Thickening Supercritical CO2 with π-Stacked Co-Polymers: Molecular Insights into the Role of Intermolecular Interaction

Vinyl Benzoate/Heptadecafluorodecyl acrylate (VBe/HFDA) co-polymers were synthesized and characterized as thickening agents for supercritical carbon dioxide (SC-CO2). The solubility and thickening capability of the co-polymer samples in SC-CO2 were evaluated by measuring cloud point pressure and relative viscosity. The molecular dynamics (MD) simulation for all atoms was employed to simulate the microscopic molecular behavior and the intermolecular interaction of co-polymer–CO2 systems. We found that the introduction of VBe group decreased the polymer–CO2 interaction and increased the polymer–polymer interaction, leading to a reduction in solubility of the co-polymers in SC-CO2. However, the co-polymer could generate more effective inter-chain interaction and generate more viscosity enhancement compared to the Poly(Heptadecafluorodecyl) (PHFDA) homopolymer due to the driving force provided by π-π stacking of the VBe groups. The optimum molar ratio value for VBe in co-polymers for the viscosity enhancement of SC-CO2 was found to be 0.33 in this work. The P(HFDA0.67-co-VBe0.33) was able to enhance the viscosity of SC-CO2 by 438 times at 5 wt. %. Less VBe content would result in a lack of intermolecular interaction, although excessive VBe content would generate more intramolecular π-π stacking and less intermolecular π-π stacking. Both conditions reduce the thickening capability of the P(HFDA-co-VBe) co-polymer. This work presented the relationship between structure and performance of the co-polymers in SC-CO2 by combining experiment and molecular simulations.


Introduction
Supercritical carbon dioxide (SC-CO 2 ) has been applied in many industrial processes due to its good diffusion, heat transfer and mass transfer properties. In unconventional oil and gas exploitation, CO 2 has been recognized as clean fracturing fluid, which has strong width generation capability [1,2]. SC-CO 2 does not damage the reservoir and possesses obvious technical advantages for the stimulation of low permeability and water-sensitive reservoir compared to hydraulic fracturing. In addition, CO 2 is easier to flow back and could replace the natural gas adsorbed in the reservoir [3,4]. The practices of the United States and Canada showed that the stimulation effect of CO 2 fracturing was especially excellent for shale gas reservoirs [5]. However, the low viscosity of SC-CO 2 has limited its capability

Preparation of Co-Polymer
The Vinyl benzoate/Heptadecafluorodecyl acrylate (VBe/HFDA) co-polymer was synthesized with AIBN as the initiator according to the procedure shown in Scheme 1 [35][36][37]. Two monomers were mixed together in a glass ampoule. AIBN (1.0 mol % relative to monomers) was added as a free radical initiator. The ampoule was sealed under reduced pressure and the polymerization was carried out at 60 • C for 24 h after the oxygen was removed. The product was dissolved in 1,1,2-trichlorotrifluoroethane and then purified twice in methanol. After this, the product collected and dried under vacuum. The co-polymers synthesized were named P(HFDA x -co-VBe y ), 'x' is the molar ratio of HFDA and y is the molar ratio of Vinyl Benzoate.
Polymers 2018, 10, x FOR PEER REVIEW 3 of 16 investigating the co-polymer-CO2 interaction energy, equilibrium conformations and radial distribution functions (RDFs), microscopic structure and intermolecular interaction of copolymer-CO2 systems were explored. The relationships of the co-polymer structure and composition with the solubility and thickening capability were revealed.

Preparation of Co-Polymer
The Vinyl benzoate/Heptadecafluorodecyl acrylate (VBe/HFDA) co-polymer was synthesized with AIBN as the initiator according to the procedure shown in Scheme 1 [35][36][37]. Two monomers were mixed together in a glass ampoule. AIBN (1.0 mol % relative to monomers) was added as a free radical initiator. The ampoule was sealed under reduced pressure and the polymerization was carried out at 60 °C for 24 h after the oxygen was removed. The product was dissolved in 1,1,2trichlorotrifluoroethane and then purified twice in methanol. After this, the product collected and dried under vacuum. The co-polymers synthesized were named P(HFDAx-co-VBey), 'x' is the molar ratio of HFDA and y is the molar ratio of Vinyl Benzoate. Scheme 1. Synthetic procedure of the P(HFDA-co-VBe) co-polymer, where x: the molar ratio of HFDA and y: the molar ratio of VBe.

Nuclear Magnetic Resonance (NMR) Spectroscopy
1 H-NMR spectrum of the co-polymer was recorded by Bruker 400 MHz Nuclear Magnetic Resonance Spectrometer (Bruker, Karlsruhe, Germany) with 1,1,2-tritriuorotrichloroethane and Chloroform-d used as the solvent at 20 °C. The spectra were used to analyze the co-polymerization ratio. The co-polymerization ratio of the two monomers was obtained by the integral relative intensity of the chemical shifts of the H atoms belonging to different characteristic proton groups [32][33][34][35][36].

