Comparison of chromatograms obtained with and without an induced MF
The effect of induced MF by positive and negative electric currents on the separation of three drug series can be seen in Fig. 3 and Fig. S1, respectively. It is noticeable that, under both positive and negative electric currents, the main alteration in the chromatograms was related to the t, and these changes increase with increasing induced MF intensity. The applied induced MF decreased the t for all three-drug series and accelerated drug detection. Additionally, a slight variation in peak width was also observed in some chromatograms.
Figure 4 illustrates the time-dependent variation of HPLC column pressure at different electric currents: ±0.41, ±0.61, and ±0.81 A. The results indicate that the pressure changes over time are proportional to the induced MF. Consequently, the time-dependent change of pressure was greater for higher electric currents and exhibited a non-linear trend. Furthermore, these trends stabilized after a specific time for each electric. Notably, when the electric current was interrupted, the HPLC column pressure increased again, showing that the effect of induced MF on column pressure was reversible.
To evaluate the effect of induced MF on each drug, the plots of variation in t were created based on the applied electric current intensity. As shown in Fig. 5, the t values decreased further with increasing electric current intensity for both positive and negative currents. Given that the RSDs% for the t in this study ranged from 0.067 to 0.351%, it can be said that the observed changes in the chromatograms were due to the presence of induced MF. When the data points on the plots were linked as a line, the differences in absolute slope were as follows: COC > NOS > HER > PAP > TRA > KET.
Although the absolute values of the slopes for positive and negative currents are comparable within each drug, the slope for negative electric currents appears slightly larger than for positive currents, except in the case of PAP. On the other hand, the results indicate that, for KET and PAP, the relationship between the t and applied electric current is relatively linear; however, for other drugs, the R value is less than 0.918.
The effect of the induced MF on the depicted in Fig. S2 and Table S1. The results indicate that in the first and third series, when the induced MF increases, the a decrease relative to the absence of the MF (blank). Conversely, in the second series, the value decreased at currents of ± 0.41, while it began to increase in currents of ± 0.61 and ± 0.81. Therefore, the influence of induced MF on this parameter is not necessarily linear and could differ depending on the intensity and orientation of induced MF, and also on solute properties.
The graphs of R variations were plotted vs. the electric current intensity to investigate the effect of the induced MF on R. It was observed that the R of the PAP and KET separation reduced as the electric current intensity increased in comparison to the blank (Fig. S3a). However, the alterations in this parameter varied in the second and third series. The R in the separation of COC and NOS increased at electric currents ± 0.41 A and ± 0.61 A, but they decreased at electric current ± 0.81 A in comparison to the blank (Fig. S3b). The data required for the R measurement are summarized in Table S1. In the separation of TRA and HER, the R improved for electric currents of -0.41 and + 0.61, whereas a decline was observed at other electric currents (Fig. S3c). Consequently, nonlinear variations in the presence of the induced MF have also been observed in the R.
To investigate the effect of induced MFs on drugs with different polarities, the graph depicting the absolute value of the slope variations presented in Fig. 5 was plotted vs. logP. As can be observed in Fig. 6, for both positive and negative currents, HER, NOS, COC, and PAP had more alterations, suggesting that they were more affected by induced MF, while KET and TRA were less affected. These findings may be attributed to the lipophilicity of these drugs, as TRA exhibited the lowest lipophilicity and KET the highest, and both demonstrated reduced sensitivity to the induced MF, while drugs with moderate lipophilicity were more significantly influenced by induced MF. Furthermore, it was observed that while changes in both positive and negative currents exhibit similarities, slight differences were also evident.
The findings demonstrate that the induced MF changed the pressure in the HPLC column and affected chromatographic parameters (peak width, t, and R). The magnitude of these changes depends on the intensity and orientation of the induced MF, as well as the properties of the separated drugs. In the following, the possible reasons for these changes were discussed by providing evidence.
It was observed that the application of induced MF resulted in peak shifting, accelerated elution of separated drugs from the HPLC column, partial changes in peak width in some cases, and a reduction in HPLC column pressure. In this study, the employed mobile phase consists of a 65% buffer. Consequently, a significant portion of the mobile phase was water. Evidence indicates that the properties of liquids, such as viscosity, can be altered under the influence of an MF. For instance, MF can alter water's viscosity, which was explained by MF's effects on hydrogen bonding. Alterations in the viscosity of blood and crude oilare other examples of MF effects on the liquid viscosity.
