Synthesis of Linear Modified Siloxane-Based Thickeners and Study of Their Phase Behavior and Thickening Mechanism in Supercritical Carbon Dioxide

Abstract

To address critical limitations of ultra-low viscosity supercritical CO₂ fracturing fluids, including excessive fluid loss and inadequate proppant transport capacity, a series of thickeners designed to significantly enhance CO₂ viscosity were synthesized. Initially, FT-IR and ¹H NMR characterization confirmed successful chemical reactions and incorporation of both solvation-enhancing and -thickening functional groups. Subsequently, dissolution and thickening performance were evaluated using a custom-designed high-pressure vessel featuring visual observation capability, in-line viscosity monitoring, and high-temperature operation. All thickener systems exhibited excellent solubility, with 5 wt% loading elevating CO₂ viscosity to 3.68 mPa·s. Ultimately, molecular simulations performed in Materials Studio elucidated the mechanistic basis, electrostatic potential (ESP) mapping, cohesive energy density analysis, intermolecular interaction energy, and radial distribution function comparisons. These computational approaches revealed dissolution and thickening mechanisms of polymeric thickeners in CO₂.

1. Introduction

With the rapid development of the modern industrial society worldwide, the use of fossil fuels such as crude oil and natural gas has gradually increased, resulting in a large amount of CO₂ emissions [1]. In response to the rapid growth of CO₂ emissions, more attention has been paid to CO₂ capture, utilization, and storage (CCUS) research [2,3]. The global CCUS technologies have been developing for more than 40 years and has been slow to develop due to high investment costs and policy influences [4]. In recent years, there have been developments that can re-create value after CO₂ capture and storage, such as using CO₂ to flood oil [5].

With the advancement of oil and gas field development technology, the development of unconventional oil and gas resources is receiving increasing attention [6]. Compared with the problems of reservoir permeability damage exposed by traditional hydraulic fracturing technology, supercritical CO₂ fracturing technology, which has the advantages of avoiding clay swelling and water locking, enhancing fracturing expansion, easy backflow, and reducing water consumption, is regarded as an ideal fracturing technology with great application potential [7,8]. However, the widespread application of supercritical CO₂ fracturing is severely limited due to issues such as gravity separation, viscous fingering, and poor sand-carrying capacity caused by its extremely low viscosity during the fracturing process [9].

To solve the above series of problems caused by supercritical CO₂ fracturing, many scholars have conducted research on CO₂ thickening; thickening technology refers to the process of dissolving thickening agent such as fluoropolymer, siloxane polymer, hydrocarbon polymer, and surfactant dissolved in CO₂, and forming a transparent and stable homogeneous phase, so as to achieve the purpose of thickening CO₂ [6,10,11]. Among them, the solubility and thickening ability of thickeners are of paramount importance in the study of thickeners [9]. Researchers typically seek structural balance between CO₂-philic and CO₂-phobic group to achieve a dynamic balance of solubility and thickening ability [10]. Because of its strong interaction with CO₂ and good solubility, fluoropolymers have become the main CO₂ solubilizing structure and CO₂-philic substance [12,13]. Dai et al. [4] prepared a copolymer of heptafluorodecyl acrylate and styrene [P(HFDA/STY)] as a thickener for supercritical CO₂. The unique binding mode between phenyl groups on the copolymer chains and CO₂, as well as the molecular simulation radial distribution function (RDF), indicate that phenyl groups have higher aggregation and thickening abilities compared to fluorinated groups. Kilic et al. [14] studied the influence of the composition of copolymer of aromatic acrylate–fluoroacrylate on the viscosity of CO₂. It was found that the copolymer composed of 29% aromatic acrylate and 71% fluoroacrylate was the most effective CO₂ thickener. At a pressure of 15 MPa and temperature of 295 K, the thickener is miscible with CO₂, and the viscosity increased to a certain extent. While achieving a balance between the thickening and solubilizing structure of polymer thickeners, less attention has been paid to the mechanisms of thickening and solubilizing polymer and the interaction between various functional groups and CO₂.

