Poorly soluble drugs: disbalance of thermodynamic characteristics of crystal lattice and solvation

Abstract

The dissolution processes in aqueous media of poorly soluble drugs belonging to the classes of spiro derivatives, benzoic acid and its derivatives, sulfonamides, fenamates, and thiadiazoles were analyzed based on the data recently published by the author. The main criterion for the solubility analysis was the comparison of the thermodynamic characteristics of sublimation processes (state of the molecules in solids) and solvation (state of the molecules in solutions) under structural modification of the reference molecule. The characteristics of the processes under investigation were compared by the superposed diagram approach which allows complete information to be obtained about the thermodynamic state of the molecules in crystal and solution. A variety of thermodynamic paths of the molecules undergoing structural modification (design) was shown. The extreme solubility values were obtained for the considered classes of compounds which can be derived by structural modification of the substances. A classification of the drugs was suggested based on the analysis of the determinative steps of the dissolution processes: crystal or solvation controlled. Based on the investigation of 59 drugs belonging to five different classes of compounds, it was estimated that for 50.7% of the compounds the solubility processes were crystal controlled, whereas for the rest 49.3% – solvation controlled. Among all the considered compounds, a structural modification of the reference one led to a solubility enhancement only in 22.1% of the substances. And in 85% of the compounds, the dissolution processes were solvation controlled and in the remaining 15% – crystal controlled.

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1. Introduction

The problem of poor API (active pharmaceutical ingredient) solubility in aqueous media is one of the key points in the design of effective drugs.¹ Approximately 40% of drugs on the market in European countries, US and Japan are practically insoluble.² Moreover, 75% of drug development candidates have low solubility based on the Biopharmaceutics Classification System (BCS).³ Poor solubility of a potential drug compound significantly reduces the bioavailability and leads to increasing doses in order to reach therapeutic effect. Sometimes the mentioned growth of doses can initiate side effects. There is a wide range of approaches aimed at solubility enhancement of poorly soluble drugs in the pharmaceutical industry. The most widespread among them are using cyclodextrin–drug systems,⁴ cocrystals,⁵ drugs incorporated into phospholipid vesicles⁶ and so on. The application of different polymorphic forms for solubility improvement should also be mentioned.⁷ The solubility ratios for eighty polymorphous forms (98.8% of compounds from the database including 81 pairs of polymorphic modifications) vary between 1 and 5, and only one compound (1.2%) has the solubility ratio higher than 5. Meanwhile, the problems of solubility improvement through molecular structural modification are of great interest to scientists. What are the limitations and the potential of such approach in terms of the top solubility enhancement limits? The problem itself is very complicated as it is associated with precise description of the compounds both in crystal state and in solution. Thermodynamically, compound solubility is determined by the difference between the Gibbs energy necessary to disrupt the crystal lattice to bring it into gas phase (sublimation process) and the term describing solvation/hydration process (transfer molecule from gas to solvent). Small changes in the substituents on the drug molecule can yield significant changes in its crystal structure and lattice energy. Therefore, it is important to consider the sublimation part of the thermodynamic cycle in order to identify compounds with the desired physicochemical properties and biological activity. At the last five years the quantum-chemical approaches based on thermodynamic methods like COSMO-RS, COSMO-SAC, SMD etc.⁸ were developed actively. The overall prediction accuracy for the five drugs (considered in ref. 8) amounts to 0.49 log mol fraction solubility, which is about the typical error bar for COSMO-RS solubility predictions. Furthermore, COSMO-RS is known to perform well for prediction of activity coefficients and solubilities in solvent mixtures.^9,10 A huge number of papers dealing with the creation of correlation models for solubility prediction by using different descriptors have been published by now. It should be mentioned, that some authors try to apply for description of solubility process the thermodynamic cycle including the fusion/melting and a mixing processes. One from the most popular equation here is the general solubility equation proposed by Yalkowsky and co-workers.^11,12 In this case the melting point has been introduced for imitation/characterization of the crystal lattice energy, whereas the (octanol–water) partition coefficient modulates/characterizes the solvation/mixing term. The big disadvantage the rest of QSPR works is no common logical line at development correlation models with descriptors determining both the solid state characteristics and the parameters of molecules in the solution (solvation processes). Usually, the descriptors are selected based on a single criterion – the optimal description of solubility. We do not want to emphasize all the existing approaches to predicting substance solubility. But it should be noted that new experimental data on thermodynamic parameters of the sublimation process of drug compounds have increased the interest to creating models which can predict these functions.¹³ Besides, new possibilities have been recently found for the description/prediction of solvation thermodynamic functions of organic molecules,^14–16 which enables the evaluation of solubility parameters by using the present information about the solid state of these compounds. An interesting work by Docherty et al.¹⁷ should be marked out, that attempts to classify the molecular crystal dissolution based on the analysis of the solvation energy and lattice energy strength. We have also tried to contribute to this area of investigations by analyzing the literature experimental data. The main aim of the present work is to analyze and systematize the thermodynamic parameters of sublimation and hydration/solvation processes (as the main processes determining solubility) of certain compound classes (described by us previously) and to reveal the regularities of these characteristics alteration caused by structural modification of the reference compounds.

2. Materials and methods

2.1. Methods

2.1.1. Sublimation experiments. Sublimation experiments were carried out by the transpiration method as described elsewhere.¹⁸ In brief: a stream of an inert gas passes above the sample at a constant temperature and at a known slow constant flow rate in order to achieve saturation of the carrier gas with the vapor of the substance under investigation. The vapor is condensed at some point downstream, and the mass of sublimate and its purity are determined. The vapor pressure over the sample at this temperature can be calculated by the amount of the sublimated sample and the volume of the inert gas used. The scheme of the equipment is presented at ESI (Scheme 1SI†).

The equipment was calibrated using benzoic acid. The standard value of sublimation enthalpy obtained here was ΔH⁰_sub = 90.5 ± 0.3 J mol⁻¹. This was in good agreement with the value recommended by IUPAC of ΔH⁰_sub = 89.7 ± 0.5 J mol⁻¹.¹⁹ The saturated vapor pressures were measured 5 times at each temperature with the standard deviation being within 3–5%. Because the saturated vapor pressure of the investigated compounds was low, it could be assumed that the heat capacity change of the vapor with temperature was so small that it could be neglected. The experimentally determined vapor pressure data could be described in (ln(P); 1/T) co-ordinates in the following way:

ln(P) = A + B/T (1)

The value of the sublimation enthalpy was calculated by the Clausius–Clapeyron equation:

ΔH_sub^T = RT²∂(ln P)/∂(T) (2)

whereas the sublimation entropy at the given temperature T was calculated from the following relation:

ΔS_sub^T = (ΔH_sub^T − ΔG_sub^T)/T (3)

with ΔG_sub^T = −RT ln(P/P₀), where P₀ is the standard pressure of 1 × 10⁵ Pa.

