Kinetics of Polymer Network Formation by Nitroxide-Mediated Radical Copolymerization of Styrene/Divinylbenzene in Supercritical Carbon Dioxide

: The kinetics of nitroxide-mediated dispersion copolymerization with crosslinking of styrene (STY) and divinylbenzene (DVB) in supercritical carbon dioxide (scCO 2 ) is addressed experimentally. 2,2,6,6-Tetramethylpiperidinyl-1-oxy (TEMPO) and dibenzoyl peroxide (BPO) were used as nitroxide controller and initiator, respectively. A high-pressure cell with lateral sapphire windows at 120 ◦ C and 207 bar was used to carry out the polymerizations. The nitroxide-mediated homopolymerization (NMP) of STY, as well as the conventional radical copolymerization (FRC) of STY/DVB, at the same conditions were also carried out as reference and for comparison purposes. The effect of nitroxide content on polymerization rate, evolution of molecular weight averages, gel fraction, and swelling index was studied.


Introduction
The properties of polymeric materials with tridimensional network structures produced by conventional free radical copolymerization with crosslinking (FRC) of vinyl and divinyl monomers make them relevant for many technological applications. The best performance in these applications is obtained when the materials possess homogeneous structures. Unfortunately, the FRC of vinyl/divinyl monomers usually leads to highly heterogeneous microstructures due to the inherent characteristics of this method, which include slow initiation, fast propagation, high termination rates, and large dispersities (Ð) of the molar mass of primary chains. Cyclization and compositional drift promote the formation of highly compact crosslinked regions mixed with looser ones, which add to the highly heterogeneous nature of polymer networks synthesized by this route [1].
Although recent studies focused on the synthesis of polymer networks in the presence of RDRP controllers, such as the synthesis of soft, elastomeric, non-tacky polymer networks; combining RAFT synthesis of the network followed by photo-induced ATRP grafting of side chains [59]; the development of a novel class of acrylic acid (AA)-based superabsorbent polymers (SAPs) with improved absorption performance by applying iodine transfer polymerization (ITP) [60]; the assessment of the advantages of RDRP polymer networks over conventional FRC ones for 3D printing [61]; and the development of a photoinduced free radical-promoted cationic RAFT polymerization method using the direct photolysis of the RAFT agent as a radical source, which was further combined with photo-INIFERTER RAFT polymerization to prepare polymer networks [62], have been reported lately (2019-2022), none of them have been carried out in scCO 2 , and none of them have used NMP chemistry.
In this contribution we report the nitroxide-mediated copolymerization with crosslinking of STY and DVB in scCO 2 using 2,2,6,6-Tetramethylpiperidine-1-oxy (TEMPO) and dibenzoyl peroxide (BPO) as the nitroxide controller and initiator, respectively. A highpressure cell with lateral sapphire windows at 120 • C and 207 bar was used as the reaction vessel. The motivation and background for this study is contained in a patent generated in our group [55].

Reaction System
The polymerization system, shown in Figure 1, was similar to the one used in our previous systems on (co)polymerizations carried out in sc-CO 2 [2,54,63,64]. The copolymerizations in scCO 2 proceeded in a 38 mL high-pressure cell. A Dual Syringe Pump System was used to feed CO 2 into the vessel and bring it to supercritical conditions. Monomers (8 g), initiator, TEMPO, stabilizer, and a magnetic stirring bar were placed inside the reactor. A slow flow of CO 2 was used to purge the reactor. It was then pressurized with CO 2 until a pre-defined pressure, lower than the desired reaction pressure, was reached. After that, the reactor was heated using heating tape (heating elements distributed homogeneously between flexible molded sheets of silicon) until the set reaction temperature (T = 120 • C) was reached and maintained. Pressure was then increased to the required reaction pres-sure (P = 207 bar) by loading additional CO 2 . The reaction mixture was stirred using the magnetic bar. The polymerization went on until the desired time elapsed.
Processes 2022, 10, x FOR PEER REVIEW 3 of 13 homogeneously between flexible molded sheets of silicon) until the set reaction temperature (T = 120 °C) was reached and maintained. Pressure was then increased to the required reaction pressure (P = 207 bar) by loading additional CO2. The reaction mixture was stirred using the magnetic bar. The polymerization went on until the desired time elapsed. Figure 1. Sketch of the reacting system for NMC of styrene and divinylbenzene in scCO2.

