Introduction

Mesalazineor 5-aminosalicylic acid (5-ASA), with the chemical formula C7H7NO3 and molecular weight 153.137 (g/mol) is used to treat inflammatory bowel disease. Drug particles can be made smaller to improve their biological absorption. Using a mill, spray dryer, and freeze dryer are some outdated techniques for managing particle size reduction. Owing to elevated temperature and mechanical strain in these techniques, there exists a potential for altering the material’s composition. The traditional techniques for regulating and reducing the size of medication particles were replaced by new ones such as using supercritical fluid to micronize or nano sized drugs.

Depending on how soluble it is in the supercritical fluid, there are various ways to micronize a drug. RESS (rapid expansion of supercritical solution) is applied if the medication dissolves readily in the supercritical fluid1,2,3,4. Techniques based on the anti-solvent properties of the supercritical fluids are used when the drug exhibits poor solubility. The “gas antisolvent (GAS)”5,6,7,8,9, “supercritical antisolvent (SAS)”10,11,12, “solution-enhanced dispersion by supercritical fluid (SEDS)”13,14, and “aerosol solvent extraction system (ASES)”15 are considered among the techniques based on the antisolvent properties of the supercritical fluids. The distinctive characteristics of carbon dioxide (CO2) have resulted in its extensive application in the supercritical state. CO2 is non-toxic, non-flammable, and has a low critical temperature and moderate critical pressure16,17.

The solubility of many drugs was measured in the laboratory using supercritical carbon dioxide (scCO2)16,18,19,20,21,22,23,24. Table 1 illustrates the solubility of some pharmaceuticals in scCO₂ without cosolvent, sort from 2021 to 2024. Nevertheless, the use of scCO2 has some limitations. Due to its non-polarity, carbon dioxide exhibits limited interaction with various solutes and solvents. The resolution of this issue can be achieved by incorporating a cosolvent25,26. Methanol has been employed as a cosolvent in conjunction with scCO2 to check the solubility of ketoconazole, sertraline hydrochloride, letrozole, phenylthiophene acid, capecitabine, clozapine, among others27,28,29,30,31. Other cosolvents such as ethanol, dimethyl sulfoxide (DMSO), and acetone have been used to improve the solubility of nystatin, chlorothiazide, eflucimibe and acetazolamide in scCO232,33,34,35,36,37.

Table 1 Some research on the solubility of various pharmaceutical compound in scCO2.
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In this framework, the solubility of mesalazine in scCO2 was determined at different temperatures and pressure values. The effect of adding DMSO at 2% on mesalazine solubility in scCO2 was investigated. The experimental solubility data of mesalazine in the binary and ternary systems, was correlated with the utilization of a new association model. Further, multiple density models were considered to model the solubility of mesalazine in scCO2, including Méndez-Santiago and Teja (MST)134,135, Chrastil136, Bartle et al.137, Kumar and Johnston (KJ)138, Jouyban et al.139,140, Bian et al.141, González et al.142, Garlapati–Madras143, Soltani-Mazloumi144, and Sodeifian-Sajadian28. The model’s parameters were acquired, and the efficacy of the model’s predictions was assessed using the average absolute relative deviation (AARD (%)).

Methods

Materials

In this project, mesalazine (CAS (Chemical Abstracts Service) number 89-57-6) with a purity of 99% was provided by Julian Kimia Sanat company (Tabriz, Iran). The Merck Chemical Company (Germany) supplied the DMSO. CO2 was purchased from the Iranian Aboghadareh Company. Formula, structure, molecular weight, CAS Number, melting and boiling temperature, and λmax were listed in Table 2. Table 3 displays the purity levels for the original and final mass fractions, along with the origins and techniques employed for analysis.

Table 2 The structure and the physical–chemical properties of mesalazine.
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Table 3 The purities, sources, and analysis methods of the used materials.
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Solubility measurement

The setup (Fig. 1) considered for the determination of mesalazine solubility in scCO2 includes the following equipment: spectrophotometer, CO2 feeding tank, air-driven compressor (Finac, China), CO2-aimed high-pressure pump, specifically an air-driven liquid pump of type M64 manufactured by Shine east, a refrigeration unit, a magnetic stirrer working at 200 rpm, filter, flow control valves (needle, back-pressure, and metering valves), equilibrium high-pressure cell and oven. The potential contamination of the CO2 introduced from the tank was eliminated by its passage through a molecular filter. The CO2 flow was liquefied by its cooling into a refrigerator working at − 15\(^\circ \text{C},\text{ previous}\) entering into the high-pressure pump. A magnetic stirrer homogenized the binary (mesalazine and scCO2) and ternary mesalazine (scCO2, and 2.0 mol% DMSO) systems.

Fig. 1
figure 1

Schematic diagram of experimental apparatus.

