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Sorption Quantification through the Magnetic Response of Paramagnetic Metal-Organic Frameworks (MOFs) to External Magnetic Fields

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Rubén Pérez-Aguirre and Oscar Castillo

Submitted: 30 September 2025 Reviewed: 07 October 2025 Published: 12 January 2026

DOI: 10.5772/intechopen.1013520

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Sorption Theoretical Aspects and Practical Applications Edited by Tatyana I. Shabatina and Yana A. Gromova

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Sorption - Theoretical Aspects and Practical Applications

Tatyana I. Shabatina and Yana A. Gromova

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Abstract

It has been known for a long time that materials with paramagnetic behavior are weakly attracted to external magnetic fields. However, this phenomenon hasnot received significant attention in the context of porous paramagnetic materials (metal-organic frameworks, MOFs, and supramolecularly assembled metal-organic frameworks, SMOFs), the composition of which depends on adsorption processes. In this sense, paramagnetic MOF particles that are immersed in a liquid medium can be moved, or even kept motionless, by strong external magnetic fields without falling down. The required magnetic field varies for each MOF and with each adsorption process, as the composition– and therefore the mass accumulated in the pores– varies. Consequently, the threshold at which this stasis of the particles happens is correlated with the quantity of adsorbate captured by the paramagnetic porous material. Two devices have been developed : one uses electromagnets, and the other uses permanent magnets as the source of the magnetic field. When electromagnets are used, the applied current can modulate the strength of the magnetic field, whereas when permanent magnets are used, it is modulated by displacing the sample from the magnet. In both cases, the specific instrument can provide a precise determination of the magnetic field strength (H) or distance (D) at which the stasis phenomenon ends. Theoretical analysis and experimental evidence indicate that both parameters correlate with the amount of mass loaded into the adsorbent, enabling its determination. The theoretical background, a detailed description of the devices, and examples of their application are provided.

Keywords

  • sorption
  • quantification technique
  • paramagnetism
  • MOFs
  • SMOFs

1. Introduction

The sorption phenomenon requires characterization techniques categorized into two groups: gas-phase and liquid-phase. Methods for characterizing sorption processes involving species in the gas phase, such as volumetric and gravimetric techniques, have been in use for a long time and are now ubiquitous in modern laboratories [1, 2]. Other techniques using ellipsometry [3], pycnometry [4], X-ray reflectometry [5], and magnetoelastic resonators have also been proposed for gas sorption characterization [6, 7].

However, characterizing the sorption of species dissolved in a liquid medium still relies on techniques that indirectly determine the sorption by measuring the concentration of the species in the solution before and after the addition of the adsorbent [8–13]. The difference between these values provides an estimate of the amount of the species captured by the adsorbent. This indirect analysis, which does not focus on the adsorbent, can lead to shortcomings. For instance, if the species to be captured are not fully dissolved in the liquid medium, which is relatively common in natural or industrial environments, the results can be inaccurate. Additionally, this approach requires access to the initial and final solutions. In other words, it is not possible to determine the amount adsorbed if only the adsorbent sample is available. Another issue arises when the amount of adsorbent is too small to significantly alter the concentrations of species in the liquid medium. For example, this would occur if the adsorption experiment were performed directly in a river, lake, or sea. In all these situations, determining the amount captured would require the captured species to be transferred to a liquid medium by desorption, ensuring complete desorption (which is not always trivial), or the complete sample to be digested (a destructive procedure). Another disadvantage of the indirect approach is that the concentration of the species in solution must be determined, which may require different analytical techniques (HPLC, GC, UV/Vis, NMR, etc.). These techniques often require specific procedures and calibrations that are not easily accessible and can be very time-consuming when working with different species.

