2.1 Materials

1H, 1H-Perfluorooctyl acrylate (purity > 0.970; CAS 307–98-2) and 1H, 1H-Perfluorooctyl methacrylate (purity > 0.970; CAS 3934–23-4) were obtained from Alfa Aesar Company. Carbon dioxide (purity > 0.999) was purchased form Deok Yang Company. All the materials were utilized as obtained in this research work. The complete details of the utilized materials related to this study is presented in the Table 1. The schematic illustration of the investigated chemicals is presented in Fig. 1.

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Fig. 1

Chemical structure of (a) 1H, 1H-perfluorooctyl acrylate and (b) 1H, 1H-perfluorooctyl methacrylate.

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2.2 Device setup and working process

The equipment operated to analyze the phase behavior of two different monomers under S_C-CO₂ were performed same as our previous works (Dhamodharan et al., 2022; Kwon et al., 2022; Ghoderao et al., 2022; Ghoderao et al., 2022; Choo et al., 2019). The essential component of the equipment consists of a variable-volume view (3 V) cell, and high-pressure (HP) generator. A thick and strong glass window is associated with the front of the 3 V cell to observe the phase changes. Normally, the thawed (liquid) monomers was passed through the cell roughly ± 0.002 g by the assist of a syringe; then the bare cell is cleansed by numerous trails with N₂ gas to eliminate pinches of organic matters and unwanted air particles. Afterward, CO₂ supplied to the operating 3 V cell roughly ± 0.004 g by the use of a HP bomb. Then the blend inside the 3 V cell compressed to the necessitous pressure by the assist of a wheel type piston.

The 3 V cell pressure was valued with a Heise gauge (having a highest pressure of 34.0 MPa, model CM-53920, made by Dresser Ind.) precise to ± 0.02 MPa. A digital meter (accurate to ± 0.005 %, model 7563, made by Yokogawa), was utilized to monitor the 3 V cell temperature and the maintained temperature was less than ± 0.2 K. A borescope (made by Olympus Corp) built-in with a camera is enclosed side to the glass window to observe phase changes via computer. The light diffusion in the 3 V cell was sustained by a fiberoptic wire associated to an elevated-density illuminator and the borescope. The monomers inside the 3 V cell were robustly blended by the support of a magnetic stirrer, which is operated by an external unit. Firstly, the monomer content compressed to a homogenous phase at steady temperature. The homogeneous phase inside the cell continued at the desired temperature for more than half an hour to accomplish phase equilibrium. Then, the 3 V cell pressure was slightly abridged till a two phases attains. The bubble and dew points were measured, while the first vapor bubble forms and while the earliest teeny mist observed inside the 3 V cell. By changing the pressure and temperature till the critical opalescence, the critical points are marked. The sketch demonstration of the equipment was presented in the Fig. 2.

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Fig. 2

The detailed pictorial representation of experimental apparatus utilized in this research work (McHugh and Krukonis, 1994).

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3.1 Experimentation

The laboratory trial data of the PFOA + S_C-CO₂ and PFOMA + S_C-CO₂ systems were investigated, and the experiment was replicated using the HP equipment at a temperature (T), pressure (p), and mole fraction (x) of 0.2 K, 0.02 MPa, and 0.002, respectively. The solubility isotherms of the PFOA + S_C-CO₂ and PFOMA + S_C-CO₂ systems with a change in temperatures from 313.2 K to 393.2 K were constructed depending on the outcomes with two sovereign factors with an estimated error of less than ± 0.1%.

The lab-based trail data of p, composition (x) isotherms at various temperatures, such as 313.2 K to 393.2 K and several pressures raise from 3.31 to 16.84 MPa for the PFOA + S_C-CO₂ system. Fig. 3a and Table 2 shows the lab-based trail data of PFOA + S_C-CO₂ system. The Fig. 3a, exposes that, described BP pressure rises with the rise in temperature which is attributes of type-I phase behavior (Byun, 2017; Lee et al., 2018). As shown in Fig. 3a, the critical p of the PFOA + S_C-CO₂ system is rising in regard to the increasing temperature, that is the early critical pressure was noted at 13.43 MPa in regard to 353.2 K, then the elevated pressure value of 16.36 MPa was accomplished at 393.2 K, which evidence that the critical point (CP) of the PFOA + S_C-CO₂ system rises with respect to raising T.