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In each test, 2000 \(\text{mg}\) of mesalazine was added to the cell (300 mL). A magnetic stirrer was applied to homogenize the solution in scCO2. In the tests that used DMSO as cosolvent, a certain amount of DMSO (2% mol) and 2000 mg of mesalazine were put at the bottom of the equilibrium cell. The temperature was adjusted using an oven. Then, the system was compressed to the working pressure. The CO2 was compressed to the proper pressure before being supplied to the cell. The preliminary test suggested that the static time was 170 min. After reaching the equilibrium condition (170 min), the injection loop was filled with saturated scCO2 (300 µL ± 0.3% µL) using a three-valve device with two positions (VI–VIII). After changing the injection valve, the loop can be placed within the collecting vial to hold onto a certain volume of DMSO (solvent). In four plans, this method is summed up in Fig. 1. A static time should be traced by the loop being filled. So, the valve (VI) is open. VI is closed after the loop is filled. The VII is then opened. After the loop is placed in the gather vial, VIII is opened, and one milliliter of DMSO is used to wash both the loop and all of the lines. The procedure was repeated three times for each data point. The solution was collected in the final volume of 5 mL (± 0.2%). UV spectrophotometry (Jenway UV–V fitted with a quartz cell) measured the absorbance at a maximum wavelength (λmax). From the solute concentration, the solubility was determined using the alignment bend and the UV absorbance. The approach’s applicability was validated by the calibration curve (Abs = 0.021 C+ 0.009) and the appropriate linear connection of the regression results over a broad range of concentrations. The λmax of mesalazine was 363 nm.

The solubility and equilibrium mole fraction \({\text{S}}\left( {\frac{{\text{g}}}{{\text{L}}}} \right)\), and y2 of mesalazine in scCO2 were determined at as follows18,19,21,145:

$$y_{2} = \frac{{n_{solute} }}{{n_{solute} + n_{{CO_{2} }} }}$$
(1)
$${n}_{solute}=\frac{{C}_{s}\left(\frac{g}{L}\right)\times {V}_{s}\left(L\right)}{{M}_{s}\left(\frac{g}{mol}\right)}$$
(2)
$${n}_{{CO}_{2}}=\frac{{V}_{l}\left(L\right)\times \rho \left(\frac{g}{L}\right)}{{M}_{{CO}_{2}}\left(\frac{g}{mol}\right)}$$
(3)

In Eq. (2) Cs is the mesalazine concentration \(\left(\frac{\text{g}}{\text{L}}\right)\) in the collecting vial. nCO2 and nsolute also explain the CO2 and solute mole in the loop, respectively. Vs \(\left(\text{L}\right)\) and Vl \(\left(\text{L}\right)\) denoted the collecting vial and loop volumes, respectively. Concentration of mesalazine in the scCO2 was defined as18,19,21:

$$S\left(\frac{g}{L}\right)=\frac{{C}_{s}\left(\frac{g}{L}\right)\times {V}_{s }\left(L\right)}{{V}_{l}\left(L\right)}$$
(4)

The concentration of mesalazine (S) also can be computed by Eq. (5):

$$S=\frac{\rho \times {M}_{S} \times {y}_{2}}{{ M}_{{CO}_{2}} \times \left(1-{y}_{2}\right)}$$
(5)

The following equation was obtained by replacing Eqs. (2) and (3) in Eq. (1):

$${y}_{2}= \frac{{C}_{s}\left(\frac{g}{L}\right)\times {V}_{s}\left(L\right)\times {M}_{{CO}_{2}}\left(\frac{g}{mol}\right)}{{C}_{s}\left(\frac{g}{L}\right)\times {V}_{s}\left(L\right)\times {M}_{{CO}_{2}}\left(\frac{g}{mol}\right)+ {V}_{l}\left(L\right)\times \rho \left(\frac{g}{L}\right)\times {M}_{s}\left(\frac{g}{mol}\right)}$$
(6)

Equation (7) represents the mesalazine mole fraction in the ternary system (adding DMSO):

$${\text{y}}_{2}^{\prime } = \frac{{n_{solute} }}{{n_{solute} + n_{{CO_{2} }} + n_{co - solvent} }}$$
(7)
$${n}_{co-solvent}= \frac{{m}_{co-solvent}\left(intheloop\right)}{{M}_{co-solvent}}$$
(8)
$${n}_{{CO}_{2}}= \frac{{m}_{{CO}_{2}}\left(intheloop\right)}{{M}_{{CO}_{2}}}$$
(9)
$${n}_{solute}=\frac{{C}_{s}\left(\frac{g}{L}\right)\times {V}_{s}\left(L\right)}{{M}_{s\left(solute\right)}\left(\frac{g}{mol}\right)}$$
(10)

Modeling

Association model without cosolvent

A detailed derivation of the following mathematical expression can be found in recent literature20. Equation (11) shows the final form of the solubility model:

$$y_{2} = \frac{{\left( {\frac{P}{{P^{ * } }}} \right)^{{\left( {\kappa - 1} \right)}} \exp \left( {N_{1} + {{N_{2} } \mathord{\left/ {\vphantom {{N_{2} } T}} \right. \kern-0pt} T} + N_{3} \rho + N_{4} \ln \left( T \right)} \right)}}{{1 + \kappa \left( {\frac{P}{{P^{ * } }}} \right)^{{\left( {\kappa - 1} \right)}} \exp \left( {N_{1} + {{N_{2} } \mathord{\left/ {\vphantom {{N_{2} } T}} \right. \kern-0pt} T} + N_{3} \rho + N_{4} \ln \left( T \right)} \right)}}$$
(11)

When a plot is made \(\ln ((y_{2} /(1 - \kappa y_{2} ))) - (\kappa - 1)\ln \left( {P/P^{ * } } \right) - N_{1} - N_{2} /T - N_{4} \ln \left( T \right)\) against density. The solubility data without a cosolvent exhibit a linear relationship, indicating that the novel association model is applicable to these data.