For experimental reasons, sublimation data were obtained at elevated temperatures. However, in comparison with effusion methods, the temperatures were much lower, which made extrapolation to room conditions easier. In order to further improve the extrapolation to room conditions, we estimated the heat capacities (C_p,cr²⁹⁸-value) of the crystals using the additive scheme proposed by Chickos et al.²⁰ Heat capacity was introduced as a correction for the recalculation of the sublimation enthalpy ΔH_sub^T-value at 298 K (ΔH_sub²⁹⁸-value), according to the equation:²⁰

ΔH_sub²⁹⁸ = ΔH_sub^T + ΔH_cor = ΔH_sub^T + (0.75 + 0.15C_p,cr²⁹⁸)(T − 298.15) (4)

2.1.2. Solubility experiments. All the experiments were carried out by the isothermal saturation method at (298 ± 0.1) K in water. The solid phase was removed by isothermal filtration (Acrodisc CR syringe filter, PTFE, 0.2 μm pore size) or centrifugation (Biofuge pico). The experimental results were reported as an average value of at least three replicated experiments. The molar solubilities of drugs were measured spectrophotometrically with an accuracy of (2 to 3)% using a protocol described previously.²¹ The bottom phase at the solubility experiments, which has been in equilibrium with the solution studied, has been checked by DSC, TG and XRPD experiments. The crystal structure of the bottom phase corresponds to the crystal structure of the initial compound (unsolvated and unhydrated phases).

2.1.3. Calculation of solvation characteristics. Solubility process can be represented as two independent processes: sublimation (molecule transfer from the solid phase to the gas one) and solvation/hydration (molecule transfer from gas to solution/aqueous solution). The thermodynamic cycle can be described by the equation:

ΔY⁰_sol = ΔY⁰_sub + ΔY⁰_solv (5)

where ΔY⁰ is a standard change of any of the thermodynamic functions (G, H, S) of solubility (ΔY⁰_sol), sublimation (ΔY⁰_sub) and solvation (ΔY⁰_solv) processes. Knowing the thermodynamic parameters of the dissolution and sublimation processes, one can easily calculate analogous functions of the solvation process.

2.2. Compounds

The objects of the investigation were those compounds, the sublimation, dissolution, and solvation/hydration processes of which had been studied. For convenience, all the compounds were divided into groups/clusters of similar structures. Each group included the reference compound and a certain set of its derivatives. Logically, such segmentation can be comparable with the process of structural variation of the “lead” compound for obtaining the “head” substance. As the compounds of different clusters have essential differences in the structure and, respectively, in the properties, (in order to make a comparison/analysis of the properties on a comparable scale) the properties were analyzed on a relative scale (i.e. in relation to the reference compound in each cluster (marked (1))). The following sets of compounds were chosen as the clusters (Fig. 1): SP1 – spiro derivatives type 1 (SP1-1–SP1-3);²² SP2 – spiro derivatives type 2 (SP2-1–SP2-11);^21,23 BA – benzoic acid and its derivatives (BA-1–BA-8);^24–26 BC – bicycles (BC-1–BC-11);^27–29 SA1 – sulfonamides type 1 (SA1-1–SA1-11);^30–33 SA2 – sulfonamides type 2 (SA2-1–SA2-5);^34,35 F – N-phenyl-anthranilic acid and their derivatives (fenamates) (F-1–F-6);^36–38 T – thiadiazoles (T-1–T-12).^39–42 Solubility data of the studied compounds are summarized at ESI (Table 1SI†).

Fig. 1 Structural formulas of the compounds studied: (a) SP1 – spiro derivatives type 1 (SP1-1–SP1-3); (b) SP2 – spiro derivatives type 2 (SP2-1–SP2-11); (c) BA – benzoic acid and its derivatives (BA-1–BA-8); (d) BC – bicycles (BC-1–BC-11); (e) SA1 – sulfonamides type 1 (SA1-1–SA1-11); (f) SA2 – sulfonamides type 2 (SA2-1–SA2-5); (g) F – N-phenyl-anthranilic acid and their derivatives (fenamates) (F-1–F-6); (h) T – thiadiazoles (T-1–T-12).

3. Results and discussion

3.1. Diagram approach

Let us consider the hydration and dissolution processes for the chosen compounds in buffer pH 7.4. To analyze sublimation, solvation (further, the term solvation will be used instead of the term hydration) and solubility characteristics, we use a diagram approach which consists in the following. All the obtained experimental values are placed on a diagram (Fig. 2) in the coordinates of the sublimation Gibbs energy difference (OY-coordinate) versus the hydration/solvation Gibbs energy difference (OX-coordinate) of the substituted compound (in the range of the chosen groups) to the reference one. For convenience, all the diagram space can be divided into eight sectors, which are restricted by four straight lines: axes OX, OY (red dotted lines) and two bisectors (black thin lines). Sector I (s-L-y) corresponds to the situation when a variation of the reference molecule structure leads to an increase in the sublimation Gibbs energy (saturated vapor pressures reduction) and growth of the molecule hydration/solvation. And enhancing the hydration of the modified molecule does not exceed the Gibbs energy sublimation increase term that is expressed in a solubility decrease (the dotted black lines in Fig. 2 correspond to the isoenergetic curves of the solubility Gibbs energy – the substance solubility characteristics). The experimental points in sector I can be presented by a histogram (Fig. 3a).

Fig. 2 Experimental data in the coordinates of the sublimation Gibbs energy difference (OY-coordinate) versus the solvation Gibbs energy difference (OX-coordinate) of the substituted compound (in the range of the chosen groups) to the reference one. Description of the diagram sees the text. Legend: black/white circle – SP1; black/white triangle – SP2; red circle – BA; square black – BC; triangle blue – SA1; blue hexahedron – SA2; black circle – F; red/white circle – T.

Fig. 3 Histograms correspond to the defined sectors of the diagram on Fig. 2.

Sector II (s-L-x) corresponds to the case when a structural variation of the reference molecule leads to the growth of the sublimation Gibbs energy and a decrease in the molecule solvation. And the sublimation term exceeds the solvation in absolute magnitude (Fig. 3b). Sector III (x-L-v) is analogous to sector II, the difference consists only in alignment between the sublimation and solvation terms: the last term exceeds the first one (Fig. 3c). The sublimation and solvation energies grow synchronously and decrease the solubility of the modified molecule as compared to the reference one.

Sector IV (v-L-z) corresponds to the case when a structural variation of the reference molecule leads to an increase in the sublimation Gibbs energy (growth of the saturated vapor pressures) and decrease (in absolute magnitude) in the molecule solvation. And the sublimation term (in absolute magnitude) does not exceed the hydration term, which leads to a decrease in the modified molecule solubility (Fig. 3d). Sector V (z-L-t) corresponds to the case when the variation of the reference molecule structure leads to a decrease in the sublimation Gibbs energy (the saturated vapor pressures increase) and a decrease in the molecular solvation. But, in contrast to the previous case, the sublimation term exceeds the solvation one, which leads to an increase in the modified molecule solubility (Fig. 3e).

Sector VI (w-L-t) corresponds to the case when the structural variation of the reference molecule leads to a sublimation Gibbs energy decrease (the saturated vapor pressures growth) and an increase in the molecule solvation. And the sublimation term exceeds the solvation one (in absolute magnitude), which leads to an increase in the modified molecule solubility (Fig. 3f). A similar pattern is observed in sector VII (u-L-w) with the only difference being that the solvation term exceeds the sublimation one in absolute magnitude (Fig. 3g).

Finally, sector VIII (y-L-u) corresponds to the case when the structural variation of the reference molecule leads to an increase in the sublimation Gibbs energy (a decrease in the saturated vapor pressures) and an enhancement of the molecule solvation. The solvation term exceeds the sublimation one in absolute magnitude (Fig. 3h).

