Kinetic features of the adsorption of menthol enantiomers on o-toluylic acid and CsCuCl 3 crystals with supramolecular chirality

. Chirality plays a key role in modern science because it is the distinguishing feature of molecules and crystals. The spontaneous emergence of chirality in the absence of detectable chiral physical and chemical sources has recently advanced significantly due to the deracemization of conglomerates through Viedma rip-ening. As a result, systems based on supramolecular chirality are obtained. Of particular importance to this type of chirality is the fact that supramolecular chirality underlies the formation of life on Earth. One manifestation of supramolecular chirality is enantiomorphic crystals. Previously, we studied the mechanism of supramolecular chiral recognition for enantiomorphic crystals in the case of adsorption of optically active substances on them. However


Introduction
Chirality is an inherent property of natural materials, including minerals, organic molecules, and biological structures.Chirality can be identified both in molecules and in supramolecular formations, such as crystals [1].Pasteur was the first, who noticed the analogy between crystals and molecules in this context.He realized that the non-identity of a crystal (or a molecule) with its own specular reflection is due to what he called dissymmetry.It is known that the two enantiomers differ in their physiological effects: one enantiomer may be an effective drug, while the other may be toxic.Therefore, the development of new methods for chiral recognition and separation of optical isomers is of practical importance for drugs and biologically active compounds design.In chromatography, in the most cases, enantiomers are separated by interaction with a chiral selector, which is either fixed to a solid substrate or added to the mobile phase.As a result of the interaction, diastereomeric complexes are formed between the enantiomers of the analyzed substance and the chiral selector.They differ in physical and chemical characteristics.Due to this approach, more than 50 years ago Davankov [2,3] and Gil-Av [4] performed the first chromatographic separations of enantiomers.Enantioselective stationary phases based on cyclodextrins have been used in gas chromatography for several decades.Cyclodextrins occupy a leading position in chiral GC, but many challenges require more selective chiral stationary phases.
In this context, concepts based on supramolecular chirality were tempting.Supramolecular chirality implies a dissymmetric arrangement of molecular components in a non-covalent assembly.Elements with this type of chirality can be obtained as a result of a certain spatial arrangement of molecules [5].In this case, they have higher levels of hierarchy than simple molecules -they consist of several layers of molecules or atoms.Chiral supramolecular structures can be formed from both chiral and achiral molecules.The latter can be used either in the case of an external source of chirality, or by spontaneous violation of chiral equilibrium.Enantiomorphic crystals are the examples of elements with supramolecular chirality.These objects is usually obtained by crystallization of optically pure substances [6].However, in some cases optically pure crystals can also be obtained from molecular achiral compounds.Such crystals are suitable for studying the effect of supramolecular chiral recognition, because there is no effect of chiral molecular recognition.
Among a lot of methods for obtaining individual enantiopure crystals from a racemic or achiral solution, the method of Viedma ripening has shown the greatest reliability.In this process, the ratio of the crystallization centers of the two optical forms is disrupted by continuous grinding of the suspension.Further, the Frank autocatalytic process leads to a complete shift in the chiral equilibrium: the crystals of one of the enantiomorphs completely dissolve and the other enantiomorph crystallizes.
Previously, Viedma ripening was successfully applied to obtain enantiomorphic crystals of achiral molecules.These crystals were studied for their ability to recognize enantiomers in adsorption processes.It was found that the chiral recognition of enantiomers was caused by different energies of lateral interactions of adsorbate on the crystal surface.So there was a difference in the thermodynamic characteristics of the adsorption of enantiomers.However, it was previously determined that the Van Deemter curves for optical isomers have differed.Therefore, 660 there may also be differences in the rate of adsorption of enantiomers.However, this phenomenon has not been thoroughly studied.
In this paper, the kinetics of menthol enantiomers adsorption on o-toluic acid and CsCuCl3 crystals with supramolecular chirality was studied.Various models have been used to describe kinetic curves, such as Lagergren's pseudo-first-order model, Ho and McKay's pseudo-second-order model, and the Еlovich model simplified by Chen and Clayton.Boyd model of film diffusion [12] and Weber-Morris [13] and Dumwald-Wagner [14] models dealing with intraparticle diffusion were used as well.