On the basis of modified siloxane as a thickening group, this study introduces fluorinated groups as solubilizing groups to synthesize fluorinated modified siloxane thickeners. The solubility and thickening ability of fluorinated groups, modified siloxanes, and their copolymers were tested and characterized by infrared and nuclear magnetic resonance, and the microscopic behavior of fluorinated groups, modified siloxanes, and their copolymers in supercritical CO₂ was studied using full atomic molecular dynamics simulation. The mechanism of action of different groups was explored, providing ideas for the molecular design of CO₂ thickeners in the future.

2. Chemicals and Methods

2.1. Chemicals

Concentrated sulfuric acid, sodium carbonate, trimethylolpropane trimethacrylate, isocyanuric acid triallyl ester, tetramethyldisiloxane (HMM), octamethylcyclotetrasiloxane (D4), azodiisobutyronitrile, and chloroplatinic acid were purchased from Chengdu Kelong Co., Ltd., Chengdu, China. All the chemicals were used as received without further purification. CO₂ and N₂ were sourced from Chengdu Xindu Jinnengda Gas Co., Ltd., Chengdu, China.

2.2. Synthesis of Linear Modified Silicone-Based Supercritical CO₂ Thickener

2.2.1. Preparation of Silicon Hydrogen-Terminated Linear Polysiloxane

Under the conditions of 90 °C and concentrated sulfuric acid as a catalyst, 1 g of HMM and 50 g of D4 were polymerized in a N₂ atmosphere for 12 h to obtain silicon hydrogen-terminated linear siloxane. Subsequently, sodium carbonate was added to filter out the sulfuric acid catalyst, followed by vacuum distillation to remove impurities, resulting in a silicon hydrogen-terminated linear polysiloxane, labeled HMM-D4. The synthesis route is shown in Figure 1.

2.2.2. Synthesis of Supercritical CO₂ Copolymer Thickeners

A quantity of trimethylolpropane triacrylate or triallyl isocyanurate was added to a three-necked flask, stirred and heated to 70 °C, and then chloroplatinic acid was added for activation for 2 h. Subsequently, a certain amount of HMM-D4 was added to the flask (the molar ratio of siloxane to acrylic ester was 1:2) under stirring conditions. After 4 h, chloroplatinic acid was separated by precipitation with anhydrous methanol, and the low boiling impurities were removed by vacuum distillation on a rotary evaporator to obtain a yellow liquid, which was the final copolymer thickener, named SHTT or SHTA. The synthesis route is shown in Figure 2.

2.2.3. Modification of SHTT and SHTA

An amount of 0.001 g of azobisisobutyronitrile was added to 25 g of SHTT or SHTA. After activation for 2 h, 3.885 g of fluorinated acrylate was added under stirring conditions. The modified SHTT and SHTA product was obtained by condensation reflux reaction at a temperature of 80 °C for 6 h and named SHTTF and SHTAF. The modification route is shown in Figure 3.

2.3. Characterization

The chemical structure of copolymers and modified copolymers was characterized by FT-IR and ¹H NMR. The FT-IR spectrum of the copolymers was recorded using a Nicolet Nexus 170SX FT-IR (Madison, WI, USA) on KBr tablets. The ¹H NMR spectrum of copolymers and modified copolymers were investigated using a Bruker 400 MHZ NMR spectrometer (Japan Electronics Corporation, Tokyo, Japan) using deuterated chloroform as the solvent.

2.4. Solubility and Thickening Properties of Copolymers and Modified Copolymers

The solubility and thickening properties of copolymers and modified copolymers were investigated using a visualization supercritical CO₂ fracturing fluid evaluation device. The schematic diagram of the experimental device is shown in Figure 4. The experimental steps were as follows.

(1)

Accurately weigh the required thickener and add it to the intermediate container.

(2)

Seal the visual reaction vessel and heat it to the measurement temperature.

(3)

Inject CO₂ to 0.5 MPa and then reduce the pressure. Repeat this cycle 5 times to expel the air inside the visual reaction vessel.

(4)

Use an ISCO pump to inject the weighed thickener in the intermediate container into the visual reaction vessel.

(5)

Use a CO₂ gas booster pump to pressurize CO₂ to the pressure required for the experiment. The physical property parameters of CO₂ were referenced from the software REFPROP (version 9.1).