Product Characterization
Monomer conversion was determined from gravimetry. Gel content and Swelling Index (SI) were obtained gravimetrically from mass fractions separated by ultracentrifugation, using the same centrifuge as in our previous study [2]. Centrifugation at 18,000 RPM took place for one hour. Molecular weight averages of the soluble fractions were measured by gel permeation chromatography (GPC). The same GPC equipment described in Jaramillo-Soto et al. [2] was used. THF was filtered and used as the eluent at a flow rate of 1 mL/min. Polymer solutions of ±0.2 wt.% were prepared and allowed to dissolve for 24 h. They were then micro filtered using injection volumes of 100 to 200 μL.

Operating Conditions and Cases Analyzed
The objective of this study was to analyze the kinetics of polymer network formation by nitroxide mediated copolymerization (NMC) of styrene and divinylbenzene carried out in scCO2. FRP and NMP of STY and conventional FRC of STY/DVB were also considered in the study as reference systems useful in the analysis. The polymerizations reported in this study, which are summarized in Table 1, proceeded at a temperature (T) of 120 °C and pressure (P) of 207 bar, using Krytox 257 FSL as a stabilizer. The chemical structure of Krytox 257 FSL is shown in Scheme 1. As shown in Table 1, eight case studies were considered in this contribution, all carried out in scCO2. Case 1 deals with FRP of STY, whereas Case 2 concerns the NMP of STY, and Case 3 refers to conventional FRC of STY DVB. These three cases are reference cases. Cases 4 to 8 concern the NMC of STY and DVB at different crosslinker and controller concentrations.

Product Characterization
Monomer conversion was determined from gravimetry. Gel content and Swelling Index (SI) were obtained gravimetrically from mass fractions separated by ultracentrifugation, using the same centrifuge as in our previous study [2]. Centrifugation at 18,000 RPM took place for one hour. Molecular weight averages of the soluble fractions were measured by gel permeation chromatography (GPC). The same GPC equipment described in Jaramillo-Soto et al. [2] was used. THF was filtered and used as the eluent at a flow rate of 1 mL/min. Polymer solutions of ±0.2 wt.% were prepared and allowed to dissolve for 24 h. They were then micro filtered using injection volumes of 100 to 200 µL.

Operating Conditions and Cases Analyzed
The objective of this study was to analyze the kinetics of polymer network formation by nitroxide mediated copolymerization (NMC) of styrene and divinylbenzene carried out in scCO 2 . FRP and NMP of STY and conventional FRC of STY/DVB were also considered in the study as reference systems useful in the analysis. The polymerizations reported in this study, which are summarized in Table 1, proceeded at a temperature (T) of 120 • C and pressure (P) of 207 bar, using Krytox 257 FSL as a stabilizer. The chemical structure of Krytox 257 FSL is shown in Scheme 1. As shown in Table 1, eight case studies were considered in this contribution, all carried out in scCO 2 . Case 1 deals with FRP of STY, whereas Case 2 concerns the NMP of STY, and Case 3 refers to conventional FRC of STY DVB. These three cases are reference cases. Cases 4 to 8 concern the NMC of STY and DVB at different crosslinker and controller concentrations. in this study, which are summarized in Table 1, proceeded at a temperature (T) of 120 °C and pressure (P) of 207 bar, using Krytox 257 FSL as a stabilizer. The chemical structure of Krytox 257 FSL is shown in Scheme 1. As shown in Table 1, eight case studies were considered in this contribution, all carried out in scCO2. Case 1 deals with FRP of STY, whereas Case 2 concerns the NMP of STY, and Case 3 refers to conventional FRC of STY DVB. These three cases are reference cases. Cases 4 to 8 concern the NMC of STY and DVB at different crosslinker and controller concentrations.