New association model with cosolvent system

A solvate complex \(AB_{\kappa } C_{\gamma }\) in equilibrium with the gaseous system is formed if a single molecule of solute (A) combines with molecules of solvent (B) and molecules of cosolvent (C). Table 3 displays the purity levels for the beginning and final mass fractions, as well as the sources and analysis methods used146,147.

$$A + \kappa \;B + \gamma \;C \Leftrightarrow AB_{\kappa } C_{\gamma }$$
(12)

Equation (13) expresses the equilibrium constant (\({K}_{f})\) by considering the fugacity of each individual component.

$${k}_{f=}\frac{{\left(\raisebox{1ex}{${\widehat{f}}_{A{B}_{k}{C}_{\gamma }}$}\!\left/ \!\raisebox{-1ex}{${f}_{A{B}_{k}{C}_{\gamma }}^{*}$}\right.\right)}_{Scp}}{{\left(\frac{{\widehat{f}}_{A}}{{f}_{A}^{*}}\right)}_{S}{\left({\left(\frac{{\widehat{f}}_{B}}{{f}_{B}^{*}}\right)}^{k}\right)}_{ScP}{\left(\frac{{\widehat{f}}_{C}}{{f}_{C}^{*}}\right)}^{\gamma }}$$
(13)

where subscript ScP stands for the supercritical phase, S stands for the solute phase and \(f^{*}\) denotes reference fugacity.

Following are the expressions for the fugacity of each phase148,149.

$$\hat{f}_{A} = y_{A} \hat{\varphi }_{A} P$$
(14)
$$\hat{f}_{B} = y_{B} \hat{\varphi }_{B} P$$
(15)
$$\hat{f}_{C} = y_{C} \hat{\varphi }_{C} P$$
(16)
$$\hat{f}_{{AB_{\kappa } C_{\gamma } }} = y_{{AB_{\kappa } C_{\gamma } }} \hat{\varphi }_{{AB_{\kappa } C_{\gamma } }} P$$
(17)
$$f_{{AB_{\kappa } C_{\gamma } }}^{*} = \varphi_{{AB_{\kappa } C_{\gamma } }}^{*} \;P^{*}$$
(18)
$$f_{A}^{*} = \varphi_{A}^{*} \;P^{*}$$
(19)
$$f_{B}^{*} = \varphi_{B}^{*} \;P^{*}$$
(20)
$$f_{C}^{*} = \varphi_{C}^{*} \;P^{*}$$
(21)

The main assumption is that the fluid-phase component does not dissolve in the solid, which means that the solid is completely pure. Solute A is present in a state of association in ScP.

$$y_{B} + y_{C} + y_{{AB_{\kappa } C_{\gamma } }} = 1$$
(22)

where \(y_{B} ,y_{C} ,y_{{AB_{\kappa } C_{\gamma } }}\) are the mole fraction of the solvents and the solvate complex, respectively.

The solute (A)at equilibrium exists in an associating state, then solubility in scCO2150.

$$y^{\prime}_{2} = \frac{{y_{{AB_{\kappa } C_{\gamma } }} }}{{1 + \kappa_{eff} \;y_{{AB_{\kappa } C_{\gamma } }} }}$$
(23)

The previous equation assumes that solute A is in its standard state, defined as a pure solute at the system’s pressure (P) and temperature (T).

$$\hat{f}_{A} = f_{A}$$
(24)

Fugacity of A (pure solute) is expressed as,

$$f_{A} = P_{A}^{sub} \exp \left( {\frac{{V_{A} (P - P_{A}^{sub} )}}{RT}} \right)$$
(25)

The sublimation pressure of the pure solid is denoted by \(P_{A}^{sub}\), while the molar volume at system conditions is denoted by \(V_{A}\).

Combining Eqs. (14) to (21) and Eq. (25) with Eq. (13) gives Eq. (26)

$$K_{f} = \frac{{\left( {\frac{{y_{{AB_{\kappa } C_{\lambda } }} \hat{\varphi }_{{AB_{\kappa } C_{\gamma } }} P}}{{\varphi_{{AB_{\kappa } C_{\gamma } }}^{ * } P^{ * } }}} \right)}}{{\left( {\frac{{P_{A}^{sub} \exp \left( {\frac{{V_{A} \left( {P - P_{A}^{sub} } \right)}}{RT}} \right)}}{{\varphi_{A}^{*} P^{*} }}} \right)\;\left( {\frac{{y_{B} \hat{\varphi }_{B} P}}{{\varphi_{B}^{*} P^{*} }}} \right)^{\kappa } \left( {\frac{{y_{c} \hat{\varphi }_{C} P}}{{\varphi_{C}^{*} P^{*} }}} \right)^{\gamma } }}$$
(26)

The fugacity coefficient of the solvate complex can be represented using Henry’s constant.