(6)

Start mechanical stirring at the bottom of the visual reaction vessel (stirring speed range: 0–1350 rpm). Stir at a constant speed for at least 40 min to promote the dissolution of the thickener and form a transparent and homogeneous solution. (The dissolution of the thickener in supercritical CO₂ was observed through the front viewing window using an external LED light source placed behind the rear viewing window. High solubility of the thickener was indicated when the mixed fluid inside the visual reaction vessel became clear (the reference object was clearly visible).)

(7)

A circulating water vacuum pump was used to evacuate the Cambridge online viscometer.

(8)

Open the intake valve of the online viscometer to allow the completely dissolved thickener solution from step (6) to enter. Meanwhile, manually and slowly adjust the volume of the visual reaction vessel to maintain a stable system pressure. Use a data acquisition system to obtain viscosity data.

(9)

After the test is completed, direct the system into the waste liquid collection device. Simultaneously, clean the equipment and wait for the next experiment.

2.5. Molecular Simulation Study

Molecular simulation techniques were employed to investigate the thickening mechanisms of supercritical CO₂ thickener, utilizing the Material Studio (version 2023) software package. The Compass force field, which is widely applied in recent years and known for its high accuracy, was selected to calculate the interparticle interactions [5,15,16,17]. Within the Amorphous Cell module, simulation systems containing CO₂ molecules and modified silicone-based thickener molecules were constructed. Three-dimensional periodic boundary conditions were applied to simulate the supercritical state. The system underwent sequential structural optimization and annealing to obtain the minimum energy conformation. Subsequently, equilibrium molecular dynamics (MD) calculations were performed under the NPT ensemble for both CO₂ and the thickener polymer, resulting in stable structures for subsequent studies [5,18].

Table 1. The repetitive unit structures of different thickeners (yellow, white, gray, red, blue, and purple denote silicon, hydrogen, carbon, oxygen, fluorine, and nitrogen atoms, respectively).

Name	Molecular Structure
CO2
SHTT
SHTA
SHTTF
SHTAF

lists the detailed information and optimized structures of the different monomers and modified silicone-based thickeners used in the simulations. The simulation process is listed below:

(1)

A model was constructed based on the molecular structures presented in Table 1. Force field charges were assigned, and the configuration with the lowest energy was selected for geometric optimization using the Forcite module.

(2)

The model obtained from the initial geometric optimization was subjected to annealing using the Forcite module. The system went through 10 annealing cycles, starting from 313.15 K, ramping up to 500 K, and then returning to 313.15 K to reach system equilibrium.

(3)

Under the NPT ensemble, the desired temperature and pressure conditions (305.15 K, 10 MPa) were set. The Andersen thermostat and Berendsen barostat were employed, respectively. The time step was set to 1 fs, and the total simulation duration was 500 ps. In the aforementioned molecular dynamics process, one frame was output every 5 ps, and the data from the last 100 ps were used for subsequent data analysis.

2.5.1. Cohesive Energy Density (CED)

It is defined as the energy required to overcome the intermolecular force in 1 mole of a condensed matter substance quantitatively characterized in the interactions between polymer molecules [19]. And the solubility parameter (δ) is defined as the square root of CED [20].

$$E=-E_{inter}=E_{van}+E_{elect}+E_{other}$$

(1)

$$CED={\displaystyle \frac{E}{V}}$$

(2)

$$\delta =\sqrt{CED}=\sqrt{{\displaystyle \frac{E}{V}}}$$

(3)

where the CED is the cohesive energy density, J/m³; E is the energy of the substance, kJ/mol; V is the molar volume of the substance, L/mol; δ is the solubility parameter, (J/m³)^1/2; E_inter is the total intermolecular energy of the system (kJ/mol); E_van is the energy from van der Waals interactions (kJ/mol); and E_elect is the energy from electrostatic interactions (kJ/mol).

2.5.2. Interaction Energy

The interaction energy serves to quantitatively characterize the strength of interactions between the polymer and CO₂. A larger absolute magnitude of the interaction energy indicates stronger interactions between the polymer and CO₂ [1].

$$E_{int}=E_{polymer+{CO}_2}-(E_{polymer}+E_{{CO}_2})$$

(4)

where E_int is the polymer–CO₂ interaction energy, (kJ/mol); E_polymer+CO2 is the total energy of the polymer–CO₂ system (kJ/mol); E_polymer is the energy of the polymer (kJ/mol); and E_CO2 is the energy of CO₂, kJ/mol.