It is well-known that MF can change the fluids' molecular structure. A study examining the effect of external MF on ammonia absorption in refrigeration systems has demonstrated that the applied MF decreases the viscosity of the ammonia-water solution after magnetization. In addition, a more intense MF and a longer exposure time result in a more significant decrease in viscosity. Here, the Lorentz force and the breakdown of hydrogen bonds in the microstructure were believed to be responsible for variations in viscosity. In this study, an increase in the applied induced MF resulted in a further reduction of HPLC column pressure and a more rapid elution of the drugs. This issue may be due to the effect of the induced MF on the mobile phase polarity (solvent's ability to solve dissolved charged or dipolar species and viscosity (related to intermolecular forces, which can alter its elution ability. Thus, it may be concluded that the impact of induced MF on the mobile phase properties is the starting point for changes in chromatographic parameters.
In HPLC, separation occurs due to the varying distribution of elution between the mobile phase (solvent) and the stationary phase (column). The separation mechanism can operate in various modes, depending on the characteristics of both phases. Based on their polarity, chromatography is classified into two main types: normal-phase and reversed-phase. In reversed-phase chromatography, ACN is used as a common mobile phase, and variations in temperature and composition influence the process's efficiency. The diffusion of molecules in the mobile phase during reversed-phase chromatography is dependent on the nature of both the molecules and the solvent. So, the viscosity of the solvent has an important role in this context, and it is crucial to manage this parameter (by reducing it).
Viscosity variations that could lead to inadequate separation and increased operating pressures can be prevented by controlling the temperature and concentration. On the other hand, it is generally accepted that hydrostatic pressure can alter viscosity. Equation 1 is utilized for calculating the pressure in chromatography, and the relationship between different parameters is formulated in it. Here, the variables include length (L), linear velocity (u, where and representing the void time), viscosity (, where ), temperature (T, where ), permeability constant (), and particle size (). In this equation, is a function of T and composition (x) and is denoted as .
According to the literature, apart from hydrogen bonding, there is a dipole-dipole interaction between water and ACN, and the intensity of this interaction changes with the application of pressure.
Here, a mixture of buffer and ACN was utilized as the mobile phase, and temperature fluctuations were controlled by the cooling system. Given that pressure and viscosity in chromatographic systems are interconnected by Eq. 1, and assuming other variables remain constant, the reason for changes can be explained as follows: the application of the induced MF alters the pressure in the HPLC column. Thus, the changes in mobile phase viscosity may be the primary reason for this variation, which can be explained by the effect of induced MF on hydrogen bonding and dipole-dipole interactions between mobile phase components.
From a more in-depth perspective, the viscosity of microstructures has been found to depend on the characteristics, which are based on theoretical models that are also applicable to water. These characteristics include density, the molar mass of a substance, molecular length (both linear and nonlinear), friction coefficient (dependent on molecular mobility and diffusion), free volume, the potential energy of molecular interactions, the internal energy of evaporation, Avogadro's number, pressure, and temperature. Other studies have also demonstrated the correlation between pressure and viscosity in organic liquids.
According to the Stokes-Einstein equation, the solution viscosity is predicted to have a reverse influence on the diffusion coefficient of solutes. The reduced plate height and reduced linear velocity values, which are employed for assessing a chromatographic column's performance, can be determined correctly with the diffusion coefficient. Therefore, these changes can be viewed from the perspective that the induced MF has changed the viscosity, which in turn affects the solutes' diffusion coefficient, t, and R, and finally the separation efficiency.
Studying the relationship between pressure and viscosity from a thermodynamic aspect is fascinating. According to the Gibbs phase law, a system in thermodynamic equilibrium has two degrees of freedom if the liquid with a constant composition is stable or metastable. In this case, temperature and pressure can be defined as independent factors that influence the system's properties, and viscosity is considered a function of these factors:
When a liquid has a positive coefficient of thermal expansion -- a characteristic that most liquids fulfill at atmospheric pressure -- it can be written:
According to these relationships, the viscosity of the isobaric process must decrease with rising temperature and increase under isothermal conditions with increasing pressure. Additionally, providing consideration of viscosity as a function of pressure and temperature, i.e., the following can be stated:
Consequently, based on the thermodynamic relationships among viscosity, temperature, and pressure, it can be suggested that the application of induced MF probably affected the viscosity of the mobile phase and altered the pressure within the HPLC column.
Research demonstrated that the entering of strong external fields into a body significantly influences its thermodynamic properties. Examine a linearly isotropic and homogeneous continuum that is uniformly magnetized. This continuum's entropy S, volume V, mass N, and internal energy U are its defining characteristics when there is no field present. So, it can be written that:
Here, T, P and are temperature, pressure, and chemical potential, respectively.