Therefore, it would be helpful to develop a universal quantification technique for sorption that is similar to the volumetric and gravimetric techniques used for gases. This would involve identifying a property of the adsorbent that changes during the sorption process. One obvious property to consider is the mass increase of the solid adsorbent that occurs during sorption. However, measuring the mass increase of the adsorbent in liquid applications is very complex for two reasons. Firstly, the adsorbent particles are immersed in a liquid, so the initial and final masses must be weighed while ensuring that no sorbent is lost during the process. Secondly, even if all the solvent is removed from the liquid medium, the adsorbent’s weight depends on the amount of solvent contained in its pores, which varies according to the room conditions and drying procedure. Consequently, this method has never been established for quantifying sorption in liquid media. Nevertheless, a new type of porous material has emerged since the beginning of this millennium: metal-organic frameworks (MOFs), which are 3D crystalline structures containing interconnected pores and consisting of inorganic and organic components.

In fact, the number of these materials and their applications has increased exponentially since their discovery. The inorganic component consists of a metal center or a metal oxide/hydroxide polynuclear unit (secondary building unit, SBU), which often involves paramagnetic metal atoms such as Mn2⁺, Cr3⁺, Ni2⁺, Fe3⁺, Co2⁺, Cu2⁺ and lanthanides. These paramagnetic MOFs have a small magnetic response to an external magnetic field; even Earth’s gravity surpasses the force exerted by the external magnetic field, meaning the particles of these MOFs do not move, even when a strong magnet is placed in proximity. However, under conditions of weakened gravity—i.e., when immersed in a liquid—this weak force is sufficient to hold the particles of this material adhered to the lower pole of a relatively strong magnet (Figure 1). The required magnetic field for this phenomenon to occur varies depending on the paramagnetic MOF and the sorbate mass loading.

Figure 1.

Paramagnetic particles are attached by strong magnetic fields of an electromagnet while immersed in a liquid medium.

Two related techniques and measuring devices have been developed based on this phenomenon to quantify the adsorbed mass in paramagnetic porous materials submerged in a liquid medium [14, 15]. As will be detailed below, these techniques perform the measurement directly in the liquid medium by means of density changes in the porous materials. Since they are based on an intensive property, the measurement is independent of the amount of adsorbent used or the fraction utilized. They are universal with respect to the sorbate, and calibration is performed on the adsorbent rather than on the sorbate (there is no need for calibration for every sorbate/analyte). Below, we provide an overview of both techniques and the measuring devices, as well as examples of their application in areas such as water remediation, drug delivery, and CO2 capture.

2. Theoretical background

The magnetic sustentation phenomenon described above can be explained by the balance of three fundamental forces acting on the adsorbent particles: the magnetic force, buoyancy (or flotation), and gravity. The magnetic force (Eq. (1)) [16, 17] can be expressed as a function of the magnetic susceptibility of the adsorbent material and the external magnetic field, provided that the particles are small enough (i.e., <1 mm). At the bottom edge of the magnet pole, the magnetic force pushes the paramagnetic particles of the MOF upwards. The gravitational force (Eq. (2)) pulls the particles downwards. The buoyancy force (Eq. (3)), generated by the liquid medium, keeps the MOF particles in suspension by pushing them upwards.

Fmagnetism=µmm∇(H)=µm⋅χMMWFρF·VF·H·∇HE1
Fgravity=M·g=(MF+Mvoid)⋅g=(VF⋅ρF+VM⋅ρM+Vsolvent⋅ρsolvent′)⋅gE2
Fbuoyancy=(VF·ρsolvent+Vvoid⋅ρsolvent)⋅gE3

In these equations, an arbitrary distinction can be made between the mass, molecular mass, density, and volume parameters corresponding to the framework of the adsorbent material (MF,MWF,VF and ρF)) and those corresponding to the void (Mvoid,Vvoid). The void is also divided between the adsorbate (MM,MWM,VM and ρM) and the solvent molecules (Vsolvent and ρsolvent′) that occupy it. As the adsorbate molecules are considered diamagnetic, their contribution to the magnetic attraction force can be ignored. Fortunately, most potential adsorbates meet this requirement. The other parameters are the magnetic permeability of the medium that surrounds the particle (µm), the particle's magnetic dipole moment (m), the molar susceptibility (χM), the magnetic field gradient (∇H)) the magnetic field (H), the solvent density (ρS), the density of the solvent when placed inside the MOF voids of the (ρsolvent′) and the gravitational acceleration of the Earth (g).

