Investigating the Effect of Pore Size Distribution on the Sorption Types and the Adsorption-Deformation Characteristics of Porous Continua: The Case of Adsorption on Carbonaceous Materials

Abstract

In the chemical industry and in the manufacturing sector, the adsorption properties of porous materials have been proven to be of great interest for the removal of impurities from liquid and gas media. While it is acknowledged that significant progress and literature production have been developed in this field, there have been adsorption studies that failed to further advance our knowledge in generating a better understanding of the prevailing sorption types and dominant adsorption processes. Therefore, this review study has focused on porous materials, their sorption types and their adsorption properties, further investigating the adsorption properties of porous materials at either solid–gas and solid–liquid interfaces, underscoring both the properties of the materials, the characterization and the correlation between the porosity and the adsorption capacity, as well as the emergent interactions between the adsorbent and adsorbate molecules, including the adsorption mechanisms, the types of sorption and the kinetic and thermodynamic information conveyed.

1. Introduction

The literature describes a mild and straightforward protocol for creating graphene-based porous materials. This protocol is crucial for effective pore design development. As a result, it is critical for the development of graphene-based porous materials with adjustable surface areas. In the relevant literature, intercalating fluorinated graphene (FG) in alignment with the detected reactive CF bonds on graphene sheets with various amine-terminated molecules has been studied [1]. Graphene sheets are porous materials that function as building blocks, while the role of the pillar is played by diamines covalently bonded to the graphene framework. Diamines can be successfully grafted onto the graphene sheets under varied grafting ratios, based on FG reduction levels and considering the chemical reactivity of the diamines; the latter are chemically anchored at one end, thus differentially reacting at the other end and supporting three distinct conformations of graphene derivatives [1].

A notable study introduced a new type of oil-water separation material: thermoplastic polyurethane (TPU) porous material. This material boasts excellent properties, including low density, a high specific surface area and superior oil-water separation performance. However, the effectiveness of TPU porous materials is often hindered by various factors. Conducting numerous experiments to examine the relationship between these factors and adsorption performance can be both costly and time-consuming. To mitigate this, machine learning (ML) techniques have been employed to model and predict experimental outcomes [2]. In this study, an integrated hybrid model was developed to forecast the adsorption performance of materials, thereby reducing the need for some experiments [2]. These models demonstrated high prediction accuracy and effectively elucidated the impact of both single-factor and multi-factor characteristics on material properties [2].

The experimental section on slow-release materials highlights their ability to control the gradual release of drugs. Extensive research has been conducted on polymer-based slow-release materials, but issues such as poor stability and difficulty in controlling the release of components persist. Diatomite mineral, known for its light weight, small volume and stable physical and chemical properties, was used to develop a series of diatomite-based porous slow-release materials to explore their adsorption-release performance. The resulting slow-release materials exhibited excellent porous structures and adsorption-release properties [3]. The maximum adsorption capacity reached 217.86 mg/g at 25 °C, with release limits of 60.04% and 80.2%, respectively. The slow-release duration extended up to 25 days, effectively reducing phoxim residues. According to the Ritger-Peppas model fitting results, the release process was governed by a Fickian diffusion mechanism [3].

The exploration of adsorption properties in innovative carbon materials, particularly sibunites, marks an exciting frontier. Sibunites are mesoporous materials characterized by highly developed pore surfaces. To understand their porous structure, benzene vapor adsorption isotherms were employed. Upon reviewing the primary methods for calculating the porous structure parameters of sibunites, it was evident that even minimal micropore presence could skew the results. Thus, the Dubinin-Zaverina equation emerged as the optimal method for assessing mesopore surfaces. Water vapor adsorption experiments corroborated the calculated surface parameters of sibunites [4].

Investigating the adsorption traits of different porous materials was essential for the removal of trace mercury from syngas or coal gas generated via coal gasification. In coal gas, mercury exists either attached to particulate dust or vaporized at high temperatures within the synthetic gas. The presence of mercury and other heavy metals in syngas can poison catalysts in downstream processes, such as syngas-to-fuel conversion, resulting in catalyst deactivation. Furthermore, mercury emissions into the atmosphere can severely harm the environment [5].

Another study emphasized the significance of understanding gas storage and separation by utilizing known structure-property relationships through computer-aided design and extensive computer simulations. The development of enhanced porous materials hinges on gathering and comparing adsorption data from numerous materials, yet the interpretation of this data remains challenging. To address this issue, the authors introduced a novel computational method that maps the structure-property spaces of porous materials, proving beneficial for adsorption-driven applications [6].

A pivotal element in the study of porous materials involves identifying substituents that can act as cationic components within porous crystal compounds, particularly those created from azamacrocyclic nickel(II) complexes and the 1,3,5-benzenetricarboxylate anion. Recognizing the significant effects on the adsorption behavior of water, methane and n-hexane vapor is crucial. The experimental compounds demonstrated reversible changes during adsorption and desorption within the crystal lattices, as well as stoichiometric reactions with water vapor, though they exhibited relatively low hydrolytic stability under high humidity [7].

In another notable study, researchers simultaneously estimated the specific surface area and micropore volume of a hybrid alcogel (both organic and inorganic). Through non-isothermal adsorption with cyclopentane across a temperature range of 333–313 K, the study outlined how effectively adsorption data can describe the specific adsorbate/adsorbent system, modeled as a combination of meso- and macropore BET and micropore Dubinin-Radushkevitch (DR) frameworks [8].

The Zn–BTB metal-organic framework (MOF) structure was synthesized using a solvothermal method. Utilizing the theory of the volume filling of micropores, methane adsorption equilibria were calculated for the Zn–BTB sample across temperatures of 243–313 K and pressures up to 35 MPa. The differential molar isosteric heats of adsorption were subsequently determined, with a maximum methane adsorption capacity of around 14.5 mmol/g at 8 MPa and 243 K [9].

Hierarchical porous carbon materials derived from cork were produced through an eco-friendly method that involved air activation, eliminating the need for templates or chemical agents. The influence of air activation on the texture and surface properties of the carbon materials was analyzed using various characterization techniques [10]. The results indicated that air oxidation significantly enhanced the surface area and hierarchical porous structure of the carbon materials, along with increasing the number of oxygen-containing functional groups on their surfaces [10]. These materials showed excellent dye removal capabilities, highlighting the potential of porous carbon derived from biomass for wastewater treatment applications [10].

2. Methodology and Bibliometric Analysis

The methodology of this study has been based on a literature search at the Scopus database in the middle of 2024, with a time period from 1980 up to the present day. The key phrase in the “article title” was “porous materials” together with the word “adsorption”. This literature search retrieved 292 documents that were organized and allocated in six separate clusters: “subject area”, “document type”, “source title” (top 20), “keyword” (top 30), “country-territory” (top 25) and “open access”. The visual and arithmetic representation of findings is shown below in Figure 1, Figure 2, Figure 3 and Figure 4 and

Table 1. Documents allocation per “source title” (top-20). Source: Authors’ own study.

#	Source Title	Number of Documents
1	Microporous And Mesoporous Materials	11
2	Langmuir	11
3	Journal Of Colloid And Interface Science	8
4	Journal Of Chemical Physics	7
5	Colloids And Surfaces A Physicochemical And Engineering Aspects	6
6	Journal Of Porous Materials	5
7	Journal Of Physical Chemistry C	5
8	Aiche Journal	5
9	Studies In Surface Science And Catalysis	4
10	Rsc Advances	4
11	Journal Of Hazardous Materials	4
12	Industrial And Engineering Chemistry Research	4
13	Chemical Engineering Journal	4
14	Materials Research Society Symposium Proceedings	3
15	Journal Of Physical Chemistry B	3
16	Fluid Phase Equilibria	3
17	Chemical Communications	3
18	Bulletin Of The Chinese Ceramic Society	3
19	Aiche Annual Meeting Conference Proceedings	3
20	Xiandai Huagong Modern Chemical Industry	2

and

Table 2. Documents allocation per “country-territory” (top-25). Source: Authors’ own study.

#	Source Title	Number of Documents
1	China	111
2	United States	66
3	France	27
4	United Kingdom	18
5	Germany	12
6	Russian Federation	9
7	Japan	8
8	India	8
9	Australia	8
10	Taiwan	7
11	Thailand	6
12	South Korea	6
13	Poland	6
14	Malaysia	6
15	Spain	5
16	Netherlands	5
17	Undefined	4
18	Mexico	4
19	Belgium	4
20	Viet Nam	3
21	Saudi Arabia	3
22	Czech Republic	3
23	Canada	3
24	Brazil	3
25	Ukraine	2

.