Experimental part
O-toluic acid crystals (99%, Sigma Aldrich, China, CAS No. 118-90-1) and CsCuCl3 were selected as the compounds for crystallization.The latter were obtained by the reaction of CuCl2 (>99%, Reachim, St. Petersburg, Russia, 7447-39-4) and CsCl (>99%, Reachim, St. Petersburg, Russia, 7647-17-8) To obtain homochiral crystals, the method of Viedma ripening was used.To obtain enantiopure crystals of o-toluic acid, 17 g of o-toluic acid were dissolved in 160 ml of acetonitrile.9 g of glass beads were added to create a "mill" effect.The resulting suspension was stirred at a speed of 1000 rpm for 2 hours, and then left to ripe for two days [7].
To obtain CsCuCl3 crystals, a saturated solution containing 57.2 g of CsCl in acidified water was gradually added to a solution containing 110.8 g of CuCl2 at 32˚C (pH=1.39).The resulting solution was intensively stirred in the presence of glass beads at a speed of 1300 rpm.Then the temperature was reduced to room temperature and stirring was continued for 2 days.The solution was left for 7 days in an open flask to complete the autocatalytic process.The suspension was filtered, and the resulting precipitate was dried in a desiccator over CaCl2 for a day.After that, the adsorbent was additionally dried in a nitrogen stream for an hour.
As a result, crystals of a characteristic garnet-black color were obtained.
The specific surface area of the crystals is several m 2 /g.For this reason, the value of adsorption on crystals is too small for reliable chiral discrimination determination.Therefore, to increase the specific surface area, the obtained crystals were applied on the surface of ASKG silica gel (Reachim, St. Petersburg, Russia, CAS No. 112926-00-8).To apply o-toluylic acid, 220 ml of acetonitrile and 10 g of crystals were added to 50 g of ASCG silica gel.The suspension was stirred for 2 hours, and then the precipitate was filtered and dried.To apply CsCuCl3 crystals, a saturated solution of CsCl in acidified water was gradually added to the CuCl2 solution with continuous stirring (pH=1.39).5 g of previously obtained CsCuCl3 crystals were added to the solution, then stirred for 30 minutes.Then 50 g of silica gel was added.The stirred solution was evaporated at room temperature until stirring became impossible.
The adsorption of menthol enantiomers from solutions was studied using the following algorithm.A 0.5 g silica gel sample modified with o-toluic acid or CsCuCl3 was added to a solution of D-or L-menthol in nheptane.The volume of the solution was 20 ml.The concentration of menthol in the case of studying the adsorption activity of o-toluic acid was 70 µg / ml; for CsCuCl3 -220 µg/ml.The choice of menthol concentrations was determined by the analysis of previously obtained data [8].The concentration was chosen when the difference in the adsorption of enantiomers by modified enantiomorphic silica gel crystals was maximal.The volume of the analyzed substance was 5 µl.To obtain kinetic adsorption curves, samples were taken after adding the sorbent for certain periods of time.
The amount of the adsorbed substance was determined using a Crystall-5000.The equilibrium adsorption value (a, µmol/g) was calculated as follows:  = ( 0 −  )  , (1) where c0 was the concentration before adsorption of µg/ml; cx was the concentration after adsorption, µg/ml; V was n-heptane volume, ml, M was the molecular weight of menthol, g/mol, and m is the mass of the adsorbent.The relative standard deviation for adsorption values did not exceed: on CsCuCl3 for L-menthol -2.3%, for D-menthol -3.3%, on o-toluic acid for L-menthol -4.6%, for D-menthol -9.8%.
The kinetic curves were approximated using pseudo-first-order Lagergren, pseudosecond-order Ho and McKay models, as well as the Elovich model, as well as Boyd, Weber-Morris and Dumwald-Wagner diffusion models.
The pseudo-first-order Lagergrenian equation in linear form looks like this [9]: where  was the adsorption value when the adsorption equilibrium was reached,  was the adsorption value at time t, and k1 was the pseudo-first-order rate constant, min -1 .From a physicochemical point of view, a pseudofirst-order model will describe experimental data only if the adsorption is limited by the transport of molecules from solution to adsorbent.This is because the model describes cases of film diffusion, which controls the rate of adsorption during the first few minutes in experiments with mixing [10].
The pseudo-second-order equation of Ho and McKay [11] in the integrated form, can calculated as follows [12]: where k2 is the pseudo-second-order adsorption rate constant, g/(µmol•min).
This equation allows us to consider not only the sorbate-sorbent interactions, but also the intermolecular interactions of the adsorbed substances, which determines the high adequacy of using the kinetic model of Ho and McKay.
The Elovich equation is often used to describe the kinetics of adsorption of substances in heterogeneous systems, with considering the sorption capacity.The Elovich equation simplified by Chen and Clayton [13], has the following form: where α was the initial adsorption rate constant, µmol/(g•min); β was the desorption constant, µmol/g.This equation was previously successfully used to describe the chemisorption of gas molecules on a sorbent.A general explanation of this form of kinetic law involves a change in the chemisorption energy depending on the surface coverage.But in recent years this equation has been widely used to describe the kinetics of gas adsorption by solids [20].For the primary distinction between intraand external diffusion limitation of adsorption the diffusion models of Boyd and Weber-Morris can be used.The Boyd equation, proposed in 1947, suggested that the film diffusion is the rate limiting step.The equation can be written as follows: where  1 (min −1 ) is liquid film diffusion constant [21].Weber-Morris model assumed that the intraparticle diffusion is the sole rate-limiting step.In this case, the amount of adsorbed substance was linked with adsorption time by the following equation: where kint is the intraparticle diffusion rate constant.Additionally, a Dumwald-Wagner model was used: , (7) where K (min −1 ) is the rate constant of adsorption.