At the end of the measurement process, the conditions under which the final particles fall correspond to a situation where the gravitational force is balanced by the upward forces of magnetic attraction and buoyancy, Eq. (4):

Fmagnetism=Fgravity−FbuoyancyE4

By substituting Eq. (1–3) into Eq. (4), we obtain Eq. (5):

μ m ⋅ χ M M W F ⋅ ρ F ⋅ V F ⋅H⋅∇H=[ V F ⋅ ρ F + V M ⋅ ρ M +( V void − void V M )⋅ ρ ′ solvent ]⋅g−( V F ⋅ ρ solvent + V void ⋅ ρ solvent )⋅g E5

This equation can be expressed as Eq. (6):

µm·χMMWF·ρF·H·∇H=[(ρF-ρsolvent)+VMVF·(ρM-ρ'solvent)+VvoidVF·(ρ'solvent-ρsolvent)·]gE6

In contrast, VF and VM can be detailed as:

VF=MFρF=n·MWFρFandVM=MMρM=n·x·MWMρM

Where n is the number of moles of the MOF framework’s empirical formula in the particle, and x is the fraction of adsorbed adsorbate molecules per MOF empirical formula. MWF and MWM represent the formula and molecular weights of the MOF and the adsorbate molecule, respectively.

The ratio of the volumes of the captured adsorbate (VM) to the adsorbent (VF) is given in Eq. (7).

VMVF=x·MWM·ρFMWF·ρME7

Which is applied to Eq. (6) to derive Eq. (8):

x·MWM=µm·χM·ρM(ρM−ρsolvent′)·gH·∇H−(ρF−ρsolvent)(ρM−ρsolvent′)⋅MWF⋅ρMρF−VvoidVF⋅(ρsolvent′−ρsolvent)(ρM−ρsolvent′)·MWF⋅ρMρFE8

Considering that all parameters except "H·∇H" and “x·MWM" are constant, the previous equation can be transformed into Eq. (9):

x·MWM=A·H·∇H−BE9

It is possible to define MM(F)=x·MWM, where MM(F) is the amount of adsorbate mass trapped per adsorbent formula, to produce Eq. (10). This establishes a linear relationship involving the captured mass and the H·∇H product when the particles fall.

MM(F)=A·H·∇H−BE10

At this point, it is necessary to develop devices that can control and measure the H·∇H product during a sustentation experiment. While measuring such a magnitude can be challenging, if these devices are designed to correlate with another, more easily measurable property of the H·∇H product, a viable adsorption quantification technique can be achieved.

3. Measuring devices

In order to change the H ·∇H product in a precise and reproducible way, a measuring device based on the sustentation of paramagnetic MOF particles must have the capacity to do so. This can be achieved in two ways:

  1. Electromagnets can be used to control the magnetic field strength and, consequently, the H·∇H product by controlling the applied electric current. The parameter being determined is the critical magnetic field (the magnetic field value at which the last particles are detached).

  2. Permanent magnets can be used, with the distance to the sample being precisely controlled. The parameter being determined is the critical distance (D), which is the lateral distance value at which the last particles tumble.

This section will detail each device and explain how the applied electric current or distance to the sample correlates with the H·∇H product.

Figure 2 shows a schematic description of the sustentation phenomenon and the electromagnet-based device. This measurement device is based on a parallel-aligned dipole electromagnet. In this device, the MOF particles are submerged in the corresponding solvent within a glass test-tube. The measurement procedure begins with the test tube positioned between the electromagnet’s poles in the area where the magnetic field is at its maximum. The particles clump together and stick to the lower part of the magnetic pole.

Figure 2.

Magnetic sustentation measurement procedure. a) Transition from a magnetic field (where particles aggregate) to a lower critical magnetic field (particles falls). b) Schematic description of the MOF aggregate. c) Forces taking place on the particle/aggregate. d) Effect of the amount of trapped mass on the critical magnetic field. e) Experimental magnetic sustentation device. f) Example of zif-67(co) particles adhered to the bottom of the electromagnet poles.

