3.1.6. FT-IR Studies

FT-IR studies predict the possible interaction between the drug and the excipients. FT-IR spectra (Figure 2) of pure PRX, its physical mixture and optimized formulation depicted all the characteristic IR peaks corresponding to their functional groups as reported in the literature. (Table 5).

**Figure 2.** Overlain FT-IR spectra of PRX (A), physical mixture of PRX and PVP K30® (B), physical mixture of PRX and Poloxamer 188® (C), physical mixture of PRX and mannitol (D), physical mixture of PRX, PVP K30®, Poloxamer 188® and mannitol (E), and freeze-dried optimized formulation (NS9) (F).


**Table 5.** Interpretation data of the FT-IR spectral analysis.

All the characteristic peaks were observed in the IR spectra of pure PRX and in the physical mixture of PRX, poloxamer 188®, PVP K 30®, and mannitol. This indicates that there is no interaction between the PRX and excipients.

### *3.2. Preparation of NS*

PRX NS was prepared by the antisolvent-precipitation technique. The aqueous phase containing suitable polymer and stabilizer (PVP K30® and Poloxamer 188®) was used as the antisolvent and dichloromethane was used as a solvent.

#### 3.2.1. Full Factorial Design

The experimental design shown in Table 1 is a factorial design for two variables at three different levels using −1, 0, and +1 corresponding to a 32 full factorial design. It is possible to evaluate the impact of distinct variables (primary effects) and their second-order effects using this efficient second-order experimental design with a small number of tests. Further, this design has the advantage of calculating the quadratic response surface, which is not estimable using a factorial design at two levels. A full factorial design was used to carefully evaluate the variables.

Data from the experimental runs were subjected to regression and graphical analysis, which produced the equations in Table 6 with F ratios that were statistically significant (*p* < 0.05) and Adj-R<sup>2</sup> values in the range of 0.7–1. The data were well-fit by these model equations.

**Table 6.** Results of statistical analysis of the 32 full factorial experimental design.


The significance of the effect on particle size (Y1) was established using ANOVA and the linear regression equation fit to the data was:

$$\chi\_1 = 326.56 - 70.50 \times \chi\_1 - 41.67 \times \chi\_2 \tag{2}$$

As the stabilizer concentration and stirring speed rise, respectively, the negative sign at coefficients X1 and X2 indicate a reduction in particle size. Because super-saturation occurs with increasing drug concentration in the aqueous phase and leads to fast precipitation on diffusion, particle size was reduced. In order to prevent agglomeration, the drug particles were reduced in size up to nanosized ranges and well-protected by a stabilizer. Moreover, considerable stabilizer upholds Oswald's ripening while too little stabilizer causes agglomeration or aggregation and increases particle size (a phenomenon in which smaller particles get smaller due to more solubility, and larger particles become larger through re-precipitation of small particles on it). The stabilizer concentration was found to be ideal between 0.2 and 0.6 percent. The same observation has been reported by Ahire et al. [24]. The increase in the stirring speed also results in the reduction in the particle size.

The effect on solubility (Y2) was established to be meaningful by ANOVA and the linear regression equation fit to the data was:

$$\mathbf{Y}\_2 = 67.23 + 11.80 \times \mathbf{X}\_1 + 6.36 \times \mathbf{X}\_2 \tag{3}$$

Poor wetting of the drug surface is a sign of hydrophobicity, which contributes to low solubility. As a result of this, the particles agglomerate instead of dispersing. Because of the increased surface area brought on by the reduction in particle size, the drug's solubility in the NS was enhanced shown in Figure 3. The increase in solubility (Y2) is predicted by the positive coefficient of X1 and X2 as the stabilizer concentration and stirring speed, respectively.

#### 3.2.2. Formulation Optimization Using the Desirability Function

The pharmaceutical formulation is optimized by studying the effects of different levels of variables on the responses. During the optimization process, all measured responses that can have an impact on the product's quality were taken into account. Considering the effect of stabilizer concentration (0.5%) and stirring speed of 2600 rpm and manipulating data from Table 6 it was observed that the optimized formulation (NS9) showed a decrease in particle size (228 nm) and high solubility (87.28 μg/mL).

**Figure 3.** Linear and 3D response surface plot for independent variable's effects on the response particle size (**A**,**B**), respectively, and on response solubility (**C**,**D**), respectively.