The magnetic energy, which is uniformly stored in a linear continuum in the presence of the field, is provided by:
As a consequence, the external MF contributes an additional term to the internal energy and Gibbs energy, introduces a new state parameter in thermodynamics, and enhances the system's degrees of freedom.
In HPLC, solute retention is typically expressed through the capacity factor (), which is directly proportional to the equilibrium constant (K) as follows:
Here, is proportionality constant and defined as the stationary phase volume divided by the mobile phase volume. The Gibbs free energy is related to K by Eq. 13 (where T is the absolute temperature and R is the gas constant) and is linked to standard enthalpies and entropies by Eq. 14:
The can be defined in terms of standard enthalpies and entropies of transfer from mobile to stationary phase by combining Eqs. (12-14):
Thus, by integrating the influence of thermodynamics on solute retention and, alternatively, the effect of MF on thermodynamic parameters, its influence on the chromatographic system could be validated.
The impact of induced MF on viscosity could be caused by its effect on intermolecular forces. As a result, the properties of the mobile phase and its elution performance can be directly affected by the induced MF, which correlates with the findings of this study. Applying induced MFs that decrease the pressure in the HPLC column can reduce the polarity of the mobile phase and coordinate its properties more closely to the properties of organic solvents, enhancing elution performance in a reversed-phase HPLC, and consequently changing the drug distribution between the two phases. Thus, the combination of these changes has altered the t, , and R. Consequently, to elucidate the reason for the alterations observed in the presence of induced MF, multiple aspects must be considered.
The results indicated that the application of induced MF with different intensities and orientations can alter the performance of the chromatographic system. So, employing MFs to modify the design of these systems seems an interesting approach. For example, regarding the influence of induced MFs on column pressure, the chromatographic system's efficiency can be altered by MFs, instead of altering the effective particle size (column packing material) in the column. This significantly decreases the expenses related to the safety and design of the chromatographic devices and columns.
In addition, it was observed that the application of induced MF caused a decrease in column pressure with time (Fig. 4). Studies show that, compared to gas chromatography, HPLC requires a larger pressure drop to reach a given linear velocity. Therefore, solvent mixtures are often used as the mobile phase in HPLC to modify solvent polarity and enhance column performance. For instance, it has been demonstrated that in liquid-solid chromatography, a 2-fold increase in column efficiency was induced by a 2.5-fold reduction in mobile-phase viscosity. Therefore, low-viscosity liquid mobile phases are recommended in liquid-solid chromatography. However, the ranges of conventional liquid-mobile-phase viscosities are constrained, and the solvents available are limited due to the solvent strength criteria for separation. It is clear that in reversed-phase column chromatography, column pressure decreases as the proportion of organic solvent in the mobile phase increases. The results showed that MF induction probably caused a reduction in the viscosity and polarity of the buffer-ACN mixture, consequently affecting the elution performance of the mobile phase. However, by removing the induced MF, the column pressure increased again with a trend that depended on the induced MF intensity. This subject demonstrates the reversibility of the induced MF's effect on column pressure. Additionally, the column pressure variations can be controlled by altering the induced MF intensity and time. This point represents another approach to utilizing induced MFs in the gradient elution programming without altering the solvent composition percentages, requiring consideration in future research. Of course, it should be noted that gradient elution with an MF necessitates both experimental and computational research because of the gradual increase in column pressure over time in induced MF. To do this, an MF of suitable intensity must be induced in a core (chromatographic column) with adequate relative permeability to improve time pressure variations and enable gradient elution.
Table S2 presents the structure, lipophilicity, and molecular weight of the drugs. Induced MF exhibited varying effects on drug separation. To understand the reason for these variations, it is necessary to investigate how MF affects the compounds.
It is well-known that many compounds experience structural alterations in response to variations in composition, temperature, or pressure. Nonetheless, creating a structural phase transition induced by an external MF is a unique approach. An MF can interact with a freely rotating molecule in the ground electronic state with zero orbital and spin-electronic angular momentum. Therefore, it is clear that electrons can be influenced by an MF. Apart from the electron cloud created by the aromatic ring, all these drugs have free electrons. The variation in the number of free electrons and the number of aromatic rings in drug structures could be responsible for the different effects of the induced MF on them.