Differential Scanning Calorimetry
To evaluate the chain flexibility, glass transition temperature of the co-polymers as measured using the Mettler-Toledo Differential Scanning Calorimeter (Mettler Toledo, Zurich, Switzerland) under the N2 atmosphere. The heating rate and the cooling rate were 10 °C/min [22][23][24]. Each sample was measured three times, taking the average of the last two as the result. Resonance Spectrometer (Bruker, Karlsruhe, Germany) with 1,1,2-tritriuorotrichloroethane and Chloroform-d used as the solvent at 20 • C. The spectra were used to analyze the co-polymerization ratio. The co-polymerization ratio of the two monomers was obtained by the integral relative intensity of the chemical shifts of the H atoms belonging to different characteristic proton groups [32][33][34][35][36].

Differential Scanning Calorimetry
To evaluate the chain flexibility, glass transition temperature of the co-polymers as measured using the Mettler-Toledo Differential Scanning Calorimeter (Mettler Toledo, Zurich, Switzerland) under the N 2 atmosphere. The heating rate and the cooling rate were 10 • C/min [22][23][24]. Each sample was measured three times, taking the average of the last two as the result.

Molar Mass Analysis
Six solutions with different concentrations of the co-polymer sample was dissolved in 1,1,2-trichlorotrifluoroethane, before being filtered through a 0.8-µm filter. The absolute refractive index increments of co-polymer sample, d n /d c , were determined by the Optilab rEX extended differential refractive index detector, while the molar mass of the co-polymer sample was measured by Static The surface tension of the co-polymers was determined to evaluate the polymer-polymer interactions. The solution of polymer with 1,1,2-trifluorotriochloroethane was spin-coated on a glass substrate at a rotational speed of 2000 rpm. A homogeneous polymer film was obtained after drying. The contact angles of water-polymer and hexadecane-polymer were measured by DSAHT Contact Angle Meter (KRÜSS GmbH, Hamburg, Germany). After this, the surface tension of the co-polymers was calculated by the two-liquid method to evaluate the polymer-polymer interaction [36,[45][46][47].

Cloud Point and Viscosity Measurements
The core part used for cloud point and viscosity measurements was the high temperature and high pressure visual unit, which is shown in Scheme 2. The visual windows were made of quartz glass and the supporting pressure is 30 MPa. The temperature was controlled by oil bath. The volume of the unit could be changed by moving the piston, which had a moving distance that was determined by displacement meter.

Molar Mass Analysis
Six solutions with different concentrations of the co-polymer sample was dissolved in 1,1,2trichlorotrifluoroethane, before being filtered through a 0.8-μm filter. The absolute refractive index increments of co-polymer sample, dn/dc, were determined by the Optilab rEX extended differential refractive index detector, while the molar mass of the co-polymer sample was measured by Static Light Scattering (SLS) with Wyatt DAWN HELEOS Multi-Angle Laser Light Scatter (Wyatt Technology, Santa Barbara, CA, USA). The light scattering data was measured through a fixed 18angle detector display simultaneously [38][39][40][41][42][43][44].

Surface Tension Measurements
The surface tension of the co-polymers was determined to evaluate the polymer-polymer interactions. The solution of polymer with 1,1,2-trifluorotriochloroethane was spin-coated on a glass substrate at a rotational speed of 2000 rpm. A homogeneous polymer film was obtained after drying. The contact angles of water-polymer and hexadecane-polymer were measured by DSAHT Contact Angle Meter (KRÜSS GmbH, Hamburg, Germany). After this, the surface tension of the co-polymers was calculated by the two-liquid method to evaluate the polymer-polymer interaction [36,[45][46][47].