It should be mentioned that the variants of the molecule modification when the experimental points belong to sectors VI and VII (Fig. 3f and g), apply to the most favorable and “stable” ones in terms of result achievement (solubility enhancement), as this process at the same time changes the crystal lattice in the direction of the sublimation Gibbs energy decrease (due to the competition between the enthalpy and entropy terms which can also be analyzed) and improves the solvation parameters of the modified molecule. Thus, the proposed approach allows us to analyze the influence of molecule structural modifications on the thermodynamic parameters of the sublimation, solvation and solubility processes in a simple and clear way.

Sectors I, II, V and VI correspond to the crystal controlled processes. In other words, the processes of crystal structure recrystallization (which are initiated by the molecule modification), have a bigger effect on the Gibbs energy of the resulting process (dissolution) than the change of the solvation characteristics. As opposed to this fact, sectors III, IV, VII and VIII correspond to the solvation controlled processes.

3.2. Spiro derivatives

The spiro-derivatives selected for analysis can be divided into two groups for convenience. The first group includes compounds SP1-1–SP1-3 (spiro type I), in which SP1-1 is assigned as a reference substance. The second group consists of compounds SP2-1–SP2-11 (spiro type II), in which SP2-1 is set as a reference substance. Such division is rather conventional and is primarily determined by the necessity of more detailed control of the changes taking place in the crystal lattice and in the solution under structural modification of the reference compound. The described procedure is most effective if the reference molecule is maximally similar to the structures of the analyzed group.

3.2.1. Spiro type I. Analysis of the considered spiro-derivatives has shown that only one substance with improved solubility (SP1-3) can be obtained by structural modification of the reference substance (SP1-1). This compound belongs to sector VIII, which testifies to the increase in the sublimation Gibbs energy (the saturated vapor pressure of the molecular crystal decreases) due to the structural modification, whereas, the solvation Gibbs energy reduces (grows in absolute magnitude). The solvation contribution (in absolute magnitude) exceeds the sublimation one. Interestingly, the compound (SP1-2) (i.e. the only difference from the previous case is in the chain length: methyl- and ethyl-substituents) is located in sector IV. It means that the structural modification of the reference compound, on the one hand, leads to a sublimation energy decrease and, on the other – to a reduction (in absolute magnitude) of the solvation term. In total, the former exceeds the latter, which decreases the solubility of the modified substance. This case can be attributed to the solvation controlled processes under structural modification of the reference molecule. This terminology correlates with the one proposed by the authors.¹⁷

For more detailed analysis of crystal structure variations under structural modification of the molecule, the following approach (used by us previously⁴³) was proposed. The Gibbs energy of the process (sublimation or solvation) can be expressed as two terms (enthalpy and entropy) and, to simplify the analysis, it is presented as a diagram where the OX axis corresponds to the change of the enthalpy term in comparison with the reference compound, whereas, the OY axis – to the change of the entropy one (Fig. 4a and b). The dotted lines correspond to the isoenergetic curves of the process Gibbs energy (sublimation or solvation). If the diagrams are divided into sectors (like the mode presented above), they can be coupled in the following way: sectors I, II, V and VI correspond to the entropy driven processes, whereas sectors III, IV, VII and VIII – to the enthalpy driven ones.

Fig. 4 Diagram where the OX axis corresponds to the change of the enthalpy term in comparison with the reference compound for SP1, whereas, the OY axis – to the change of the entropy one. The dotted lines correspond to the isoenergetic curves of the process Gibbs energy (sublimation (a) or solvation (b)).

Then, to facilitate the analysis, we combine all the diagrams together (Fig. 5). Each diagram provides the whole information on the studied processes for the certain substance. Arabic numerals (Fig. 5) correspond to the number of the compound studied (conditionally, these numerals are represented in the first column in Fig. 5). The symbol of the diagram for the sublimation processes of the certain compound (coordinates TΔS_sub − ΔH_sub) is the following one after the number of the compound in the considered line (the second column in Fig. 5). On this diagram the sectors are marked by Roman numerals (correspondently to the symbols for these diagrams introduced before). The filled sector corresponds to the position of the experimental values on the diagram. More to the right (in the selected line) of the sublimation diagram it is located the analogous diagram for the solvation processes (coordinates TΔS_solv − ΔH_solv) (the third column in Fig. 5). The numbers of the sectors are not marked here (to avoid cluttering the figure), but these numbers are fully coincide with those on the sublimation diagram. The filled sector corresponds to the position of the analyzed compound. Finally, the diagram (ΔG_sub − ΔG_solv) is the last in the line belong to the analyzed substance (column 4). The symbols here are similar to those in the previous diagrams. Thus, the presented scheme allows us to get the maximal thermodynamic information about the processes determining the solubility of the compound in the considered buffer under the structural modification of the substance.

Fig. 5 Combined diagrams for SP1 (spiro derivatives type 1). The first column corresponds to the numeration of the analyzed compounds, the second one – to the sublimation processes diagrams (coordinates TΔS_sub − ΔH_sub), the third one – to the solvation processes diagrams (coordinates TΔS_solv − ΔH_solv) and, finally, the fourth one – to the total dependence diagram (ΔG_sub − ΔG_solv). The filled sector corresponds to the position of the experimental values on the diagram.

The only compound in which the solubility was improved compared to the reference value is SP1-3. As it follows from Fig. 5 (it was mentioned above), the solubility process is solvation controlled. And when the reference substance is structurally modified, the sublimation Gibbs energy slightly increases due to the growth of the sublimation enthalpy and decrease (negative value) in the sublimation entropy. The entropy term exceeds in absolute magnitude the enthalpy one (entropy driven process – sector V). The solvation process is also entropy driven (sector II): the solvation enthalpy decreases (in absolute magnitude, i.e. the interaction with the solvent molecules weakens), and the solvation entropy grows (i.e. the solution disorder increases). And the entropy term exceeds the enthalpy one. Thus, both the sublimation and the solvation processes are entropy determined, and the resulting dissolution process is solvation controlled.

3.2.2. Spiro type II. Only one compound (SP2-6) in the considered group (SP2) reveals a solubility growth as a result of the structural modification of the reference substance (Fig. 6 and 1SIa–c†). The solubility process for this compound is solvation controlled, as well as for (SP2-4) and (SP2-9) ones. For the rest substances the dissolution processes are crystal controlled. For compound (SP2-6) (under the structural modification of the reference substance) the following alterations of the crystal lattice take place. The sublimation Gibbs energy grows considerably (decrease in the saturated vapor pressure) due to the sublimation enthalpy increase (crystal lattice energy growth) and practically constant entropy term. The sublimation process is enthalpy driven. In its turn, the solvation Gibbs energy of (SP2-6) decreases considerably (the sign is taken into account) in comparison with the reference substance (sector VIII; the solvation is improved). All the described events are caused by the solvation enthalpy reduction (increasing in absolute magnitude: strengthening the interaction of the dissolved molecule with the solvent ones) and the entropy term decrease. The enthalpy term exceeds the entropy one, which makes the solvation process enthalpy driven. As the solvation Gibbs energy (negative value) exceeds in absolute magnitude the sublimation Gibbs energy (positive value), and the resulting process (dissolution) is solvation controlled.

Fig. 6 Combined diagrams for SP2 (spiro derivatives type 2) (see legend of Fig. 5).

