Dissolution thermodynamics and solubility prediction of satranidazole in mono-solvent systems at various temperatures using a single determination

ABSTRACT

The reported mole fraction solubility data of satranidazole (SAT) in 18 mono-solvents at five different temperatures (T = 293.2K to 313.2 K) and atmospheric pressure (p = 0.1MPa) collected from the literature were revisited from another physicochemical point of view. The solubility of SAT in 12 mono-solvents was correlated by a newly developed model and six mono-solvents were excluded from correlation due to the non-availability of solvent parameters. Additionally, apparent thermodynamic quantities of dissolution and mixing were calculated based on the van’t Hoff and Gibbs equations by using mole fraction solubilities and reported enthalpy and temperature of fusion of SAT. Results were interpreted in terms of possible intermolecular interactions.

KEYWORDS:

• Solubility
• satranidazole
• Jouyban model
• Simulation
• dissolution thermodynamics

1. Introduction

Satranidazole (SAT) or 1-methane sulphonyl-3-(1-methyl-5-nitro-2-imidazolyl)-2-imidazolidinone has low water solubility and high permeability drug which is classified as a class II drug according to the biopharmaceutics classification system. It is used in the treatment of amoebic liver abscess, giardiasis and trichomoniasis, since it possesses potent broad spectrum antiprotozoal activity against Entamoebia histolytica, Treponema vaginalis and Giardia intestinalis [1–4].

The solubility data of SAT in methanol (MeOH), ethanol (EtOH), 1-propanol (1-PrOH), 2-propanol (2-PrOH), formamide, 1,4-dioxane, N,N-dimethyl formamide (DMF), N,N-dimethyl acetamide (DMA), dimethyl sulphoxide (DMSO), N-methyl-2-pyrrolidone (NMP), ethylene glycol (EG), propylene glycol (PG), 1,4-butanediol (BDOH), glycerine, polyethylene glycol-200 (PEG-200), PEG-400, PEG-600, and water was reported in our earlier work [5]. Different mathematical models have been used to correlate the experimental solubility of SAT in the mono-solvents at various temperatures; including the van’t Hoff model, Apelblat model, Buchowski-Ksiazczak model, and a polynomial empirical model [5]. These models were applied for solubility of SAT in each solvent at various temperatures separately. In a recently proposed model [6], one may correlate the solubility of a given drug in different mono-solvents at various temperatures employing the physico-chemical properties of the solvents. Therefore, in this short work, the previously reported mole fraction solubility of SAT in above-mentioned mono-solvents at T = 293.2 to 313.2 K at 0.1 MPa atmospheric pressure were simulated using the proposed model. Moreover, apparent thermodynamic quantities of dissolution and mixing of SAT in all the neat solvents were calculated by means of previously described procedures.

2. Computational methods

The experimental solubility data of SAT in MeOH, EtOH, 1-PrOH, 2-PrOH, 1,4-dioxane, DMF, DMA, DMSO, NMP, EG, PG, and water at different temperatures was fitted to the general form of the recently proposed model:

(1) $ln{x}_T=\left({\alpha }_0+\sum _{\mathit{i}=1}^5{\alpha }_{\mathit{i},\mathit{AP}}\mathit{A}{P}_i+\sum _{\mathit{i}=1}^3{\alpha }_{\mathit{i},\mathit{HP}}\mathit{H}{P}_i+\sum _{\mathit{i}=1}^4{\alpha }_{\mathit{i},\mathit{CP}}\mathit{C}{P}_i\right)+\left(\frac{{\beta }_0+\sum _{\mathit{i}=1}^5{\beta }_{\mathit{i},\mathit{AP}}\mathit{A}{P}_i+\sum _{\mathit{i}=1}^3{\beta }_{\mathit{i},\mathit{HP}}\mathit{H}{P}_i+\sum _{\mathit{i}=1}^4{\beta }_{\mathit{i},\mathit{CP}}\mathit{C}{P}_i}{\mathit{T}}\right)$(1)

where α and β terms are the model constants. The intercept and slope of the van’t Hoff equation (α and β terms) and the solvation parameters of the mono-solvents, i.e. Abraham solvation parameters (AP_i), Hansen solubility parameters (HP_i) and Catalan parameters (CP_i) were combined to build up a correlative model [6]. The numerical values of AP_i, HP_i and CP_i for the investigated solvents are listed in Table 1. The most significant (p < 0.05) independent variables obtained from the regression analysis of the solubility data of SAT dissolved in the investigated mono-solvents were included in the trained model. It should be noted that formamide, BDOH, glycerin, and PEGs 200, 400 and 600 were excluded from this analysis since at least one of the AP_i, HP_i and CP_i parameters was not available for these mono-solvents.

Table 1. The numerical values for the solvent’s properties.