Cloud Point and Viscosity Measurements
The core part used for cloud point and viscosity measurements was the high temperature and high pressure visual unit, which is shown in Scheme 2. The visual windows were made of quartz glass and the supporting pressure is 30 MPa. The temperature was controlled by oil bath. The volume of the unit could be changed by moving the piston, which had a moving distance that was determined by displacement meter. The polymer-CO2 mixture was stirred for 30 min to form a homogeneous system after being heated to the desired temperature, before the piston was moved to bring the system to the desired pressure. The polymer-CO2 system was a single phase under the initial conditions after having achieved phase equilibrium. After this, the piston was moved slowly to increase the volume of the unit under constant temperature, before decreasing the pressure until mist appeared. The pressure at which the mist appeared exactly was the cloud point pressure [48,49]. The phase transitions of the CO2-polymer system under a constant temperature were shown in Figure 1. The cloud point pressure was determined by repeating three measurements. The polymer-CO 2 mixture was stirred for 30 min to form a homogeneous system after being heated to the desired temperature, before the piston was moved to bring the system to the desired pressure. The polymer-CO 2 system was a single phase under the initial conditions after having achieved phase equilibrium. After this, the piston was moved slowly to increase the volume of the unit under constant temperature, before decreasing the pressure until mist appeared. The pressure at which the mist appeared exactly was the cloud point pressure [48,49]. The phase transitions of the CO 2 -polymer system under a constant temperature were shown in Figure 1. The cloud point pressure was determined by repeating three measurements. The pitching device at the top of the device could put aluminum ball into the visual unit. At the pressures above the cloud point pressure, the process of aluminum ball passing through the visual windows was captured by the high-speed camera at 2000 frames per second and used for the viscosity calculation. The viscosity of CO2 and polymer-CO2 mixture were calculated by Equation (1) under the pressures above the cloud point pressure [50,51]: where α and β are the thermal expansion coefficient and the compression coefficient of the visual unit; Tr and Pr are the reference temperature and pressure; ρl and ρs are the density of the solution and the ball respectively; t is the settling time; and A is the apparatus constant. The ratio of the CO2-polymer viscosity to the CO2 viscosity at the same temperature and pressure, which is also known as the relative viscosity was used to evaluate the viscosification of the co-polymer [21]. The relative viscosity was obtained by Equation (2): where ηmix is the viscosity of the CO2-polymer mixture and 2 CO η is the viscosity of CO2.

Molecular Dynamics Simulation
Two types of systems, which are namely the system with eight chains of co-polymer as well as the co-polymer-CO2 system with eight chains of co-polymer and 2000 molecules of CO2, were simulated by the Material Studio 7.0 (MS) package. All the force-field parameters of CO2 and polymers were determined by the COMPASS force-field. Firstly, HFDA and VBe repeat units were established. Four molecular modelings of P(HFDA-co-VBe) random co-polymers were constructed with different molar ratios of HFDA to VBe. PHFDA homopolymer was constructed with HFDA repeat units. The molecular modeling of P(HFDA-co-VBe) co-polymer is shown in Scheme 3.
Then, CO2 and polymer molecules were optimized by the Smart Minimizer of the Discover module. After this, the systems were constructed by the Amorphous Cell module. This module makes the boxes have periodic boundary conditions and constructs quasi-infinite system to represent the macro system precisely. The different systems simulated are shown in Table 1. The pitching device at the top of the device could put aluminum ball into the visual unit. At the pressures above the cloud point pressure, the process of aluminum ball passing through the visual windows was captured by the high-speed camera at 2000 frames per second and used for the viscosity calculation. The viscosity of CO 2 and polymer-CO 2 mixture were calculated by Equation (1) under the pressures above the cloud point pressure [50,51]: where α and β are the thermal expansion coefficient and the compression coefficient of the visual unit; T r and P r are the reference temperature and pressure; ρ l and ρ s are the density of the solution and the ball respectively; t is the settling time; and A is the apparatus constant. The ratio of the CO 2 -polymer viscosity to the CO 2 viscosity at the same temperature and pressure, which is also known as the relative viscosity was used to evaluate the viscosification of the co-polymer [21]. The relative viscosity was obtained by Equation (2): where η mix is the viscosity of the CO 2 -polymer mixture and η CO 2 is the viscosity of CO 2 .

Molecular Dynamics Simulation
Two types of systems, which are namely the system with eight chains of co-polymer as well as the co-polymer-CO 2 system with eight chains of co-polymer and 2000 molecules of CO 2 , were simulated by the Material Studio 7.0 (MS) package. All the force-field parameters of CO 2 and polymers were determined by the COMPASS force-field. Firstly, HFDA and VBe repeat units were established. Four molecular modelings of P(HFDA-co-VBe) random co-polymers were constructed with different molar ratios of HFDA to VBe. PHFDA homopolymer was constructed with HFDA repeat units. The molecular modeling of P(HFDA-co-VBe) co-polymer is shown in Scheme 3.
Then, CO 2 and polymer molecules were optimized by the Smart Minimizer of the Discover module. After this, the systems were constructed by the Amorphous Cell module. This module makes the boxes have periodic boundary conditions and constructs quasi-infinite system to represent the macro system precisely. The different systems simulated are shown in Table 1. Polymers 2018, 10, x FOR PEER REVIEW 6 of 16 Scheme 3. The molecular modeling of P(HFDA-co-VBe) co-polymer. Five cycles of annealing calculation from 300 to 500 K was calculated by Anneal in the Forcite module to delay the systems. The optimized conformation of co-polymer-CO2 system is shown in Figure 2.   Five cycles of annealing calculation from 300 to 500 K was calculated by Anneal in the Forcite module to delay the systems. The optimized conformation of co-polymer-CO 2 system is shown in Figure 2.  Five cycles of annealing calculation from 300 to 500 K was calculated by Anneal in the Forcite module to delay the systems. The optimized conformation of co-polymer-CO2 system is shown in Figure 2.  using the Ewald summing algorithm and the van der Waals interactions were calculated using the atom-based summation. The time step was 1 fs and the frame output interval was 5000 ps. Andersen method was used for the temperature control and Berendsen method was used for the pressure control [33,34]. The final 500 ps equilibrium conformations were used for data analysis.