Comparison of Base Case of NMC of STY/DVB (Case 4) against Reference Situations (Cases 1-3)
A comparison of a representative formulation of NMC of STY/DVB in scCO 2 (Case 4) against the reference situations of FRP of STY (Case 1), NMP of STY (Case 2), and FRC of STY/DVB (Case 3) is shown in Figure 2. As expected, the slowest case is the NMP of STY (Case 2), where the controller slows down the polymerization rate and there is no crosslinker which accelerates it, and the fastest case corresponds to the conventional FRC of STY/DVB, where opposite conditions prevail. Intermediate between these two are the NMC of STY/DVB (Case 4), which is the second slowest system, and the FRP of STY (Case 1). In this situation, the reduced polymerization rate caused by the controller dominates over the action of the crosslinker.

Comparison of Base Case of NMC of STY/DVB (Case 4) against Reference Situations (Cases 1-3)
A comparison of a representative formulation of NMC of STY/DVB in scCO2 (Case 4) against the reference situations of FRP of STY (Case 1), NMP of STY (Case 2), and FRC of STY/DVB (Case 3) is shown in Figure 2. As expected, the slowest case is the NMP of STY (Case 2), where the controller slows down the polymerization rate and there is no crosslinker which accelerates it, and the fastest case corresponds to the conventional FRC of STY/DVB, where opposite conditions prevail. Intermediate between these two are the NMC of STY/DVB (Case 4), which is the second slowest system, and the FRP of STY (Case 1). In this situation, the reduced polymerization rate caused by the controller dominates over the action of the crosslinker.

Effect of Crosslinker Content on Polymerization Rate and Evolution of Molecular Weight Averages
The NMC of STY/DVB with a [TEMPO]/[BPO] ratio of 1.1 was taken as a base formulation to study the effect of DVB content on the polymerization rate (Figure 3), molecular weight development (Figures 4 and 5), gel fraction versus conversion, and the SI versus conversion. It is observed in Figure 3 that the polymerization proceeds faster as the amount of DVB crosslinker in the formulation is increased.