Based on Figure 2 it is demonstrated that almost 78% of the total documents have been published as “Articles”, followed by the less commonly reported formats, such as reviews and book chapters.

Based on Figure 1, it can be noted that there were conceptually overlapping subject areas; thus, a grouping of all “homogeneous” subject areas was made and included in Figure 1. These clusters of subject areas are:

-

Chemistry: including the fields of Chemistry, Chemical Engineering;

-

Engineering: including the fields of Engineering, Materials Science;

-

Biosciences: including the fields of “Biochemistry, Genetics and Molecular Biology”, “Agricultural and Biological Sciences”, “Medicine”, “Pharmacology, Toxicology and Pharmaceutics”, “Immunology and Microbiology”.

The other fields have been kept as they were in the literature search results, thus formulating 13 fields in total. Furthermore, it was observed that the top four entries (that accounted for 30% of the total entries) corresponded to 87% of the total documents retrieved, which corresponded to a total of 655 documents. This observation was slightly different if no homogeneity was applied, as if the documents were considered “per se”, then the subject area of Chemistry should correspond to 50% of the total reported documents, followed by the subject areas of Chemical Engineering, Material Science, Physics and Astronomy and Engineering. In such a case, the 528 items in the top five subject areas should cover 80% of the total documents (655 in total).

Another significant outcome of the bibliometric analysis, as shown in Table 1, is the fact that the most popular source titles are those directly related to porous material advancements, interface phenomena, chemicals, physics and physical chemical publications. This finding also disclosed a more balanced and smooth decline in the number of documents reported, implying a research focus and prioritization of the “experimental chemistry” behind the operation and functionality of porous materials, comparing other dimensions such as environmental concerns and energy-intensiveness, as well as the scalability prospects offered to real-world applications, i.e., manufacturing and industrial applications. This “Chemistry” research priority is also reported in Figure 3, in which the top 30 keywords are identified.

In Figure 4, there are noteworthy instances in the literature of a move toward open access published research comparing subscription-issued journals and enabling greater technological know-how and advancement in both academia and industry nationally and globally. In an attempt to organize and represent an indicative technological background of the role of adsorption of porous media and the sorption behavior reported, a corpus of representative technologies, identified adsorption characteristics, kinetics and research outlines, as well as advantages and disadvantages, are all collectively presented in

Table 3. A collective roadmap of co-evaluating adsorption kinetics of porous media. Source: Authors’ own study that was based on the relevant literature.