	Abraham parameters
Mono-solvent	c	e	s	a	b	v
1,4-Dioxane	0.10	0.35	−0.08	−0.56	−4.80	4.17
DMA	−0.27	0.08	0.21	0.92	−5.00	4.56
DMF	−0.31	−0.06	0.34	0.36	−4.90	4.49
DMSO	−0.19	0.33	0.79	−1.30	−4.50	3.36
EG	−0.27	0.58	−0.51	0.72	−2.60	2.73
EtOH	0.22	0.47	−1.00	0.33	−3.60	3.86
2-PrOH	0.10	0.34	−1.00	0.41	−3.80	4.03
MeOH	0.28	0.33	−0.71	0.24	−3.30	3.55
NMP	0.15	0.53	0.23	0.84	−4.80	3.67
PG	−0.15	0.75	−0.97	0.68	−3.10	3.25
1-PrOH	0.14	0.41	−1.00	0.25	−3.80	3.99
Water	−0.99	0.58	2.55	3.81	4.84	−0.87
	Hansen parameters
	δD	δP	δH
1,4-Dioxane	19.00	1.80	7.40
DMA	16.80	11.50	10.20
DMF	17.40	13.70	11.30
DMSO	18.40	16.40	10.20
EG	12.40	16.00	33.50
EtOH	15.80	8.80	19.40
2-PrOH	13.00	10.40	15.70
MeOH	15.10	12.30	22.30
NMP	15.10	10.30	14.60
PG	12.80	14.20	28.00
1-PrOH	16.00	6.80	17.40
Water	15.50	16.00	42.30
	Catalan parameters
	SP	SdP	SA	SB
1,4-Dioxane	0.74	0.31	0.00	0.44
DMA	0.76	0.99	0.03	0.65
DMF	0.76	0.98	0.03	0.61
DMSO	0.83	1.00	0.07	0.65
EG	0.78	0.91	0.72	0.53
EtOH	0.63	0.78	0.40	0.66
2-PrOH	0.63	0.81	0.28	0.83
MeOH	0.61	0.90	0.61	0.55
NMP	0.81	0.96	0.02	0.61
PG	0.73	0.89	0.48	0.60
1-PrOH	0.66	0.75	0.37	0.78
Water	0.68	1.00	1.06	0.03
	KAT-LSER parameters
	α^a	β^a	π*^a	δ1/MPa^1/2 b
1,4-Dioxane	0.00	0.35	0.55	20.47
DMA	0.00	0.76	0.88	22.77
DMF	0.00	0.69	0.88	24.86
DMSO	0.00	0.75	1.00	26.68
EG	0.90	0.52	0.92
EtOH	0.86	0.75	0.54
2-PrOH	0.76	0.84	0.48	23.58
MeOH	0.98	0.66	0.60	29.61
NMP	0.00	0.77	0.92	25.35
PG	0.83	0.78	0.76	29.52
1-PrOH	0.84	0.9	0.52	24.45
Water	1.17	0.47	1.09	48.82

^aα, β, and π* values were taken from [https://doi.org/10.1039/cs9932200409].

^bC.M. Hansen, Hansen Solubility Parameters: a User’s Handbook, 2 ed., Taylor and Francis, Hoboken, 2012.

The calculated solubility data of SAT was used to compute the mean percentage deviation (MPD) values by:

(2) $\mathit{MPD}=\frac{100}{N}\sum _{\mathit{\hspace{0.17em}}}^{\mathit{\hspace{0.17em}}}\mathit{\hspace{0.17em}}\left(\frac{\left|x_T^{C\mathrm{alulated}}-x_T^{\hspace{0.17em}}\right|}{x_T^{\hspace{0.17em}}}\right)$(2)

where N is the number of data points in each set. The accuracy of the proposed model was compared with those of previous models [5]. To test the prediction capability of the proposed model, it was trained using one datum in each mono-solvent at one temperature, then the rest of data points were predicted and the results were compared with those of similar models taken from the literature [7]. The predictive model employing only one datum in its training process is:

(3) $-ln{x}_T=-ln{x}_{\hspace{0.17em}}^i+ln\left[\frac{V_2{\phi }_1^2{\left({\delta }_1-{\delta }_2\right)}^2}{\mathit{RT}}\right]+\mathit{F}$(3)

where xⁱ is the ideal mole fraction solubility of SAT, V₂ is the molar volume of SAT, ${\phi }_1^2$is the volume fraction of the solvent which is very close to unity and may be replaced with 1, δ₁ and δ₂ are the Hildebrand solubility parameters of the solvent and SAT, F is the model constant. The V₂ and δ₂ values were calculated using Fedors’ group contribution [8] and were 160.1 cm³·mol⁻¹ and 28.3 MPa^1/2, respectively (Table 2). The xⁱ value could be used from experimentally derived data or could be computed employing the melting temperature datum (T_m) and by using:

(4) $-ln{x}_{\hspace{0.17em}}^i=\frac{0.02303{\left(T_m-\mathit{T}\right)}^2}{\mathit{T}ln\left(\frac{T_m}{\mathit{T}}\right)}$(4)

Table 2. Application of the Fedors’ method to estimate internal energy, molar volume, and Hildebrand solubility parameter of satranidazole.

Group	Group number	ΔU°/kJ mol^−1	V/cm^3 mol^−1
–CH3	2	2 × 4.71 = 9.42	2 × 33.5 = 67.0
–CH2–	2	2 × 4.94 = 9.88	2 × 16.1 = 32.2
–CH=	1	4.31	13.5
>C=	2	2 × 4.31 = 8.62	2 × −5.5 = −11.0
5 atoms ring closure	2	2 × 1.05 = 2.10	2 × 16.0 = 32.0
Conjugation in ring	2	2 × 1.67 = 3.34	2 × −2.2 = −4.4
–N<	2	2 × 4.20 = 8.40	2 × −9.0 = −18.0
–N=	1	11.70	5.0
–CON<	1	29.50	−7.7
–NO2 aromatic	1	15.36	32.0
–SO2–	1	25.60	19.5
		Σ ΔU° = 128.23	Σ V = 160.1
		δ3 = (128,230/160.1)^1/2 = 28.3 MPa^1/2

The F value could be computed using a single experimental solubility datum in each mono-solvent using:

(5) $\mathit{F}=-ln{x}_T+ln{x}_{\hspace{0.17em}}^i-ln\left[\frac{V_2{\phi }_1^2{\left({\delta }_1-{\delta }_2\right)}^2}{\mathit{RT}}\right]$(5)

The numerical value of xⁱ derived from experimental solubility data for SAT is taken from a previous paper [5] and was also computed using Equation 4(4) $-ln{x}_{\hspace{0.17em}}^i=\frac{0.02303{\left(T_m-\mathit{T}\right)}^2}{\mathit{T}ln\left(\frac{T_m}{\mathit{T}}\right)}$(4) .