Then, the magnetic field is slowly decreased, causing the particles to fall into smaller aggregates. The process begins with the particles that are more loosely attached to the glass walls of the test tube (i.e., those located farther from the magnetic pole). Finally, the last particles – those that are directly attached to the glass wall – fall down. The magnetic field obtained where the final detachment occurs is defined as the critical magnetic field. This parameter corresponds to the minimum magnetic field value required to hold the particles in place before gravity overcomes magnetic attraction and they are no longer suspended by the magnetic poles.

According to Eq. (10), the values obtained for an adsorbent loaded with different amounts of mass should lie on a straight line in a captured mass versus H·∇H plot. The H·∇H product value along the vertical profile of the electromagnet pole was measured using a Hall effect sensor (see Figure 3a), which revealed that the maximum attraction force occurs at the pole’s edge – the very spot where the particles are held during experimentation – and that this value rises with the applied electric current. However, the magnetic field value at the center of the electromagnet pole is easier to measure, and its correlation with the H·∇H product can be determined (see Figure 3b). When the two electromagnets are placed in a parallel configuration facing opposite poles, the dependence of H·∇H on H is not linear across the whole range. Nevertheless, it follows a quasi-linear dependence across more limited ranges, such as those observed in the magnetic sustentation experiments. Consequently, Eq. (10) can be rewritten as Eq. (11):

Figure 3.

a) H and H·∇H profile along the black line on the electromagnet pole. The different colors indicate the applied current intensity, increasing from 0.0 to 2.5 A in 0.1 A increments. b) The dependence of H·∇H on the magnetic field at the center of the pole. The graph on the left shows a second-order polynomial fit to the entire magnetic field range, while the graph on the right shows a linear fit within a shorter range typical of the observed variations during the adsorption processes.

MM(F)=A'·H−B'E11

Another way to modify the magnetic field (H) and the H·∇H product is to control the distance between the pole and the sample holder. The greater the distance, the smaller the magnetic field and the H·∇H product. This approach means that an electromagnet is no longer necessary, as cheaper rare-earth permanent magnets can be used instead. However, the measuring device must be set up differently to allow the sample holder to be displaced slowly and smoothly with respect to the magnetic pole while simultaneously measuring the separation distance precisely.

Figure 4a shows a schematic description of the measuring device, which is based on the use of permanent magnets and the measurement of the distance between the magnet and the sample holder. The device consists of a methacrylate base with an indentation of the same width and length as the U-shaped magnetic steel frame. This frame can be positioned in the indentation so that it cannot move or shift. A linear actuator is then attached to the methacrylate support between the permanent magnets, and a methacrylate plate with a hole is attached to the actuator’s shaft. This enables control of the distance to the magnet’s surface when a test tube containing MOF particles immersed in a liquid is inserted into the hole. The aim is to modify the H⋅∇H product using lateral displacement until the particles fall (see Figure 4b).

Figure 4.

a) A schematic depiction of the measuring device based on permanent magnets, highlighting its key components. b) A representative image of the measuring process. Initially, the sample holder touches the magnet pole, with the paramagnetic particles of the adsorbent attaching to the bottom part of the pole. With the help of the linear actuator, the sample holder is displaced laterally until the final particles detach from the transparent sample holder walls and fall (right). The lateral distance at which these particles fall defines the distance (D) parameter, which is characteristic of each porous material and the mass of adsorbate loaded. The linear actuator provides an easy reading of this lateral distance.

Again, the value of the H⋅∇H product at the bottom part of the permanent magnet was measured using a Hall effect sensor at different lateral displacements. This made it possible to determine the correlation of this product with respect to the critical distance (D). The H⋅∇H vs D plot showed that there is no linearity across the full range of lateral displacement in the parallel configuration of the permanent poles. However, quasi-linear dependence can be assumed for smaller ranges, such as those observed during the magnetic sustentation experiments (Figure 5). Therefore, Eq. (10) can be rewritten for this device as Eq. (12):

Figure 5.

On the left: the H·∇H product variation with respect to the magnetic field, H, at the center of the pole. On the right: linear fits within the range observed for each MOF during the magnetic sustentation experiments.