2.5.3. Radial Distribution Function (RDF)

The RDF is commonly used to investigate the microscopic structure of systems and evaluate intermolecular interactions. It typically represents the probability density of finding a molecule (or atom) of A at a specific distance from a molecule (or atom) of B [21] calculated as

$$g_{AB}(r)={\displaystyle \frac{1}{{\rho }_{AB}·4\pi r·{∆}_r}}{\displaystyle \frac{\sum _{j=1}^{N_{AB}}{∆N}_{AB}(r\to r+∆r)}{N_{AB}}}$$

(5)

where $g_{AB}\left(r\right)$ is the radial distribution function value; $N_{AB}$ is the number of species A and B (molecules or atoms) in the system; $∆r$ is the distance interval width; ${∆N}_{AB}$ is the number of B particles (or A particles) found within the distance range r~r + Δr from a central A particle (or B particle); and ${\rho }_{AB}$ is the density of system.

3. Results and Discussion

3.1. Characterization of Supercritical CO₂ Thickener

3.1.1. FT-IR

Figure 5 shows the FT-IR spectra of HMM-D4, SHTT, and SHTA. The FT-IR spectra of HMM-D4 primarily exhibit characteristic peaks including the Si-CH₃ stretching vibration at 1257 cm⁻¹, Si-O stretching vibration at 1064 cm⁻¹ and 1052 cm⁻¹, and the Si-C stretching vibration at 797 cm⁻¹. As the hydrosilylation reaction progresses, the characteristic peaks of HMM-D4 are still retained in the infrared spectra of the obtained thickeners SHTT and SHTA. However, the intensities of the peaks corresponding to the Si-CH₃ stretching vibration at 1257 cm⁻¹ and the Si-O stretching vibration at 1052 cm⁻¹ are significantly reduced [22]. Additionally, new peaks emerge at 1680 cm⁻¹ (C=C stretching vibration of CH₂=CH–), 1719 cm⁻¹ (C=O stretching vibration), and 1447 cm⁻¹ (bending vibration of saturated C–H bonds in –CH₂– and –CH₃ groups) [23,24]. Based on the above analysis, the appearance of new characteristic peaks in the infrared spectra of the thickeners SHTT and SHTA corresponds to the changes in functional groups during the hydrosilylation reaction [17]. This conclusion is consistent with the previous research results of Tang et al. [22] and Liu et al. [17,19].

3.1.2. ¹H NMR

Figure 6 shows the ¹H NMR spectra of the thickener copolymers. The peak at 7.26 ppm corresponds to the residual protons in the solvent CDCl₃. For SHTT (Figure 6a), key signals include alkenyl protons (CH₂=C(CH₃)C=O–) at 5.5–6.2 ppm, methylene protons (–(CH₂)₃CCH₂CH₃) at 3.9–4.2 ppm, methyl protons (CH₂=C(CH₃)C=O–) at 1.94 ppm, methylene protons of the ethyl group (–(CH₂)₃CCH₂CH₃) at 1.2 ppm, methylene and methyl protons (O=C–CH(CH₃)CH₂Si–) at 0.89–0.98 ppm, and methyl protons bonded to silicon (Si–CH₃) at 0.1–0.2 ppm. For SHTA (Figure 6b), key signals include methine proton (–NCH₂CH=CH₂) at 5.8–5.93 ppm, alkenyl protons (–NCH₂CH=CH₂) at 5.2–5.34 ppm, methylene protons of the allyl group (–CH₂–) at 4.4–4.6 ppm, methylene protons adjacent to silicon (Si–CH₂CH₂–) at 1.2–1.6 ppm, and methyl protons bonded to silicon (Si–CH₃) at 0–0.2 ppm [17,19].

Compared with SHTT (Figure 6a), in SHTTF (Figure 6c), peaks corresponding to the hydrogen atoms of the methylene group adjacent to the oxygen atom in –O–CH₂–CH₂–C₈F₁₇ appear at δ = 3.9–4.2 ppm, and peaks corresponding to the hydrogen atoms of the methylene group adjacent to the fluorine atoms in –O–CH₂–CH₂–C₈F₁₇ appear at δ = 1.7–1.94 ppm. Similarly, in SHTAF (Figure 6d), the peak corresponding to the hydrogen atoms of the methylene group adjacent to the oxygen atom in –O–CH₂–CH₂–C₈F₁₇ appears at δ = 4.2 ppm, and the peak corresponding to the hydrogen atoms of the methylene group adjacent to the fluorine atoms in –O–CH₂–CH₂–C₈F₁₇ appears at δ = 1.7–1.96 ppm. Similar to the findings of Dai et al. [4] and Sun et al. [13], the changes in the values of these characteristic peaks correspond to the changes in the corresponding functional groups after the introduction of fluorides. Combining the previous infrared analysis and the above NMR results, it indicates the successful preparation of the thickener copolymers.