Synthesis and Characterization
The experimental results of the synthesis and physical properties of the co-polymer samples are shown in Table 2. With the enhancement of the molar ratio of VBe, the surface tension and glass transition temperature increased gradually. The molar mass measurement results showed that the differences of molar mass between the co-polymer samples were small, so the effects of molar mass on cloud point pressure and viscosification were not considered in this paper. The co-polymer compositions were determined by comparing the peak intensities of phenyl protons at 6.8 and 7.1 ppm (a and b) and methylene protons at 1.9 ppm (h). Taking the spectrum of P(HFDA 0.87 -co-VBe 0.13 ) shown in Figure 3a as an example, the chemical shift of the H atoms in HFDA group at the point h was in the range of 1.8-2.0 ppm, while the chemical shift of the H atoms in VBe group at the point a and b was in the range of 6.5-7.2 ppm. The integral relative intensity of the peaks of h to a + b, was equal to the molar ratio of the two groups, which was HFDA/VBe = x:y = h/2:(a + b)/5 = 0.87:0.13 [32][33][34][35][36]. The co-polymerization ratios of the other co-polymers were obtained by the same method, which is shown in Figure 3b-d.

Solubility of Co-Polymers in SC-CO 2
The cloud point pressure of the co-polymer-CO 2 solution with mass concentration at 308.2 K and temperature at 1 wt. % of concentration are shown in Figure 4. As observed in Figure 4a, the cloud point pressures of the co-polymers gradually enhanced with an increase in the mass concentration. The cloud point curves also reflected the influence of the VBe molar ratio on cloud point pressures. With an increase in the molar ratio of VBe, the cloud point pressures of the co-polymers increased rapidly. It seemed that the VBe content had greater effect than the mass concentration in determining the solubility of the co-polymers. The cloud point pressure of the co-polymers increased with an increase in temperature, which is shown in Figure 4b. With the temperature rose from 308.2 K to 328.2 K, the cloud point pressures of the four co-polymers were found to increase by about 5 MPa equivalently. Obviously, the temperature has a significant effect on the solubility of the co-polymers in SC-CO 2 . This may be related to the change of CO 2 properties caused by the change in temperature. When the temperature rose, the density and dielectric constant of CO 2 decreased, so its dissolubility decreased [52]. To counteract the downfall of CO 2 dissolubility, the pressure must be increased to enhance the co-polymer-CO 2 interactions, which helped to balance the intermolecular interactions in the solutions [53]. the pressure must be increased to enhance the co-polymer-CO2 interactions, which helped to balance the intermolecular interactions in the solutions [53].  The radial distribution function (RDF) is a common function used to study the microstructures and evaluate the intermolecular interactions, which refers to the spherically symmetric distribution probability of other particles in a space centered on a given particle. This can be calculated as follows [54,55]: where gαβ(r) is the value of radial distribution function, Nα is the number of α particles; Nβ is the number of β particle; V is the volume of box simulated; and niβ(r) is the number of β particles in the space of (r, r + Δr) centered on α particles. the pressure must be increased to enhance the co-polymer-CO2 interactions, which helped to balance the intermolecular interactions in the solutions [53].  The radial distribution function (RDF) is a common function used to study the microstructures and evaluate the intermolecular interactions, which refers to the spherically symmetric distribution probability of other particles in a space centered on a given particle. This can be calculated as follows [54,55]: where gαβ(r) is the value of radial distribution function, Nα is the number of α particles; Nβ is the number of β particle; V is the volume of box simulated; and niβ(r) is the number of β particles in the space of (r, r + Δr) centered on α particles. The radial distribution function (RDF) is a common function used to study the microstructures and evaluate the intermolecular interactions, which refers to the spherically symmetric distribution probability of other particles in a space centered on a given particle. This can be calculated as follows [54,55]: where g α β (r) is the value of radial distribution function, N α is the number of α particles; N β is the number of β particle; V is the volume of box simulated; and n iβ (r) is the number of β particles in the space of (r, r + ∆r) centered on α particles. Solvation plays an important role in controlling the solubility of polymer in SC-CO 2 [56]. The solvation behavior of the polymer in SC-CO 2 depends on the relative strength of the solute-solvent interaction to the solvent-solvent interaction [57]. The enrichment or dispersion of CO 2 around the polymer would determine the tendency of the polymer to gather or disperse in CO 2 [58]. Intermolecular RDF has been used to evaluate the miscibility of polymer-solvent systems by investigating the solvation behavior. If the RDF values of atom pairs between polymer and solvent are greater than or almost equal to those of polymers, indicating the richness of the solvent around the polymer, the polymer would dissolve easily and may exhibit good solubility in the solvent [19,59,60]. The RDF statistical results for the C of the polymer-C of the polymer and C of the polymer-C of CO 2 are shown in Figure 5.