No #	Adsorption Type	Kinetics—Main Idea	Advantages (+), Disadvantages (-), Key-Aspects of Analysis and Findings	Ref. # (First Author Last Name, Year of Publication)
1	B/N co-doped porous carbon materials with rich microporous structure	Investigating CO2 adsorption properties of B/N co-doped porous carbon materials	+ Exceptional CO2 adsorption properties + Cycling stability + CO2/N2 selectivity + Outstanding porous structure + Efficient synergistic effect of the regular distribution of B and N atoms in the material	[11] Chen, J.X., Li, J.H. and Bao, A. (2023).
2	Surface-modified materials based on porous biochar	Studying the effect of surface modification on the properties of porous biochar and its adsorption properties for 2,4-dichlorophenoxyacetic acid	+ Biochar modified with various substances, such as nZVI (nano zero-valent iron), shows effective adsorption capabilities for 2,4-D, indicating high efficiency + Surface modifications of biochar allow high versatility + Biochar is an environmentally friendly adsorbent compared to synthetic materials + Biochar has various functional groups that interact with 2,4-D and improve its absorption efficiency - Biochar and its modifications show decreased efficiency over time - Complex regeneration process of biochar - The active surface sites of biochar can potentially become saturated with contaminants - Each biochar type varies in its absorption efficiency	[12] Zhu, L., Zhao, N., Tong, L., Lv, Y. and Li, G. (2018).
3	Cadmium ion (Cd2⁺) on chitosan beads that have undergone acylation and crosslinking processes	Determining if N-acylation and crosslinking can significantly influence the material properties and cadmium ion adsorption capacity of chitosan beads	+ Cadmium ion on chitosan beads that have undergone N-acylation show increased adsorption capacity + Crosslinking with glutaric dialdehyde improves the stability of the chitosan beads in acidic environments - Crosslinking the N-acylated chitosan beads reduces their saturation adsorption capacity - Crosslinking reduces the crushing strength of the chitosan beads, making them more brittle	[13] Hsien, T.-Y. and Rorrer, G.L. (1995).
4	Technological use of the gravimetric method through CCl4 and NH3 adsorption studies under two different relative pressure ranges. This is a study on nano-scaled porous carbons	Investigating the adsorption properties of nano-porous carbon materials in low and high relative pressures by using CCl4 and NH3 adsorption isotherms	+ Nano-scaled porous carbons show enhanced adsorption capacity due to their large internal surface areas and pore volumes + Nano-scaled porous carbons can be tailored for selective adsorption - Nano-scaled porous carbons present different limited adsorption efficiency for certain compounds such as NH3 adsorption - Nano-porous carbon materials adsorption capacity is heavily dependent on the surface chemistry and presence of oxygen functional groups, at low relative pressures	[14] Lee, W.H., Park, J.S., Sok, J.H. and Reucroft, P.J. (2005).
5	Adsorptions of acid orange II dye from aqueous solution at different genipin contents, adsorption times and pH values	Preparing chitosan/gelatin porous materials with interpenetrating polymer networks (IPN) and porous dual structures and studying their properties on dye adsorption	+ Chitosan/gelatin porous materials show high adsorption capacity for anionic dyes + Chitosan/gelatin porous materials show pH-sensitive adsorption and desorption behaviors, and thus they present efficient dye removal and potential recyclability + Chitosan/gelatin porous materials have simple preparation processes + Chitosan/gelatin porous materials can show improved stability and mechanical strength after crosslinking with genipin + Chitosan, gelatin and genipin are environmentally friendly materials - Chitosan tends to dissolve in acidic conditions - The production and use of genipin as a cross-linker can be costly - Chitosan/gelatin porous materials present incomplete desorption properties	[15] Cui, L., Xiong, Z., Guo, Y., Liu, Y., Zhao, J., Zhang, C. and Zhu, P. (2015).
6	Nanoporous carbon materials (NCMs) adsorption processes and properties	Exploring how the chemical functionalization of porous carbon-based materials can adjust their properties and tailor their performance in adsorption-related applications	+ Chemical functionalization improves the adsorption efficiency of nanoporous carbon materials (NCMs) + Functionalized NCMs show improved performance in electrochemical energy storage applications + NCMs can be used as effective catalysts after chemical functionalization + NCMs become more versatile after chemical functionalization + Chemical functionalization of NCMs can lead to more useful and advanced applications, such as selective CO2 capture - It is very challenging for NCMs to achieve uniform and controlled functionalization - NCMs are characterized by the complexity of their chemical reactions - NCMs require unique and often more complex synthetic strategies for functionalization - Difficulty in controlling the functionalization of NCMs, therefore their adsorption performance and properties in general are less predictable	[16] Perovic, M., Qin, Q. and Oschatz, M. (2020).
7	Adsorption properties of porous materials from clays	Studying the possibility of using porous materials from clays as adsorbents of volatile organic compounds (VOCs) or for the purification of methane, e.g., for upgrading natural or landfill gas	+ Porous materials from clays prepared by gallery-templated synthesis exhibit high surface areas and significant micropore volumes that enhance their adsorption capacity + Porous materials from clays show high potential for adsorbing volatile organic compounds (VOCs) and high efficiency in separating gases such as natural gas + Porous materials from clays exhibit high thermal stability + Porous materials from clays have hydrophobic characteristics that enhance their adsorption efficiency, especially for organic compounds in humid environments - These materials have complex and possibly expensive synthesis and preparation processes - Pores characterization of porous materials from clays is difficult, and thus so is the understanding and optimization of their adsorption properties - Questionable consistency and predictability of their performance in adsorption processes due to their lack of long-range order	[17] Pires, J., Araújo, A.C., Carvalho, A.P., Pinto, M.L., González-Calbet, J.M. and Ramírez-Castellanos, J. (2004).
8	Structure and iodine adsorption properties of porphyrin-cucurbituril organic molecular porous material	Studying the structure and the iodine adsorption behaviour of this porphyrin-cucurbituril supramolecular structure	+ Porphyrin-cucurbituril complex demonstrates high specificity and selectivity in adsorption + This material can maintain its stability and robustness and therefore its structural integrity under various environmental conditions + Porphyrin-cucurbituril exhibits effective adsorption properties for iodine, which is important for environmental and industrial applications + This material shows enhanced photophysical and electrochemical properties that make it useful in applications such as sensors and catalytic processes - This material has complex and expensive synthesis and preparation processes - Its adsorption efficiency may be limited to certain types of guest molecules - Porphyrin-cucurbituril complex presents limited solubility in various solvents	[18] Xiao, X., Li, W. and Jiang, J. (2013).
9	Thermodynamic property surfaces for R507A, R134a and n-Butane adsorption on pitch-based carbonaceous porous material (Maxsorb III)	Computing and studying the entropy, enthalpy, internal energy and heat of adsorption as a function of pressure, temperature and the amount of adsorbate for the thermodynamic property surfaces of R507A, R134a and n-butane on pitch-based carbonaceous porous material (Maxsorb III)	+ The thermodynamic property surfaces of R507A, R134a and n-butane on pitch-based carbonaceous porous material (Maxsorb III) offer a comprehensive thermodynamic analysis + The thermodynamic property surfaces of R507A, R134a and n-butane on pitch-based carbonaceous porous material (Maxsorb III) are particularly useful for analyzing adsorption cooling cycles and enhancing the design and performance of adsorption chillers and cryocoolers + Pitch-based carbonaceous porous material (Maxsorb III) leads to better adsorption capacity for R507A, R134a and n-butane compared to other adsorbents such as silica gel or zeolite + These thermodynamic property surfaces can help in the development of efficient gas storage systems + The creation of adsorption isotherms from thermodynamic properties can be crucial for applications in gas purification and separation - The development of thermodynamic property surfaces is characterized by complexity, thus it can be a time-consuming and a costly process - These surfaces present high variability in their adsorption energy, making them difficult to understand - Maxsorb III adsorbent surfaces can lead to non-uniform adsorption properties due to their heterogeneity - These thermodynamic property surfaces present specificity to adsorbent-adsorbate pairs, which may limit the generalizability of their findings to other materials and adsorbates - The determination of these surfaces heavily relies on experimental data that may not always be readily accessible or reproducible in different settings	[19] Chakraborty, A., Saha, B.B., Ng, K.C., El-Sharkawy, I.I. and Koyama, S. (2010).
10	Acetaminophen adsorption performance of new biobased carbon materials that have been created by implementing sustainable, facile and different single-step pyrolysis chemical methods (KOH, ZnCl2, ZnSO4 and MgCl2) using Norway spruce bark as a suitable and efficient carbon precursor	Creating new biomass-based carbon materials (BBPMs) as adsorbents via facile, sustainable and different single-step pyrolysis chemical methods (KOH, ZnCl2, ZnSO4 and MgCl2) using Norway spruce bark as a suitable and efficient carbon precursor and studying the effects of each chemical activator on the physicochemical structure of these materials as well as the performance of each chemical activator on the acetaminophen adsorption	+ These new biomass-based carbon materials (BBPMs) have a high specific surface area, which is beneficial for their adsorption efficiency + The activation of BBPMs with different chemical activators such as KOH, ZnCl2, ZnSO4 and MgCl2 gives them a great variety of useful properties and applications + Norway spruce is a sustainable and low-cost carbon precursor + These new biomass-based carbon materials (BBPMs) have been proven to be efficient pollutant removers due to their very fast adsorption performance of acetaminophen + BBPMs show good regeneration capability + BBPMs present high hydrophobic capabilities that can be advantageous in specific applications where water repellency is desired + Their adsorption process involves multiple mechanisms that can improve their effectiveness and versatility - Selecting the appropriate chemical activator for these BBPMs can be a complex and difficult process - Some of their chemical activators such as ZnCl2 and ZnSO4 can pose health and environmental risks if they are not handled properly - Single-step pyrolysis chemical methods cause significant energy consumption - Scaling up the production of BBPMs from laboratory-scale production to industrial levels may be challenging and difficult - BBPMs present high hydrophobic capabilities that can be disadvantageous too, as long as they limit the applicability of these materials in aqueous environments	[20] Dos Reis, G.S., Guy, M., Mathieu, M., Jebrane, M., Lima, E.C., Thyrel, M., Dotto, G.L. and Larsson, S.H. (2022).