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Fig. 3

The laboratory experimental results of pressure-composition isotherm for as-proposed binary models. (a) × 1H, 1H-perfluorooctyl acrylate + (1-x) SC-CO2 model at various temperatures such as ●, 313.2.K; ■, 333.2.K; ▲, 353.2.K; ▾, 373.2.K; ◆, 393.2.K. (b) × 1H, 1H-perfluorooctyl methacrylate + (1-x) SC-CO2 model at various temperatures such as ●, 313.2 K; ■, 333.2 K; ▲, 353.2 K; ▾, 373.2 K; ◆, 393.2 K.

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Similarly, the PFOMA + S_C-CO₂ model was also carried out with the various temperatures and difference pressures same as PFOA + S_C-CO₂ model. The studied lab-based investigational data of the PFOMA + S_C-CO₂ system is presented in the Fig. 3b and Table 3. The Fig. 3a, exposes that, described BP pressure rises with the rise in temperature which is attributes of type-I BP (Byun, 2017; Lee et al., 2018). In addition, there was a notable decrease in the solubility of the monomer in CO₂ with increase T at a fixed pressure range. Nevertheless, as shown in Fig. 3 (a-b), both two-component models demonstrate type-I model and possibly there were no three phases achieved at various operated temperatures in both the models.

3.2 Computational analysis

The PR EOS model was utilized for comparison with the obtained laboratory trail values such as the BP, dew point (DP), and CP of the isothermal phase behavior, and the formulas used are expressed below:

The vdW1 rules are expressed below,

Fig. 4a shows the comparison of the laboratory trail and PR EOS assessed values of the PFOA + S_C-CO₂ system at T = 353.2 K. The red dots indicate the laboratory trail data counts, and the red mark displays a good fit of computational analysis data obtained by the aid of PR EOS. The blue marks imply outcomes obtained using $k_{\mathit{ij}}=0.0,{\eta }_{\mathit{ij}}=0.0$ , whereas the red mark indicate outcomes obtained using the matched $k_{\mathit{ij}}$ and ${\eta }_{\mathit{ij}}$ . The independent interaction parameter of the PR EOS exposes good match with the laboratory trail data at 353.2 K. The PR EOS, adjusted value for PFOA + S_C-CO₂ system are ${\eta }_{\mathit{ij}}$  = 0.0, $k_{\mathit{ij}}$  = 0.075 at 353.2 K.

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Fig. 4

The comparative study analysis of experimental and PR EOS simulated results of as-proposed binary mixtures models. (a) Plot of pressure against mole fraction to illustrate the comparison of experimental data (symbols) for the (1H, 1H-perfluorooctyl acrylate + S_C-CO2) {(1-x) S_C-CO2 + x (C₁₁H₅F₁₅O₂)} model with calculations obtained from the PR EOS by ${\mathrm{\kappa }}_{\mathrm{i}\mathrm{j}}$ and ${\mathrm{\eta }}_{\mathrm{i}\mathrm{j}}$ set equal to zero (dashed lines), and ${\mathrm{\kappa }}_{\mathrm{i}\mathrm{j}}$ equal to 0.075 and ${\mathrm{\eta }}_{\mathrm{i}\mathrm{j}}$ equal to 0.0 (solid lines) at T-353.2 K. (b) 1H, 1H-perfluorooctyl acrylate + S_C-CO2 {(1-x) S_C-CO2 + x (C₁₁H₅F₁₅O₂)}.

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Fig. 4b, demonstrating the competitive discussion of lab-made trail and computational analysis data of the p-x isotherms at various temperatures (313.2 to 393.2) K for the PFOA + S_C-CO₂ system engaged using the adjusted data of the sovereign factors of $k_{\mathit{ij}}$ and ${\eta }_{\mathit{ij}}$ calculated at T = 353.2 K. In agreement with the Fig. 4b, the lab-based investigational results, and the PR EOS adjusted data of the PFOA + S_C-CO₂ system shows a decent agreement. The RMSD (%) of all the laboratory trial T was 5.08 % for 70 data counts.