3.2. Phase Behavior

The phase behavior of SHTT and SHTTF in ScCO₂ was investigated using visualized reaction vessel as shown in Figure 4, with results presented in Figure 7 and

Table 2. Phase behavior and dissolution pressure of thickeners (SHTT and SHTTF) in CO₂ under different temperatures and pressures.

System	Temperature (°C)/Pressure (MPa)				Dissolution Pressure (MPa)
	25 °C, 7.5 MPa	32 °C, 7.5 MPa	32 °C, 10 MPa	32 °C, 7.5 MPa
SHTT-CO2	a1	a2	a3	a4	9.2
	Clarified	Turbid, reference object not visible	Clear and transparent	Turbid, reference object visible
SHTTF-CO2	b1	b2	b3	b4	8.6
	Clarified	Turbid, reference object not visible	Clear and transparent	Turbid, reference object visible

. The observation revealed that the system remained clear and transparent under stirred conditions at 25 °C and 7.5 MPa, allowing distinct visibility of the reference wire behind the observation window (Figure 7(a₁,b₁)). When stirring was initiated at 32° C and 7.5 MPa, the system turned turbid as temperature increase intensified molecular thermal motion, promoting gradual dissolution of the thickener and completely obscuring the reference wire (Figure 7(a₂,b₂)). Upon maintaining the temperature while slowly increasing pressure to 10 MPa, the thickener became fully dissolved in ScCO₂, accompanied by brightening of the solubility phase diagram and restored visibility of the reference wire (Figure 7(a₃,b₃)). When pressure was reduced back to 7.5 MPa, the system appeared more turbid than in Figure 7(a₃,b₃) at 32 °C and 10 MPa but retained better clarity than in Figure 7(a₂,b₂), suggesting that although pressure decreased, the polymeric thickener remained dissolved in supercritical CO₂ without complete precipitation [15]. During this process, the dissolution pressures of SHTT-CO₂ and SHTTF-CO₂ were measured to be 9.2 MPa and 8.6 MPa, respectively. The dissolution pressure is defined as the pressure at which the thin-line reference changes from visible to invisible during the pressure reduction process starting from 10 MPa (the measurement is repeated three times, and the average value is taken) [17,19].

3.3. Thickening Ability

The thickening ability of SHTT, SHTA, SHTTF, and SHTAF were investigated at 32 °C and 10 MPa, and the results are shown in Figure 8 and

Table 3. The original viscosity data of supercritical CO₂ thickened by different contents and types of thickeners at 32 °C and 10 MPa.

Temperature (°C)/Pressure (MPa)		System	SHTT-CO2	SHTA-CO2	SHTTF-CO2	SHTAF-CO2
	Content (wt%)		Viscosity (mPa·s)
32 °C, 10 MPa	0		0.06335 (REFPROP)
	1		0.823	0.355	2.026	1.564
	2		1.027	0.539	2.612	1.636
	3		1.234	0.66	2.951	1.986
	4		1.378	0.85	3.396	2.47
	5		1.512	1.162	3.68	2.676

. All ScCO₂ fracturing fluid systems with different thickeners exhibited the same trend. Based on the literature review, a good thickener should achieve a thickening ratio of 10~100 times (compared to pure CO₂) at a low concentration (0~5 wt%) and achieve excellent solubility while maintaining thickening performance, cost-effectiveness, and safety [9,10]. Based on this, in this study, the authors will investigate the concentration of the additive (thickener) in the range of 0~5 wt%. The viscosity of ScCO₂ increased with higher thickener content. However, fluorinated modified copolymers (SHTTF, SHTAF) demonstrated a significantly stronger impact on ScCO₂ viscosity than SHTT and SHTA, highlighting its superior thickening capacity. For instance, adding 5 wt% SHTTF increased the viscosity of CO₂ to 3.68 mPa·s. At the initial stage of adding SHTT or SHTA, the system contained only a small number of thickener molecules, resulting in limited van der Waals interactions and hydrogen bonding between CO₂ molecules and the thickener. This formed a sparse spatial network structure. As the thickener content increased—particularly with fluorinated thickeners like SHTTF and SHTAF—more modified siloxane polymers dissolved in CO₂. This enhanced the interactions between CO₂ molecules and thickener molecules, leading to the formation of a denser microscopic spatial network structure [16,19]. Consequently, the apparent viscosity of CO₂ increased macroscopically.