One may also calculate the solubility of SAT in different mono-solvents at 298.15 K using KAT-LSER model which is commonly used in the recent papers [9–12] for mathematical representation of the solute-solvent interactions in the solution. The KAT-LSER model is:

(6) $ln{x}_{298.15}=c_0+c_1{\pi }^{\ast }+c_2\mathit{\alpha }+c_3\mathit{\beta }+c_4\left(\frac{V_2{\delta }_2^2}{100\mathit{RT}}\right)$(6)

where R is the universal gas constant, the terms c₂α and c₃β account for the specific interaction energies; c₁π* expresses the non-specific interaction energy; $c_4\left(\frac{V_2{\delta }_2^2}{100\mathit{RT}}\right)$ represents the cavity term that demonstrates the solvent-solvent molecular interactions. The coefficients of the KAT-LSER model, c_{i = 0–4}, are the model constants [9–12]. We also applied KAT-LSER model for representing the solubility data at various temperatures since there is a T term to present temperature effects.

In addition to correlative analyses using the above mentioned models, the models also were trained using a single point solubility data in each mono-solvent and then the trained were used to predict the rest of data points. The main advantage of this numerical analysis is that it could reduce the number of experiments which is an important issue in high-throughput screening studies.

3. Results and discussion

3.1. Satranidazole solubility correlation

The obtained correlative model for representing the solubility of SAT in the mono-solvents at various temperatures is:

(7) $\begin{array}{rl}& ln{x}_T=\left(-72.082-2.887\mathit{c}-7.570\mathit{s}+2.764\mathit{a}-0.683{\delta }_D+124.845\mathit{SP}\right)\\ & +\left(\frac{\begin{array}{c}21452.869-792.566e+1887.508s-1646.957a-229.234{\delta }_P+25.576{\delta }_H\\ -33285.7\mathit{SP}+5738.270\mathit{SdP}-2442.658\mathit{SA}-4640.382\mathit{SB}\end{array}}{\mathit{T}}\right)\\ & \end{array}$(7)

which correlated the solubility data of SAT with the MPD of 4.1 ± 2.9% (N = 60). The smallest MPD was observed for water (1.98%) and the largest one was obtained for 2-propanol (7.13%). Details of the MPD values for this equation and other equations are listed in Table 3. The overall MPDs for polynomial empirical (0.43%) < Apelblat (0.86%) < Buchowski-Ksiazczak (1.45%) < van’t Hoff (1.54%) < Jouyban (4.10%) < Equation 3(3) $-ln{x}_T=-ln{x}_{\hspace{0.17em}}^i+ln\left[\frac{V_2{\phi }_1^2{\left({\delta }_1-{\delta }_2\right)}^2}{\mathit{RT}}\right]+\mathit{F}$(3) (10.46%) < Equation 6(6) $ln{x}_{298.15}=c_0+c_1{\pi }^{\ast }+c_2\mathit{\alpha }+c_3\mathit{\beta }+c_4\left(\frac{V_2{\delta }_2^2}{100\mathit{RT}}\right)$(6) (only for T = 298.2 K) (33.33%) and Equation 7(7) $\begin{array}{rl}& ln{x}_T=\left(-72.082-2.887\mathit{c}-7.570\mathit{s}+2.764\mathit{a}-0.683{\delta }_D+124.845\mathit{SP}\right)\\ & +\left(\frac{\begin{array}{c}21452.869-792.566e+1887.508s-1646.957a-229.234{\delta }_P+25.576{\delta }_H\\ -33285.7\mathit{SP}+5738.270\mathit{SdP}-2442.658\mathit{SA}-4640.382\mathit{SB}\end{array}}{\mathit{T}}\right)\\ & \end{array}$(7) (for all temperatures) (41.21%). It should be noted that the van’t Hoff, Apelblat, Buchowski-Ksiazczak and the polynomial empirical models correlate the solubility of SAT in a given mono-solvent at various temperatures, and Equation 1(1) $ln{x}_T=\left({\alpha }_0+\sum _{\mathit{i}=1}^5{\alpha }_{\mathit{i},\mathit{AP}}\mathit{A}{P}_i+\sum _{\mathit{i}=1}^3{\alpha }_{\mathit{i},\mathit{HP}}\mathit{H}{P}_i+\sum _{\mathit{i}=1}^4{\alpha }_{\mathit{i},\mathit{CP}}\mathit{C}{P}_i\right)+\left(\frac{{\beta }_0+\sum _{\mathit{i}=1}^5{\beta }_{\mathit{i},\mathit{AP}}\mathit{A}{P}_i+\sum _{\mathit{i}=1}^3{\beta }_{\mathit{i},\mathit{HP}}\mathit{H}{P}_i+\sum _{\mathit{i}=1}^4{\beta }_{\mathit{i},\mathit{CP}}\mathit{C}{P}_i}{\mathit{T}}\right)$(1) , Equation 3(3) $-ln{x}_T=-ln{x}_{\hspace{0.17em}}^i+ln\left[\frac{V_2{\phi }_1^2{\left({\delta }_1-{\delta }_2\right)}^2}{\mathit{RT}}\right]+\mathit{F}$(3) and Equation 7(7) $\begin{array}{rl}& ln{x}_T=\left(-72.082-2.887\mathit{c}-7.570\mathit{s}+2.764\mathit{a}-0.683{\delta }_D+124.845\mathit{SP}\right)\\ & +\left(\frac{\begin{array}{c}21452.869-792.566e+1887.508s-1646.957a-229.234{\delta }_P+25.576{\delta }_H\\ -33285.7\mathit{SP}+5738.270\mathit{SdP}-2442.658\mathit{SA}-4640.382\mathit{SB}\end{array}}{\mathit{T}}\right)\\ & \end{array}$(7) correlate the solubility of SAT in all mono-solvents at various temperatures. Therefore, it is logical to compare the accuracy of these two sets of models within their sub-groups. Concerning this point, the Apelblat was the most accurate model from subgroup I and Equation 1(1) $ln{x}_T=\left({\alpha }_0+\sum _{\mathit{i}=1}^5{\alpha }_{\mathit{i},\mathit{AP}}\mathit{A}{P}_i+\sum _{\mathit{i}=1}^3{\alpha }_{\mathit{i},\mathit{HP}}\mathit{H}{P}_i+\sum _{\mathit{i}=1}^4{\alpha }_{\mathit{i},\mathit{CP}}\mathit{C}{P}_i\right)+\left(\frac{{\beta }_0+\sum _{\mathit{i}=1}^5{\beta }_{\mathit{i},\mathit{AP}}\mathit{A}{P}_i+\sum _{\mathit{i}=1}^3{\beta }_{\mathit{i},\mathit{HP}}\mathit{H}{P}_i+\sum _{\mathit{i}=1}^4{\beta }_{\mathit{i},\mathit{CP}}\mathit{C}{P}_i}{\mathit{T}}\right)$(1) was the best model from subgroup II. However these MPDs could be considered within an acceptable error range when compared with the relative standard deviation of the repeated solubility measurements which is usually < 10%.