For the other 9 compounds, the structural modifications of the reference molecule lead to a solubility decrease. Meanwhile, the analysis of the diagrams (Fig. 6 and SIa–c†), clearly demonstrates the existence of four different thermodynamic paths (variations of the sublimation and solvation parameters of the substance), leading to the observed result. This fact once again proves the complicated nature of the dissolution processes. Besides compound (SP2-6), for two substances (SP2-4) and (SP2-9) the dissolution processes are solvation controlled. Moreover, for the other two ones, the thermodynamic paths are equal. For these compounds the processes of crystal lattice change under the reference compound structural modification can be described in the following manner. The sublimation Gibbs energy slightly decreases (the saturated vapor pressure increases) due to the reduction of the sublimation enthalpy (diminution of the crystal lattice energy) and the decrease in the entropy term (ordering the molecules in the crystal). And the entropy term exceeds the enthalpy one (in absolute magnitude), which corresponds to the entropy driven sublimation process (sector VI, Fig. 4a). For the solvation processes a growth of the Gibbs energies is observed (a solvation decrease), with their values exceeding those of the sublimation processes, which corresponds to the solvation controlled solubility processes. The solvation processes are enthalpy driven: the solvation enthalpy decreases in absolute magnitude (the interaction solute–solvent energy reduction) and the entropy term grows (increasing the disordering of the solute into the solvent).

Crystal controlled solubility process. The dissolution processes of compounds (SP2-2, SP2-3, SP2-5, SP2-7, SP2-8, SP2-10, SP2-11) are crystal controlled. And there are three different thermodynamic paths describing these processes (Fig. 6 and 1SIa–c†). For compounds (SP2-2, SP2-3, SP2-5, SP2-8, SP2-11) the dissolution process is described by one path. The changes in the crystal can be characterized in the following manner. The structural modification of the reference substance results in the sublimation Gibbs energy growth (the saturated vapor pressure decreases) due to the growth of the sublimation enthalpy (the crystal lattice energy increase) and the increment of the entropy term (molecules disordering in the crystal). Both terms act nonsynchronously (in different directions) and the former exceeds the latter (sector III – enthalpy driven sublimation processes). In contrast to the sublimation processes, the solvation ones have negative Gibbs energy values (under the structural modification of the reference compound). The solvation enthalpy reduces (negative sign), increasing in absolute magnitude (strengthening of the solute–solvent molecules interaction). In its turn, the entropy term decreases (enhancing the solution ordering). The processes are characterized as enthalpy driven (sector VII).

For compounds (SP2-7) and (SP2-10), the sublimation processes are entropy driven (sector VI) as opposed to the compounds considered above. And if the entropy term decreases for both substances under the structural modification of the reference molecule (ordering of the crystal molecules), the behavior of the enthalpy terms is different. For compound (SP2-7), the enthalpy term decreases (reducing the crystal lattice energy), whereas for (SP2-10) – increases. The solvation processes for (SP2-7) and (SP2-10) are also different. The structural modification of the reference molecule leads to a slight decrease in the solvation Gibbs energy of (SP2-7) (the molecules are solvated to a greater extent), whereas for (SP2-10), the opposite trend is observed. For both compounds, the solvation enthalpies decrease in absolute magnitude (weakening the energy of the solute–solvent interaction), whereas the entropy solvation terms increase (enhancing the solution disorder). The essential difference between the considered compounds is the relationship between the enthalpy and entropy terms: in (SP2-7) the latter ones prevail (entropy driven solvation processes – sector II), whereas in (SP2-10) – the former ones (enthalpy driven solvation processes – sector III).

3.3. Benzoic acid derivatives

In the capacity of BA derivatives we consider acetylsalicylic acid, three isomers of methoxy- and acetylamino-benzoic acid (Fig. 1). The summarized diagrams of the sublimation, solvation processes and Gibbs energies are presented in Fig. 7. A more detailed description of these diagrams is given in the ESI (Fig. 2SIa–c†). For compounds (BA-2, BA-3, BA-4) we have managed to slightly increase the solubility compared to the reference compound (benzoic acid) and these processes are solvation controlled. But for the rest substances an insignificant decrease in the solubility is observed and the processes are crystal controlled. All the considered compounds have three different thermodynamic paths (Fig. 7).

Fig. 7 Combined diagrams for BA (benzoic acid and its derivatives) (see legend of Fig. 5).

The structural modification of benzoic acid by methoxy groups makes the crystal lattices of all three isomers more thermodynamically stable (the saturated vapor pressure reduces) as compared to the reference compound (Fig. 2SIb†). Such behavior is determined by the increase both in the sublimation enthalpy (crystal lattice energy) and the entropy term, with the former exceeding the latter (sector III – enthalpy driven). On the other hand, the solvation processes of the isomers are described by the experimental values located in sector VII (Fig. 2SIc†): an increase (in absolute magnitude) in both the solvation enthalpies and the entropy term (system ordering). The first contributions exceed the second ones, which leads to enthalpy driven processes (as in the case of sublimation processes). Superposition of the described processes results in better solubility of ortho- and meta-isomers (sector VIII diagram of Gibbs energies), than of the remaining isomer (sector I).

As it was mentioned above, the acetylamino-benzoic acid isomers ((BA-6)–(BA-8)) do not reveal better solubility as compared to the reference compound (benzoic acid). Their thermodynamic paths are similar to that of compound (BA-5) (Fig. 7). The essential difference of the thermodynamic functions of the sublimation and solvation processes of meta- and para-isomers from the ortho-isomer can be attributed to the formation of additional hydrogen bonds in the molecules of the first two ones in crystal and solution. Meanwhile, the solvation terms do not exceed the sublimation ones, which results in the solubility values reduction.

3.4. Bicycle derivatives

A 4-F phenyl derivative was chosen as the reference compound to study the influence of the structural modification of the bicycle derivatives (BC) molecules on the thermodynamic sublimation, solvation and solubility processes. This choice is explained by the absence of experimental data about the unsubstituted phenyl derivative. Meanwhile, the choice of the reference compound does not affect the conclusions made because the geometric characteristics of the fluorine atom differ slightly from those of the hydrogen atom.

The thermodynamic paths of the considered processes are represented in Fig. 8 and 3SIa–c.†

Fig. 8 Combined diagrams for BC (bicycles) (see legend of Fig. 5).

None of the investigated compounds under the reference substance structural modification leads to the solubility improvement. On the other hand, the solubility of most of the compounds slightly decreases and does not exceed 7 kJ mol⁻¹ (Gibbs energy scale) compared to the reference substance (which corresponds to a ten-fold solubility decrease). As it follows from Fig. 8 (Fig. 3SIa†), all the compounds in coordinates ΔG_sub vs. ΔG_solv belong to two sectors only: I – crystal controlled ((BC-3)–(BC-4), (BC-7)–(BC-11)) and IV – solvation controlled (BC-2, BC-6). In their turn, crystal controlled compounds are divided into two groups (according to the thermodynamic paths): the first contains compounds (BC-3) and (BC-5) in which the structural modification of the molecule results in entropy driven processes both in the crystal lattice and during solvation. Whereas the second group (BC-4, BC-7–BC-11) contains compounds in which the structural modification of the molecule results in the enthalpy driven processes both in the crystal lattice and during solvation.

3.5. Sulfonamides

All the sulfonamides selected for the analysis were divided into two clusters for convenience (Fig. 1). The first cluster contained compounds with NH₂-group in the para-position of the first phenyl ring (sulfonamides type 1: SA1). And the second one included substances which did not belong to the first group (sulfonamides type 2: SA2).