Under experimental conditions of 32 °C and 5 wt% thickener dosage, the effect of pressures on the viscosity of CO₂ thickened by various agents was studied, with results shown in Figure 9 and

Table 4. The original viscosity data of supercritical CO₂ thickened by different types of thickeners under different pressures at 32 °C with a thickener content of 5 wt%.

Temperature (°C)/Content (wt%)		System	SHTT-CO2	SHTA-CO2	SHTTF-CO2	SHTAF-CO2
	Pressure (MPa)		Viscosity (mPa·s)
32 °C, 5 wt%	7.5		1.312	0.9	3.334	2.495
	10		1.512	1.162	3.68	2.676
	12.5		1.69	1.28	3.785	2.96
	15		1.803	1.56	3.9	3.27
	17.5		1.905	1.77	4.102	3.34

. The viscosity of thickened CO₂ increased with rising pressure, with SHTTF demonstrating the optimal thickening performance. The likely reasons are (1) the incorporation of fluoride groups enhances the solubility of the modified siloxane polymer in CO₂; (2) during pressurization, decreasing intermolecular distances facilitate the formation of hydrogen bonding through Lewis acid–base pairing. These two effects work synergistically, manifesting macroscopically as an increase in CO₂ viscosity [19,25].

Figure 10 presents the curves depicting the influence of temperature on the thickening capacity of various thickeners for the CO₂ system (

Table 5. The original viscosity data of supercritical CO₂ thickened by different types of thickeners at different temperatures under 10 MPa with a thickener content of 5 wt%.

Pressure (MPa)/Content (wt%)		System	SHTT-CO2	SHTA-CO2	SHTTF-CO2	SHTAF-CO2
	Temperature (°C)		Viscosity (mPa·s)
10 MPa, 5 wt%	32		1.512	1.162	3.68	2.676
	36		1.36	0.985	3.51	2.33
	40		1.11	0.81	3.09	2.17
	44		0.934	0.523	2.77	1.79
	48		0.8	0.4	2.49	1.31

shows the original data corresponding to Figure 10). The results indicate that the viscosity of CO₂ thickened by SHTT, SHTA, SHTTF, and SHTAF declined progressively with increasing temperature. This occurs because, at lower temperatures, the three-dimensional network structures formed by molecular intertwining are insufficient to counteract the disruption of the network structure induced by the temperature rise, as well as the detrimental effect on viscosity caused by the breakdown of Lewis acid–base pairs [12,26].

To further clarify the gap between the thickener prepared in this study and similar thickeners in the current literature,

Table 6. Under different experimental conditions (content, cosolvent, temperature, pressure), the viscosity data of this study are compared with those of similar thickeners in the existing literature [31].

Thickener	Concentration (wt%)	Cosolvent (wt%)	Experimental Condition	Viscosity (mPa·s)	Ref.
HBD-1	5	no	32 °C/8 MPa	3.4	[17]
HBD-2	5	no	32 °C/8 MPa	4.3
SHTTF	5	no	32 °C/10 MPa	3.68	This study
HS-1	5	no	32 °C/10 MPa	0.8	[19]
HS-2	5	no	32 °C/10 MPa	2.7
HS-3	5	no	32 °C/10 MPa	3.0
PDMS (350 mPa·s)	5	10 wt% toluene	42 °C/20 MPa	1.5	[27]
SiO2/HBD-2	5 wt% HBD-2 + 1 wt% SiO2	no	32 °C/10 MPa	5.82	[16]
EEPDMS	3	9 wt% toluene	30 °C/8 MPa	1.3	[28,29]
Ester-branched polydimethylsiloxane	2.5	7.5 wt% n-hexane	30 °C/12 MPa	1.65	[30]