MM(F)=A''⋅D−B''E12

Although the two measuring devices are based on the same phenomenon and have the same theoretical background, the way they accomplish the modification of the magnetic field (H) and the H⋅∇H product differs: i) by applying an electrical current to electromagnets, or ii) by measuring the distance to permanent magnets. These two approaches result in differences in the performance and cost of the measuring devices. Electromagnets can generate stronger magnetic fields (up to 2.0 T) than permanent magnets (up to 0.6 T), which implies that materials with a very weak paramagnetic response will necessarily require an electromagnet-based device. That said, it is worth mentioning that, to date, we have not identified a paramagnetic adsorbent whose adsorption values cannot be measured by both devices. However, the materials and equipment required to build the devices are far more expensive when an electromagnet is needed than when permanent magnets are used.

4. Experimental validation and examples of applications

The above equations suggest that the endpoint of the measurements should be independent of the size or morphology of the adsorbent particles. This is a key feature of the technique that requires experimental validation. To this end, an electromagnet was used to take measurements on three samples of MIL-88A(Fe) porous material of diverse sizes (1.5, 4.4, and 5.7 μm) and morphologies, Figure 6. The results obtained from samples of the compound with different particle sizes show no significant differences in the measured critical magnetic fields [18].

Figure 6.

The critical magnetic field parameter of three MIL-88A(Fe) samples.

The linear dependence of the captured mass on the H⋅∇H product was verified using a supramolecularly assembled MOF (SMOF) with the formula [Cu6Cr(μ-adeninato)6(μ3-OH)6(μ-OH2)6](SO4)1.5, which can capture a variety of molecules (Figure 7a). In agreement with the theoretical prediction, plotting the captured mass of each molecule —determined from the initial and final solution concentrations— and the measured H⋅∇H product at which the last particles detach from the sample holder wall shows a strong linear correlation. Therefore, the value at which the adsorbent particles detach from the wall of the sample holder in both devices can be used as qualitative or quantitative evidence of the adsorption process. For qualitative analysis, it is only necessary to measure the endpoint value for the pristine adsorbent and for the adsorbent loaded with sorbate. The greater the deviation, the greater the amount of sorbate being loaded (Figure 7b). The quantitative approach requires a calibration procedure to be carried out in advance, in which samples of the adsorbent with known mass-loading values are measured in one of these devices to generate the corresponding calibration line. This is the same procedure that was described above for validating the linear dependence. Once this calibration line has been established, the mass loading of any sorbate can be determined by extrapolating the measured endpoint value directly onto the calibration straight line.

Figure 7.

(a) Linear correlation between the percentage of adsorbed mass and the measured H·∇H value at which the adsorbent particles detach from the electromagnet pole. (b) Comparison of the measured critical magnetic fields between the pristine adsorbent (Ø) and those exposed to different adsorbates.

Another feature of the method is that, according to the theoretical background, the liquid media does not necessarily need to be aqueous media. In that sense, two MOFs were selected: MOF-74(Cu) and MIL-88A(Fe) to accomplish their calibration in water and ethanol, respectively. As can be seen in Figure 8, both in water or ethanol, a calibration straight line is achieved experimentally, supporting the universality of the technique with respect to the solvent.

Figure 8.

Calibration curves obtained using UV-VIS spectroscopy for the quantification of DMF, DMSO, and TMU, along with values for the other adsorbates: a) MIL-88A(Fe) in solvent water and b) MOF-74(Cu) in solvent ethanol. Ø indicates the experiment using pure water or ethanol, respectively.