Table 3. The MPD values for correlation of the solubility of SAT in different mono-solvents at various temperatures using various models.

Solvent	van’t Hoff^a	Apelblat^a	Buchowski-Ksiazczak^a	Polynomial empirical^a	Equation 1(1) $ln{x}_T=\left({\alpha }_0+\sum _{\mathit{i}=1}^5{\alpha }_{\mathit{i},\mathit{AP}}\mathit{A}{P}_i+\sum _{\mathit{i}=1}^3{\alpha }_{\mathit{i},\mathit{HP}}\mathit{H}{P}_i+\sum _{\mathit{i}=1}^4{\alpha }_{\mathit{i},\mathit{CP}}\mathit{C}{P}_i\right)+\left(\frac{{\beta }_0+\sum _{\mathit{i}=1}^5{\beta }_{\mathit{i},\mathit{AP}}\mathit{A}{P}_i+\sum _{\mathit{i}=1}^3{\beta }_{\mathit{i},\mathit{HP}}\mathit{H}{P}_i+\sum _{\mathit{i}=1}^4{\beta }_{\mathit{i},\mathit{CP}}\mathit{C}{P}_i}{\mathit{T}}\right)$(1)	Equation 3^b(3) $-ln{x}_T=-ln{x}_{\hspace{0.17em}}^i+ln\left[\frac{V_2{\phi }_1^2{\left({\delta }_1-{\delta }_2\right)}^2}{\mathit{RT}}\right]+\mathit{F}$(3)	Equation 6^c	Equation 7^d
1,4-Dioxane	1.37	0.95	1.40	0.90	4.17	2.00	9.10	19.33
DMA	1.09	0.61	0.85	0.33	3.60	5.07	69.84	87.61
DMF	1.81	0.96	1.50	0.32	2.74	5.19	12.76	19.43
DMSO	1.45	0.29	1.29	0.31	4.62	3.89	18.69	37.86
EG	1.35	1.45	1.29	0.37	3.53	29.68	87.72	82.01
EtOH	1.20	0.73	1.22	0.80	2.54	1.47	3.36	14.86
2-PrOH	1.89	0.75	1.81	0.82	7.13	3.53	45.87	49.94
MeOH	1.80	0.48	1.69	0.10	6.12	7.71	39.14	36.58
NMP	1.93	1.75	1.92	0.64	5.98	29.11	54.90	55.72
PG	1.72	1.86	1.62	0.38	3.37	28.59	30.29	42.04
1-PrOH	0.86	0.27	0.80	<0.005	3.46	1.76	26.21	30.89
Water	1.98	0.24	1.98	0.14	1.98	7.55	2.12	18.25
Overall:	1.54	0.86	1.45	0.43	4.10	10.46	33.33	41.21

^aMPD data taken from a previous work [5].

^bxⁱ was calculated using Equation 4(4) $-ln{x}_{\hspace{0.17em}}^i=\frac{0.02303{\left(T_m-\mathit{T}\right)}^2}{\mathit{T}ln\left(\frac{T_m}{\mathit{T}}\right)}$(4)

^cOnly for T = 298.2 K.

^dFor all temperatures.