Fig. 5a shows a comparative study analysis of laboratory trail and simulated p-x isotherms for the PFOMA + S_C-CO₂ system at T = 353.2 K. The red dots denote to lab-based investigational results, and the red line indicates that the laboratory results were well matched with the simulated values obtained using PR EOS. The blue mark indicates the outcomes obtained using $k_{\mathit{ij}}=0.0,{\eta }_{\mathit{ij}}=0.0$ whereas the red marks represent the outcomes obtained using the matched $k_{\mathit{ij}}$ and ${\eta }_{\mathit{ij}}$ . The two component interaction elements of the PR EOS model were in good agreement with the laboratory trail data at 353.2 K. The PR EOS adjusted data for PFOMA + S_C-CO₂ system at T = 353.2 K were ${\eta }_{\mathit{ij}}$  = 0.0, $k_{\mathit{ij}}$ = 0.075.

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Fig. 5

The comparative study analysis of experimental and PR EOS simulated results of as-proposed binary mixtures models. (a) Plot of pressure against mole fraction to illustrate the comparison of experimental data (symbols) for the (1H, 1H-perfluorooctyl methacrylate + S_C-CO2) {(1-x) S_C-CO2 + x (C₁₂H₇F₁₅O₂)} model with calculations obtained from the PR EOS by ${\mathrm{\kappa }}_{\mathrm{i}\mathrm{j}}$ and ${\mathrm{\eta }}_{\mathrm{i}\mathrm{j}}$ set equal to zero (dashed lines), and ${\mathrm{\kappa }}_{\mathrm{i}\mathrm{j}}$ equal to 0.075 and ${\mathrm{\eta }}_{\mathrm{i}\mathrm{j}}$ equal to 0.0 (solid lines) at T-353.2 K. (b) 1H, 1H-perfluorooctyl methacrylate + S_C-CO2 {(1-x) S_C-CO2 + x (C₁₂H₇F₁₅O₂)}.

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Fig. 5b displays that the comparative discussion of laboratory trail response and computational p-x isotherms at various temperatures from 313.2 K to 393.2 K for the PFOMA + S_C-CO₂ system engaged the adjusted data of the sovereign factors of $k_{\mathit{ij}}$ and ${\eta }_{\mathit{ij}}$ lofted at T = 353.2 K. The image revealed that the obtained laboratory trail results and the PR EOS optimized data of the PFOMA + S_C-CO₂ system were well matched. The RMSD (%) of all the investigated T was 5.36 % for 58 data counts.

Fig. 6a shows the PR EOS predicted critical curve (CC) for the PFOA + S_C-CO₂ system. The red marks in Fig. 6a indicate the vapor p of the pure PFOA and CO₂, which was assessed using the Lee-Kesler approach (Peng and Robinson, 1976; Poling et al., 2001). The red dots emphasize the CP of the pure CO₂ and PFOA. The area above the blue mark indicated that the system is in one phase (fluid), and the area below indicates two phases (vapor and liquid). The blue dashed lines represent the information obtained from the PR EOS for the PFOA + S_C-CO₂ model at T = 353.2 K.

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Fig. 6

Plot of pressure against temperature for the as-proposed binary models. (a) 1H, 1H-perfluorooctyl acrylate + S_C-CO2 model. The solid lines and the solid circles represent the (vapor + liquid) lines and the critical points for pure CO₂ and 1H, 1H-perfluorooctyl acrylate. The solid squares are critical points determined from isotherms measured in this work. (b) 1H, 1H-perfluorooctyl methacrylate + S_C-CO2 model. The solid lines and the solid circles represent the (vapor + liquid) lines and the critical points for pure CO₂ and 1H, 1H-perfluorooctyl methacrylate. The solid squares are critical points determined from isotherms measured in this work.

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Fig. 6b shows the PR EOS estimated CC for the PFOMA + S_C-CO₂ system. The red lines in Fig. 6b correspond to the vapor p of the pure PFOMA and CO₂, which was assessed by the help of Lee-Kesler approach (Peng and Robinson, 1976; Poling et al., 2001). The red dots indicate the CP of the pure CO₂ and PFOMA. In Fig. 6b, the area above the blue marking represents one phase (fluid), and the below the mark represents two phases (vapor–liquid). The consequential CCs expose type-I system. The blue marking relates to the estimated data accomplished through PR EOS of the PFOMA + S_C-CO₂ system at T = 353.2 K. Moreover, the examined CCs of the as-proposed two-component models were consistent with the laboratory trail data and computational response, which was obtained using PR EOS with two alterable parameters.