4.1 Pollutant removal from aqueous media

Nowadays, emerging pollutants from pharmaceuticals, agriculture, and industry are a growing environmental concern [19]. Among these pollutants, drugs released into the environment via domestic wastewater and pharmaceutical sewage can lead to increased pollution levels that may affect living organisms [20]. Therefore, it is crucial not only to develop simple methods to remove drugs from water but also to devise effective ways to analyze their effectiveness. Of all the techniques studied so far, those based on adsorbents are considered to be among the best suited, given their high removal capacity. In this context, two paramagnetic MOFs were selected: MIL-100(Fe) and MIL-101(Cr). Due to their large pores (2.5–2.9 nm and 2.9–3.4 nm, respectively) and specific surface area (1900 m2/g and 2800–3200 m2/g respectively) both should be capable of capturing a wide variety of molecules making them ideal candidates for testing the capture of these pharmaceutical pollutants. The calibration line for each adsorbent was obtained by measuring the adsorption of simple molecules (aniline, ribose, DMF and DMSO). The results, obtained by interpolating the end-point distance for different pollutants on the calibration line, are displayed in Figure 9. They show that the wide pores of these materials can effectively trap relatively large drug-molecules, such as ibuprofen, aspirin and naproxen (25–31 wt%), among others.

Figure 9.

Graph and data of the adsorbed mass (%) versus lateral displacement d for the adsorbent materials: (a) MIL-101(Cr) and (b) MIL-100(Fe) at 30 °C. Molecules employed to determine the calibration line (dashed line) are marked with a blue circle, while molecules whose captured mass was determined by interpolation are marked with a red square. Horizontal bars indicate the corresponding standard deviation from five measurements.

4.2 Alcohol recovery from aqueous media

Recovering alcohol from low-concentration aqueous solutions is of great interest due to alcohol’s widespread use in industrial processes [21]. In this sense, the separation using adsorbents is viewed as a green and money-saving alternative to the processes traditionally used for separating alcohol/water mixtures that involve a high energy penalty. MIL-88A(Fe) is an iron-based flexible MOF with a 3D porous structure, featuring pores measuring 3.2–3.7 Å in diameter and generating a void volume of around 0.7 m3/g. Its ability to capture alcohols from water was measured in the electromagnet device using an aqueous solution containing 50 µL of some small alcohols (methanol, ethanol, n- and isopropyl alcohol, n-, sec-, iso-, and tert-butyl alcohol). As shown in Figure 10, the results indicate that the smaller the alcohol, the greater the uptake, with values ranging from almost 20 wt% for methanol to an almost negligible 4 wt% for tert-butyl alcohol. The calibration line of MIL-88A(Fe) in water is depicted in Figure 8a [22].

Figure 10.

(a) Representation of the critical magnetic field, H(T), of MIL-88A(Fe) after exposure to aqueous solutions containing different alcohols. (b) Determination of the amount of adsorbed alcohols portrayed as adsorbed mass (%) and as adsorbed molecules per MOF formula. (c) Methanol adsorption kinetics.

Additionally, the measurements were repeated for samples exposed to a higher concentration of alcohol (200 µL instead of 50 µL). The results showed pretty similar outcomes, which suggests that MIL-88A(Fe) is already at saturation at 50 µL. Furthermore, a study of the methanol adsorption kinetics was conducted using this device (Figure 10c).

4.3 Drug loading and delivery

The therapeutic application of drugs often faces challenges due to non-specific distribution, inadequate dosification, and degradation, which limit their efficacy [23]. Two main approaches are employed to overcome these issues: using derivatives of the active substance and incorporating these active substances into porous materials. The latter approach, which involves materials such as hydrogels, zeolites, and MOFs, has shown promising results not only in the protection of the active ingredients from degradation but also in allowing a controlled release. In this context, several experiments were performed to determine the capacity of various supramolecular metal-organic frameworks (SMOFs) to be loaded with different drugs and to study the drug release kinetics of these drug-loaded SMOFs. The electromagnet-based device was used to determine the amount of drug that the SMOFs were capable of adsorbing and also to follow the desorption kinetics.