11		The shape of the isotherms determined for the carbonaceous samples AC-1 and AC-2 (being characterized by a larger content of basic groups) are type I isotherms without visible hysteresis loops, characteristic of the microporous materials in which the monolayer adsorption occurs. Practically, the isotherms overlap, suggesting only slight differences in their structural parameters. Extending the intermediate stage (from 1 to 2 h) at 400 °C made the surface of the AC-2 material slightly better developed (SBET = 346.7 m2/g, Vp = 0.179 mL/g) than the surface of the sample obtained according to procedure 1 (AC-1; SBET = 339.6 m2/g, Vp = 0.160 mL/g). From an economic point of view, this procedure is unfavorable. The Smicro values are high and indicate the large microporosity of the materials. The shape of the pore size distribution curves versus the mean radii is characteristic of the materials with homogeneous pore distribution, with a dominant pore size of Rdom-2 nm. The curves course, derived from the thermal decomposition of wheat bran (WB-ININ2), showed that the obtained biocarbons are stable up to about 450–500 °C. However, the stability depends insignificantly on the isothermal stage time (400 °C), the atmosphere (CO2 or steam) and the energy source. Clear peaks directed downwards are found on the DTG curves, confirming mass loss within a certain temperature range. These peaks are regular and wide, which prove the equal speed and temperature range of the combustion process. The DTA curves indicate the energy effects of the processes that took place. With the temperature increase, clear peaks on the curves related to the exothermic process of activated carbons combustion can be observed. The course of the curves revealed that the peak maxima were evidently “shifted” to the left, pointing out that the combustion process for the individual samples started at different times.	+ The obtained materials are characterized by the presence of both basic and acidic groups on their surface. They are mostly acidic groups, and for all materials the total number of these groups is ~1.9 mEq/g. + It was very advantageous to introduce steam in the annealing stage at 800 °C (sample: AC-1-OX). The additional steam oxidation resulted in the better development of the pores. The isotherm determined for this material is type IV, characteristic of the mesoporous materials. The clearly visible H2-type hysteresis loop indicates the presence of bottle-shaped pores. The obtained material (AC-1-OX) has a well-developed specific surface area of SBET = 594.0 m2/g and a pore volume of Vp = 0.356 mL/g. For the tested materials, the volume of sorption pores (Vtotal) and macropores (Vmacro) was also determined using methanol as an adsorbate. These values are important because the obtained materials can be used as effective adsorbents for removing contaminations from the aquatic environment and macropores play an important role as the “transport channels”. The authors noted that the obtained values of Vtotal and Vmacro were over 10 times larger than the volume of sorption pores. The activated carbon obtained in the oxidizing atmosphere of steam (Vtotal = 3.013 mL/g) was additionally modified using a microwave as an energy source (Vtotal = 2.34 mL/g), characterized by a very large total volume of pores. - Unfortunately, the additional use of microwave treatment resulted in the reduction in the sorption pores volume in the other discussed materials (Vtotal~0.947–1.031 mL/g). Significant Vtotal values resulted from the fact that methanol fills both the available sorption pores and the intergranular spaces between the carbon matter particles. - using CO2 as an activating agent promoted the formation of oxygen basic groups. The application of the additional activation with steam was not favorable for the formation of basic surface groups. SEM images presented the structure of the material pyrolized only in the presence of CO2. The oxidizing atmosphere caused the disordered particles of the carbonaceous material to burn, which made the initially heterogeneous structure to be more homogeneous under the smallest burning degree. The carbonaceous surface was rough and folded. Pyrolysis in the oxidizing steam atmosphere caused the additional burning of the carbon material, making the pores accessible and open. The use of modifications in the form of superheated steam assisted by the energy of microwave radiation resulted in the widening of the existing pores, indicating an even better ordering of the carbon structure. The oxidizing atmosphere caused the disordered particles of the carbonaceous material to burn, which made the structure more homogeneous. This material was characterized by the best-developed surface and porous structure.	[21] Charmas, B.; Ziezio, M.; Jedynak, K. (2023)
12		This study investigated magnesium slag-based porous materials (MSBPM) as an synthesized adsorbent in using alkali activation and foaming methods for the adsorption (removal of) Pb2+ in solution. The pseudo-first-order and pseudo-second-order kinetic models were used to investigate the adsorption kinetics of Pb2+ by MSBPM-H2O2 and MSBPM-Al. The porous material (MSBPM-H2O2) of high compressive strength (8.46 MPa) showed excellent Pb2+ adsorption capacity (396.11 mgg−1), obtained under the optimal conditions: a H2O2 dosage of 3%, an alkali dosage of 9%, a water glass modulus of 1.3 and a liquid–solid ratio of 0.5. Another porous material (MSBPM-Al) showed a compressive strength of 5.27 MPa and a Pb2+ adsorption capacity of 424.89 mgg-1, obtained under the optimal conditions: an aluminum powder dosage of 1.5‰, an alkali dosage of 8%, a water glass modulus of 1.0 and a liquid–solid ratio of 0.5. At a pH equal to 6, the initial Pb2+ concentrations were 200~500 mg/L; the MSBPM-H2O2 and MSBPM-Al could remove more than 99% of Pb2+ in the solution. Typically, the pseudo-first-order kinetic model better fits the initial adsorption process, where the longer the transfer time of the solute, the lower the concentration of the solution ions at the adsorption equilibrium and the greater the adsorption capacity. The pseudosecond-order kinetic model more fully describes the diffusion and adsorption process, accompanied by the formation of chemical bonds. The results indicated that the adsorption of Pb2+ by both MSBPM-H2O2 and MSBPM-Al followed the pseudo-second-order kinetic model, and the adsorption process was mainly dominated by chemical adsorption.	As the H2O2 dosage increases, the apparent density and the porosity showed a monotonic decrease and a monotonic increase, respectively, with corresponding ranges of 820~1160 kg/m3 and 61~48%. Variations in the pore structure of MSBPM with an alkali dosage of 9% were reported as well as an activator modulus of 1.3 after 28 d under the different dosages of foaming agent. As the H2O2 dosage increases, the number and size of pores increase, resulting in a loose and porous structure that is not conducive to strength development. The pore size of MSBPM foamed by H2O2 is within the range of 0.1~2.4 mm. Regarding the MSBPM-Al, the dosage of aluminum powder was negatively correlated with the compressive strength of the specimens. The pore size of MSBPM foamed by aluminum powder was within the range of 0.25~1 mm. The adsorption process of both materials followed the Langmuir isotherm model and pseudo-second-order kinetic model, indicating that the adsorption process was a single-molecule layer chemical adsorption. Indeed, the results indicated that the Langmuir model is better suited to describe the adsorption process of the adsorbent for Pb2+. Specifically, each Pb2+ molecule as an adsorbate is adsorbed onto the surface of MSBPM-H2O2 with equal adsorption activation energy, and the adsorption process is uniform and belongs to monolayer adsorption.	[22] Lu, G.; Han, J.; Chen, Y.; Xue, H.; Qiu, R.; Zhou, X.; Ma, Z., 2023
13		Due to a high risk of power outages, heat-driven adsorption chillers are gaining the attention. To increase the efficiency of the chiller, new adsorbents must be produced and examined. In this study, four newly developed silica–based porous materials were tested and compared with silica gel, an adsorber commonly paired with water. The metal organic silica (MOS) nanocomposites analysed in this study had thermal properties similar to those of commonly used silica gel. MOS samples have a thermal diffusivity coefficient in the range of 0.17–0.25 mm2/s, whereas silica gel has about 0.2 mm2/s. The highest water adsorption capacity was measured for AFSMo-Cu and was equal to 33–35%. For narrow porous silica gel, mass uptake was equal about 25%. In the case of water adsorption, it was observed that the pore size of the sorbent is essential, and adsorbents with pore sizes higher than 5 nm are recommended in working pairs with water. The highest thermal diffusivity coefficient was measured for the MPSilica sample at about 0.3 mm2/s, while the lowest was measured for silica gel at about 0.2 mm2/s for both samples. The interesting thing is that the tested sorbents were characterized by a stable value of the thermal diffusivity coefficient. In the analyzed temperature range, the thermal diffusivity coefficient in all cases was constant or slightly increased with temperature. Compared to the most commonly used adsorbent in sorption cooling devices, silica gel, the thermal diffusivity of which is 0.137 mm2/s, the thermophysical properties of the analyzed sorbents are slightly higher.	Metal-organic silica (MOS) are dynamically developing materials with significant industrial potential because of their wide range of useful properties such as high stability and resistibility to chemical changes. The mesoporous structure of the silica matrix and the extensive surface area of about 1500 m2/g enables it to obtain material with high sorption capacity. Metal-organic silica nanocomposites are characterised by a noticeable active surface area, exceeding 1000 m2/g in some cases, but in the literature, MOS with a lower BET surface area was also reported. However, it was noted that for porous materials with a developed surface area, e.g., MOFs, a BET surface area exceeding 7000 m2/g is an indicator of the potential for the use of sorbents in adsorption chillers. The modification of MOS properties is performed through the introduction of additional atoms or functional groups. The unique features of MOS make them candidates for a variety of applications, such as wastewater treatment, CO2 sequestration, catalysis, as heavy metal adsorbents and other toxic contaminants detectors and adsorbents.	[23] Sztekler, K.; Mlonka-Mędrala, A.; Khdary, N.H.; Kalawa, W.; Nowak, W.; Mika, Ł., 2023
14		Hyper-crosslinked porous polymers (HCLPs) have gained attention because of their high surface area and porosity, low density, high chemical and thermal stability and excellent adsorption capabilities in comparison to other porous materials. Herein, we report the synthesis, characterization and gas (particularly CO2) adsorption performance of a series of novel styrene-based HCLPs. The materials were prepared in two steps. The first step involved the radical copolymerization of divinylbenzene (DVB) and 4-vinylbenzyl chloride (VBC), a non-porous gel-type polymer, which was then modified by hyper-crosslinking, generating micropores with a high surface area of more than 700 m2 g−1. The texture properties of pure and functionalized porous polymers HCLPPs. The value range of the examined samples were: SBET(m2 g−1): 277–757, Smeso (m2 g−1): 93–310, Vtot (mm3 liq g−1): 157–408, Vmicro (mm3 liq g−1): 76–226. The gas adsorption capacity of pure and functionalized porous HCLPP at 100 kPa and 25 °C was calculated as (μmol g−1): 820–110 (CO2), 130–310 (CH4), 29–90 (N2), 12–21 (H2), 12–89(O2). Compared to similar studies, the material prepared in this study showed a comparable or slightly lower CO2 adsorption capacity, but in most cases higher selectivity.	Synthesized hyper-crosslinked porous material showed a high apparent surface area and selective CO2 adsorption over CH4, N2 and H2, which significantly increased after amines functionalization. Therefore, produced porous polymers represent promising organic porous materials for CO2 uptake from gas mixtures. The results indicated that the reaction of the prepared polymer with the dendrimer was not as effective as its reaction with amines due to the partially microporous structure being too tight for the possible interaction with the branched dendrimer molecules. Based on this finding, the authors’ future proposal is the development of polymers with a mesoporous structure that may be more suitable for dendrimer loading. The prepared porous polymer structure and its amine-functionalized forms can be considered for testing as fillers into mixed-matrix membranes with improved CO2/CH4 and CO2/N2 separation performance as well. Therefore, produced porous polymers represent promising organic porous materials for CO2 uptake from gas mixtures.	[24] Setnickova, K.; Jerabek, K.; Strasak, T.; Mullerova, M.; Jandova, V.; Soukup, K.; Petrickovic, R.; Tseng, H.-H.; Uchytil, P., 2023