Table 4 listed the MPD values for various models trained using a single point experimental solubility datum. The proposed model (Equation 1(1) $ln{x}_T=\left({\alpha }_0+\sum _{\mathit{i}=1}^5{\alpha }_{\mathit{i},\mathit{AP}}\mathit{A}{P}_i+\sum _{\mathit{i}=1}^3{\alpha }_{\mathit{i},\mathit{HP}}\mathit{H}{P}_i+\sum _{\mathit{i}=1}^4{\alpha }_{\mathit{i},\mathit{CP}}\mathit{C}{P}_i\right)+\left(\frac{{\beta }_0+\sum _{\mathit{i}=1}^5{\beta }_{\mathit{i},\mathit{AP}}\mathit{A}{P}_i+\sum _{\mathit{i}=1}^3{\beta }_{\mathit{i},\mathit{HP}}\mathit{H}{P}_i+\sum _{\mathit{i}=1}^4{\beta }_{\mathit{i},\mathit{CP}}\mathit{C}{P}_i}{\mathit{T}}\right)$(1) ) provided the best predictions MPD (5.91%) for SAT solubility data in DMA and the worst MPD (40.91%) for water and the overall MPD was 19.33%. For Equation 3(3) $-ln{x}_T=-ln{x}_{\hspace{0.17em}}^i+ln\left[\frac{V_2{\phi }_1^2{\left({\delta }_1-{\delta }_2\right)}^2}{\mathit{RT}}\right]+\mathit{F}$(3) , there were two possibilities; 1) to use the experimentally derived xⁱ values taken from a previous paper [5], and 2) to calculate the xⁱ values employing Equation 4(4) $-ln{x}_{\hspace{0.17em}}^i=\frac{0.02303{\left(T_m-\mathit{T}\right)}^2}{\mathit{T}ln\left(\frac{T_m}{\mathit{T}}\right)}$(4) . The most accurate MPDs using the first and the second procedures were obtained for MeOH (1.76%) and EtOH (1.72%), the less accurate MPDs were for NMP (42.04%) and EG (37.00%) and the overall MPDs of 15.46 and 13.00%, respectively. Although there is no significant difference among overall MPDs of Equation 3(3) $-ln{x}_T=-ln{x}_{\hspace{0.17em}}^i+ln\left[\frac{V_2{\phi }_1^2{\left({\delta }_1-{\delta }_2\right)}^2}{\mathit{RT}}\right]+\mathit{F}$(3) using two procedures, the second procedure is preferred since it does not require any more experimental effort and knowledge of SAT’s melting point is enough. The KAT-LSER provided the minimum, maximum and the overall MPDs of 8.09% (for DMSO), 60.90% (for DMA) and 37.92%. The most accurate overall MPD value was obtained for Equation 3(3) $-ln{x}_T=-ln{x}_{\hspace{0.17em}}^i+ln\left[\frac{V_2{\phi }_1^2{\left({\delta }_1-{\delta }_2\right)}^2}{\mathit{RT}}\right]+\mathit{F}$(3) (procedure II) and the worst one for KAT-LSER model. Equation 3(3) $-ln{x}_T=-ln{x}_{\hspace{0.17em}}^i+ln\left[\frac{V_2{\phi }_1^2{\left({\delta }_1-{\delta }_2\right)}^2}{\mathit{RT}}\right]+\mathit{F}$(3) uses an empirical non-ideality parameter of F, the KAT-LSER is used to provide physico-chemical justifications for the solute-solvent interactions and usually was used to correlate the data at 298.2 K. Equation 1(1) $ln{x}_T=\left({\alpha }_0+\sum _{\mathit{i}=1}^5{\alpha }_{\mathit{i},\mathit{AP}}\mathit{A}{P}_i+\sum _{\mathit{i}=1}^3{\alpha }_{\mathit{i},\mathit{HP}}\mathit{H}{P}_i+\sum _{\mathit{i}=1}^4{\alpha }_{\mathit{i},\mathit{CP}}\mathit{C}{P}_i\right)+\left(\frac{{\beta }_0+\sum _{\mathit{i}=1}^5{\beta }_{\mathit{i},\mathit{AP}}\mathit{A}{P}_i+\sum _{\mathit{i}=1}^3{\beta }_{\mathit{i},\mathit{HP}}\mathit{H}{P}_i+\sum _{\mathit{i}=1}^4{\beta }_{\mathit{i},\mathit{CP}}\mathit{C}{P}_i}{\mathit{T}}\right)$(1) could be considered as a model with acceptable accuracy and providing some information on the enthalpic and entropic changes in the solution.

Table 4. The MPD values for prediction of the solubility of SAT in different mono-solvents at various temperatures using various models trained using a single solubility datum in each mono-solvent.

Solvent	Equation 1(1) $ln{x}_T=\left({\alpha }_0+\sum _{\mathit{i}=1}^5{\alpha }_{\mathit{i},\mathit{AP}}\mathit{A}{P}_i+\sum _{\mathit{i}=1}^3{\alpha }_{\mathit{i},\mathit{HP}}\mathit{H}{P}_i+\sum _{\mathit{i}=1}^4{\alpha }_{\mathit{i},\mathit{CP}}\mathit{C}{P}_i\right)+\left(\frac{{\beta }_0+\sum _{\mathit{i}=1}^5{\beta }_{\mathit{i},\mathit{AP}}\mathit{A}{P}_i+\sum _{\mathit{i}=1}^3{\beta }_{\mathit{i},\mathit{HP}}\mathit{H}{P}_i+\sum _{\mathit{i}=1}^4{\beta }_{\mathit{i},\mathit{CP}}\mathit{C}{P}_i}{\mathit{T}}\right)$(1)	Equation 3^a(3) $-ln{x}_T=-ln{x}_{\hspace{0.17em}}^i+ln\left[\frac{V_2{\phi }_1^2{\left({\delta }_1-{\delta }_2\right)}^2}{\mathit{RT}}\right]+\mathit{F}$(3)	Equation 3^b(3) $-ln{x}_T=-ln{x}_{\hspace{0.17em}}^i+ln\left[\frac{V_2{\phi }_1^2{\left({\delta }_1-{\delta }_2\right)}^2}{\mathit{RT}}\right]+\mathit{F}$(3)	Equation 6(6) $ln{x}_{298.15}=c_0+c_1{\pi }^{\ast }+c_2\mathit{\alpha }+c_3\mathit{\beta }+c_4\left(\frac{V_2{\delta }_2^2}{100\mathit{RT}}\right)$(6)
1,4-Dioxane	12.46	7.71	2.48	23.37
DMA	5.91	12.53	6.25	60.90
DMF	11.14	11.14	6.37	18.73
DMSO	29.19	5.69	4.75	8.09
EG	13.14	41.77	37.00	56.89
EtOH	14.99	6.80	1.72	18.45
2-PrOH	22.86	3.64	4.32	59.91
MeOH	27.97	1.76	9.60	36.01
NMP	22.84	42.04	36.34	69.53
PG	15.65	40.59	35.70	47.90
1-PrOH	14.89	8.15	2.14	34.00
Water	40.91	3.65	9.36	21.31
Overall:	19.33	15.46	13.00	37.92