and Figure 11 present the detailed viscosity data of similar thickeners under different experimental conditions in the literature and a 3D intuitive comparison diagram, respectively. Overall, the SHTTF thickener prepared in our study exhibits relatively excellent CO₂ thickening ability, which is superior to the reported HBD-1 thickener (32 °C/8 MPa) [17], HS series thickeners (32 °C/10 MPa) [19], PDMS (42 °C/20 MPa) [27], EEPDMS (30 °C/8 MPa) [28,29], and Ester-branched polydimethylsiloxane (30 °C/12 MPa) [30]. In addition, it is worth mentioning that, in comparison with the thickeners in these references, no cosolvent was added in this study. However, there is still a significant gap in the thickening ability between the thickener in this study and the reported HBD-2 [17] and SiO₂/HBD-2 thickeners [16] in the literature, which is exactly the direction of our future efforts (structure optimization, compounding of different types of thickeners, or introduction of nanomaterials).

3.4. Thickening Mechanisms

3.4.1. Molecular Electrostatic Potential Map

Figure 12 shows the electrostatic potential distribution of CO₂ molecules and modified siloxane thickeners. In CO₂, negative charges concentrate on oxygen atoms, whereas positive charges in both modified siloxane and fluorinated modified siloxane thickeners distribute evenly across carbon-containing groups [32]. Simultaneously, the electrostatic potential at polymerization sites between modified siloxane and fluorides (Figure 12d,e) appears slightly higher than that of surrounding functional groups [15]. Consequently, both modified and fluorinated modified siloxane thickeners can bind with CO₂ molecules through electrostatic attraction [1,15].

3.4.2. CED and Δ

CED and δ are commonly employed to characterize intermolecular interactions in polymers. CED is defined as the energy required to vaporize one mole of a condensed substance per unit volume, overcoming intermolecular forces, which primarily reflects inter-group interactions [33]. Relevant studies demonstrate that polymers with lower CED exhibit higher solubility in CO₂. Furthermore, smaller differences between polymer and CO₂ solubility parameters correlate with enhanced dissolution performance of the polymer in CO₂ [34]. The CED and δ of CO₂ and thickened CO₂ system are tabulated in

Table 7. CED and δ of CO₂ and thickened CO₂ at 40 °C and 10 MPa.

System	Evan/(J/m3)	Eelect/(J/m3)	Eother/(J/m3)	CED/(J/m3)	δ/(J/m3)1/2	Δδ/(J/m3)1/2
CO2	7.958 × 107	5.629 × 107	3.033 × 106	1.389 × 108	11.777	0
SHTT-CO2	1.365 × 108	9.910 × 107	5.454 × 106	2.411 × 108	15.512	3.735
SHTA-CO2	1.369 × 108	9.938 × 107	5.413 × 106	2.417 × 108	15.507	3.730
SHTTF-CO2	7.202 × 107	4.727 × 107	2.803 × 106	1.221 × 108	11.036	0.741
SHTAF-CO2	6.082 × 107	3.986 × 107	2.305 × 106	1.030 × 108	10.119	1.658

, all four thickener polymers show minor δ differences with CO₂. Among these, SHTTF exhibits the smallest δ difference with CO₂, confirming its optimal solubility in the CO₂ system.

3.4.3. Intermolecular Interaction Energy

Interaction energy (E_int) quantitatively characterizes the strength of interactions between polymers and CO₂ molecules (calculated via Equation (4)) [18,35]. A larger absolute value of E_int indicates stronger polymer–CO₂ interactions, which enhances polymer solubility in CO₂ [33,36]. As shown in

Table 8. Intermolecular interaction energy between thickener and CO₂ (4 repeating units of the thickener + 1000 CO₂ molecules).