$$\hat{\varphi }_{{AB_{\kappa } C_{\gamma } }} = H_{2}^{eff}$$
(27)
$$\begin{aligned} \ln \left( {K_{f} } \right) = & \ln \left( {y_{{AB_{\kappa } }} } \right) + \ln \left( {H_{2}^{eff} } \right) + \ln \left( {{{\hat{\varphi }_{{AB_{\kappa } C_{\gamma } }} } \mathord{\left/ {\vphantom {{\hat{\varphi }_{{AB_{\kappa } C_{\gamma } }} } {\varphi_{{AB_{\kappa } C_{\gamma } }}^{ * } }}} \right. \kern-0pt} {\varphi_{{AB_{\kappa } C_{\gamma } }}^{ * } }}} \right) + \ln \left( {{P \mathord{\left/ {\vphantom {P {P^{ * } }}} \right. \kern-0pt} {P^{ * } }}} \right) + \ln \left( {\varphi_{A}^{ * } } \right) - \ln \left( {{{P_{A}^{sub} } \mathord{\left/ {\vphantom {{P_{A}^{sub} } {P^{ * } }}} \right. \kern-0pt} {P^{ * } }}} \right) - \frac{{V_{A} \left( {P - P_{A}^{sub} } \right)}}{RT} \\ & - \kappa \ln \left( {y_{B} } \right) - \kappa \ln \left( {{{\hat{\varphi }_{B} } \mathord{\left/ {\vphantom {{\hat{\varphi }_{B} } {\varphi_{B}^{ * } }}} \right. \kern-0pt} {\varphi_{B}^{ * } }}} \right) - \kappa \ln \left( {{P \mathord{\left/ {\vphantom {P {P^{ * } }}} \right. \kern-0pt} {P^{ * } }}} \right) - \gamma \ln \left( {y_{C} } \right) - \gamma \ln \left( {{{\hat{\varphi }_{C} } \mathord{\left/ {\vphantom {{\hat{\varphi }_{C} } {\varphi_{C}^{ * } }}} \right. \kern-0pt} {\varphi_{C}^{ * } }}} \right) - \gamma \ln \left( {{P \mathord{\left/ {\vphantom {P {P^{ * } }}} \right. \kern-0pt} {P^{ * } }}} \right) \\ \end{aligned}$$
(28)

Effective Henry’s constant may be established in terms of density and cosolvent as follows

$$\ln \left( {H_{2}^{eff} } \right) = \ln \left( {f_{s} } \right) + \frac{{\left( {D + E\rho + Fy_{C} } \right)}}{RT}$$
(29)

\(K_{f}\) may be expressed as

$$\ln \left( {K_{f} } \right) = {{\Delta H_{s} } \mathord{\left/ {\vphantom {{\Delta H_{s} } {RT}}} \right. \kern-0pt} {RT}} + q_{s}$$
(30)

The heat of solvation in the previous equation was expressed as \(\Delta H_{s}\), meanwhile qs is a constant.\({\raise0.7ex\hbox{${V_{A} P}$} \!\mathord{\left/ {\vphantom {{V_{A} P} {RT}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${RT}$}}\) may be expressed as \({\raise0.7ex\hbox{${ZV_{A} \rho }$} \!\mathord{\left/ {\vphantom {{ZV_{A} \rho } M}}\right.\kern-0pt} \!\lower0.7ex\hbox{$M$}}\). The equation represents the density (\(\rho\)) of scCO2, which depends on the variables of pressure, temperature, and composition.

Then Eq. (28) may be expressed as:

$$\begin{aligned} \ln \left( {y_{{AB_{\kappa } C_{\gamma } }} } \right) = & \kappa \ln \left( {y_{B} } \right) + \left( {\kappa + \gamma - 1} \right)\ln \left( {{P \mathord{\left/ {\vphantom {P {P^{ * } }}} \right. \kern-0pt} {P^{ * } }}} \right) + \gamma \ln \left( {y_{C} } \right) = \ln \left( {\frac{{\hat{\varphi }_{s} }}{{\varphi_{{AB_{\kappa } C_{\gamma } }}^{ * } }}} \right) + \ln \left( {\frac{{P_{A}^{sub} }}{{P^{ * } }}} \right) + \frac{{ZV_{A} \rho }}{M} + \kappa \ln \left( {\frac{{\hat{\varphi }_{B} }}{{\varphi_{B}^{ * } }}} \right) \\ & + \gamma \ln \left( {\frac{{\hat{\varphi }_{C} }}{{\varphi_{C}^{ * } }}} \right) - \ln \left( {\varphi_{A}^{ * } } \right) + \frac{{\Delta H_{S} }}{RT} + q_{s} + \frac{{\left( {D + E\rho + Fy_{C} } \right)}}{RT} \\ \end{aligned}$$
(31)

Equation (32) represents the sublimation pressure149,150.

$$R\ln \left( {\frac{{P_{A}^{sub} }}{{P^{ * } }}} \right) = \beta + \frac{\gamma }{T} + \Delta_{sub} \delta \ln \left( {\frac{T}{298.15}} \right)$$
(32)

where \(\beta\), \(\gamma\) and \(\Delta_{sub} \delta\) are temperature independent parameters.