^axⁱ derived from experimental solubility data was used [5].

^bxⁱ was calculated using Equation 4(4) $-ln{x}_{\hspace{0.17em}}^i=\frac{0.02303{\left(T_m-\mathit{T}\right)}^2}{\mathit{T}ln\left(\frac{T_m}{\mathit{T}}\right)}$(4) .

3.2. Apparent thermodynamic quantities of dissolution

All the apparent thermodynamic quantities of dissolution of SAT in all mono-solvents were estimated at the harmonic mean temperature (T_hm), which in turn was calculated by using Equation 17(17) ${\mathrm{\Delta }}_{\mathrm{fus}}{S}^{{\mathit{T}}_{\mathrm{hm}}}={\mathrm{\Delta }}_{\mathrm{fus}}{S}^{{\mathit{T}}_{\mathrm{fus}}}-\mathrm{\Delta }{C}_{p}ln\left(\frac{{\mathit{T}}_{\mathrm{fus}}}{T_{\mathrm{hm}}}\right)$(17) [13]:

(8) $T_{\mathrm{hm}}=\frac{n}{\sum _{\mathit{i}=1}^n\left(\frac{1}{T}\right)}$(8)

where, n = 5 is the number of temperatures studied. Thus, from T = (293.2 to 313.2) K, the obtained T_hm value is 303.0 K. In this way, the apparent standard enthalpic changes for SAT dissolution processes (∆_solnH°) were obtained by means of the modified van’t Hoff equation, as [14,15]:

(9) ${\left(\frac{\mathrm{\partial }ln{x}_2}{\mathrm{\partial }\left(1/\mathit{T}-1/T_{\mathrm{hm}}\right)}\right)}_{\mathit{P}}=-\frac{{\mathrm{\Delta }}_{\mathrm{soln}}{H}^{\circ }}{\mathit{R}}$(9)

The apparent standard Gibbs energy changes for the SAT dissolution processes (∆_solnG°) were calculated by means of:

(10) ${\mathrm{\Delta }}_{\mathrm{soln}}{G}^{\circ }=-\mathit{R}\cdot T_{\mathrm{hm}}\cdot \mathrm{intercept}$(10)

Here, the intercepts used are those obtained in the respective linear regressions of ln x₂ vs. (1/T − 1/T_hm). Linear regressions with determination coefficients higher than 0.99 were obtained in all cases [16–18]. Standard apparent entropic changes for SAT dissolution processes (∆_solnS°) were obtained from the respective ∆_solnH° and ∆_solnG° values by using Equation 17(17) ${\mathrm{\Delta }}_{\mathrm{fus}}{S}^{{\mathit{T}}_{\mathrm{hm}}}={\mathrm{\Delta }}_{\mathrm{fus}}{S}^{{\mathit{T}}_{\mathrm{fus}}}-\mathrm{\Delta }{C}_{p}ln\left(\frac{{\mathit{T}}_{\mathrm{fus}}}{T_{\mathrm{hm}}}\right)$(17) [15]:

(11) ${\mathrm{\Delta }}_{\mathrm{soln}}{S}_{\hspace{0.17em}}^{\mathrm{o}}=\frac{\left({\mathrm{\Delta }}_{\mathrm{soln}}{H}^{\circ }-{\mathrm{\Delta }}_{\mathrm{soln}}{G}^{\circ }\right)}{T_{\mathrm{hm}}}$(11)

Table 5 summarises the standard apparent molar thermodynamic functions for dissolution processes of SAT in all mono-solvents at T_hm = 303.0 K.

Table 5. Apparent thermodynamic parameters for dissolution behaviour of satranidazole in 17 mono-solvents and water at T_hm = 303.0 K.