For the system of P(HFDA 0.87 -co-VBe 0.13 )-CO 2 , the RDF curve of C of the polymer-C of CO 2 was almost equal to that of C of the polymer-C of the polymer as observed in Figure 5a. For the other three co-polymers, the RDF curves of C of the polymer-C of CO 2 became significantly lower than that of C of the polymer-C of the polymer as shown in Figure 5b-d. With an increase in VBe content, the curve gaps between C of the polymer-C of CO 2 and C of the polymer-C of the polymer increased gradually. The RDF results showed that the co-polymers with lower VBe content were more likely to be surrounded and solvated by CO 2 , thus indicating that they were more soluble in CO 2 . Solvation plays an important role in controlling the solubility of polymer in SC-CO2 [56]. The solvation behavior of the polymer in SC-CO2 depends on the relative strength of the solute-solvent interaction to the solvent-solvent interaction [57]. The enrichment or dispersion of CO2 around the polymer would determine the tendency of the polymer to gather or disperse in CO2 [58]. Intermolecular RDF has been used to evaluate the miscibility of polymer-solvent systems by investigating the solvation behavior. If the RDF values of atom pairs between polymer and solvent are greater than or almost equal to those of polymers, indicating the richness of the solvent around the polymer, the polymer would dissolve easily and may exhibit good solubility in the solvent [19,59,60]. The RDF statistical results for the C of the polymer-C of the polymer and C of the polymer-C of CO2 are shown in Figure 5. For the system of P(HFDA0.87-co-VBe0.13)-CO2, the RDF curve of C of the polymer-C of CO2 was almost equal to that of C of the polymer-C of the polymer as observed in Figure 5a. For the other three co-polymers, the RDF curves of C of the polymer-C of CO2 became significantly lower than that of C of the polymer-C of the polymer as shown in Figure 5b-d. With an increase in VBe content, the curve gaps between C of the polymer-C of CO2 and C of the polymer-C of the polymer increased gradually. The RDF results showed that the co-polymers with lower VBe content were more likely to be surrounded and solvated by CO2, thus indicating that they were more soluble in CO2. Generally speaking, the solubility of polymers in SC-CO2 is dominated by polymer-CO2 interactions, polymer-polymer interaction and chain flexibility. The CO2-soluble polymers have strong polymer-CO2 interaction and weak polymer-polymer interactions, which is reflected by low surface tension. In addition, the high chain flexibility results in the polymers exhibiting the high entropy of mixing in CO2, which is reflected by the low glass transition temperature (Tg). The experimental results in Table 2 showed that with an increase of the molar ratio of VBe, the surface tension and Tg increased gradually, which indicated that the enhancement of polymer-polymer interaction and the decrease of chain flexibility. The polymer-CO2 interaction strength could be characterized by the interaction energy quantitatively, with a greater absolute value of the interaction energy indicating a stronger polymer-CO2 interaction. The interaction energies of co-polymer-CO2 and PHFDA-CO2 were examined by MD. As shown in Table 3, the interaction energy of PHFDA-CO2 was significantly greater than those of the four co-polymers. The interaction energy of co-polymer-CO2 trended downward along with the VBe molar ratio. This indicated that the import of VBe weakened the co-polymer-CO2 interaction. Generally speaking, the solubility of polymers in SC-CO 2 is dominated by polymer-CO 2 interactions, polymer-polymer interaction and chain flexibility. The CO 2 -soluble polymers have strong polymer-CO 2 interaction and weak polymer-polymer interactions, which is reflected by low surface tension. In addition, the high chain flexibility results in the polymers exhibiting the high entropy of mixing in CO 2 , which is reflected by the low glass transition temperature (T g ). The experimental results in Table 2 showed that with an increase of the molar ratio of VBe, the surface tension and T g increased gradually, which indicated that the enhancement of polymer-polymer interaction and the decrease of chain flexibility. The polymer-CO 2 interaction strength could be characterized by the interaction energy quantitatively, with a greater absolute value of the interaction energy indicating a stronger polymer-CO 2 interaction. The interaction energies of co-polymer-CO 2 and PHFDA-CO 2 were examined by MD. As shown in Table 3, the interaction energy of PHFDA-CO 2 was significantly greater than those of the four co-polymers. The interaction energy of co-polymer-CO 2 trended downward along with the VBe molar ratio. This indicated that the import of VBe weakened the co-polymer-CO 2 interaction. In summary, with an increase in VBe content, the co-polymer-CO 2 interaction energy decreased, the polymer-polymer interaction enhanced, the chain flexibility declined and resulted in unfavorable entropy of mixing, which resulted in a decrease the co-polymer solubility and an increase in the cloud point pressure of the co-polymer-CO 2 system.