.

Based on Table 3 above, as well as taking into consideration the relevant literature, it can be signified that typical equations apply to adsorption equations and calculations [21], but a similar calculation process is also applied to all relevant literature sources:

qe = ((C0 − Ce) × V)/m

(1)

where: qe—the amount of adsorbate per 1 g of adsorbent at equilibrium [mg g⁻¹]; C0—the initial concentration of the adsorbate [mg L⁻¹]; Ce—the equilibrium concentration of the adsorbated [mg L⁻¹]; V—the adsorbate solution volume [L]; m—the sample weight [g].

The full description of kinetic process refers to the linear form equations of the PFO (Equation (2)), PSO (Equation (3)), Elovich kinetic model (Equation (4)) and intraparticle diffusion model (Equation (5)):

ln(qe − qt) = lnqe − k₁t

(2)

t/qt = 1/(k₂ × qe₂) + t/qe

(3)

qt = 1/β ln (αβ) + 1/β lnt

(4)

qt = kd t^1/2+ C

(5)

where: qt—the amount of adsorbed substance per 1 g of adsorbent after time t [mg g⁻¹]; qe—the amount of adsorbed dye per 1 g of adsorbent at equilibrium [mg g⁻¹]; k₁—the reaction rate constant [h−1]; k₂—the reaction rate constant [g mg⁻¹ h⁻¹]; —the initial adsorption rate [mg g⁻¹ h⁻¹]; β—the desorption constant [g mg⁻¹]; kd—the intraparticle diffusion rate constant [mg g⁻¹ h^1/2]; C—the boundary layer thickness [mg g⁻¹]; t—the adsorption time [h].

The determination of the adsorption isotherm is actually described by the use of the adsorption isotherms, the Langmuir (Equation (6)) and Freundlich (Equation (7)) models:

Ce/qe = 1/q_m × Ce + 1/q_m × K_L

(6)

logqe = logK_F + 1/n ×logCe

(7)

where: qe—the amount of adsorbed substance per g of adsorbent in the equilibrium state [mg g⁻¹]; qm—the maximum amount of adsorbate [mg g⁻¹]; Ce—the equilibrium concentration of the dye solution [mg L⁻¹]; K_L—the Langmuir adsorption equilibrium constant [L mg⁻¹]; K_F—the Freundlich constant, which indicates the adsorption capacity [mg^1–1/n (dm³)^1/n g⁻¹]; n—the Freundlich adsorption intensity constant.

The main experimental results showed the mixed adsorption capacity of the adsorbents, comparing each case result with the relevant literature findings. In this context, in the case of Pb²⁺, the adsorption capacity reached 353.9 mgg⁻¹ and the removal rate was 88.03% [22]. In similar studies, the use of sodium hydroxide and slag as raw materials to prepare geopolymer microsphere adsorbents achieved high adsorption capacities in aqueous solutions, reaching 335.43 mgg⁻¹, 414.38 mgg⁻¹ and 91.21 mgg⁻¹ for Cu²⁺, Ni²⁺ and Co²⁺, respectively. The adsorption process conformed to the pseudo-second-order kinetic model and the Langmuir isotherm model [22]. Other critical parameters of the relevant studies are the cost-effectiveness and the efficiencies achieved [22].

Electrostatic attraction and ion exchange were the main mechanisms for the adsorption of metal cations. For cations with the same charge number, the ion radius was inversely proportional to the cation exchange and adsorption capacity. Among cations with different charge numbers, cations with lower ion potential were more easily adsorbed on the gel surface. In summary, geopolymer has been proven to be an effective adsorbent, but its disadvantage is that the geopolymer structure is relatively dense and the adsorption efficiency is low. Therefore, the preparation of porous geopolymer is proposed to improve the adsorption capacity of heavy metal ions [22]. In the following

Table 4. Advantageous and disadvantageous characteristics of typical non-carbonaceous adsorbent materials. Source: Based on [25].

Type of Material	Indicative Examples	Advantages	Disadvantages
Zeolites	NaY, 13X	Large micropores/mesopores, medium CO2 adsorption capacity at room temperature, low production cost	Low CO2 adsorption capacity, moisture-sensitivity, high energy consumption
Porous silica materials	M41S, SBA-n, AMS	High specific surface area, pore volume and good thermal and mechanical properties	High molecular diffusion resistance, decreased adsorption capacity at high temperature
Metal organic frameworks (MOFs)	M-MOF-74, IRMOF-6, USO-2-Ni, Zn4O (BDC)3, (MOF-5), USO-1-Al (MIL-53)	Ease of controlling pore sizes, high selectivity of CO2, large specific surface area	Low CO2 adsorption capacity at partial pressure, complicated synthesis process, moisture sensitivity, unstable at high temperature, high production cost
Metal oxides-based adsorbents	CaO, MgO	Dry chemical adsorbents, adsorption/desorption at medium to high temperatures	High energy consumption, complicated process, high cost for regeneration

, selected types of non-carbonaceous materials serving as adsorbents are presented, pointing out their most important advantages and disadvantages.

3. Case Study: Adsorption Behavior on Porous Carbonaceous Materials

In this case study, a “reverse” problem has attracted the current research interest: that the adsorbate matter (not the adsorbent matter) is carbonaceous. In such a case, there are certain economical and technical properties that have to be presented in order to select the best solid adsorbent candidate for a particular carbonaceous capture application. For research convenience, the most studied carbonaceous material today is carbon dioxide (CO₂), and for this material, the following criteria can be met [25]. Actually, the routes and the adsorption logic are similar to those of carbonaceous adsorbents in aqueous solutions, offering useful insights into the sorption mechanisms developed in similar experimental or industrial-commercial applications.

-

The adsorption capacity of CO₂: The equilibrium adsorption capacity is represented by the equilibrium adsorption isotherm of a sorbent material. The adsorption capacity is a crucial characteristic of adsorption, not only because it causes a reduction in the sorbent quantity, but also when considering the cost of the applied process. In order to enhance the adsorption capacity of solid sorbents, functionalization has been developed through existing monoethanolamine (MEA) [25]. The CO₂ working capacity of the sorbent can be ranged at 2–4 mmol/g [25].

-

Selectivity for CO₂: CO₂ adsorption selectivity means the sorption uptake ratio of a target gas species compared to another type (for example, N₂) is/are contained in a gaseous mixture under specific operation conditions. Therefore, CO₂ adsorption selectivity is linked with the purity of the adsorbed gas in the effluent [25]. Since the purity of CO₂ influences transportation and sequestration, it is an important criterion that contributes to CO₂ sequestration [25].

-

Adsorption and desorption kinetics: The quick time taken to employ adsorption/desorption kinetics for CO₂ is attributed to the fact that this adsorption/desorption cycle can control the whole cycle time of a fixed-bed adsorption system. Indeed, fast kinetics are inducing a sharp CO₂ breakthrough curve in which effluent CO₂ concentration changes are measured as a function of time, while slow kinetics should provide a distended breakthrough curve. However, both fast and slow adsorption and desorption kinetics are impacting the amount of sorbent required. In functionalized solid sorbents, the overall kinetics of CO₂ adsorption are mainly bounded by the existing functional groups as well as the mass transfer or diffusional resistance of the gas phase through the sorbent structures. The porous support structures of functionalized solid sorbents can be further tailored to minimize diffusional resistance. Fast CO₂ adsorption/desorption also implies less need to capture a given volume of flue gas [25].

-

Mechanical strength of sorbent particles: This property refers to the stable microstructure and morphological structures in adsorption and regeneration steps that each sorbent must sustain. Otherwise, disintegration of the sorbent particles should be reported due to the high volumetric flow rate of flue gas, vibration, and temperature. The disintegration of the sorbent particles could also occur due to abrasion or crushing. Therefore, sufficient mechanical strength of sorbent particles is required to keep the CO₂ capture process cost-effective [25].

-

Chemical stability/tolerance towards impurities: The stability of solid CO₂ capture sorbents, such as amine-functionalized sorbents, is dependent on the oxidizing environment of flue gas and should be resistant to common flue gas contaminants [25].

-

Regeneration of sorbents: The regeneration of the sorbent is energy-saving, and is one of the most important parameters required to improve energy efficiency [25]. Regeneration achievement can be accomplished through the adjustment of the thermodynamics of CO₂-solid adsorbent interactions [25]. Considering regeneration, physisorption is mostly favored over chemisorption, since chemisorption requires high energy consumption for regeneration.

-

Sorbent costs: The production cost is a key aspect when considering industrial applications for reasonable gas selectivity and adsorption performance [25].

In the following

Table 5. Chemisorption and physisorption characteristics. Source: Based on [25].