Solvent	ΔsolnG° (kJ·mol^−1)	ΔsolnH° (kJ·mol^−1)	ΔsolnS° (J·K^−1·mol^−1)	TΔsolnS° (kJ·mol^−1)	ζH	ζTS
Methanol	18.54	22.85	14.22	4.31	0.841	0.159
Ethanol	18.78	31.13	40.75	12.35	0.716	0.284
1-Propanol	18.95	32.54	44.87	13.60	0.705	0.295
2-Propanol	19.43	27.99	28.27	8.57	0.766	0.234
Formamide	6.56	32.40	85.27	25.84	0.556	0.444
1,4-Dioxane	11.01	31.85	68.78	20.84	0.604	0.396
DMF	6.84	34.98	92.87	28.14	0.554	0.446
DMA	7.08	36.91	98.44	29.83	0.553	0.447
DMSO	6.29	26.41	66.41	20.12	0.568	0.432
NMP	4.40	59.06	180.37	54.66	0.519	0.481
EG	15.34	69.85	179.87	54.51	0.562	0.438
PG	14.28	68.33	178.36	54.05	0.558	0.442
1,4-Butanediol	15.99	46.12	99.42	30.13	0.605	0.395
Glycerin	17.45	20.91	11.41	3.46	0.858	0.142
PEG-200	10.57	45.68	115.87	35.11	0.565	0.435
PEG-400	9.36	50.54	135.89	41.18	0.551	0.449
PEG-600	8.83	51.66	141.34	42.83	0.547	0.453
Water	31.49	21.64	−32.53	−9.86	0.687	0.313

Apparent standard Gibbs energies, enthalpies and entropies relative to SAT dissolution processes are positive in all organic solvents as shown in Table 5, which implies endothermic and entropy-driven dissolution processes. Otherwise, in neat water apparent Gibbs energy and enthalpy of dissolution are positive but dissolution entropy is negative, probably owing hydrophobic hydration around the non-polar moieties of SAT, which involves ‘icebergs’ formation reducing entropy. Additionally, the relative contributions by enthalpy (ζ_H) and entropy (ζ_TS) towards SAT dissolution processes were calculated by means of the following equations [19]:

(12) ${\zeta }_H=\frac{\left|{\mathrm{\Delta }}_{\mathrm{soln}}{H}^{\circ }\right|}{\left|{\mathrm{\Delta }}_{\mathrm{soln}}{H}^{\circ }\right|+\left|\mathit{T}{\mathrm{\Delta }}_{\mathrm{soln}}{S}^{\circ }\right|}$(12)

(13) ${\zeta }_{\mathit{TS}}=\frac{\left|\mathit{T}{\mathrm{\Delta }}_{\mathrm{soln}}{S}^{\circ }\right|}{\left|{\mathrm{\Delta }}_{\mathrm{soln}}{H}^{\circ }\right|+\left|\mathit{T}{\mathrm{\Delta }}_{\mathrm{soln}}{S}^{\circ }\right|}$(13)

As shown in Table 5 the main contributor to the positive standard apparent molar Gibbs energies of SAT dissolution processes was the positive enthalpy, which demonstrates the energetic predominance.

3.3. Apparent thermodynamic quantities of mixing

Global dissolution processes of SAT in all the neat solvents may also be represented by means of the following hypothetical process:

Solute_(Solid) at T → Solute_(Solid) at T_fus → Solute_(Liquid) at T_fus → Solute_(Liquid) at T → Solute_(Solution) at T

Here the hypothetical stages are as follows: i) the heating and melting of SAT at T_fus = 461.83 K [20], ii) the cooling of SAT to the considered temperature (T_hm = 303.0 K), and iii) the subsequent mixing of both the hypothetical SAT super-cooled liquid and the solvent system under consideration at T_hm = 303.0 K [21]. This allowed us the calculation of the individual thermodynamic contributions by fusion and mixing towards the overall SAT individual dissolution processes, by means of the following equations:

(14) ${\mathrm{\Delta }}_{\mathrm{soln}}{H}^{\circ }={\mathrm{\Delta }}_{\mathrm{fus}}{H}^{{\mathit{T}}_{\mathrm{hm}}}+{\mathrm{\Delta }}_{\mathrm{mix}}{H}^{\circ }$(14)

(15) ${\mathrm{\Delta }}_{\mathrm{soln}}{S}^{\circ }={\mathrm{\Delta }}_{\mathrm{fus}}{S}^{{\mathit{T}}_{\mathrm{hm}}}+{\mathrm{\Delta }}_{\mathrm{mix}}{S}^{\circ }$(15)

where ${\mathrm{\Delta }}_{\mathrm{fus}}{H}^{{\mathit{T}}_{\mathrm{hm}}}$and ${\mathrm{\Delta }}_{\mathrm{fus}}{S}^{{\mathit{T}}_{\mathrm{hm}}}$ indicate the thermodynamic quantities of SAT fusion and its cooling at T_hm = 307.8 K. In turn, these two functions were calculated by means of Equation 16(16) ${\mathrm{\Delta }}_{\mathrm{fus}}{H}^{{\mathit{T}}_{\mathrm{hm}}}={\mathrm{\Delta }}_{\mathrm{fus}}{H}^{{\mathit{T}}_{\mathrm{fus}}}-\mathrm{\Delta }{C}_p\left(T_{\mathrm{fus}}-T_{\mathrm{hm}}\right)$(16) and 17(17) ${\mathrm{\Delta }}_{\mathrm{fus}}{S}^{{\mathit{T}}_{\mathrm{hm}}}={\mathrm{\Delta }}_{\mathrm{fus}}{S}^{{\mathit{T}}_{\mathrm{fus}}}-\mathrm{\Delta }{C}_{p}ln\left(\frac{{\mathit{T}}_{\mathrm{fus}}}{T_{\mathrm{hm}}}\right)$(17) , respectively [22]. ΔC_p is approached as the entropy of fusion by means of the quotient of fusion enthalpy and absolute temperature of fusion (ΔH_f/T_f), with reported values, i.e. 32.49 kJ·mol⁻¹ and 461.83 K [20], obtaining the value 70.34 J·mol⁻¹·K⁻¹.