Thickening Capability of Co-Polymers in SC-CO 2
The variations of the relative viscosity of the co-polymer-CO 2 solutions against mass concentration at 308.2 K and 30 MPa were used to evaluate the viscosification, which is shown in Figure 6. This indicated that all the co-polymers could thicken SC-CO 2 and the thickening capability increased with greater mass concentration. Unlike the solubility, the thickening capability did not vary with the VBe molar ratio linearly with a maximum occurring at 33.0 mol %. The P(HFDA 0.67 -co-VBe 0.33 ) could enhance the viscosity of SC-CO 2 by 438 times at 5 wt. %. The P(HFDA 0.87 -co-VBe 0.13 ) with lower content of VBe did not enhance the viscosity of SC-CO 2 significantly, while the thickening capabilities of P(HFDA 0.29 -co-VBe 0.71 ) and P(HFDA 0.50 -co-VBe 0.50 ) with higher content of VBe were also limited.  In summary, with an increase in VBe content, the co-polymer-CO2 interaction energy decreased, the polymer-polymer interaction enhanced, the chain flexibility declined and resulted in unfavorable entropy of mixing, which resulted in a decrease the co-polymer solubility and an increase in the cloud point pressure of the co-polymer-CO2 system.

Thickening Capability of Co-Polymers in SC-CO2
The variations of the relative viscosity of the co-polymer-CO2 solutions against mass concentration at 308.2 K and 30 MPa were used to evaluate the viscosification, which is shown in Figure 6. This indicated that all the co-polymers could thicken SC-CO2 and the thickening capability increased with greater mass concentration. Unlike the solubility, the thickening capability did not vary with the VBe molar ratio linearly with a maximum occurring at 33.0 mol %. The P(HFDA0.67-co-VBe0.33) could enhance the viscosity of SC-CO2 by 438 times at 5 wt. %. The P(HFDA0.87-co-VBe0.13) with lower content of VBe did not enhance the viscosity of SC-CO2 significantly, while the thickening capabilities of P(HFDA0.29-co-VBe0.71) and P(HFDA0.50-co-VBe0.50) with higher content of VBe were also limited.  Figure 7a,b showed the relative viscosity of co-polymer-CO2 solution with 2 wt. % of concentration versus temperature at 30 MPa and versus pressure at 35 °C, respectively. As shown in the figure, the relative viscosity diminished with an increase in temperature, although this was enhanced with an increase in pressure. With an increase in temperature, the dissolubility of CO2 decreased, the co-polymer chains crimped, and the size of hydrodynamics became smaller, so the degree of intermolecular association decreased, leading to a decrease in thickening capability. At higher pressures, the solubility parameter and dissolubility of CO2 was enhanced [52,53], and the copolymer chains were more stretched in solution, with the larger hydrodynamic size allowing the generation of stronger thickening capability through more intermolecular association.  Figure 7a,b showed the relative viscosity of co-polymer-CO 2 solution with 2 wt. % of concentration versus temperature at 30 MPa and versus pressure at 35 • C, respectively. As shown in the figure, the relative viscosity diminished with an increase in temperature, although this was enhanced with an increase in pressure. With an increase in temperature, the dissolubility of CO 2 decreased, the co-polymer chains crimped, and the size of hydrodynamics became smaller, so the degree of intermolecular association decreased, leading to a decrease in thickening capability. At higher pressures, the solubility parameter and dissolubility of CO 2 was enhanced [52,53], and the co-polymer chains were more stretched in solution, with the larger hydrodynamic size allowing the generation of stronger thickening capability through more intermolecular association. To understand the thickening capability of the co-polymers intuitively, the equilibrium conformations of the co-polymers and the PHFDA in SC-CO2 obtained by molecular dynamics simulation were analyzed. As shown in Figure 8, there was no effective aggregation between the polymer chains for the PHFDA. The co-polymers containing VBe groups exhibited aggregation between polymer chains in different levels. It may be inferred that PHFDA lacked the basic power of triggering intermolecular association due to the weak polymer-polymer interaction, while the VBe group in the co-polymers could provide the driving power. The most obvious intermolecular association was initiated by P(HFDA0.67-co-VBe0.33), which formed effective molecular aggregates. The P(HFDA0.87-co-VBe0.13) with lower VBe content exhibited less inter-chain aggregation compared to P(HFDA0.67-co-VBe0.33). It was inferred that its poor thickening capabilities rooted in the lack intermolecular aggregation was due to the shortage of VBe groups. However, the excess of VBe groups would generate more intramolecular π-π stacking and a decrease in intermolecular π-π stacking, just as the equilibrium conformations shown in Figure 8. Therefore, the thickening capabilities of P(HFDA0.50-co-VBe0.50) and P(HFDA0.29-co-VBe0.71) with higher VBe content were not as good as P(HFDA0.67-co-VBe0.33). In this work, 33.0 mol % of VBe content of the co-polymer was the optimum value for generating the strongest intermolecular association and thus the best thickening performance.  