The insignificance of sublimation pressures (~ 10–4) and molar volume of solid solutes (~ 10–4) permit to discard the term \(\frac{{V_{A} P_{A}^{sub} }}{RT}\)(~ 10–9). Therefore, it is possible to approximate the density of the solution to be equal to the density of the supercritical fluid. Solubility of solids is much less than 1 thus \(\ln \left( {y_{B} } \right)\) treated as approximately zero. Thus, the combination of Eqs. (30) and (31) reduces to Eq. (33)

$$\ln \left( {y_{{AB_{\kappa } C_{\gamma } }} } \right) = \left( {\kappa + \gamma - 1} \right)\ln \left( {{P \mathord{\left/ {\vphantom {P {P^{ * } }}} \right. \kern-0pt} {P^{ * } }}} \right) + \gamma \ln \left( {y_{C} } \right) + \frac{{\left( {A_{0} + A_{1} \rho + A_{2} y_{C} } \right)}}{T} + A_{3} \rho + A_{4} \ln \left( T \right) + A_{5}$$
(33)

where \(A_{0} = \frac{{\Delta H_{s} }}{R} + \frac{D}{R} + \frac{\gamma }{R}\), \(A_{1} = {E \mathord{\left/ {\vphantom {E R}} \right. \kern-0pt} R}\), \(A_{2} = \frac{F}{R}\), \(A_{3} = \frac{{ZV_{A} }}{M}\)\(A_{4} = \frac{{\Delta_{sub} \delta }}{R}\) \(A_{5} = - \ln \left( {\frac{{\left( {{{\varphi_{A}^{ * } \;\hat{\varphi }_{s} } \mathord{\left/ {\vphantom {{\varphi_{A}^{ * } \;\hat{\varphi }_{s} } {\varphi_{{AB_{\kappa } C_{\gamma } }}^{ * } }}} \right. \kern-0pt} {\varphi_{{AB_{\kappa } C_{\gamma } }}^{ * } }}} \right)}}{{\left( {{{\hat{\varphi }_{B} } \mathord{\left/ {\vphantom {{\hat{\varphi }_{B} } {\varphi_{B}^{ * } }}} \right. \kern-0pt} {\varphi_{B}^{ * } }}} \right)^{\kappa } \left( {{{\hat{\varphi }_{V} } \mathord{\left/ {\vphantom {{\hat{\varphi }_{V} } {\varphi_{C}^{ * } }}} \right. \kern-0pt} {\varphi_{C}^{ * } }}} \right)^{\gamma } }}} \right)\)\(+ q_{s} + \frac{\beta }{R} - \frac{{\Delta_{sub} \delta \ln \left( {298.15} \right)}}{R}\).

Equation (33) may be written as Eq. (34)

$$y_{{AB_{\kappa } C_{\gamma } }} = \left( {\frac{P}{{P^{ * } }}} \right)^{{\left( {\kappa + \gamma - 1} \right)}} \left( {y_{c} } \right)^{\gamma } \exp \left( {\frac{{A_{0} }}{T} + A_{1} \frac{\rho }{T} + A_{2} \frac{{y_{c} }}{T} + A_{3} \rho + A_{4} \ln \left( T \right) + A_{5} } \right)$$
(34)

Combining Eqs. (23) and (34) gives expression for solubility Eq. (35)

$$y_{2}^{\prime } = \frac{{\left( {\frac{P}{{P^{ * } }}} \right)^{{\left( {\kappa + \gamma - 1} \right)}} \left( {y_{C} } \right)^{\gamma } \exp \left( {\frac{{A_{0} }}{T} + A_{1} \frac{\rho }{T} + A_{2} \frac{{y_{c} }}{T} + A_{3} \rho + A_{4} \ln \left( T \right) + A_{5} } \right)}}{{1 + k_{eff} \left( {\frac{P}{{P^{*} }}} \right)^{{\left( {\kappa + \gamma - 1} \right)}} \left( {y_{C} } \right)^{\gamma } \exp \left( {\frac{{A_{0} }}{T} + A_{1} \frac{\rho }{T} + A_{2} \frac{{y_{c} }}{T} + A_{3} \rho + A_{4} \ln \left( T \right) + A_{5} } \right)}}$$
(35)

Equation (35) shows that the solubility when cosolvents are present is influenced by factors such as density, temperature, association numbers, and cosolvent concentration being (i.e.,\(y_{2}^{\prime } = y_{2}^{\prime } (\rho_{1} ,T,\kappa ,\gamma ,k_{eff} ,y_{C} )\)) dimensionally consistent. Hence forth, this equation shall be referred to as the novel association model for cosolvent systems. The model constants in Eq. (35) were assumed to be temperature-independent and were determined by regression analysis using experimental data. For a fixed cosolvent composition a linear plot is obtained when the data \({{\left( {\ln \left( {{{y_{2}^{\prime } } \mathord{\left/ {\vphantom {{y_{2}^{\prime } } {\left( {1 - \kappa \;y_{2}^{\prime } } \right)}}} \right. \kern-0pt} {\left( {1 - \kappa \;y_{2}^{\prime } } \right)}}} \right) - \left( {\kappa + \gamma - 1} \right)\ln \left( {{P \mathord{\left/ {\vphantom {P {P^{ * } }}} \right. \kern-0pt} {P^{ * } }}} \right) - \gamma \ln \left( {y_{c} } \right) - {{A_{0} } \mathord{\left/ {\vphantom {{A_{0} } {T - {{A_{2} y_{c} } \mathord{\left/ {\vphantom {{A_{2} y_{c} } T}} \right. \kern-0pt} T} - A_{4} \ln \left( T \right) - A_{5} }}} \right. \kern-0pt} {T - {{A_{2} y_{c} } \mathord{\left/ {\vphantom {{A_{2} y_{c} } T}} \right. \kern-0pt} T} - A_{4} \ln \left( T \right) - A_{5} }}} \right)} \mathord{\left/ {\vphantom {{\left( {\ln \left( {{{y_{2}^{\prime } } \mathord{\left/ {\vphantom {{y_{2}^{\prime } } {\left( {1 - \kappa \;y_{2}^{\prime } } \right)}}} \right. \kern-0pt} {\left( {1 - \kappa \;y_{2}^{\prime } } \right)}}} \right) - \left( {\kappa + \gamma - 1} \right)\ln \left( {{P \mathord{\left/ {\vphantom {P {P^{ * } }}} \right. \kern-0pt} {P^{ * } }}} \right) - \gamma \ln \left( {y_{c} } \right) - {{A_{0} } \mathord{\left/ {\vphantom {{A_{0} } {T - {{A_{2} y_{c} } \mathord{\left/ {\vphantom {{A_{2} y_{c} } T}} \right. \kern-0pt} T} - A_{4} \ln \left( T \right) - A_{5} }}} \right. \kern-0pt} {T - {{A_{2} y_{c} } \mathord{\left/ {\vphantom {{A_{2} y_{c} } T}} \right. \kern-0pt} T} - A_{4} \ln \left( T \right) - A_{5} }}} \right)} {\left( {{{A_{1} } \mathord{\left/ {\vphantom {{A_{1} } T}} \right. \kern-0pt} T} + A_{3} } \right)}}} \right. \kern-0pt} {\left( {{{A_{1} } \mathord{\left/ {\vphantom {{A_{1} } T}} \right. \kern-0pt} T} + A_{3} } \right)}}\) is graphically represented against density. This indicates that the new association model is applicable to modeling solids solubility data when a cosolvent is present.