For this purpose, two different SMOFs were selected: [Cu7(μ-adeninato)6(μ3-OH)6(μ-OH2)6](naphthalene-2,6-dicarboxylate)—now called Cu7ADNap—and the previously reported Cu6Cr. The two compounds contain the same wheel-shaped heptanuclear entity, in which the central metal atom, which can be Cu2+ or Cr3+ is connected to six external Cu2+ centers through hydroxide bridges. These external metal centers are bridged among themselves by adeninato ligands and coordinated water molecules. The resulting polynuclear discrete entity is positively charged and requires the presence of anions to maintain neutrality. Depending on the characteristics of the anion, the resulting supramolecular crystal structure differs, giving rise to porous materials. The selected drugs were the antibiotic 4-aminosalicylic acid (4-ASA), the anti-inflammatory for bowel diseases 5-aminosalicylic acid (5-ASA), the antitumoral 5-fluorouracil (5-FU), the antiarthritic allopurinol (ALLO), and theobromine (THEO), historically employed as a diuretic, bronchodilator, and vasodilator. The quantification of the drug loading was completed as previously explained (Figure 11) [24, 25].

Figure 11.

Graph and data of the adsorbed mass(%) versus critical magnetic field (H) for the adsorbent materials: (a) Cu7ADNap and (b) Cu6Cr. Molecules employed to determine the calibration line (straight black line) are marked with a blue or green circle, while molecules whose captured mass was determined by interpolation are marked with a red square.

In addition to this, the drug release kinetics were also measured with the device. The desorption process was carried out on SMOFs that were previously loaded with the corresponding drug by placing them in 5 mL of water at 35 °C. Afterward, the critical magnetic field was measured at different times in order to determine the kinetics of the drug release. After each measurement, the aqueous medium was replaced. In the case of compound Cu7ADNap the desorption curves show that nearly half of the loaded drug of 5-FU and ALLO is released in the first 2 − 3 h, while 4-ASA and 5-ASA are released after 6 − 7 h, following pseudo-first-order kinetics. Compound Cu6Cr also follows pseudo-first-order kinetics with t1/2 values ranging between 2 and 5 h (Figure 12).

Figure 12.

Desorption isotherms of the drug-loaded samples for compound Cu6Cr. Inset: fitting of the first 6 hours of the desorption process to a first-order kinetic.

4.4 CO2 capture from water

The ability of SMOF Cu6Cr to capture CO2 from water was also tested [26]. The coordinated adeninato ligands provide protonable positions and a flexible structure, making this compound a promising candidate for this application. In this sense, the electromagnet-based device was used together with conventional weighing. This combination allows both the verification of CO2 capture and the determination of the chemical species in which it is captured. The following procedure was followed to determine the amount of CO2 captured from water using the magnetic sustentation technique (Figure 13a). Fifty milligrams of Cu6Cr compound were added to a glass flask containing 50 ml of water. The flask was then sealed with a septum, and two needles were inserted: one as the CO2 inlet and the other as the outlet. CO2 was bubbled through the solution for 1 hour with a flow rate of 300 ml/min at 293 K. The aqueous medium containing the Cu6Cr particles was then transferred to the magnetic sustentation measuring device to determine the amount of CO2 mass captured on the particles by interpolation on the Cu6Cr calibration line. In order to gravimetrically determine the amount of CO2 captured, a slightly different setup was used (Figure 13b; see more details in Ref. 22).

Figure 13.

(a) Experimental setup for determining CO2 uptake from water using the magnetic sustentation technique. (b) Experimental setup for gravimetrically determining CO2 uptake.

As previously mentioned, the magnetic sustentation technique allows the determination of the adsorbate mass that has been captured by the porous material. In contrast, the gravimetric technique measures the total amount of CO2 stored in the water-plus-porous-material system. Consequently, the two techniques are complementary, and they do not necessarily provide equal results. It is true that physisorption of CO2 and carbamate formation should provide identical values, but the capture of CO2 in the form of HCO3-/adenine adduct must necessarily imply that the magnetic sustentation technique obtains a greater mass capture value than the gravimetric method. This hypothesis is corroborated by the measurements obtained at 20 °C (Table 1).

Gravimetric measurement Magnetic sustentation
Δmass (mg) Δmass excess (mg) CO2 (%) CO2/Cu6Cr H2CO3 (%) H2CO3/Cu6Cr
Cu6Cr 500 mg/50 mL 118.7 ± 4.0 85.7 ± 4.3 17.1 ± 0.9 6.4 ± 0.3 22.3 ± 2.6 5.9 ± 0.7
Water 50 mL 33 ± 1.7 - ~0 -

Table 1.