To understand the thickening capability of the co-polymers intuitively, the equilibrium conformations of the co-polymers and the PHFDA in SC-CO 2 obtained by molecular dynamics simulation were analyzed. As shown in Figure 8, there was no effective aggregation between the polymer chains for the PHFDA. The co-polymers containing VBe groups exhibited aggregation between polymer chains in different levels. It may be inferred that PHFDA lacked the basic power of triggering intermolecular association due to the weak polymer-polymer interaction, while the VBe group in the co-polymers could provide the driving power. The most obvious intermolecular association was initiated by P(HFDA 0.67 -co-VBe 0.33 ), which formed effective molecular aggregates. The P(HFDA 0.87 -co-VBe 0.13 ) with lower VBe content exhibited less inter-chain aggregation compared to P(HFDA 0.67 -co-VBe 0.33 ). It was inferred that its poor thickening capabilities rooted in the lack intermolecular aggregation was due to the shortage of VBe groups. However, the excess of VBe groups would generate more intramolecular π-π stacking and a decrease in intermolecular π-π stacking, just as the equilibrium conformations shown in Figure 8. Therefore, the thickening capabilities of P(HFDA 0.50 -co-VBe 0.50 ) and P(HFDA 0.29 -co-VBe 0.71 ) with higher VBe content were not as good as P(HFDA 0.67 -co-VBe 0.33 ). In this work, 33.0 mol % of VBe content of the co-polymer was the optimum value for generating the strongest intermolecular association and thus the best thickening performance. To understand the thickening capability of the co-polymers intuitively, the equilibrium conformations of the co-polymers and the PHFDA in SC-CO2 obtained by molecular dynamics simulation were analyzed. As shown in Figure 8, there was no effective aggregation between the polymer chains for the PHFDA. The co-polymers containing VBe groups exhibited aggregation between polymer chains in different levels. It may be inferred that PHFDA lacked the basic power of triggering intermolecular association due to the weak polymer-polymer interaction, while the VBe group in the co-polymers could provide the driving power. The most obvious intermolecular association was initiated by P(HFDA0.67-co-VBe0.33), which formed effective molecular aggregates. The P(HFDA0.87-co-VBe0.13) with lower VBe content exhibited less inter-chain aggregation compared to P(HFDA0.67-co-VBe0.33). It was inferred that its poor thickening capabilities rooted in the lack intermolecular aggregation was due to the shortage of VBe groups. However, the excess of VBe groups would generate more intramolecular π-π stacking and a decrease in intermolecular π-π stacking, just as the equilibrium conformations shown in Figure 8. Therefore, the thickening capabilities of P(HFDA0.50-co-VBe0.50) and P(HFDA0.29-co-VBe0.71) with higher VBe content were not as good as P(HFDA0.67-co-VBe0.33). In this work, 33.0 mol % of VBe content of the co-polymer was the optimum value for generating the strongest intermolecular association and thus the best thickening performance.  The peak position and peak value of the radial distribution function could indicate the strength of the inter-group interaction indirectly. A smaller peak position and higher peak value represented the stronger interaction strength. Intermolecular RDFs for C-C pairs of the VBe groups and F-F pairs of the HFDA groups were used to further investigate the microstructure of the four co-polymer-CO 2 systems quantitatively, with the results shown in Figure 9. As shown in Figure 9a, the distance of the RDF curves that achieved the values of greater than zero was about 2.9 Å. This indicated that the intermolecular interactions of VBe groups in the co-polymers were dominated by van der Waals forces. The RDF values and positions of the peaks were significantly different for the four polymer-CO 2 systems. The RDF curve peak of P(HFDA 0.67 -co-VBe 0.33 ) was the highest, while a peak appeared at the distance of 4.9 Å. The RDF curve peak heights of P(HFDA 0.87 -co-VBe 0.13 ) and P(HFDA 0.50 -co-VBe 0.50 ) were almost the same, but the peak of the former appeared at 10.7 Å, which was farther away than the 6.5 Å of the latter. No peak could be observed in the RDF curve of P(HFDA 0.29 -co-VBe 0.71 ), which had the smallest RDF value. As shown in Figure 9b, all the curves showed similar trend and no obvious peak was observed. This indicated that the intermolecular interaction between HFDA groups in co-polymer was not strong enough to generate effective intermolecular associations. It may be related to the strong electronegativity and fluorine repulsion of F atoms in the HFDA group. By comparing the data in Figures 5 and 9, it is not difficult to find that intermolecular aggregation occurs between the VBe groups not between HFDA groups. According to the results of experiments and simulations, the thickening capabilities of the co-polymers in SC-CO 2 should be attributed to the π-π stacking of VBe group.
Polymers 2018, 10, x FOR PEER REVIEW 12 of 16 The peak position and peak value of the radial distribution function could indicate the strength of the inter-group interaction indirectly. A smaller peak position and higher peak value represented the stronger interaction strength. Intermolecular RDFs for C-C pairs of the VBe groups and F-F pairs of the HFDA groups were used to further investigate the microstructure of the four co-polymer-CO2 systems quantitatively, with the results shown in Figure 9. As shown in Figure 9a, the distance of the RDF curves that achieved the values of greater than zero was about 2.9 Å. This indicated that the intermolecular interactions of VBe groups in the co-polymers were dominated by van der Waals forces. The RDF values and positions of the peaks were significantly different for the four polymer-CO2 systems. The RDF curve peak of P(HFDA0.67-co-VBe0.33) was the highest, while a peak appeared at the distance of 4.9 Å. The RDF curve peak heights of P(HFDA0.87-co-VBe0.13) and P(HFDA0.50-co-VBe0.50) were almost the same, but the peak of the former appeared at 10.7 Å, which was farther away than the 6.5 Å of the latter. No peak could be observed in the RDF curve of P(HFDA0.29-co-VBe0.71), which had the smallest RDF value. As shown in Figure 9b, all the curves showed similar trend and no obvious peak was observed. This indicated that the intermolecular interaction between HFDA groups in co-polymer was not strong enough to generate effective intermolecular associations. It may be related to the strong electronegativity and fluorine repulsion of F atoms in the HFDA group. By comparing the data in Figures 5 and 9, it is not difficult to find that intermolecular aggregation occurs between the VBe groups not between HFDA groups. According to the results of experiments and simulations, the thickening capabilities of the co-polymers in SC-CO2 should be attributed to the π-π stacking of VBe group.

