*2.3. Solubility Measurement*

The solubility of florfenicol in methanol + water, ethanol + water, 1-propanol + water, and isopropanol + water was determined using a gravimetric method [14] in this work. The mass fraction of alcohol in four kinds of binary solvents varies from *ω*<sup>A</sup> = 0 to 1, with an interval of 0.1. The experimental procedures are described as follows: firstly, 10 mL of binary solvents was added into a 20 mL glass vial and placed into a big jacket vessel in which the temperature was controlled by a high-precision constant temperature water bath (XOYS-2009, accuracy: ± 0.1 K). After the temperature of the mixture solvents remained stable, an excess amount of florfenicol solid was added to the glass vial. The mixture in the sealed vial was continuously stirred using magnetic stirring for 12 h to achieve solid–liquid equilibrium. The duration of 12 h is determined by a preliminary experiment. Then, the stirring was stopped and the suspension was left for another 1 h to assure the undissolved solids settle down completely. The supernatant was then drawn out using a syringe fitted with a Millipore filter (0.45 μm), which was precooled/preheated to the measurement

temperature. After that, the supernatant was transferred into a pre-weighed glass beaker rapidly. Then the beaker with supernatant inside was weighed again using an analytical balance (AL204-C, Metter Toledo, Zurich, Switzerland) with an accuracy of ±0.0001 g. Finally, the beaker was dried in a vacuum oven (type DZF-2BC, Tianjin Taisite Instrument Co., Ltd., Tianjin, China) at 313.15K and weighed periodically until the weight did not change. All the experiments were repeated at least three times to reduce accidental errors and the average value of three measurements was used to calculate the mole ratio fraction solubility of florfenicol (*x*F) according to Equation (1).

$$\mathbf{x\_F} = \frac{m\_\mathrm{F}/\mathbf{M\_F}}{m\_\mathrm{F}/\mathbf{M\_F} + m\_\mathrm{w}/\mathbf{M\_W} + m\_\mathrm{A}/\mathbf{M\_A}} \tag{1}$$

where *m*F, *m*w, and *m*<sup>A</sup> represent the mass of florfenicol, water, and alcohol solvents (methanol, ethanol, 1-propanol, or isopropanol), respectively. MF, Mw, and MA represent the molar mass of florfenicol, water, and alcohol solvents (methanol, ethanol, 1-propanol, or isopropanol), respectively.

After the solubility measurement experiments, the undissolved florfenicol solid in the equilibrium saturated solution was filtered and tested by PXRD.

#### **3. Theoretical Basis**

A variety of thermodynamic models have been proposed to correlate solubility data. These models can be used to check the accuracy of the determined data and describe the solid–liquid phase equilibrium relationship in the solution. In this work, the experimental solubility data were correlated by the modified Apelblat model, CNIBS/R-K model, the Jouyban–Acree model, and the NRTL model.

#### *3.1. Modified Apelblat Model*

The modified Apelblat model was proposed by Apelblat et al. [15,16] and can be used to correlate the solid–liquid equilibrium solubility of the solute in pure solvents and binary solvents. This semi-empirical model is applied to describe the relationship between mole fraction solubility and temperature. The equation is expressed as follows:

$$
\ln \mathbf{x}\_{\overline{\mathbf{F}}} = A + \frac{B}{T} + C \ln T \tag{2}
$$

where *x*<sup>F</sup> is the mole fraction solubility of the solute. *T* is the absolute temperature. *A*, *B*, and *C* are model parameters.

#### *3.2. CNIBS/R-K Model*

The CNIBS/R-K model was proposed by Acree et al. [17,18] and is used to study the solid–liquid equilibrium solubility of the solutes in binary solvents. This equation describes the relationship between mole fraction solubility of solute and solvent composition. The equation is defined as Equation (3):

$$\ln \mathbf{x}\_{\overline{\mathbb{F}}} = \mathbf{x}\_{\overline{a}} \ln X\_{\overline{a}} + \mathbf{x}\_{\overline{b}} \ln X\_{\overline{b}} + \mathbf{x}\_{\overline{a}} \mathbf{x}\_{\overline{b}} \sum\_{i=0}^{N} S\_i \left(\mathbf{x}\_{\overline{a}} - \mathbf{x}\_{\overline{b}}\right)^{i} \tag{3}$$

where *Xa* and *Xb* refer to the saturated mole solubility of the solute in a pure solvent *a* and *b* at the same temperature, respectively. *xa* and *xb* are the initial mole fraction composition of solvent *a* and *b* in binary solvent mixtures in the absence of solute. The *Si* is the model parameter and *N* refers to the amount of solvent. For the binary solvent system, the value of *N* is 2 and *xa* = 1−*xb*. Therefore, Equation (3) can be simplified to Equation (4):

$$\ln \mathbf{x}\_{\rm F} = B\_0 + B\_1 \mathbf{x}\_a + B\_2 \mathbf{x}\_a^2 + B\_3 \mathbf{x}\_a^3 + B\_4 \mathbf{x}\_a^4 \tag{4}$$

where *B*0, *B*1, *B*2, *B*3, and *B*<sup>4</sup> are model parameters.