Effect of Crosslinker Content on Polymerization Rate and Evolution of Molecular Weight Averages
The NMC of STY/DVB with a [TEMPO]/[BPO] ratio of 1.1 was taken as a base formulation to study the effect of DVB content on the polymerization rate (Figure 3), molecular weight development (Figures 4 and 5), gel fraction versus conversion, and the SI versus conversion. It is observed in Figure 3 that the polymerization proceeds faster as the amount of DVB crosslinker in the formulation is increased.          Although not all the samples were characterized for molecular weight development, a linear relationship between number average molecular weight (M n ) and conversion is observed in Figure 4 (see trending line) for Case 5 of Table 1. The data point at 20% monomer conversion seems to deviate from the linear trend. As observed in Figure 5, which shows a plot of weight average molecular weight (M w ) versus conversion, the gelation point occurs precisely between 20% and 25% monomer conversion, a situation that may explain the deviation from the linear trend. It is clearly observed in Figure 5 that M w increases sharply during the pre-gelation period until the gelation point is reached, and then decreases for the sol fraction during the post-gelation period (see the trending lines), behavior typical for a system with polymer network formation.
Experimental profiles of gel percentage versus monomer conversion at three levels of crosslinker are shown in Figure 6. The exact occurrence of the gelation points is not captured with precision, but the qualitative trend, illustrated by the trending lines, is clear: the gelation point occurs sooner when the concentration of DVB is increased. The gelation point for the system with 3 wt.% DVB content (Case 6) occurs between 5 and 10% monomer conversion; it occurs between 15 and 20% monomer conversion for the system with 1.5 wt.% DVB content (Case 5) and it takes place between 20 and 30% conversion for the system with 1 wt.% DVB content (Case 4). According to Figure 5, the gelation point for Case 4 takes place at about 25% conversion, which agrees with the gelation point observed in Figure 6. Although not all the samples were characterized for molecular weight development, a linear relationship between number average molecular weight (Mn) and conversion is observed in Figure 4 (see trending line) for Case 5 of Table 1. The data point at 20% monomer conversion seems to deviate from the linear trend. As observed in Figure 5, which shows a plot of weight average molecular weight (Mw) versus conversion, the gelation point occurs precisely between 20% and 25% monomer conversion, a situation that may explain the deviation from the linear trend. It is clearly observed in Figure 5 that Mw increases sharply during the pre-gelation period until the gelation point is reached, and then decreases for the sol fraction during the post-gelation period (see the trending lines), behavior typical for a system with polymer network formation.
Experimental profiles of gel percentage versus monomer conversion at three levels of crosslinker are shown in Figure 6. The exact occurrence of the gelation points is not captured with precision, but the qualitative trend, illustrated by the trending lines, is clear: the gelation point occurs sooner when the concentration of DVB is increased. The gelation point for the system with 3 wt.% DVB content (Case 6) occurs between 5 and 10% monomer conversion; it occurs between 15 and 20% monomer conversion for the system with 1.5 wt.% DVB content (Case 5) and it takes place between 20 and 30% conversion for the system with 1 wt.% DVB content (Case 4). According to Figure 5, the gelation point for Case 4 takes place at about 25% conversion, which agrees with the gelation point observed in Figure 6. As shown in Figure 7, the swelling index (SI) is very low before the gelation point. As shown by the trending lines, a sudden increase in the SI around the gel point vicinity and then a gradual decrease after the gelation period is observed for both situations (Cases 4 and 5). Open markers in Figure 7 are repeats of polymerization. Although it is not observed clearly, most of the solid markers are repeats of the measurement for a single sample. These results show that the repeatability of the technique is good, and the reproducibility, understood as replication of the experiments in the same laboratory, is rather large. The gelation points inferred from Figure 7 are slightly higher than those obtained from Figures 5 and 6, but the qualitative trend is correct, since the gelation point at the lower As shown in Figure 7, the swelling index (SI) is very low before the gelation point. As shown by the trending lines, a sudden increase in the SI around the gel point vicinity and then a gradual decrease after the gelation period is observed for both situations (Cases 4 and 5). Open markers in Figure 7 are repeats of polymerization. Although it is not observed clearly, most of the solid markers are repeats of the measurement for a single sample. These results show that the repeatability of the technique is good, and the reproducibility, understood as replication of the experiments in the same laboratory, is rather large. The gelation points inferred from

Effect of TEMPO Content on Polymerization Rate and Molecular Weight Development
Cases 3, 4, 7, and 8 of Table 1, all of them with [DVB] = 1 wt.%, were used to analyze the effect of controller (TEMPO) content on the NMC of STY/DVB at T = 120 °C and P = 207 bar. It is observed in Figure 8 that increasing TEMPO content in the reacting mixture results in decreased polymerization rates (slower conversion versus time profiles), a result which is expected in RDRPs. It is shown in Figure 9 that the Mn versus conversion (x) profiles for Cases 7 and 8 follow linear trends, with the case with lower TEMPO content reaching slightly higher molecular weights.

Effect of TEMPO Content on Polymerization Rate and Molecular Weight Development
Cases 3, 4, 7, and 8 of Table 1, all of them with [DVB] = 1 wt.%, were used to analyze the effect of controller (TEMPO) content on the NMC of STY/DVB at T = 120 • C and P = 207 bar. It is observed in Figure 8 that increasing TEMPO content in the reacting mixture results in decreased polymerization rates (slower conversion versus time profiles), a result which is expected in RDRPs.