Conclusions
Four P(HFDA-co-VBe) co-polymers with different compositions were synthesized and evaluated. The molecular models of co-polymer-CO2 systems were established to study the molecular behaviors and intermolecular interactions by the all-atom MD simulation. We found that the π-π stacking of the VBe group played a decisive role in thickening SC-CO2. The solubility of the co-polymers decreased with an increase in VBe content, while the thickening capability did not vary with the VBe molar ratio linearly. The relative viscosity of the co-polymers reached its maximum of 438 at a VBe molar ratio of 33.0% in this work. Less VBe content resulted in the lack of intermolecular π-π stacking, while excessive VBe content generated more intramolecular π-π stacking and less intermolecular π-π stacking. This work provided the molecular insights into the relationship of copolymer structure with the activity by the study of intermolecular interactions. The thickening capability of ternary co-polymer or polymer surfactant in SC-CO2 will be discussed in future studies.

Conclusions
Four P(HFDA-co-VBe) co-polymers with different compositions were synthesized and evaluated. The molecular models of co-polymer-CO 2 systems were established to study the molecular behaviors and intermolecular interactions by the all-atom MD simulation. We found that the π-π stacking of the VBe group played a decisive role in thickening SC-CO 2 . The solubility of the co-polymers decreased with an increase in VBe content, while the thickening capability did not vary with the VBe molar ratio linearly. The relative viscosity of the co-polymers reached its maximum of 438 at a VBe molar ratio of 33.0% in this work. Less VBe content resulted in the lack of intermolecular π-π stacking, while excessive VBe content generated more intramolecular π-π stacking and less intermolecular π-π stacking. This work provided the molecular insights into the relationship of co-polymer structure with the activity by the study of intermolecular interactions. The thickening capability of ternary co-polymer or polymer surfactant in SC-CO 2 will be discussed in future studies.