The utilization of nuclear magnetic resonance (NMR) to evaluate the aromaticity of compounds based on the magnetic response of a molecule in an external MF is a known approach. When an external MF is applied to a delocalized electron system, it produces an induced MF with a long-range. Thus, the presence of aromatic rings in drugs caused them to be susceptible to induced MFs. However, it was observed that drugs would exhibit different responses to the induced MF due to structural differences (Table S2).
Bohr's simple model explains why matter interacts with the MF. An MF generates microscopic current loops around the nuclei, which subsequently induce MFs in matter. Depending on the paramagnetic or diamagnetic properties of the matter, this induced MF may be parallel with or opposite to the direction of the applied MF. When a substance is exposed to an MF, it creates a magnetization M, also known as the magnetic dipole moment per unit volume, which is directly proportional to the applied field H and the material's magnetic susceptibility:
Molar susceptibility or , is the most common manner to describe magnetic susceptibility. Here, represents molar volume. The applied field H and the material's magnetic permeability define the magnetic induction B in a medium:
The vacuum permeability () and the relative permeability () of the medium multiply to yield the magnetic permeability ():
As the applied field H is adjusted by the magnetization M that the medium obtains, the magnetic induction B in a medium can be expressed. Consequently, the following expression (Eq. 16) can be used to explain the relationship between the applied field H and the magnetic induction B in the sample:
The number of magnetic moments (atoms) per volume N and the intensities of elementary magnetic moments determine the magnetization M that a material gains in an MF. On the other hand, magnetic moments are dependent on the matter's intrinsic properties, including the closeness of electrons to the nucleus and the induced MF intensity. Thus, the different effects of induced MF on drugs can be explained by differences in magnetic susceptibility and magnetic moment.
The results indicate that the induced MF orientation had a slight effect on the t, , R, and slope alternations. As shown in Fig. S4, the mobile phase and induced MF were oriented in the same direction for positive currents and in the opposite direction for negative currents. MF orientation can influence phenomena differently. Therefore, the slight variations in the orientations of induced MF may be linked to its different effects on the properties of the mobile phase and drugs.
Slight changes in peak width resulting from the application of the induced MF were also observed in some chromatograms. Literature evidence indicates that MF can influence mass transfer and diffusion. Consequently, the influence of induced MF on separation efficiency can be explained as follows: the effect of induced MF on mass transfer and diffusion, which subsequently alters separation efficiency by affecting the height of theoretical plates, as described by the Van Deemter equation, and consequently, changes selectivity factor (α) and the number of theoretical plates (N) (Table S1).
The possibility of a change in the drug distribution between the stationary and mobile phases due to the applied induced MF is another factor to consider. Hydrophobicity is the basis for the separation of molecules in reversed-phase HPLC. The solute molecule from the mobile phase interacted hydrophobically with the immobilized hydrophobic stationary phase to cause the separation. The influence of induced MF on altering the properties of the mobile phase, as previously discussed, along with its effect on the solutes, can lead to changes in these hydrophobic interactions and the change in solute distribution between the mobile phase and the stationary phase. The magnitude of these changes can be different based on the induced MF intensity and orientation, the structure of drugs, and their interaction with both the mobile phase and the stationary phase.
TRA and KET, which possessed the lowest molecular weights (MW=263.37 g/mol and MW=237.72 g/mol) and had the lowest and highest lipophilicity (logP =1.34 and logP =3.12), exhibited less susceptibility to induced MF (Fig. 6). Figure 5a and f, representing the variations in t for both positive and negative currents, show that the absolute value of the slopes for TRA and KET is less than 0.48 and less than 0.23, respectively. This issue may reflect the influence of drug molecular weight and lipophilicity on its susceptibility to induced MF, as reported in previous studies. On the other hand, the presence of a single aromatic ring in both drugs may reduce their MF susceptibility.
The results indicated that for PAP, COC, NOS, and HER, the absolute values of the slopes for both positive and negative currents ranged from 0.8187 to 0.8412, 0.9228 to 0.9447, 0.9131 to 0.9434, and 0.8315 to 0.8698, respectively (Fig. 5b-e). Comparison of the drugs demonstrated that the induced MF significantly influenced the changes in the t for COC and NOS. As a result, drugs with a higher molecular weight and medium lipophilicity were more susceptible to being affected by induced MF. In addition, the structures of these drugs contain a greater number of heteroatoms and aromatic rings, which could be the reason for their increased susceptibility to induced MF.
However, since the drugs differ structurally, their interactions with the mobile phase, which is also affected by induced MF, can change. This issue could partly explain why drugs behave differently under an induced MF. Finally, it is essential to note that the correlations between the induced MF effect and the examined parameters are not necessarily linear.