Effect of TEMPO Content on Polymerization Rate and Molecular Weight Development
Cases 3, 4, 7, and 8 of Table 1, all of them with [DVB] = 1 wt.%, were used to analyze the effect of controller (TEMPO) content on the NMC of STY/DVB at T = 120 °C and P = 207 bar. It is observed in Figure 8 that increasing TEMPO content in the reacting mixture results in decreased polymerization rates (slower conversion versus time profiles), a result which is expected in RDRPs. It is shown in Figure 9 that the Mn versus conversion (x) profiles for Cases 7 and 8 follow linear trends, with the case with lower TEMPO content reaching slightly higher molecular weights. It is shown in Figure 9 that the M n versus conversion (x) profiles for Cases 7 and 8 follow linear trends, with the case with lower TEMPO content reaching slightly higher molecular weights.   Figure 10; one of them (x = 0.1) seems to correspond to an increasing profile for the pre-gelation period, and the other (x = 0.33) to a decreasing profile for the postgelation period (see solid black trending lines). This indicates that the gelation point for Case 4 occurs between 15 and 25% monomer conversion. In the case at [TEMPO]/[BPO] = 1.6, there are three data points at conversions lower than 20% monomer conversion, which shows an increasing trend that agrees with the increasing trend of a crosslinking system for the pre-gelation period. The data point at x = 0.3 seems to correspond to a decreasing profile for the post-gelation period. This behavior is illustrated with the short-dashed red trending lines. The gelation point for Case 7 occurs between 15 and 28% monomer conversion. In the system at [TEMPO]/[BPO] = 3 (Case 8), although the data points are scattered, all of them seem to follow the increasing trend of a profile during the pre-gelation period. As indicated by the long-dashed green trending line, it seems that the gelation point was not reached before 24 h, which was the maximum time where samples were taken.   Figure 10; one of them (x = 0.1) seems to correspond to an increasing profile for the pre-gelation period, and the other (x = 0.33) to a decreasing profile for the post-gelation period (see solid black trending lines). This indicates that the gelation point for Case 4 occurs between 15 and 25% monomer conversion. In the case at [TEMPO]/[BPO] = 1.6, there are three data points at conversions lower than 20% monomer conversion, which shows an increasing trend that agrees with the increasing trend of a crosslinking system for the pre-gelation period. The data point at x = 0.3 seems to correspond to a decreasing profile for the post-gelation period. This behavior is illustrated with the short-dashed red trending lines. The gelation point for Case 7 occurs between 15 and 28% monomer conversion. In the system at [TEMPO]/[BPO] = 3 (Case 8), although the data points are scattered, all of them seem to follow the increasing trend of a profile during the pre-gelation period. As indicated by the long-dashed green trending line, it seems that the gelation point was not reached before 24 h, which was the maximum time where samples were taken.   Figure 10; one of them (x = 0.1) seems to correspond to an increasing profile for the pre-gelation period, and the other (x = 0.33) to a decreasing profile for the postgelation period (see solid black trending lines). This indicates that the gelation point for Case 4 occurs between 15 and 25% monomer conversion. In the case at [TEMPO]/[BPO] = 1.6, there are three data points at conversions lower than 20% monomer conversion, which shows an increasing trend that agrees with the increasing trend of a crosslinking system for the pre-gelation period. The data point at x = 0.3 seems to correspond to a decreasing profile for the post-gelation period. This behavior is illustrated with the short-dashed red trending lines. The gelation point for Case 7 occurs between 15 and 28% monomer conversion. In the system at [TEMPO]/[BPO] = 3 (Case 8), although the data points are scattered, all of them seem to follow the increasing trend of a profile during the pre-gelation period. As indicated by the long-dashed green trending line, it seems that the gelation point was not reached before 24 h, which was the maximum time where samples were taken.  Figure 11 shows the profiles of gel percentage versus conversion. As expected, gelation is delayed as the amount of TEMPO is increased. From the data points at low conversions, it can be inferred that the gelation point in the absence of a controller (Case 3) occurs very early during the polymerization (no data point available); gelation occurs between 5 and 10% monomer conversion for Case 4 and between 13 and 25% for Case 7. The colored trending lines of Figure 11 provide an easier way to visualize these results.  Figure 11 shows the profiles of gel percentage versus conversion. As expected, gelation is delayed as the amount of TEMPO is increased. From the data points at low conversions, it can be inferred that the gelation point in the absence of a controller (Case 3) occurs very early during the polymerization (no data point available); gelation occurs between 5 and 10% monomer conversion for Case 4 and between 13 and 25% for Case 7. The colored trending lines of Figure 11 provide an easier way to visualize these results. The results of the SI versus conversion shown in Figure 12 confirm that gelation did not take place during the time that the polymerization was monitored in Case 6, the one with [TEMPO]/[BPO] = 3 (green trending line and green squares). On the other hand, the SI for Case 7 increased abruptly and then decreased between 20 and 30% monomer conversion, which indicates that gelation took place in that interval, in agreement with what was observed in Figures 10 and 11 (see red trending line and red diamonds). The results of the SI versus conversion shown in Figure 12 confirm that gelation did not take place during the time that the polymerization was monitored in Case 6, the one with [TEMPO]/[BPO] = 3 (green trending line and green squares). On the other hand, the SI for Case 7 increased abruptly and then decreased between 20 and 30% monomer conversion, which indicates that gelation took place in that interval, in agreement with what was observed in Figures 10 and 11 (see red trending line and red diamonds).  Figure 11 shows the profiles of gel percentage versus conversion. As expected, gelation is delayed as the amount of TEMPO is increased. From the data points at low conversions, it can be inferred that the gelation point in the absence of a controller (Case 3) occurs very early during the polymerization (no data point available); gelation occurs between 5 and 10% monomer conversion for Case 4 and between 13 and 25% for Case 7. The colored trending lines of Figure 11 provide an easier way to visualize these results. The results of the SI versus conversion shown in Figure 12 confirm that gelation did not take place during the time that the polymerization was monitored in Case 6, the one with [TEMPO]/[BPO] = 3 (green trending line and green squares). On the other hand, the SI for Case 7 increased abruptly and then decreased between 20 and 30% monomer conversion, which indicates that gelation took place in that interval, in agreement with what was observed in Figures 10 and 11 (see red trending line and red diamonds).