3.5.1. Sulfonamides type 1. As it has been shown by us previously,^33,35 NH₂-group facilitates an essential complication of the hydrogen bonds network topology in the crystals (as compared to the unsubstituted molecules – SA2), that is reflected on their thermodynamic characteristics for the sublimation and solvation processes. As a consequence, there is a large variety of thermodynamic paths in this group of compounds (practically each compound has its own path), given in Fig. 9.

Fig. 9 Combined diagrams for SA1 (sulfonamides type 1) (see legend of Fig. 5).

A 4-Cl-phenyl derivative was selected as a reference substance to study the influence of the structural modification of the sulfonamides molecules on the sublimation, solvation and solubility thermodynamic processes. Such choice is explained by the absence of experimental data about the unsubstituted phenyl derivative. Meanwhile, the selection of the reference compound does not affect the conclusion made because this compound (in terms of Tanimoto similarity index) characterizes the structures of the analyzed cluster of structurally similar substances quite well.

The structural modification of the reference molecule results in the solubility enhancement in three compounds (SA1-7, SA1-8, SA1-9) (Fig. 9 and 4SIa–c†). For compounds (8) and (9), the dissolution processes are solvation controlled, and for compound (SA1-7) – crystal controlled. The other substances demonstrate a solubility reduction as compared to the reference molecule, and for compounds (SA1-3), (SA1-4) and (SA1-6), the dissolution processes are crystal controlled, while for (SA1-2), (SA1-5), (SA1-10) and (SA1-11) ones – solvation controlled.

Compounds with reduced solubility. The compounds with the crystal controlled solubility processes and with reduced solubility values as compared to the reference one (SA1-3, SA1-4, SA1-6) are divided into two thermodynamic paths. The first path includes compounds (SA1-3) and (SA1-6), in which under the molecule modification the enthalpy driven processes take place both in the crystal lattice and during solvation. The second path consists of substance (SA1-4), in which the enthalpy driven processes take place in the crystal lattice and the entropy driven ones – during solvation under the structural modification.

The compounds with the solvation controlled dissolution processes and reduced solubility values in comparison with the reference one (SA1-2, SA1-5, SA1-10, SA1-11) are divided into four thermodynamic paths (each compound has an individual path). For compound (SA1-2), under the reference molecule modification the entropy driven processes (reduction of the sublimation Gibbs energy determined by the increase in both enthalpy and entropy with the latter prevailing over the former) take place both in the crystal lattice and during solvation (decrease in the absolute value of the solvation enthalpy and entropy with the latter prevailing over former).

For substance (SA1-5), the modification of the reference molecule results in the enthalpy driven process (decrease in the sublimation Gibbs energy which is determined by the reduction of the enthalpy term and the increase in the entropy one with the former term prevailing over the latter) in the crystal lattice and the entropy driven process during solvation (with a decrease in the solvation enthalpy and entropy absolute values with the latter prevailing over the former).

For compound (SA1-10), under the structural modification of the reference molecule the enthalpy driven process (increase of the sublimation Gibbs energy which is determined by the growth of the enthalpy and entropy terms with the former prevailing over the latter) in the crystal lattice and the entropy driven process during solvation (with the decrease in the solvation enthalpy and entropy absolute values with the latter prevailing over the former) take place.

For substance (SA1-11), the structural modification of the reference molecule leads to the enthalpy driven process (decrease in the sublimation Gibbs energy determined by the reduction of the enthalpy and entropy terms with the former prevailing over the latter) in the crystal lattice and the enthalpy driven process during solvation (with a decrease in the solvation enthalpy and entropy absolute values with the former prevailing over the latter).

Compounds with improved solubility. The compounds with the solvation controlled solubility processes and enhanced solubility values as compared to the reference substance solubility ones (SA1-8, SA1-9) have two thermodynamic paths. For substance (SA1-8), under the reference molecule modification, the enthalpy driven processes (increasing the sublimation Gibbs energy determined by the enhancement of the enthalpy and entropy terms with the former prevailing over the latter) both in the crystal lattice and during solvation (growth of the absolute values of the solvation enthalpy and decrease in the solvation entropy with the former prevailing over the latter).

For compound (SA1-9), under the reference molecule modification the entropy driven processes (growth of the sublimation Gibbs energy determined by the decrease in enthalpy and entropy terms with the latter term prevailing over the former) both in the crystal lattice and during solvation (constant solvation enthalpy value and increase in the solvation entropy) take place.

Finally, for compound (SA1-7), the reference molecule modification makes process entropy driven (a small decrease in the sublimation Gibbs energy determined by the increase in the enthalpy and entropy terms with the latter prevailing over the former) in the crystal lattice, whereas, during solvation the process becomes enthalpy driven (growth of the solvation enthalpy and entropy terms in absolute magnitude with the former prevailing over the latter).

Thus, by analyzing the structural modification of sulfonamides as an example it has been shown there is a wide range of thermodynamic paths describing the processes in crystals and solutions. It is not yet possible to definitely predict the path, and it will probably take time to collect and analyze the representative base of experimental data.

3.5.2. Sulfonamides type 2. As noted in the previous section, sulfonamides were divided for convenience into two clusters (Fig. 1), so here we will focus on the analysis of sulfonamides type 2 (without an amino group in the first phenyl ring: SA2). Unlike the first group, the reference compound has no substituents in the phenyl moiety. Each of the compounds considered has its own thermodynamic path (Fig. 10). It should be noted that for all the selected compounds the processes of dissolution are solvation controlled (Fig. 5SIa–c†). However, the solubility enhancement under the reference compound structural modification is only observed in compound (SA2-5). Analysis of thermodynamic path shows that the reference substance modification significantly increases the Gibbs energy of sublimation (reduced saturated vapor pressure) due to the increase in both the sublimation enthalpy and entropy terms with the former prevailing over the latter (enthalpy driven process). Apparently, this is due to the presence of a nitro group, which contributes to the formation of complex hydrogen bonds networks (crystal lattice energy increase). In turn, the Gibbs energy of solvation is significantly reduced (compared to the reference compound) due to a stronger interaction of the dissolved molecule with the solvent (an increase in the solvation enthalpy in absolute magnitude) and a small increase in the solvation entropy term (enthalpy driven solvation process). Thus, the NO₂-group has a greater influence on the solvation processes, compared to the processes taking place in the crystal lattice.

Fig. 10 Combined diagrams for SA2 (sulfonamides type 2) (see legend of Fig. 5).

Introduction of the Cl-atoms in the ortho-(SA2-2) and para-(SA2-4) position of the second phenyl ring of the reference compound leads to a solubility decline, and the dissolution processes are solvation controlled. However, the thermodynamic paths of Cl-isomers differ. Although for the two isomers, the same (small) decrease in the sublimation Gibbs energy in the crystal (increased vapor pressure) is observed, meanwhile, this result is achieved in different ways. For the ortho-isomer a slight increase in enthalpy (energy of the crystal lattice) and sublimation entropy is observed with the latter prevailing over the former (entropy driven process) in comparison with the reference compound. And for the para-isomer the enthalpy and entropy term decreases with the former prevailing over the latter (enthalpy driven process). For both isomers the solvation Gibbs energy increases as compared to the reference compound (process worsening). Moreover, this occurs due to the reduction of the solvation enthalpy (reduction in the interaction between the solute and solvent), and to the increase in the entropy term (with the former prevailing over the latter – enthalpy driven processes).