Results and discussion
On Figure 1 the kinetic curves of the adsorption of D-menthol and L-menthol on silica gel modified with o-toluic acid crystals, obtained under Viedma ripening conditions, were shown.As can be seen from the presented data, the kinetic curves of enantiomers adsorption have differed.Before reaching equilibrium, D-menthol was adsorbed more strongly than L-menthol.Thus, after 2 minutes, the L-menthol adsorption was 14.8 µmol/g, while the adsorption of D-menthol was 15.7 µmol/g.The enantioselectivity coefficient α, calculated as the ratio of higher adsorption to lower adsorption, was 1.06.After 4 minutes, the largest difference in adsorption values was observed.They were 15.8 and 16.8 µmol/g for L-menthol and Dmenthol, respectively (α=1.07).At the 6th minute, the adsorption value of L-menthol was 16.7 µmol/g, D-menthol -17.3 µg/ml (α=1.04).By 8 minutes, adsorption-desorption equilibrium was reached, and no differences in adsorption values were observed.Thus, the analysis of the obtained kinetic curves made it possible to assume differences in the adsorption rate.As can be seen from the obtained data, the adsorption curves of menthol enantiomers have also differed.It should be noted that the time of establishment of adsorption equilibrium between the modified samples has differed too.Thus, in the case of CsCuCl3, adsorption equilibrium was established already at 20 s, which is 24 times faster than in the sample with o-toluic acid.
The t-test was used to prove the relevance of the difference in the adsorption values of enantiomers.This statistical method consists in proposing and testing a null hypothesis about the coincidence of two sets of parallel data by comparing the experimental values of the t-test and the extreme boundary value tabulated depending on the number of measurements and the confidence level.If the experimental value is below the extreme value (α=0.05), this indicates that the two values  are different.In this work, the null hypothesis was the assumption that the adsorption values of menthol enantiomers belong to the same sample set.Using the t-test, the adsorption values of menthol enantiomers on enantiomorphic crystals of o-toluic acid and CsCuCl3 were processed until equilibrium was reached.Previously, the dispersions of all experimental data were checked for homogeneity using the F-test.In all cases, the dispersions were homogeneous.The obtained data of the p values of the t-test are given in Table 1.As can be seen from the obtained values, the difference in adsorption values is statistically significant for the sample modified with both o-toluic acid and CsCuCl3.Thus, the fact of the difference between the kinetic curves of menthol enantiomers adsorption on the studied adsorbent samples was confirmed.
In the case of menthols adsorption on silica gel modified with CsCuCl3, due to the high rate of establishment of adsorption-desorption equilibrium, the use of various kinetic models was difficult.Therefore, the experimental curves were approximated only for the adsorption of menthols on silica gel modified with o-toluic acid.
In Figure 3, the kinetics of menthols adsorption in the coordinates of Lagergren's pseudo-first-order model was described.It can be seen from the figure, that the adsorption kinetics was adequately described only for D-menthol.This was confirmed by high correlation coefficients (Table 3).Hence, in the case of D-menthol, the limiting stage was the diffusion to the adsorbent, and in the case of L-menthol, it can be otherwise.By Lagergren's model, the rate constants of adsorption were calculated (Table 3).For L-menthol the rate constant was 0.7766 min -1 , while for D-menthol it was 0.4781 min -1 .
Ho and McKay's pseudo-second order equation is widely used to describe the kinetic laws of adsorption.The plotting of curves (Fig. 4) in the t/a -t coordinates makes it possible to analyze the experimental data from the point of view of the Ho and McKay rate model.As can be seen from the graph, this model was able to adequately describe the experimental data on the adsorption kinetics for both D-and L-menthol.The results of the determination made it possible to calculate the reaction rate constants equal to 0.08 g/(μmol•min) and 0.17 g/(μmol•min) for L-Menthol and D-Menthol, respectively.
The Elovich model, simplified by Chen and Clayton [15], was used to estimate the adsorption and desorption constants.Data linearization in the coordinates of the Elovich model also did not cause difficulties (Fig. 5).The equation constants can be determined by drawing the dependence a -lg t from the slope and the segment cut off by the straight line on the y-axis.The initial rate constant (α) of adsorption and desorption constant (β) for L-menthol were 820 µmol/g•min and 0.51 µmol respectively, while for D-menthol α and β were 386000 µmol/g min and 0.85 µmol/g, respectively.From the data obtained, it is noticeable that the adsorption equilibrium in the case of both samples is shifted to the right.The dependence in the values of the adsorption rate constants has coincided with the previous methods -D-menthol was adsorbed faster than L-.Differences were observed only in the ratio of rate constants.
The Lagergren, Ho and McKay and Elovich models were used only for comparing adsorption rate constants of enantiomers.
From the data obtained one can see the different kinetics of adsorption for enantiomers.Enantiomer diffusion in solution should be equal because of solvent achiral nature.So, if diffusion was rate-limiting step, no enantioselectivity should be observed.One can conclude that the rate-limiting step was adsorption.
From this insight, it is interesting to analyze the results of curve approximation using the diffusion models.Thus, Boyd model describes diffusion out of particle, but it has approximated the experimental data with high correlation coefficients.Moreover, the kinetic coefficients for enantiomers have differed.The Weber-Morris model wasn't fit data well, unlike of Dumwald-Wagner equation (see Fig. 4).The last has shown the best fitting among the diffusion models used.Non-linearity a -t1/2 dependences in the coordinates of the Weber-Morris equation could indicate a potential mixed-diffusion mechanism of adsorption kinetics, when the process cannot uniquely limited by external or internal diffusion.
So, there can be two points of view on kinetic mechanism.From the one hand, the results of approximation can indicate the mixed mechanism, with diffusion and adsorption rate are closed to each other.In the other hand, the absence of dependence between the fitting results of pseudo-first-and pseudo-first -order rate equations and kinetic mechanisms was thoroughly proved by Khamizov [22][23][24].So there is a question, how we can trust to use the fitting quality to making conclusions about kinetic mechanism.Maybe a good fitting of experimental