Technology Classification	Type of Sorption	Indicative Examples	Efficiency (%, in Descending Order)
Absorption	Chemical: Chemical reaction occurs between the solid sorbents and CO2. Chemisorption sustains high selectively, but it is also characterized by slow reactivity, being also energy-intensive for recycling and for the breaking of the chemical bonds.	Amines, Caustics	>90
Absorption	Physical: Depends on the physical properties of CO2 and the ability to engage in noncovalent interactions with the solid sorbent. Physisorption bonds are that of weak Vander-walls forces-London and Dispersion forces, also developed inside pore walls. Physisorption sustains the advantageous characteristics such as fast and high selectivity and working capacity, requiring also low recycling energy. However, there has also been reported a poor selectivity in binary or mixed gas applications.	Selexol, Rectisol, fluorinated solvents	>90
Adsorption	Chemical	Metal Oxides, Si based materials	>85
Adsorption	Physical	Carbons, Zeolites, Si based materials	>85
Membrane-based	Organic (celluloses, polyamides)	Polyphenyleneoxide, Polydimethylsiloxane	>80
Membrane-based	Inorganic	Ceramics of metallic fabrication	>80

, the chemisorption and physisorption definitions and descriptions of functionality, as well as typical examples and reported efficiencies, are presented.

The chemical absorption of CO₂ is more suitable than physical absorption owing to its high adsorption capacity, relatively easy synthesis routes and lower regeneration energy requirements. Among many chemisorbents, SiO₂-based adsorbents, including amine-functionalized SiO₂, support higher CO₂ selectivity and adsorption capacities, making them ideal candidates for CO₂ capture. However, the performance of currently available amine-functionalized SiO₂ needs to be further developed and improved in terms of stability, gas selectivity and resistivity to thermal degradation. Furthermore, major financial, technical and environmental barriers and prospects are associated with porous silica-based materials during the scalability process [25].

In the following

Table 6. A representative cluster of studies on carbonaceous porous materials in the process of adsorption. Source: Based on a synthesis of the relevant literature.

No #	Thematic Area	Ref. #
10	Organic and Biochar	[26,27,28,29,30,31,32,33,34,35]
8	Pharmaceutical-antibiotics	[36,37,38,39,40,41,42,43]
5	Inorganic and Metals	[44,45,46,47,48]
4	Waste	[49,50,51,52]
1	Pesticides	[53]

, a representative cluster of studies that are relevant to carbonaceous porous materials used in adsorption processes has been provided. Furthermore, the full development of this case study also contains the following subsections: “Adsorption and Porosity” and “Adsorption Kinetics and Isotherms”, which can be studied in alignment with the conveyed information in Table 3, Table 4, Table 5 and Table 6 accordingly.

The contents of Table 6 were determined through a literature search using the Scopus database using the keywords “carbonaceous materials” and “sorption” in the article title. Then, a total of 28 documents were retrieved, which were further organized in alignment with the following 5 thematic areas. These thematic areas have been presented in descending order of studies containing -which is aligned with the descending order of number of studies mentioned as “No #” per thematic area, in Table 6: organic and biochar; pharmaceutical-antibiotics; inorganic and metals; waste; pesticides.

The document allocation also contained some overlapping thematic areas; thus, their placement was made only once in Table 6, considering the priority field keyword that these overlapping documents featured. Based on the outcomes of Table 6, it can be argued that the main research focus was directed on organic and pharmaceutical applications of removing pollutants using carbonaceous adsorbent materials, while the inorganic, waste and pesticide studies attracted less research attention.

3.1. Adsorption and Porosity

Based on Table 3, Table 4, Table 5 and Table 6, it can be inferred that carbonaceous materials were used in the adsorption process. In recent years, adsorption has become the most widely used method for water and wastewater treatment. This is a relatively cheap method and does not require expensive and complicated equipment [21].

If the rectilinear relationship does not pass through the origin of the coordinate system, it means that intra-particle diffusion is involved in the adsorption process, but this is not a speed-controlling step in the adsorption process. In the case of multi-linear relationship types, the intra-particle diffusion model shows that there are two or more stages that make up and determine the adsorption process: (a) the first (the fastest) stage is related to the external surface adsorption—the adsorbed molecules move from the solution to the surface of the adsorbent by diffusion through the boundary layer (diffusion in the boundary film); (b) the second stage includes the gradual diffusion of the adsorbate through the pores of the adsorbent (intra-particle diffusion); (c) the third stage is a state of equilibrium that includes very slow diffusion of the adsorbate from the larger pores to the smaller ones (micropores) [21].

Another important study on porosity examined the modified porous sorbents of energy storage and heat transformation capability, which were utilized to examine water adsorption properties by measurements through thermogravimetry (TG), differential thermogravimetry (DTG), microcalorimetry, water adsorption isotherms and storage tests. A chabazite type, a dealuminated faujasite type zeolite and a mesostructured aluminosilicate were coordinated and evaluated for common zeolites X, Y and silica gel, showing that the optimum lattice composition as well as the pore architecture can effectively characterize and disclose the detected hydrophilic properties and the concurring beneficial steep isotherm [54].

In addition to water, the mercury adsorption capacities of zeolite, activated carbon and copper-loaded alumina were examined to evaluate their effectiveness in extracting mercury from the gas phase [5]. During the adsorption experiments, the mercury concentration in the nitrogen gas was maintained at approximately 70 ppbv to study the adsorption properties of the materials. The variation in mercury concentration was monitored over time at the outlet of an adsorption column containing about 5 g of the porous adsorbent. Throughout the tests, the adsorption column was held at room temperature. Among the various porous adsorbents tested, activated carbon exhibited a superior capacity for mercury adsorption. In contrast, zeolite, despite its relatively high surface area, showed diminished adsorption performance. Copper-loaded alumina also demonstrated some capacity for mercury adsorption, but its overall performance was inadequate [5]. The effective removal of gaseous mercury posed a challenge, as the short residence time of mercury within the adsorption column made the adsorption rate a critical consideration. Among the adsorbents with high surface areas, only activated carbon delivered satisfactory results, indicating that a larger surface area does not necessarily correlate with better mercury adsorption. Rather, the presence of specific functional groups on the adsorbent surface seems to play a more critical role. Therefore, a detailed analysis of the functional groups present on activated carbon, along with the identification of those most effective for mercury adsorption, could pave the way for developing a highly efficient mercury adsorbent [5].

Among the studies on novel materials, a noteworthy achievement involved the successful preparation of a new porous adsorption material (PAM) derived from raw coal slag. This material was characterized using various techniques, including nitrogen adsorption-desorption isotherms, thermogravimetric analysis (TGA), Fourier transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), transmission electron microscopy (TEM) and X-ray diffraction (XRD) measurements [25]. The PAM was synthesized with a remarkable yield of 99.20 wt.% at 90 °C over a duration of 4 h, utilizing a Ca/Si molar ratio of 0.75:1. According to the Langmuir model, the PAM exhibited a maximum phenol adsorption capacity of 63.78 mg/g. Thermodynamic analyses indicated that the adsorption process was exothermic, thermodynamically feasible, spontaneous and chemically controlled [55].

Exploring the potential applications of plant-based materials, such as tobacco stems, researchers have developed a comprehensive method combining fermentation, microwave drying, agglomeration, semi-carbonization and modification, with KOH serving as the modifier [56]. The resulting porous materials were examined through scanning electron microscopy, specific surface area analysis, pore analysis and infrared analysis, determining their structural characteristics and properties when developing adsorption isotherm models, their kinetics and the thermodynamics of phenol solutions [56]. The study indicated optimal conditions for the production of porous materials, characterized by a typical porous structure enriched with numerous cavities and pores due to KOH modification. These materials exhibited higher specific surface areas and pore volumes [56]. Furthermore, they contained abundant functional groups, such as -OH and -CH, enhancing their potential for organic compound adsorption. The phenol solution adsorption isotherm was successfully modeled using the Freundlich isotherm equation, while the quasi-second-order kinetic model was found to be suitable for the adsorption process. Additionally, thermodynamic studies confirmed that the adsorption was predominantly physical and exothermic in nature [56].

3.2. Adsorption Kinetics and Isotherms

In the case of the adsorption process, kinetics has been proven to be an extremely important step in enabling researchers to determine the substance absorption rate, e.g., from the liquid phase by the adsorbent particles. Therefore, kinetics represents the adsorption efficiency of a given adsorbent, thus supporting the identification of its potential applications. However, it should be taken into account that adsorption is a complex process involving electrostatic, chemical and physical interactions. Subsequently, the rate of adsorption of pollutants depends, inter alia, on the contact time of the adsorbent and the solution, as well as on the diffusion process [21].