Conclusions
Polymer networks synthesized by FRC of STY/DVB in scCO 2 , at 120 • C and 207 bar, in a high-pressure cell with lateral sapphire windows are reported for the first time. The novelty of this process includes the combination of three technological aspects: (a) synthesis of polymer networks; (b) use of RDRP chemistry for the synthesis of controlled polymer microstructures; and (c) the use of scCO 2 as a green route to carry out the polymerization. The results obtained confirmed that crosslinking and gelation took place, that the presence of TEMPO slowed down the polymerization and delayed the occurrence of the gelation point, and that growth was less disordered than in conventional FRC. The reduced rate of polymerization is observed in the conversion versus time profiles, where higher conversions are reached when the amount of TEMPO is reduced. The effect of TEMPO delaying the occurrence of gelation is clearly observed in the M w versus conversion, SI versus conversion, and gel fraction versus conversion profiles.
The nature of the reactor did not allow obtaining more abundant and precise experimental data but did allow us to prove the concept that we proposed earlier for RAFT copolymerization of STY/DVB in scCO 2 [2,54,55] to the case of NMC of vinyl/divinyl monomers in scCO 2 . Namely, polymer networks with different kinetic behavior during the polymerization (slower polymerization rates and delayed gelation) and less heterogeneous crosslink density distributions are obtained when TEMPO is used as a controller, and the material is easily dried by depressurization of the reactor. Our experimental data do not provide direct information on the homogeneity of the polymer network, but the linear relationship between M n and conversion suggests that less heterogeneous are indeed produced when TEMPO is included in the formulation. This is an issue that requires further analysis in future studies on the topic.

Patents
The contents of this manuscript are related to the scope of patent MX/a/2013/009053: "Polímeros con estructura de red de baja densidad y proceso de obtención de los mismos mediante polimerización radicálica por desactivación reversible en fluidos comprimidos"

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.