System	${\mathit{E}}_{{\mathit{P}\mathit{o}\mathit{l}\mathit{y}\mathit{m}\mathit{e}\mathit{r}-\mathit{C}\mathit{O}}_2}$/(kcal/mol)	${\mathit{E}}_{\mathit{P}\mathit{o}\mathit{l}\mathit{y}\mathit{m}\mathit{e}\mathit{r}}$/(kcal/mol)	${\mathit{E}}_{{\mathit{C}\mathit{O}}_2}$/(kcal/mol)	Eint/(kcal/mol)
SHTT-CO2	−2449.962372	−1406.236231	−846.918705	−196.807436
SHTA-CO2	−2205.395479	−1181.816535	−847.726976	−175.851968
SHTTF-CO2	−1635.494087	−390.389668	−1028.260001	−216.844418
SHTAF-CO2	−1473.056476	−292.508835	−977.561245	−202.986396

, in modified siloxane systems, the SHTT-CO₂ system exhibits a greater absolute E_int than the SHTA-CO₂ system, confirming superior solubility of thickener polymer SHTT in CO₂. After fluorination modification, thickener polymer SHTTF maintains stronger solubility in CO₂ than SHTAF. Based on the above interaction energy data between different thickeners and CO₂, the solubility order of different thickeners in CO₂ is as follows: SHTTF-CO₂ > SHTAF-CO₂ > SHTT-CO₂ > SHTA-CO₂. Among them, the maximum interaction energy between the thickener SHTTF and CO₂ indicates that it has the strongest polymer–CO₂ interaction with CO₂, which improves its solubility in CO₂ and thickening ability. This result corresponds to the result in the thickening ability test in Section 3.3. In addition, the reason for the enhanced polymer–CO₂ interaction may be that the interaction between the polar sites on the polymer chain and CO₂ breaks the intermolecular interaction between polymer–polymer molecules [36].

3.4.4. Radial Distribution Function (RDF)

Calculation of radial distribution functions between different thickener molecules and carbon dioxide molecules by means of trajectory files of molecular dynamics optimized system models (Figure 13a–d). Figure 14 shows the radial distribution functions between different thickeners and CO₂: (a) four repeating units of the thickener + 1000 CO₂ molecules; (b) thickener polymer chains consisting of four chains with 6, 8, and 10 repeating units of the thickener (SHTT/SHTA) + 1000 CO₂ molecules, respectively; (c) thickener polymer chains consisting of four chains with 3, 4, and 5 repeating units of the thickener (SHTTF/SHTAF) + 1000 CO₂ molecules, respectively; (d) a combination of Figure 13b,c. From the RDFs (Radial Distribution Functions) of different thickeners and CO₂ in Figure 14, it can be seen that a higher RDF value indicates better miscibility between the thickener and CO₂. From Figure 14a,d, it can be obtained that the dissolution abilities of thickeners with different types, different chain lengths, and different molecular weights in CO₂ are in the following order: SHTTF-CO₂ > SHTAF-CO₂ > SHTT-CO₂ > SHTA-CO₂. That is, the introduction of fluorocarbon chains weakens the intermolecular interactions between the thickener polymer molecules, enhancing their solubility and thickening ability [4,36]. From the RDF data in Figure 14b,c, it can be seen that as the chain length and molecular weight of the thickeners (SHTT/SHTA, SHTTF/SHTAF) increase, their dissolution abilities in CO₂ decrease. The reason for this phenomenon may be that while the increase in the chain length and molecular weight of the thickener polymer introduces more polar sites, the intermolecular interactions between polymer–polymer molecules also increase, and the interaction between the polymer and CO₂ weakens, resulting in a decrease in solubility and thickening ability [37].

4. Conclusions

(1)

Four modified silicone-based thickeners for supercritical CO₂ fracturing fluids were successfully synthesized. FT-IR and NMR characterization confirmed the successful incorporation of CO₂-philic groups into thickener molecular structures, achieving the synthesis of fluorinated silicone thickeners.

(2)

The fluorinated silicone thickeners demonstrated exceptional thickening performance and favorable solubility. At 5 wt% concentration under 10 MPa and 32 °C, they formed homogeneous mixtures with CO₂, elevating the viscosity of CO₂ to 3.68 mPa·s. Systematic experiments established positive correlations between CO₂ viscosity and both thickener concentration and pressure, while revealing an inverse relationship with temperature. The limitation of this study is that it only investigated the thickener concentrations within the range of 0~5 wt%.

(3)

Integrating experimental results with molecular simulations, the thickening mechanism was elucidated: The introduction of fluorinated compounds with carbon dioxide-affinitive moieties significantly enhances the dissolution of thickening functional-modified silicone segments in CO₂, thereby substantially increasing the viscosity of CO₂ fracturing fluids.