Finally, the introduction of two Cl-atoms (SA2-3) in the second phenyl fragment decreases the solubility of the compound in comparison with the reference one (leaving the value in the same range as for the mono-Cl-derivatives), and the dissolution process is characterized as solvation controlled. In the crystal the following changes take place. The sublimation Gibbs energy is practically unchanged as compared to the unsubstituted compound. At the same time, the enthalpy and entropy terms synchronously increase with the former slightly prevailing over the latter (enthalpy driven process). The solvation process is accompanied by an increase in the Gibbs energy by the magnitude comparable to that of mono-Cl-substituted compounds. Moreover, there is a reduction both in the solvation enthalpy (increased interaction of the dissolved molecule with the solvent), and the entropy term (system ordering) with the latter prevailing over the former (entropy driven process).

3.6. Fenamates

This group of compounds contains drug substances – fenamates (F), some of them differ from the founder of this class – N-phenyl-anthranilic acid (F-1) (for example, niflumic acid (F-3) and diclofenac (F-6)). Fig. 11 and 6SIa–c† depict the thermodynamic paths of the considered compounds. It should be noted that each compound has its own path. The reference compound modification improves the solubility except that of niflumic acid (F-3). The dissolution process in one compound (F-2) is crystal controlled, whereas in the remaining ones – solvation controlled.

Fig. 11 Combined diagrams for F (fenamates) (see legend of Fig. 5).

If we consider compounds (F-2) and (F-3), the only structural difference between them is the presence of a nitrogen atom in the conjugated system of the first phenyl ring. However, this difference materially affects the properties of the substances. Substance (F-3) is more poorly soluble than the reference compound, whereas compound (F-2) is shown to have better solubility. If we analyze the sublimation process, it is possible to conclude that the introduction of CF₃-group at the meta position of the second phenyl moiety (F-2) reduces the sublimation Gibbs energy (increases the vapor pressure) as compared to the reference substance. Such behavior is explained by the decrease in the sublimation enthalpy (decrease in the energy of the crystal lattice) and the reduction of the entropy term: both of these terms act synchronously to decrease the Gibbs energy. It should be emphasized that the enthalpy term exceeds the entropy one, so the sublimation process is enthalpy driven. For compound (F-3), the modification of the first phenyl fragment and the introduction of the CF₃-group at the meta-position of the second phenyl fragment results in an increase in the sublimation Gibbs energy (the saturated vapor pressure decrease). Such behavior is determined by the sublimation enthalpy increase (strengthening of the crystal lattice energy) as compared to the reference compound and a slight growth of the entropy term. The sublimation process, as in the previous case, is enthalpy driven. The solvation processes for (F-2) and (F-3) under the reference compound modification are similar: the solvation enthalpies decrease in absolute magnitude (the energy of the interaction of the solute molecule with the solvent decreases), whereas the entropy term increases. The entropy contributions exceed the enthalpy ones, so the solvation processes of the considered compounds are entropy driven. The ratio of the contributions differs for these compounds, which results in a lower solvation Gibbs energy (best solvation) for (F-3) in comparison with (F-2).

Let us consider compounds (F-4) and (F-5). The replacement of the methyl group of compound (F-4) by the Cl-atom (F-5) leads to a significant solubility improvement. The following processes take place under the reference molecule structural modification in crystals. The introduction of two methyl-groups into N-phenyl-anthranilic acid (molecule A is formed) results in a slight increase in the sublimation Gibbs energy (the saturated vapor pressure is decreased) in comparison with the reference molecule. This behavior is determined by increasing the enthalpy of sublimation (strengthening of the crystal lattice energy) and the entropy term increase. And the enthalpy term exceeds the entropy one, which makes the sublimation process enthalpy driven. In contrast to compound (F-4), substance (F-5) has negative values of the sublimation Gibbs energy (a saturated vapor pressure increase) compared to the reference compound. And as in compound (4), the sublimation enthalpy and entropy grow. However, unlike the previous case, the entropy term prevails over the enthalpy one, so the sublimation process is entropy driven. The solvation Gibbs energy for the two considered compounds has a positive value (they are solvated more poorly) as compared to the reference substance. However, this process for compound (F-4) is enthalpy driven, whereas for (F-5) one – entropy driven.

3.7. Thiadiazoles

The considered thiadiazoles can generally be characterized as follows. Practically all the compounds are phenyl para-substituted (T-2–T-7, T-9), two substances belong to meta-phenyl derivatives (T-10 and T-11) and two compounds are di-Cl-, Me-phenyl derivatives (T-8 and T-12). Phenyl derivative of thiadiazole was selected as a reference substance. Fig. 12 and 7SIa–c† depict the thermodynamic paths of the considered compounds. The structural modifications of the reference molecule do not improve the solubility. The dissolution processes for all the selected compounds can be divided into two groups: crystal and solvation controlled ones. All compounds have 7 different thermodynamic paths: 4 paths belong to the substances collected in pairs ((T-2, T-9); (T-3, T-4); (T-5, T-10); (T-6, T-7)) and three paths correspond to individual ones (T-8, T-11, T-12).

Fig. 12 Combined diagrams for T (thiadiazoles) (see legend of Fig. 5).

Thermodynamic paths (T-2, T-9) and (T-6, T-7) are the same in terms of describing the process of sublimation: the structural modification of the reference molecule leads to an increase in the sublimation Gibbs energy (vapor pressure reduction) by increasing the sublimation enthalpy (the crystal lattice energy growth) and an increase in the entropy term (molecular disorder in the crystal lattice). And the enthalpy term exceeds the entropy one, which makes the sublimation processes of the considered compounds enthalpy driven. On the other hand, the solvation processes of the two analyzed pairs have different patterns. The structural modification of the reference molecule produces compounds (T-2) and (T-9), and the solvation Gibbs energy slightly goes down (solvation enhancement) by decreasing the solvation enthalpy (growth in absolute magnitude – increasing the energy of the interaction of the dissolved molecule with the solvent) and by reducing the entropy term (which corresponds to better solute–solvent system order). It should be noted that the enthalpy term overweighs the entropy one, so the solvation processes in these two compounds are enthalpy driven. For the pair of compounds (T-6) and (T-7), the enthalpy and entropy terms of the solvation processes have opposite signs as compared to the previous pair. Moreover, the entropic terms exceed the enthalpy ones, which make these processes entropy driven.

The reference molecule structural modification (which produces compounds (T-5) and (T-10)) results in the following changes in the crystal lattice. The sublimation Gibbs energy increases slightly (the saturated vapor pressure decrease) and it happens due to the sublimation enthalpy increase (increasing the energy of the crystal lattice) and the entropy term growth (disordering of the molecules in the crystal lattice). And the enthalpy term exceeds the entropy one, which makes the sublimation processes of the considered compounds enthalpy driven. The solvation processes are characterized by a slight increase in the Gibbs energy (solvation deterioration) due to the solvation enthalpy reduction (increase in absolute magnitude – increasing the interaction energy of the solute molecule with the solvent), and the entropy term decrease (which corresponds to the increase in the solute–solvent system ordering degree). It should be noted that the entropy term outweighs the enthalpy one, which makes the solvation processes in these two compounds entropy driven.