In the relevant literature, it is generally known that the pseudo-first order (PFO) kinetic model describes an adsorption rate that is directly proportional to the difference between the equilibrium and instantaneous adsorbate on the adsorbent surface. In turn, the pseudo-second order (PSO) kinetic model assumes that the rate of occupancy of the accessible active sites by the adsorbate is proportional to the square of the number of vacant sites [21]. In cases where the correlation coefficient R2 can reach the highest possible value, such as 0.99, these higher values are reported by applying the pseudo-second order (PSO) equation. This means that the kinetics of the adsorbate adsorption process, such as that of methylene blue on the tested adsorbents and that of biochars, can be described by the PSO model. Model adaptation showed that the rate of adsorption can be largely interrelated to the accessibility of active centers, but not to the concentration of adsorbates in the solution [21].

Regarding the adsorption kinetics of carbonaceous adsorbents, it can also be denoted that with an increase in temperature, the values of qe and exp increase, implying that adsorption can be described as an endothermic process. In the tested pairs of adsorbates in carbonaceous adsorbent materials, the maximum adsorption capacity can be met at 303 K, indicating the influence of temperature on the adsorption process. These dependencies are grounded by the increase in the adsorbate molecules’ diffusion rate throughout the external boundary layer or the greater mobility of some adsorbate molecules at higher temperatures, which facilitates diffusion in the porous structure of activated carbons [21].

In the relevant literature, it was calculated that the greatest adsorption capacity could be achieved at temperatures of 298 K, 303 K and 308 K, which corresponded to 212.59 mg/g, 220.79 mg/g and 241.95 mg/g, respectively. Among the tested carbonaceous materials, the AC-1-OX-activated biocarbon material exhibited good adsorption properties, and had lower qe,exp values compared with the other discussed sample. Those samples characterized by a much smaller sorption capacity (152–174 mg/g) compared to the materials activated in the steam atmosphere were additionally modified by the use of microwave energy. These differences can be attributed to the characteristics of both the porous structure and the surface chemical nature [21]. Well-developed surfaces are related to the micro/mesoporous structure. Contrarily, rough surfaces explain faster and easier diffusion through pores with larger diameters, such as mesopores. Moreover, microwave treatment can extend the already existing pores, which makes it easier for the adsorbate molecules to penetrate the pores’ interior and occupy active centers [21]. Other determining factors of the adsorption phenomenon are the presence of oxygen and acidic groups; the latter can occupy some active centers that become inaccessible to the adsorbate molecules—causing a reduction in interactions between the activated carbon surface and the adsorbate molecules [21].

Complete analysis and interpretation of the adsorption process include the different influences of the surface functional groups that affect the adsorption process. In the case of the Freundlich model, the relatively smaller values of the R² compared with the Langmuir one are an indicator, together with the high K_F coefficient for all tested materials, of the strength of the interactions between the adsorbate and the adsorbent. Moreover, the n values are >2, where applicable, indicating the significant contribution of chemical adsorption [21].

The current understanding of the process and material properties of porous adsorbent materials prepared from magnesium slag is insufficient, including preparation methods, stability, durability and adsorption mechanisms. Furthermore, the potential application fields of porous magnesium slag materials need to be further expanded to fully exploit their application potential [22]. This study focuses on the utilization of magnesium slag, a solid waste, as the primary raw material by which to prepare magnesium slag-based porous materials (MSBPM) through alkali activation and foaming using H₂O₂ and aluminum powder, respectively. The effects of the foaming agent dosage, the alkali dosage and the water glass modulus on the compressive strength, apparent density and porosity of MSBPM were investigated. Furthermore, the adsorption performance of the adsorbents prepared by the two foaming methods for Pb²⁺ in an aqueous solution was studied under different conditions [22].

Based on the test results for narrow porous silica gel, it can be concluded that the adsorption isotherms for temperatures at 40 °C, 50 °C and 60 °C at water vapor saturation pressures from 10% to 100% P/P0 according to the IUPAC classification take the shape characteristic for the type IV isotherm. Both the shape of the adsorption isotherms and the maximum weight gain of the sorbent are similar in the range of the tested temperatures and equal a maximum value of 26%, on average. In the case of the desorption process, a slight hysteresis is observed, depending on the process temperature, and it is characteristic of the type IV isotherm. The hysteresis takes a shape similar to the H₂ type, which may indicate that spherical pores with numerous constrictions and open ends are present in the material [23]. Pore diameters smaller than 5 nm are considered very narrow for water sorption processes. In such a case, the ideal characteristics of adsorbents in adsorption chillers that work with water as the adsorbate phase are: a large active surface area, higher than 5 nm pore diameters and noticeable thermal conductivity coefficients [23].

Similar literature studies have introduced models that can depict chemical potential as a linear combination of gas-like and solid-like contributions, enhanced by a new fraction parameter, g, in addition to the fluidity factor from the original 2PT method [54]. This extended method, known as ext-2PT, allows for the computation of the chemical potential of an adsorbed system based on adsorption uptake. By employing an interpolation scheme, the equilibrium loading at any given gas-phase chemical potential can be determined, resulting in adsorption isotherms. The ext-2PT model has shown its efficacy through accurate predictions of methane adsorption and diffusion in two metal-organic frameworks (MOFs), IRMOF-1 and Cu-BTC, as well as in zeolite FAU with inaccessible volume. Overall, the ext-2PT model is a robust and efficient approach for simultaneously computing adsorption isotherms and diffusion coefficients using a single set of molecular dynamics (MD) simulations [57].

It can also be argued that nitrogen sorption isotherms have been reported as valuable tools to demonstrate that the surface area and pore distribution of the resulting porous materials are significantly influenced by the size and structure of the diamine pillars. Characterization of CO₂ uptake capacity revealed that ethylenediamine-intercalated FG achieved a high CO₂ uptake density of 18.0 CO₂ molecules per nm² at 0 °C and 1.1 bars, with a high adsorption heat of up to 46.1 kJ mol⁻¹ at zero coverage [1].

An important discovery in the recent literature is the interaction between water molecules and surfaces in porous systems, which is crucial in various applications such as catalysis, adsorption and electrochemical energy storage or conversion [58]. The hydrophilicity of typically non-polar carbon-based materials can be enhanced by incorporating heteroatoms, such as nitrogen. However, understanding the interaction mechanisms on a molecular level remains challenging due to the lack of porous carbons with well-defined and regular atomic structures, as well as the absence of suitable structural models for such substances. This complexity makes theoretical calculations difficult. To shed light on the interactions between nitrogen-doped carbon surfaces and water molecules, studies on water adsorption have been conducted using model materials with varying pore structures and atomic configurations [58]. Solid-state NMR spectroscopy, combined with theoretical calculations, revealed that water in nitrogen-rich C₂N materials exhibited an exceptionally strong rate of adsorption, significantly above 60 kJ mol⁻¹, which is far greater than what is typically associated with physisorption. In these porous materials, water becomes an integral part of the chemical structure, justifying the term “zeocarbons [58]”.

4. Discussion

4.1. Limitation Implications and Future Research Considerations on Porous Carbonaceous Materials

In a separate study focused on innovative materials, researchers developed a novel microporous carbon material, referred to as MUM-51, derived from waste coffee grounds through a process of carbonization followed by activation with KOH. MUM-51 was thoroughly characterized using a variety of techniques, including nitrogen adsorption-desorption at 77 K, X-ray powder diffraction, Fourier transform infrared (FTIR) spectroscopy and Raman spectroscopy. To assess its methane adsorption capabilities, experiments were performed on the synthesized adsorbent under varying pressures (up to 10 MPa) and temperatures (up to 323.15 K). The specific pore volume of the adsorbent, calculated using density functional theory (DFT), was determined to be VDFT = 1.604 cm³/g, while the Brunauer-Emmett-Teller (BET) specific surface area was found to be SBET = 3456 m²/g. At a temperature of 298.15 K and a pressure of 10 MPa, the maximum methane adsorption capacity approached 19 mmol/g. The average relative deviations between the experimental data and predictions made by the Dubinin-Radushkevich model were found to be below 3%. Moreover, the initial differential molar heat of methane adsorption on the MUM-51 adsorbent was recorded at 28.7 kJ/mol [59].

An overview of novel materials in the relevant literature highlights a study in which the authors developed an algorithm to generate random porous “pseudomaterials”. Researchers calculated the structural characteristics of these pseudomaterials, such as surface area, pore size and void fraction, along with their gas adsorption properties, through molecular simulations. The research specifically focused on void fraction and xenon (Xe) adsorption at varied pressures of 1–10 bars. In this study, they identified pseudomaterials exhibiting rare combinations of mutating void fraction and Xe adsorption in order to create new pseudomaterials. This approach determined new emerging fields of mapping the structure-property, thus supporting future gas storage and separation applications through the design of new porous materials [6].