Semiempirical density-based models

Semiempirical models can be employed to define the solubility of mesalazine in scCO2. For the binary system, the Chrastil136, Jouyban et al.140, Bian et al.141, Bartle et al.137, KJ (Kumar-Johnston)138, and MST (Mendez − Santiago − Teja)134 were considered (Table 4). For the ternary system, the MST135, Garlapati–Madras143, Sodeifian-Sajadian28, Jouyban et al.151, González et al.142, and Soltani-Mazloumi144 models were applied (Table 5).

Table 4 The semi-empirical models used in binary system.
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Table 5 The semi-empirical models used in ternary system.
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Results and discussion

The solubility of mesalazine in scCO2 was measured at temperatures ranging from 308 to 338 K and pressures ranging from 12 to 30 MPa, both with and without the presence of a cosolvent. The measured molar solubilities of mesalazine in supercritical carbon dioxide were within the range of 4.41 × 10–5 to 9.97 × 10–5 (308 K), 3.9 × 10–5 to 13.1 × 10–5 (318 K), 3.4 × 10–5 to 16 × 10–5 (328 K)and 3.3 × 10–5 to 18.4 × 10–5 (338 K). Figure 2 presents solubility data both without (Fig. 2a) and with cosolvent (Fig. 2b).

Fig. 2
figure 2

The solubility of mesalazine in scCO2 against pressure (a) without and (b) with cosolvent at different temperature 308, 318, 328, and 338 K (Each point was measured three times).

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The results reveal that the solubility of mesalazine in scCO2 increases as pressure rises while keeping the temperature constant. The observed correlation can be explained by the enhanced solubility of the supercritical solution resulting from the well-documented rise in density as pressure increases. Equal outcomes were informed in the other research18,19,21,154. The determined experimental molar solubilities in scCO2 using 2% dimethyl sulfoxide (DMSO) as cosolvent were in the range of 28.22 × 10–5 to 36.2 × 10–5 (308 K), 26.07 × 10–5 to 51.41 × 10–5 (318 K), 25.02 × 10–5 to 69.07 × 10–5 (328 K) and 25.86 × 10–5 to 82.6 × 10–5 (338 K). A significant increase in solubility of mesalazine was observed when 2% DMSO was added to scCO2.

The mole fraction values in the binary system indicate the potential utilization of gas antisolvent and supercritical antisolvent techniques to micronize mesalazine. Furthermore, the results obtained from the ternary system employing a cosolvent substantiate the assertion that alternative methods, such as RESS, can also be employed for the production of micro and nanoparticles of mesalazine.

The enhancement of the solubility was quantified as enhancement factor, E. This factor was quantified as the ratio between the solubility of the solute when cosolvent was used and the solubility without cosolvent (Eq. 36).

$$E = \frac{{{\acute{y}}_{2} }}{{y_{2} }}$$
(36)

The observed enhancement of the solubility of mesalazine varied from 3.6 to 7.9 depending on the temperature and pressure. The average increase in the solubility the presence of 2% DMSO over all the pressure at 308 K, 318 K, 328 K and 338 K were 4.91, 5.2, 5.62 and 5.8 respectively. However, the average increase in the solubility using DMSO at 2% as cosolvent over all the experimental conditions was 5.38. The comprehensive experimental findings are documented in Tables 6 and 7, as previously mentioned.

Table 6 Experimental mole fraction (y) of mesalazine in supercritical carbon dioxide.
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Table 7 The mole fraction (\({y}_{2}^{\prime}\)) of mesalazine in DMSO and scCO2 mixtures at different conditions.
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The solubility of mesalazine in supercritical carbon dioxide involves considering the interplay of physical and chemical properties, including temperature, pressure, and the use of cosolvent. This knowledge can be applied to enhance drug formulation and delivery systems using supercritical fluids. Mesalazine is a polar compound, while carbon dioxide is non-polar. In the supercritical state, CO₂ exhibits properties of both gases and liquids, which allows it to dissolve certain solutes more effectively than traditional solvents. The ability of scCO₂ to diffuse through solids and interact with solute molecules facilitates the dissolution process. The solubility of polar compounds in scCO₂ can be enhanced by the presence of polar additives or cosolvents that can interact favorably with mesalazine [31,32].