As noted above, the processes of dissolution in the pair of compounds (T-3) and (T-4) are solvation controlled. The structural modification of the reference molecule leads to the following changes in the crystal lattice. The sublimation Gibbs energy increases slightly (the saturated vapor pressure decrease) due to the sublimation enthalpy growth (increasing the energy of the crystal lattice) and the entropy term increase (disordering of the molecules in the crystal lattice). And the enthalpy term exceeds the entropy one making the sublimation processes of the compounds enthalpy driven. The solvation processes are characterized by a slight increase in the Gibbs energy (solvation deterioration) due to the solvation enthalpy reduction (increase in absolute magnitude – increasing of the interaction energy of the solute molecule with the solvent), and the entropy term decrease (which corresponds to an increase in the solute–solvent system ordering degree). It should be noted that the entropy term outweighs the enthalpy one, so the solvation processes in these two compounds are entropy driven.

Let us compare the thermodynamic paths of di-substituted phenyl thiadiazoles (T-8, T-12). The dissolution processes in them are solvation controlled. The following changes occur in the crystal lattice under the molecule structural modification. The sublimation Gibbs energy of compound (T-8) increases, whereas that of (T-12) – decreases (the vapor pressure increases). For both compounds, the sublimation enthalpy is reduced (the energy of the crystal lattice is decreased). In turn, the sublimation entropy term is also reduced (the molecules in the crystal become ordered). The essential difference between the sublimation processes is that in compound (T-8) the process is entropy driven, whereas in (T-12), it is enthalpy driven. Thus, altering the positions of the substituents of the same nature may lead to a change in the sublimation process driving forces, and, as a consequence, to Gibbs energy modification. The solvation processes of the considered compounds are similar and characterized by a slight increase in the Gibbs energy (solvation deterioration) by increasing the solvation enthalpy (a decrease in absolute magnitude – a reduction of the interaction energy between the solute molecule and the solvent) and an entropy term increase (which corresponds to the solute–solvent system disorder). It should be noted that the enthalpy term outweighs the entropy one, so the solvation processes in these two compounds are enthalpy driven.

Let us consider the thermodynamic path of the remaining compound ((T-11) – meta-Cl-derivative) in comparison with the other isomer ((T-9) – para-Cl-). The sublimation process can be described as follows. The reference molecule modification increases the sublimation Gibbs energy in both isomers (the saturated vapor pressure reduction) but this result is achieved in different ways. For para-isomer (T-9) there is a slight increase in the enthalpy (energy of the crystal lattice), and sublimation entropy with the former prevailing over the latter (enthalpy driven process). Whereas for meta-isomer (T-11), the enthalpy and the entropy terms decrease with the latter prevailing over the former (entropy driven process). The solvation processes in the investigated isomers are similar. The reference molecule modification results in the reduction of both the solvation enthalpy (an increase in absolute magnitude, i.e. strengthening of the interactions between the dissolved substance and the solvent), and the entropy terms in both isomers. The essential difference is that in the para-isomer the solvation process is enthalpy driven with a negative Gibbs energy value, whereas in the meta-isomer it is entropy driven with a positive value of the Gibbs energy.

3.8. General analysis of the experimental data

To reveal the regularities of the solubility, sublimation and solvation processes under the structural modification of the reference compounds, it was interesting to analyze the distribution of the experimental values across the sectors of the considered diagrams. We examined 8 groups of substances, each of them being a structural modification of the reference substance. Of course, not all the groups were numerous, meanwhile, the total number of the analyzed compounds reached 59 (not including the 8 reference ones). This allowed us to suggest the correctness/reasonableness of the conclusions made.

Table 1 shows the statistics of the compounds in the considered groups by the sectors of the diagram ΔG_sub(i − 1) vs. ΔG_solv(i − 1). It is easy to see that the maximal number of the experimental points (24) belongs to sector I, that is 40.6% of the total number of the substances. Then, sectors III, IV and VIII have the same number of the experimental points (9), which is 15.3% for each sector. Sector II contains 6.7% of the compounds, whereas sectors V and VII have 3.4% compounds in each. The compounds in which the solubility processes are crystal controlled (sectors I, II, V, VI) represent 50.7%. In their turn, the compounds with solvation controlled solubility processes (sectors III, IV, VII, VIII) account for 49.3%, respectively. It is evident that these two classes of the compounds are approximately the same. Thus, the explanation of the solubility variations (under structural modification) only by changing the crystal structure is wrong. Such mode can work roughly only in 50% of the cases when the solubility processes are crystal controlled.

Table 1 Distribution of the compounds studied concerning to the diagram sectors ΔG_sub(i − 1) vs. ΔG_solv(i − 1)

Groups^a	Number of compounds	Sectors
		I	II	III	IV	V	VI	VII	VIII
a SP1 – spiro derivatives (type 1); SP2 – spiro derivatives (type 2); BA – benzoic acid and its derivatives; BC – bicycles; SA1 – sulfonamides (type 1); SA2 – sulfonamides (type 2); F – N-phenyl-anthranilic acid and their derivatives (fenamates); T – thiadiazoles.
BC	10	8			2
BA	7	4							3
SA-1	10	2	1	1	3	1			2
SA-2	4			1	2				1
SP1	2				1				1
SP2	10	6	1	2					1
F	5			1		1		2	1
T	11	4	2	4	1
Total	59	24	4	9	9	2		2	9
Total (in %)	100	40.6	6.7	15.3	15.3	3.4		3.4	15.3
Crystal controlled (in %)	50.7	40.6	6.7			3.4
Solvation controlled (in %)	49.3			15.3	15.3			3.4	15.3
Solubility improve (in %)	22.1					3.4		3.4	15.3
Solubility decrease (in %)	77.9	40.6	6.7	15.3	15.3

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Among all the considered compounds, it is only in 22.1% of the compounds that the structural modification of the reference substance improves the solubility. And it most frequently happens in sector VIII (15.3% – solvation controlled solubility processes). But one should not disregard that for 3.4% of the compounds the solubility improvement is achieved by means of crystal controlled processes. In total, the solubility enhancement is 5.5 times more often achieved by solvation controlled processes than by crystal controlled ones.

Among all cases of the solubility decrease, crystal controlled processes are found 1.5 times more often than solvation controlled ones.

As the next step, we tried to analyze which combinations of the sectors for the three investigated diagrams were found most often. Table 2 shows the results of the analysis.