Figure 2
Figure2has shown the kinetic curves of adsorption on silica gel modified with CsCuCl3 crystals.As can be seen from the obtained data, the adsorption curves of menthol enantiomers have also differed.It should be noted that the time of establishment of adsorption equilibrium between the modified samples has differed too.Thus, in the case of CsCuCl3, adsorption equilibrium was established already at 20 s, which is 24 times faster than in the sample with o-toluic acid.The t-test was used to prove the relevance of the difference in the adsorption values of enantiomers.This statistical method consists in proposing and testing a null hypothesis about the coincidence of two sets of parallel data by comparing the experimental values of the t-test and the extreme boundary value tabulated depending on the number of measurements and the confidence level.If the experimental value is below the extreme value (α=0.05), this indicates that the two values

Fig. 3 .Fig. 4 .
Fig. 3. Description of the kinetics of adsorption of menthols in the coordinates of Lagergren's pseudo-first-order model.
Сорбционные и хроматографические процессы.2023.Т.23, 4. С. 657-666.Sorbtsionnye i khromatograficheskie protsessy.2023.Vol. 23, No 4. pp.657-666.ISSN 1680-0613_____________________________________________________________ 665 data by Boyd model has only a mathematical nature.ConclusionThus, the reliable differences in enantiomers adsorption values in the region before adsorption-desorption equilibrium were reached.The difference in adsorption rate constants was observed as well.It has indicated that the adsorption rate of menthol enantiomers on crystals of o-toluic acid and CsCuCl3 obtained under Viedma ripening conditions was different.This phenomenon was discovered for the first time in this work.Differences in the kinetics of adsorption of enantiomers on adsorbents with a supramolecular chiral surface open up new opportunities for developing technologies for the separation of optical isomers.

Table 1 .
Values of t-criterion and F-criterion for pairs of values of menthol adsorption on crystalsof o-toluylic acid and CsCuCl3 (critical degree of significance α=0.05)

Table 2 .
Parameters of approximation of the o-toluic acid kinetic curve by the models used