Novel association models, both with and without cosolvent, are suggested, and the efficacy of the established density models was assessed using the solubility mesalazine in scCO2 with and without cosolvent. It should be emphasized that the cosolvent model is not applicable to systems with large cosolvent concentrations in scCO2. This is because it contradicts the fundamental assumption of infinite dilution, which is used to define the solute’s fugacity in the solution in terms of the effective Henry’s constant. The parameters are acquired using the simulated annealing process. The AARD percentage was used to evaluate the accuracy of the model.

$$AARD\% = \frac{100}{{N_{i} - Z}}\mathop \sum \limits_{i = 1}^{{N_{i} }} \frac{{\left| {y_{2}^{calc} - y_{2}^{exp} } \right|}}{{y_{2}^{exp} }}$$
(37)

Z and Ni indicate the improvement parameters number for any rallies22. Adjusted correlation coefficient (Radj) was contemplated to compare the different models38,140,143:

$${R}_{adj}=\sqrt{\left|{R}^{2}-\left(\frac{Q\left(1-{R}^{2}\right)}{N-Q-1}\right)\right|}$$
(38)

Moreover, N, and Q indicates the number of data points and self-determining parameters of each equation, respectively. The R2 coefficient was employed to contrast models:

$${R}^{2}=1-\frac{{SS}_{E}}{{SS}_{T}}=1-\frac{\sum ({y}_{2 exp}-{y}_{2}{)}^{2}}{\sum ({y}_{2 exp}{)}^{2}-\frac{(\sum {y}_{2}{)}^{2}}{N}}$$
(39)

Here, \({\text{SS}}_{\text{E}}\) renders the sum square error and \({\text{SS}}_{\text{T}}\) points to the total sum of squares42. The solubility data acquired by examining new association models, both with and without cosolvents, are found to be consistent with the proposed models. Table 8 displays the additional association model parameter in addition to the statistical parameters. Figure 3a,b provide convincing evidence of the correlation between the new association model without and with cosolvent.

Table 8 New association model parameters.
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Fig. 3
figure 3

(a) New association model without cosolvent; \(\ln ({{y_{2} } \mathord{\left/ {\vphantom {{y_{2} } {\left( {1 - \kappa y_{2} } \right)}}} \right. \kern-0pt} {\left( {1 - \kappa y_{2} } \right)}}) - (\kappa - 1)\ln \left( {{P \mathord{\left/ {\vphantom {P {P^{ * } }}} \right. \kern-0pt} {P^{ * } }}} \right)\) \(- {{N_{1} - N_{2} } \mathord{\left/ {\vphantom {{N_{1} - N_{2} } {T - N_{4} \ln \left( T \right)}}} \right. \kern-0pt} {T - N_{4} \ln \left( T \right)}}\) versus density at different temperature 308, 318, 328, and 338 K. (b) New association model with cosolvent (2% DMSO); \({{\left( {\ln \left( {{{y_{2}^{\prime } } \mathord{\left/ {\vphantom {{y_{2}^{\prime } } {\left( {1 - \kappa \;y_{2}^{\prime } } \right)}}} \right. \kern-0pt} {\left( {1 - \kappa \;y_{2}^{\prime } } \right)}}} \right) - \left( {\kappa + \gamma - 1} \right)\ln \left( {{P \mathord{\left/ {\vphantom {P {P^{ * } }}} \right. \kern-0pt} {P^{ * } }}} \right) - \gamma \ln \left( {y_{c} } \right) - {{A_{0} } \mathord{\left/ {\vphantom {{A_{0} } {T - {{A_{2} y_{c} } \mathord{\left/ {\vphantom {{A_{2} y_{c} } T}} \right. \kern-0pt} T} - A_{4} \ln \left( T \right) - A_{5} }}} \right. \kern-0pt} {T - {{A_{2} y_{c} } \mathord{\left/ {\vphantom {{A_{2} y_{c} } T}} \right. \kern-0pt} T} - A_{4} \ln \left( T \right) - A_{5} }}} \right)} \mathord{\left/ {\vphantom {{\left( {\ln \left( {{{y_{2}^{\prime } } \mathord{\left/ {\vphantom {{y_{2}^{\prime } } {\left( {1 - \kappa \;y_{2}^{\prime } } \right)}}} \right. \kern-0pt} {\left( {1 - \kappa \;y_{2}^{\prime } } \right)}}} \right) - \left( {\kappa + \gamma - 1} \right)\ln \left( {{P \mathord{\left/ {\vphantom {P {P^{ * } }}} \right. \kern-0pt} {P^{ * } }}} \right) - \gamma \ln \left( {y_{c} } \right) - {{A_{0} } \mathord{\left/ {\vphantom {{A_{0} } {T - {{A_{2} y_{c} } \mathord{\left/ {\vphantom {{A_{2} y_{c} } T}} \right. \kern-0pt} T} - A_{4} \ln \left( T \right) - A_{5} }}} \right. \kern-0pt} {T - {{A_{2} y_{c} } \mathord{\left/ {\vphantom {{A_{2} y_{c} } T}} \right. \kern-0pt} T} - A_{4} \ln \left( T \right) - A_{5} }}} \right)} {\left( {{{A_{1} } \mathord{\left/ {\vphantom {{A_{1} } T}} \right. \kern-0pt} T} + A_{3} } \right)}}} \right. \kern-0pt} {\left( {{{A_{1} } \mathord{\left/ {\vphantom {{A_{1} } T}} \right. \kern-0pt} T} + A_{3} } \right)}}\) against density at different temperature 308, 318, 328, and 338 K.