Table 2 Distribution of the compounds studied concerning to the sectors for the three diagrams: TΔS_sub vs. ΔH_sub (Sub); TΔS_solv vs. ΔH_solv (Solv); ΔG_sub vs. ΔG_solv (Sub − Solv)

N	NC^a	%	Sub	Solv	Sub − Solv
a Number of compounds.
1	19	32.2	III	VII	I
2	4	6.8	III	VI	III
3	3	5	VI	III	III
4	3	5	VI	II	I
5	3	5	III	VII	VIII
6	2	3.4	VII	IV	IV
7	2	3.4	VII	III	IV
8	2	3.4	II	VI	IV
9	2	3.4	III	VI	II
10	2	3.4	III	II	I
11	1	1.7	III	II	VIII
12	1	1.7	II	VI	IV
13	1	1.7	III	VI	II
14	1	1.7	VIII	VI	IV
15	1	1.7	II	VII	V
16	1	1.7	VI	I	VIII
17	1	1.7	II	III	IV
18	1	1.7	III	VIII	VIII
19	1	1.7	V	II	VIII
20	1	1.7	IV	VII	VIII
21	1	1.7	V	III	II
22	1	1.7	VII	II	V
23	1	1.7	III	II	III
24	1	1.7	III	III	VIII
25	1	1.7	II	VI	VII
26	1	1.7	VII	VI	VII
27	1	1.7	VI	VI	III
	59	100

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It is evident that the most frequent variant (32.2%) is simultaneous position of the experimental points in the following sectors. In sector III (for sublimation processes), the reference molecule structural modification increases both the sublimation enthalpy (strengthening the crystal lattice energy) and the entropy term (disordering the molecules in the crystal lattice) with the enthalpy term prevailing over the entropy one (enthalpy driven sublimation process). In sector VII (for solvation processes) it reduces (increase in absolute magnitude) the solvation enthalpy (strengthening the solute–solvent interaction) and the entropy term (ordering the molecules in the solution) with the enthalpy term prevailing over the entropy one (enthalpy driven solvation process). In sector I (for sublimation and solvation Gibbs energies) the structural modification leads to crystal controlled solubility processes, where the sublimation Gibbs energy increases and the solvation Gibbs energy decreases, with the former prevailing over the latter. It should be noted that it is this variant of the thermodynamic path under reference compound modification that is usually analyzed in the literature and, as a rule, on this basis generalized conclusions are made. But other 67.8% variants with alternative path are practically ignored in the literature.

3.9. Absolute scale of thermodynamic characteristics for the considered compounds

In conclusion it is necessary to assess the absolute scale of the thermodynamic characteristics of the considered processes for the selected groups of the compounds. For this purpose it is enough to analyze the reference compounds themselves using the employed diagrams concerning the compound with the minimal Gibbs energy values of sublimation, solvation and dissolution. BA was selected as the above mentioned compound. The results are given in Fig. 13a–c. The dispersion interval of the solubility Gibbs energy values derived as a result of the structural modification of the reference molecule is indicated by an arrow. The maximal interval corresponds to fenamates. But it should be emphasized that not all the compounds of this group perfectly suit the structure of the reference compound (N-phenyl-anthranilic acid): for example, diclofenac and mefenamic acid do not. It is them that are responsible for the essential deviations of the solubility values. If these substances are excluded from consideration, the interval is considerably reduced (the red arrow). The narrowest range of the solubility dispersion corresponds to BA and SP1 due to insufficient representation of the compounds in this group. In the groups where the representation is sufficient, the values are approximately dispersed in the range of no more than ΔG⁰_sol = 12 kJ mol⁻¹ (which corresponds to the 145 time solubility value dispersion) and this range is approximately the same for all the indicated classes of the compounds. The only difference between these classes consists in the fact that for some compounds it is possible to improve the solubility by structural modification in the ranges of reliable variations (SA1, F, SP2 and SA2), whereas for other ones – it is impossible (T, BC). Practically all classes of the compounds intersect according to the solubility values. This fact can be taken into account while designing bioavailable drug compounds aimed at the interaction with the same biological receptors. For example, compounds T, BC, SP1 and SP2 are candidate neuroprotectors (the same class of compounds) for Alzheimer disease therapy.

Fig. 13 Diagrams for the references compounds (description sees Fig. 1) concerning to the compound with the minimal Gibbs energy values of sublimation, solvation and dissolution (benzoic acid – BA): (a) experimental data in co-coordinates (ΔG_sub(i) − ΔG_sub(BA)) vs. (ΔG_solv(i) − ΔG_solv(BA)); (b) experimental data in co-coordinates (TΔS_sub(i) − TΔS_sub(BA)) vs. (ΔH_sub(i) − ΔH_sub(BA)); (c) experimental data in co-coordinates (TΔS_solv(i) − TΔS_solv(BA)) vs. (ΔH_solv(i) − ΔH_solv(BA)).

As the substances solubility values intersect, further biological tests can be conducted using compounds with improved membrane permeability. Before “participating” in the process of membrane permeability (passive diffusion), the molecule should pass from the aqueous to the lipophilic (distribution) phase. For this purpose, the solvated molecule in the solution must “throw off” the solvation shell before the transition to the lipophilic phase (membrane). The strength of the interaction of the dissolved molecule with the solvent is characterized by the solvation Gibbs energy. Due to this fact it is necessary to choose from the presented set of the molecules those ones with the minimal values of the solvation Gibbs energy. In our case, these compounds belong to groups SP1 and BC. Here we present one of the ways to select molecules with acceptable pharmaceutical parameters. But, as a rule, these schemes are very complicated and produce ambiguous results.

4. Conclusions

Dissolution processes of poorly soluble drugs belonging to the classes of spiro derivatives, benzoic acid and its derivatives, sulfonamides, fenamates, thiadiazoles have been analyzed based on the literature data published by the author recently. The main criterion for the solubility analysis was the comparison of the thermodynamic characteristics of the sublimation processes (state of the molecules in solids) and the solvation (state of the molecules in solutions) under the reference molecule structural modification. The superposed diagram approach was used to compare the parameters of the investigated processes including simultaneous analysis of the sublimation process thermodynamic functions (analysis of the experimental data in the coordinates of TΔS⁰_sub versus ΔH⁰_sub), solvation (analysis of the experimental data in the coordinates of TΔS⁰_solv versus ΔH⁰_solv), and analysis of the experimental data in the coordinates of ΔG⁰_sub versus ΔG⁰_solv. The proposed approach enables obtaining full information about the thermodynamic state of the molecules in crystal and solution. A variety of the thermodynamic paths of the substances under structural modification of the reference molecules were shown in each group (such process can be compared to the structural variation of the “lead” compound to obtain the “head” substance). The extreme solubility values were obtained for the considered classes of the compounds which can be derived by structural modification of the substances.

A classification of the drugs was suggested based on the analysis of the controlling steps of the dissolution processes: crystal or solvation controlled ones. Based on the investigation of 59 drugs belonging to five different classes of compounds it was estimated that for 50.7% of the compounds, the solubility processes are crystal controlled, whereas for the rest 49.3% – solvation controlled. From all the considered compounds only in 22.1% of the substances, the structural modification of the reference substance led to solubility improvement. And in 85% of the compounds, the dissolution processes were solvation controlled and in the other 15% – crystal controlled.

The absolute scale of the thermodynamic parameters of the dissolution, sublimation, and solvation processes for the considered drugs was analyzed.

Acknowledgements

This work was supported by the Russian Science Foundation (No. 14-13-00640). The author would like to thank Dr Tatyana Volkova, Dr Sergey Kurkov, Dr Artem Surov, Dr Alex Manin, Dr Alex Ryzhakov, Dr Bui Kong Chin, Dr Svetlana Blokhina, Dr Angelica Sharapova, Dr Marina Ol'khovich for experimental data collection and useful discussions.

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Footnote

† Electronic supplementary information (ESI) available: Diagrams for experimental data of sublimation, solvation and dissolution processes of the spiro derivatives type 2 (SP2), benzoic acid and their derivatives (BA), bicycles (BC), sulfonamides type 1 (SA1), sulfonamides type 2 (SA2), N-phenyl-anthranilic acid and their derivatives (fenamates), thiadiazoles (T) in comparison to the reference compound are represented in Fig. 1–7SI. See DOI: 10.1039/c6ra14333d

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