentioned, is the smallest crystal structure of lithium hydroxide salt. You see the binding energy for this structure is different and lower than the other clusters in the table, almost half of the value of the similar structure i.e. Li 4 (OH) 4 . Because for this cluster, we assumed the optimal position of the carbon dioxide molecule in a position where the carbon dioxide is close to the hydroxide part of the salt. This assumption was different from the situation that existed for other clusters because in those clusters, carbon dioxide approaches the lithium atoms of the cluster from its oxygen side. The reason for this assumption is that in the crystal structure, lithium atoms are placed in the inner part of the salt structure, and the outermost part of the salt crystal is the hydroxide part placed on the lithium atoms (See part b of Fig. 2 in the supplementary file). As mentioned in the table above, the optimal distance of carbon dioxide from lithium hydroxide is about 2.1 angstroms, which means that the maximum binding energy occurs at this distance, and if the distance between carbon dioxide and salt is less than this, it will face electrostatic repulsion. This conclusion is shown schematically in Fig. 15.
In fact, the combination of carbon dioxide and lithium hydroxide can form a one-piece system in terms of electron cloud distribution, which will have the lowest possible energy in the optimum state of this electron distribution. In the combination of carbon dioxide-lithium hydroxide, the orbitals of carbon dioxide molecule will play the role of HOMO, and the orbitals of lithium hydroxide will play the role of LUMO of the compound. For this reason, the attraction between carbon dioxide and lithium hydroxide is justified, and their distance should be such that this combined system has the lowest potential energy, in other words, the two compounds are in an optimum position to each other. In Fig. 16, you can see the situation of electron cloud distribution and HOMO and LUMO orbitals in the desired combination.  Table 7. Information of the clusters, the optimal distance between the clusters and carbon dioxide, and finally the binding energy between each of the clusters and carbon dioxide in the optimal state. www.nature.com/scientificreports/ According to the charge distribution on the Mulliken scale, it is clear that the oxygens in the carbon dioxide molecule act as the negative pole and the hydrogens on the surface of the lithium hydroxide act as the positive pole of the structure, so initially there is an attraction between carbon dioxide and lithium hydroxide. However, as the carbon dioxide molecule approaches the surface of the lithium hydroxide crystal, the repulsive force between the carbon of the molecule and the hydrogen of the surface increases and decreases the attractive force. Then, as the molecule approaches the salt, the interaction force between the two turn into repulsive.

Conclusion
A remarkable difference was observed in the CO 2 adsorption behaviors on the LiOH. The effects of various operating parameters, i.e., LiOH particle size, temperature, and pressure, on the CO 2 adsorption capacity were wisely examined using the RSM method. The CO 2 uptake rapidly increased, with increasing pressure from 1 to 9 bar, and accordingly, at an equilibrium pressure of 9 bar, the maximum CO 2 uptake (318.095 mg/g) attained by  www.nature.com/scientificreports/ the LiOH solid which is significantly higher than the amount obtained in the pressure of 1 bar (156.242 mg/g). Hill isotherm model to the closest fit to the experimental data was two-parameter model. The second-order closest model to fit the experimental data was a kinetic one. An increase in temperature led to an increase in the chemical CO 2 uptake of the solid lithium hydroxide. The values of ΔH° and ΔS° were calculated from the slopes and intercepts of linear regression of Ln k d versus 1/T, based on which ΔH° = − 13,681 j/mol and ΔS° = − 72 j/ mol·K were obtained, representing that the exothermic chemical reaction is between carbon dioxide and lithium hydroxide. Also, our DFT simulations show that with the nanonization of lithium hydroxide, are formed stable atomic clusters, and the smaller the dimensions of these clusters, the greater the attraction between them and the carbon dioxide molecule.

Data availability
The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.