#### *3.3. The Jouyban–Acree Model*

The Jouyban–Acree model is a more general model that can be used to describe the effects of both solvent composition and temperature on the solid–liquid equilibrium solubility of solute [19]. Based on the CNIBS/R-K model, the temperature parameter *T* is introduced as the second variable. The equation is shown in Equation (5):

$$\ln \mathbf{x}\_{\rm F} = \mathbf{x}\_a \ln X\_a + \mathbf{x}\_b \ln X\_b + \mathbf{x}\_a \mathbf{x}\_b \sum\_{i=0}^{N} \frac{f\_i (\mathbf{x}\_a - \mathbf{x}\_b)^i}{T} \tag{5}$$

where *Ji* is a model parameter. Other symbols have the same meanings as those in the CNIBS/R-K model. By applying the Apelblat equation [20], the Jouyban–Acree model can be transformed into Equation (6):

$$\begin{split} \ln \chi\_{\mathcal{F}} &= A\_0 + \frac{A\_1}{T} + A\_2 \ln T + A\_3 \chi\_a + \frac{A\_4 \chi\_a}{T} + \frac{A\_5 \chi\_a^2}{T} \\ &+ \frac{A\_6 \chi\_d^3}{T} + \frac{A\_7 \chi\_d^4}{T} + A\_8 \chi\_d \ln T \end{split} \tag{6}$$

where *A*0~*A*<sup>8</sup> are model parameters.

#### *3.4. NRTL Model*

The NRTL model was proposed by Renon et al. and can be used to calculate the activity coefficients *γ<sup>i</sup>* of non-polar or polar miscible systems [21]. The model is expressed as follows:

$$\begin{aligned} \ln \gamma\_{i} &= \frac{\left(\mathbf{x}\_{j}\mathbf{G}\_{ji} + \mathbf{x}\_{k}\mathbf{G}\_{kj}\right)\left(\mathbf{x}\_{j}\mathbf{G}\_{ji}\mathbf{r}\_{ji} + \mathbf{x}\_{k}\mathbf{G}\_{ki}\mathbf{r}\_{ki}\right)}{\left(\mathbf{x}\_{i} + \mathbf{x}\_{j}\mathbf{G}\_{ji} + \mathbf{x}\_{k}\mathbf{G}\_{ki}\right)^{2}} + \\ &\frac{\left[\mathbf{x}\_{j}\mathbf{G}\_{ij}\mathbf{x}\_{j}^{2} + \mathbf{G}\_{ij}\mathbf{G}\_{kj}\mathbf{x}\_{j}\mathbf{x}\_{k}\left(\mathbf{r}\_{ij} - \mathbf{r}\_{kj}\right)\right]}{\left(\mathbf{x}\_{j} + \mathbf{x}\_{i}\mathbf{G}\_{ij} + \mathbf{x}\_{k}\mathbf{G}\_{kj}\right)^{2}} + \\ &\frac{\left[\mathbf{x}\_{jk}\mathbf{G}\_{jk}\mathbf{x}\_{k}^{2} + \mathbf{G}\_{ik}\mathbf{G}\_{jk}\mathbf{x}\_{j}\mathbf{x}\_{k}\left(\mathbf{r}\_{ik} - \mathbf{r}\_{jk}\right)\right]}{\left(\mathbf{x}\_{k} + \mathbf{x}\_{i}\mathbf{G}\_{ik} + \mathbf{x}\_{j}\mathbf{G}\_{jk}\right)^{2}} \end{aligned} \tag{7}$$

with

$$G\_{i\rangle} = \exp\left(-a\_{i\rangle}\tau\_{i\rangle}\right) \tag{8}$$

$$
\pi\_{ij} = \frac{\Delta g\_{ij}}{\mathcal{R}T} \tag{9}
$$

where *i* = *j*, Δ*gij* is the interaction parameter that is related to the Gibbs energy that is listed in Table 8, *Gij* and *τij* are model parameters. *αij* is a random parameter.

The calculated solubility corrected by the activity coefficient is shown as Equation (10):

$$
\ln x\_i = \frac{\Delta\_{\text{fus}}H}{R} \left( \frac{1}{T\_{\text{m}}} - \frac{1}{T} \right) - \ln \gamma\_i \tag{10}
$$

where Δfus*H* and *T*<sup>m</sup> are the melting enthalpy and melting point of florfenicol.

#### **4. Results and Discussion**

*4.1. Solid-State Characterization*

The PXRD patterns of florfenicol (Figure 2) in different solvents show that the characteristic peaks of florfenicol in the equilibrium saturated solution remained consistent with that of the raw material. This indicates that florfenicol did not undergo a phase transition during the solubility experiment. The PXRD pattern of the florfenicol in this work was consistent with the form I data in the literature [9]. The melting temperature (*T*m) and the enthalpy of fusion (Δfus*H*) of florfenicol were calculated from the DSC result (Figure 3). The melting temperature (*T*m) of florfenicol is 426.21 K and the enthalpy of fusion (Δfus*H*) of florfenicol is 34.13 kJ mol<sup>−</sup>1. These two results are consistent with the values from other literature [12].

**Figure 2.** PXRD patterns of florfenicol.

**Figure 3.** Thermal analysis spectrum (DSC) of florfenicol.