(16) ${\mathrm{\Delta }}_{\mathrm{fus}}{H}^{{\mathit{T}}_{\mathrm{hm}}}={\mathrm{\Delta }}_{\mathrm{fus}}{H}^{{\mathit{T}}_{\mathrm{fus}}}-\mathrm{\Delta }{C}_p\left(T_{\mathrm{fus}}-T_{\mathrm{hm}}\right)$(16)

(17) ${\mathrm{\Delta }}_{\mathrm{fus}}{S}^{{\mathit{T}}_{\mathrm{hm}}}={\mathrm{\Delta }}_{\mathrm{fus}}{S}^{{\mathit{T}}_{\mathrm{fus}}}-\mathrm{\Delta }{C}_{p}ln\left(\frac{{\mathit{T}}_{\mathrm{fus}}}{T_{\mathrm{hm}}}\right)$(17)

Table 6 summarises the apparent thermodynamic quantities of mixing of the hypothetical SAT as super-cooled liquid with all the neat solvents, at T_hm = 303.0 K. Apparent Gibbs energies of mixing are positive or negative depending on the solvent. As observed, the contributions by the mixing thermodynamic quantities, Δ_mixH° and Δ_mixS°, to the overall dissolution processes of SAT, are variable in sign and magnitude, depending on the solvent. Thus, Δ_mixH° are positive, except in glycerine, probably owing the weaker adhesive molecular interactions between the molecules of SAT and the molecules of solvents (namely, solute-solvent interactions) as compared to those cohesive between the molecules of solvent (namely, solvent-solvent interactions) or between the drug molecules (namely, solute-solute interactions) considered by separate. Thus, the newly formed bonds between drug and solvent molecules are not powerful enough to compensate the energy needed for breaking the original association bonds in the solvents for cavity creation amend of solute molecules separation from its original solid state. In other words, high values of the enthalpy suggest that more energy is required to overcome the cohesive force of the solute and the solvent in the dissolution process, which also indicates that the solubility is strongly dependent on temperature. The positive signs in mixing entropy values observed in some organic solvents suggests a less ordered structure, whereas negative values of entropy in some alcohols and water indicates increased order due to the solvation process in solution. This may be due to different molecular structures and space conformations between solute and solvent molecules. As SAT molecule contain groups of different nature like -N-, >C=O, -NO₂, -SO₂-, etc., the mixing of this drug in various solvents may cause various interactions such as dipole-dipole, H-bonding, hydrophobic interactions, and stereospecific effects. Due to different type and magnitude of interactions, amend the entropy increasing by the ideal process of mixing, drug (SAT) may disrupt the alignment of solvent molecules which increases entropy (like in 1-propanol, formamide, 1,4-dioxane, DMF, DMA, DMSO, NMP, EG, PG, 1,4-butanediol, PEG-200, PEG-400 and PEG-600) or form a more ordered structure (as in methanol, 2-propanol, glycerine and water) which decreases entropy.

Table 6. Apparent thermodynamic parameters for mixing behaviour of satranidazole in 17 mono-solvents and water at T_hm = 303.0 K.

Solvent	ΔmixG° (kJ·mol^−1)	ΔmixH° (kJ·mol^−1)	ΔmixS° (J·K^−1·mol^−1)	TΔmixS° (kJ·mol^−1)	ζH	ζTS
Methanol	9.57	1.54	−26.48	−8.03	0.161	0.839
Ethanol	9.80	9.82	0.05	0.01	0.999	0.001
1-Propanol	9.97	11.23	4.17	1.26	0.899	0.101
2-Propanol	10.45	6.69	−12.44	−3.77	0.639	0.361
Formamide	−2.41	11.09	44.57	13.51	0.451	0.549
1,4-Dioxane	2.03	10.54	28.08	8.51	0.553	0.447
DMF	−2.14	13.67	52.17	15.81	0.464	0.536
DMA	−1.90	15.60	57.74	17.50	0.471	0.529
DMSO	−2.69	5.10	25.71	7.79	0.396	0.604
NMP	−4.57	37.75	139.67	42.32	0.471	0.529
EG	6.37	48.54	139.17	42.17	0.535	0.465
PG	5.31	47.02	137.66	41.71	0.530	0.470
1,4-Butanediol	7.01	24.81	58.71	17.79	0.582	0.418
Glycerin	8.47	−0.40	−29.29	−8.88	0.044	0.956
PEG-200	1.60	24.37	75.16	22.78	0.517	0.483
PEG-400	0.39	29.23	95.19	28.85	0.503	0.497
PEG-600	−0.15	30.35	100.63	30.50	0.499	0.501
Water	22.52	0.33	−73.23	−22.19	0.014	0.986

4. Conclusion

The solubilities of SAT in 12 different mono-solvents were correlated/predicted using a new multiple linear regression model and the accuracies of the correlations/predictions were compared with those of similar models from the literature. Overall the proposed model provided reasonable accurate results and could be used in the pharmaceutical industry where these sort of simulated data are highly in demand. Moreover, all apparent thermodynamic quantities of dissolution in 18 mono-solvents were positive indicating endothermal and entropy-driven processes. In turn, apparent Gibbs energy and enthalpy in neat water were both positive but entropy was negative, which could be interpreted in terms of hydrophobic hydration around the non-polar moieties of this drug. Further, the main contributor to standard Gibbs free energy of dissolution process is enthalpy for the studied solvents. Otherwise, apparent thermodynamic quantities of mixing in these mono-solvents were variable in sign depending on the specific solvent.

Acknowledgments

This work was supported by the Pharmaceutical Analysis Research Center, Tabriz University of Medical Sciences, Tabriz, Iran under grant number of 67898.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by the Tabriz University of Medical Sciences [67898].