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This research aims to simulate the solubility of mesalazine in supercritical carbon dioxide both with and without the addition of a cosolvent, specifically dimethyl sulfoxide using six semiempirical correlations were applied for the binary system (Table 4), and six semiempirical correlations were investigated for the ternary system (Table 5). The findings of the semiempirical model are displayed in Table 9, together with the corresponding statistical parameters. The Fig. 4 clearly demonstrate the correlation capabilities of the semiempirical models (MST, Chrastil, Bartle, KJ, Jouyban, and Bian) for the binary system. According to Fig. 5, all of the correlations used were acceptable to modeling the solubility of mesalazine in scCO2 with DMSO as cosolvent. From the Chrastil model parameters \(\left( {a_{1} } \right)\) total enthalpy is obtained by multiplying with universal gas constant and it is calculated as 38 kJ/mol. From the Bartle model parameters \(\left( {a_{1} } \right)\) vaporization enthalpy is obtained by multiplying with universal gas constant and it is calculated as 59.6 kJ/mo. The solvation enthalpy is determined by calculating the difference in magnitude between the total enthalpy and the enthalpy of vaporization. A negative sign is assigned to indicate the estimated value, which is − 21.6 kJ/mol. A statistical method (Akaike’s Information Criterion (AIC)) was applied to assess the models. AIC is denoted as155,156,157:

$$AIC = N\ln \left( {\frac{{SS_{E} }}{N}} \right) + 2K$$
(40)
Table 9 The parameters of the semi-empirical used models.
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Fig. 4
figure 4

Correlated mesalazine solubility data, binary system ((a). MST, (b) Chrastil, (c) Bartle et al., (d) KJ, (e) Jouyban et al., and (f) Bian et al. Model) at different temperature 308, 318, 328, and 338 K without cosolvent.

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Fig. 5
figure 5

Correlated mesalazine solubility data, ternary system ((a) Gonzalez et al., (b) Garlapati-Madras, (c) Soltani-Mazloumi, (d) Sodeifian-Sajadian, (e) MST, and (f) Jouyban et al.) at different temperature 308, 318, 328, and 338 K with cosolvent.

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where K is the number of constant parameters, N displays the number of test points. When test points were less than 40), Eq. (41) was applied to calculate AIC88,156:

$${AIC}_{C}=AIC+\frac{2K\left(K+1\right)}{N-K-1}$$
(41)

The experimental determined solubility data of mesalazine in scCO2 using various density-based models. (Jouyban et al., Bartle et al., Bian et al., Chrastil, KJ, and MST) as well using anew association model. As shown in Fig. 6, the closely related model had the lowest percentage of AARD % (4.13), designating it as the optimal model for forecasting the solubility of mesalazine in scCO2. The most unpleasant model was the Bartle et al. (AARD % = 13.581). The same figure (Fig. 7) was drawn to compare the solubility of mesalazine in carbon dioxide in the presence of cosolvent. The best and worst models for predicting the mesalazine solubility in ternary system were obtained new association model and Jouyban et al. with an AARD % value of 3.36 and 7.613.

Fig. 6
figure 6

Comparison of the AARD % calculated for semi-empirical density-based and new association model of mesalazine in binary system (without cosolvent).

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Fig. 7
figure 7

Comparison of the AARD % calculated for semiempirical density-based and new association model of mesalazine in ternary system (with cosolvent).

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Conclusion

The solubility of mesalazine in scCO2 was measured under various temperature (308 K and 338 K) and pressure value (12 to 30 MPa), both with and without a cosolvent. The determined experimental molar solubilities of mesalazine in scCO2 were in the range of 4.41 × 10–5 to 9.97 × 10–5(308 K), 3.9 × 10–5 to 13.1 × 10–5(318 K), 3.4 × 10–5 to 16 × 10–5(328 K)and 3.3 × 10–5 to 18.4 × 10–5(338 K). Meanwhile, the determined experimental molar solubilities in scCO2 using 2% dimethyl sulfoxide as cosolvent were in the range of 28.22 × 10–5 to 36.2 × 10–5(308 K), 26.07 × 10–5 to 51.41 × 10–5(318 K), 25.02 × 10–5 to 69.07 × 10–5(328 K)and 25.86 × 10–5 to 82.6 × 10–5 (338 K). The mole fraction values show that the binary system uses gas and supercritical antisolvent methods. The ternary system using cosolvent confirms that other methods, such as RESS, can be used to produce micro and nanoparticles of mesalazine.

Furthermore, the measured solubilities were strongly associated with both a new association model and current semiempirical models. The newly proposed association model demonstrated a strong correlation between the data, both with and without the presence of a cosolvent, with absolute relative deviation percentages of 3.36% and 4.13% respectively. The findings demonstrated the superiority of the Bian et al. model in binary systems (with an average absolute relative deviation of 6.251%) and the Sodeifian-Sajadian model in ternary systems (with an average absolute relative deviation of 4.901%) compared to alternative models.