Comparison of gravimetric measurements and magnetic sustentation CO2/H2CO3 capture results for the Cu6Cr aqueous suspension.

Additionally, adsorption kinetics experiments were performed at 20 °C to study the capture of CO2 under different conditions: dry Cu6Cr particles exposed to dry CO2, dry Cu6Cr particles exposed to a water-saturated CO2 stream, and Cu6Cr particles submerged in water and exposed to CO2/N2 bubbling mixtures (Figure 14). The absence of CO2 capture under dry conditions confirms that capture is driven by the formation of HCO3-/adenine pairs.

Figure 14.

(a) CO2 adsorption kinetic curves at 20 °C under different conditions: Cu6Cr particles under dry CO2 flux (red), Cu6Cr particles under humid saturated CO2 flow (blue), and bubbling CO2 in an aqueous suspension of Cu6Cr particles (green). (b) Adsorption isotherm of Cu6Cr as function of CO2 percentage.

Kinetic curves of CO2 adsorption/desorption for aqueous suspensions of Cu6Cr particles were obtained at different temperatures (20, 30, and 40 °C; Figure 15) in order to calculate the activation energies corresponding to both processes. The data showed a relatively good fit to the Langmuir model, and the resulting activation energies for both processes were 21.8 kJ/mol and 41.2 kJ/mol for adsorption and desorption, respectively. The difference between these two values enabled the adsorption heat (ΔHads) for the CO2 capture process in this material to be estimated at −19.4 kJ/mol, indicating an exothermic process.

Figure 15.

(a) Kinetic curves of CO2 adsorption (left) and desorption (right) of compound Cu6Cr at three different temperatures. (b) Langmuir model fitting (see the accompanying table for the fitting details). (c) Arrhenius plots showing the calculated activation energies.

5. Conclusions

The developed techniques and devices (the one based on electromagnets and the one based on permanent magnets) allow analysis of the phenomenon of magnetic sustentation, which occurs when the particles of paramagnetic porous materials submerged in a liquid are exposed to a sufficiently strong magnetic field. The devices allow the definition of two easily measurable parameters: the critical magnetic field (H) and the critical lateral displacement (D). These parameters can be correlated with the mass loaded by porous paramagnetic materials (mainly MOFs and SMOFs). Theoretical and experimental analysis of magnetic sustentation indicates that these parameters are intensive properties that do not depend on the amount of material used for measurement. The technique can measure the adsorption of any kind of adsorbate. Nor are there limitations on the liquid medium, which can be aqueous or non-aqueous, or on the temperature at which measurements are performed. Calibration takes place on the adsorbent material, not on every adsorbate that you want to measure. The measurement procedure is quick and straightforward and does not require complex training. These techniques not only allow the determination of the amount of a substance loaded into the adsorbent but also enable additional determinations to be made, such as adsorption isotherms, adsorption/desorption kinetic studies, activation energy calculations, and testing the long-term stability of adsorbents. Overall, these techniques have great potential to transform the characterization of adsorption processes in liquids that involve paramagnetic materials such as the fascinating MOFs and their counterparts, the SMOFs.

Acknowledgments

These developments are the result of research lines funded by Eusko Jaurlaritza/Gobierno Vasco (IT1722-22; ELKARTEK program KK-2022/00032), Ministerio de Universidades and the European Union-Next Generation EU (marsa21/52, R. P. A.), and by the Spanish Ministry of Science and Innovation (PID2023-146448OB-C22, PID2022-138968NB-C22 project funded by MCIN/AEI /10.13039/501100011033/and by FEDER, a way to make Europe). We also thank G. Beobide, N. Barroso, J. B. Etxebarria, E. Maiza, S. Mena, S. Pérez, and A. Luque for their contributions to the development and testing of these devices. Human and technical support provided by SGIker (UPV/EHU, MICINN, GV/EJ, ESF) is also acknowledged.

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Written By

Rubén Pérez-Aguirre and Oscar Castillo

Submitted: 30 September 2025 Reviewed: 07 October 2025 Published: 12 January 2026

© 2026 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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