Another significant study focused on the lead adsorption properties of nano-hydroxyapatite/chitosan porous materials, which combine hydroxyapatite (HAP) and chitosan (CS) powders—both of which demonstrate good adsorption activity for Pb²⁺ ions but are challenging to separate from wastewater. The bioinspired fabrication of nano-HAP/CS porous materials (HCPMs) was achieved through a two-step process: (a) freeze-drying the brushite (DCPD)/CS porous materials (BCPMs) and (b) converting the BCPMs into HCPMs using alkaline solution treatment. The HCPMs featured interconnected, three-dimensional (3D) macropores with sizes ranging from 150 to 240 μm and a porosity of 93.0% [60]. Kinetic and isotherm studies revealed that the adsorption of Pb²⁺ ions on the HCPMs aligned well with pseudo-second-order kinetics and the Langmuir isotherm model, demonstrating their suitability for the chemical adsorption of Pb²⁺ ions from wastewater [60].

In a related study, the isotropic and anisotropic characteristics of adsorption-induced deformation in carbon adsorbents were explored [61]. A simplified model of microporous zones within carbon adsorbents was developed based on the structure dictated by raw materials and activation conditions. This model enabled the evaluation of the number of micropores (approximately 10²⁰ g⁻¹) and the number of microporous nanocrystals, referred to as elementary microporous zones (EMZ), estimated at around 10¹¹ g⁻¹ for four different carbon adsorbents with varying raw materials and activation conditions [61]. The contraction-expansion transition, along with the magnitude of contraction, was found to be temperature-dependent within a range of 216.6 to 393 K. The compressibility and tri-axial compression modulus of Sorbonorit-4 were assessed across the temperature range of 216.6 to 293 K, with both parameters exhibiting temperature-dependent behavior that could be approximated by exponential functions. Notably, the tri-axial compression modulus of Sorbonorit-4 decreased from 42 to 10 GPa, while compressibility increased fivefold within the specified temperature range [61].

Innovative hierarchical porous carbon materials (HPCs) were developed using a reactive template-induced in situ hyper-crosslinking method. This study examined how various carbonization conditions influenced the microstructure and morphology of the HPCs, as well as their ability to adsorb methylene blue (MB) [62]. The resulting HPCs exhibited a complex hierarchical structure consisting of micro-, meso- and macropores, formed through the overlapping of hollow nanospheres with microporous shells and macroporous interiors. Key factors such as carbonization temperature, duration and heating rate significantly influenced the formation of these nanostructures. The BET-specific surface area reached an impressive 2388 m²/g, with a micropore-specific surface area of 1892 m²/g [62]. Thanks to their well-structured pores, the HPCs demonstrated a methylene blue removal efficiency exceeding 99% under optimized conditions. The kinetics of adsorption were effectively modeled by a pseudo-second-order equation, while the thermodynamic behavior conformed to the Langmuir model. Additionally, this adsorption process was characterized as spontaneous and endothermic in nature [62].

4.2. Synthesizing and Designing Aspects of Adsorptive Materials Fabrication

The industrial wastewater management sector faces an urgent demand for multifunctional materials that can effectively separate both oil-in-water and water-in-oil emulsions while simultaneously adsorbing heavy metal ions. To meet this critical need, a novel three-dimensional porous material was developed, consisting of polystyrene-divinylbenzene-trimethylolpropane triacrylate/polyethyleneimine (P(St-D-T)/PEI20) [63]. This material features underliquid dual superlyophobicity and was synthesized using a one-pot high internal phase emulsion polymerization technique. The design strategy for this material integrated both hydrophilic and hydrophobic components. Cationic polyethyleneimine (PEI) was chemically grafted onto the surface of the hydrophobic P(St-D-T) porous structure via a 1,4-conjugate addition reaction. This modification endowed the material with underliquid dual superlyophobicity and introduced metal ion-chelating coordination groups. The resulting composite exhibited exceptional performance in continuously separating surfactant-stabilized oil-in-water and water-in-oil emulsions, achieving separation efficiencies of 99.4% and 97.4%, respectively, with separation flux rates of 2543 L m⁻²h⁻¹ bar⁻¹ and 8363 L m⁻²h⁻¹ bar⁻¹. Furthermore, this material displayed excellent mechanical stability and remarkable resistance to chemical degradation [63].

To conclude this section, it is worth noting the findings from two studies [64,65]. Study [64] involved the preparation of porous materials (P-Mt) using a gel casting method with nano-montmorillonite (Nano-Mt) powder. These P-Mt materials demonstrated the ability to adsorb low concentrations of Cr³⁺ from tanning wastewater [64]. When P-Mt was sintered at 600 °C, it retained effective Cr³⁺ adsorption. However, sintering temperatures exceeding 700 °C led to a significant alteration in the crystal structure and lamellar arrangement of P-Mt, resulting in reduced Cr³⁺ adsorption capacity. This indicates that 600 °C is the optimal sintering temperature for P-Mt to efficiently remove Cr³⁺ from tanning wastewater. Additionally, this method addressed issues related to the aggregation and recycling difficulties of Nano-Mt powder in liquid environments [64]. In an earlier study (published almost four decades ago), a complete computer analysis of the morphological properties of porous solid samples was obtained from gas adsorption data [65]. An interactive procedure was developed, enabling even non-specialized computer users to determine the volume and surface characteristics of samples. This method of automatic data analysis can support research laboratories interested in standard characterizations and data archives. The most important feature of this procedure was its improvement in providing calculation options without modifying the structure of the original program. It was also possible to select from different geometrical pore models that obeyed a generalized form of the Kelvin equation [65].

5. Conclusions

From a general perspective, the literature studies intended to establish the chemical principles of new types of methods, such as water chemistry, which were confined to strongly interacting sorption mechanisms, such as nanopores [55]. It is noteworthy that porous materials featuring a bimodal pore size distribution (comprising both micro and mesopores) have been successfully synthesized under ambient conditions [66]. These materials consist of uniformly sized mesoporous channels that are randomly distributed, resulting in exceptionally high surface areas and pore volumes. When examining their adsorption characteristics for water and various large organic molecules, these materials demonstrated water sorption capacities approximately 300% greater than those of traditional zeolite molecular sieves, such as zeolite 13X [66].

One of the primary features of these materials is their remarkable ability to adsorb substantial molecules, such as tetralin, at concentrations exceeding 60 wt.%, which are typically excluded by zeolites. The materials’ open architecture and extensive pore size contribute to rapid adsorption and desorption rates. These enhanced adsorption capabilities underscore the promising potential of these new materials for various applications in both adsorption and catalysis. Furthermore, the anticipated large-scale production of these mesosieve materials is expected to be both efficient and cost-effective [66].

The results of relevant research indicate that carbon material derived from waste coffee grounds possesses a high specific surface area and porosity, making it an effective adsorbent for greenhouse gases (GHGs), particularly methane [59]. A comprehensive theoretical and experimental review of published studies further highlighted that the activated carbon fibrous materials and granular activated carbon in relation to vapors of benzene, toluene, ethyl acetate and acetone are all determined by the reported porous structure and adsorption properties [67]. The porous structures of these adsorbents can be characterized by their adsorption mechanism of benzene, which serves as a standard substance, allowing for the calculation of their adsorption characteristics concerning the organic solvents examined. A strong correlation for all adsorbents was reported between their calculated and experimental characteristics. Furthermore, it was established that the adsorption properties of both activated carbon fibrous adsorbents and granular activated carbon are directly related to the molecular polarizability of the adsorptive, as well as the volume and size of the adsorbing pores [67]. In conclusion, two key insights from the bibliometric analysis were emphasized:

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The adsorption properties of polytetrafluoroethylene and silica chemically modified with an organofluoric coating match gas chromatography at low coverage compared with other hydrophobic materials, showing that polytetrafluoroethylene is a nonpolar material with the lowest energy of adsorption of all the adsorbents studied, irrespective of their chemical nature [68].

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New research efforts can focus on developing porous materials with underliquid dual superlyophobicity to address complex wastewater treatment challenges, particularly in the treatment of oily wastewater and organic pollutants in aqueous solutions [63,69,70].