Investigation of radical polymerization kinetics of poly(ethylene glycol) methacrylate hydrogels via DSC and mechanistic or isoconversional models
Monomers composed of a polymerizable methacrylate moiety connected to a short poly(ethylene) glycol (PEG) chain are versatile building-blocks for the preparation of “smart” biorelevant materials. Hydrogels based on these PEG methacrylates are a very important class of biomaterials with several applications. The radical polymerization kinetics of two such oligomers, namely poly(ethylene glycol) methacrylate (PEGMA) and poly(ethylene glycol) methyl ether methacrylate (PEGMEMA) was investigated. Experimental polymerization rate and monomer conversion data were measured using DSC operating under non-isothermal conditions, at several constant heating rates, or isothermal, at different constant reaction temperatures. Isoconversional techniques were employed to estimate the variation of the polymerization effective activation energy as a function of the extent of reaction. It was found that isothermal and non-isothermal experiments results in similar trends of the activation energy, whereas by comparison of differential to integral isoconversional methods it was postulated that in non-isothermal polymerization experiments integral methods should not be used. From comparison of the two oligomers employed in the polymerization experiments, it was clear that the presence of the terminal hydroxyl group in PEGMA compared to the methoxy group in PEGMEMA leads to different conversion time profiles and activation energies. In particular, monomer–monomer association through hydroxyl groups results in initially lower activation energy of PEGMA. As polymerization proceeds, the existence of aggregated hydroxyl structures (···OH···OH···OH···) in the PEGMA macromolecular chains result in higher activation energies and a more abrupt increase in the conversion time curve.
KeywordsPolymerization kinetics DSC Isoconversional methods PEGMA PEGMEMA
Radical polymerization usually involves vinyl monomers with at least one double bond in their structure. Polymerization of these vinyl monomers is accompanied by a significant heat release due to the addition reaction to the double bond . This polymerization enthalpy can be recorded by thermal analysis techniques, such as Differential Scanning Calorimetry (DSC) and converted to polymerization rate after some appropriate mathematical transformations . DSC has long been proven a powerful technique for measuring the variation of polymerization rate as a function of time (isothermal mode) or temperature (non-isothermal mode). It offers the advantage of continuous recording of the variation of the reaction rate, which permits the estimation and identification of specific phenomena taking place during polymerization (such as diffusion controlled, besides chemical reactions). This is very significant, since in other techniques of measuring the polymerization conversion (e.g. gravimetry, FTIR, etc.) only discrete experimental data are collected. DSC measurements can be easily carried out in a variety of experimental conditions and monomer(s) chemical structure. The latter is very important especially when polymerization leading to crosslinked structures is investigated, where other techniques, requiring the dissolution of the polymer formed, significantly fail . Use of DSC in the investigation of the isothermal bulk polymerization of a variety of monomers, including the well-studied methyl methacrylate (MMA), as well as the curing of several epoxy resins, has been reported in literature [1, 2, 3, 4, 5, 6]. Moreover, a number of papers have been published on modelling polymerization kinetics using detailed mechanistic models . However, investigations on the simulation of polymerization kinetics of vinyl monomers using isoconversional methods are rather rare .
Monomers composed of a methacrylate moiety connected to a short poly(ethylene glycol) (PEG) chain are versatile building-blocks for the preparation of “smart” biorelevant materials . Many of these monomers are commercial and can be easily polymerized by either anionic, free-radical, or controlled radical polymerization. Depending on the molecular structure of their monomer units, non linear PEG analogues can be insoluble in water, readily soluble up to 100 °C, or thermoresponsive. Thus, these polymers can be used for building a wide variety of modern materials such as biosensors, artificial tissues, smart gels for chromatography, injectable hydrogels, capsules for drug-release, antibacterial surfaces, or stationary phases for bioseparation [10, 11, 12, 13]. Although the applications of these polymeric hydrogels have been extensively considered, a detailed study on their polymerization kinetics has not been published so far.
Recently, the polymerization kinetics of 2-hydroxyethyl methacrylate (HEMA) has been extensively studied in our laboratory using DSC measurements and mechanistic or isoconversional models and compared to the corresponding of MMA [8, 14]. HEMA has a hydroxyl group in its molecule, which is responsible to hydrogen bonding and thus it presents high boiling point and hydrophilicity. PHEMA materials are used as hydrogels. The variation of the activation energy with the extent of reaction was estimated using isoconversional methods. As a step further here we investigate the polymerization kinetics of two oligomers, namely the poly(ethylene glycol) methacrylate and poly(ethylene glycol) methyl ether methacrylate in the presence of benzoylperoxide initiator. These oligomers include two parts in their molecular structure: a polymerizable methacrylate and a PEG side chain with a few number of repeated poly(ethylene oxide) units. Besides, depending on their structure may or may not have terminal hydroxyl groups. Polymerizations were carried out at several constant heating rates (non-isothermal conditions) and different constant reaction temperatures (isothermal conditions). Differential and integral isoconversional methods were employed and the results were compared. Differences in the reaction kinetics were attributed to the chemical structure of the oligomers used and the formation of side chemical bonds.
The polymerization enthalpy and conversion were calculated by integrating the area between the DSC thermograms and the baseline, which in the case of the isothermal experiments was established by extrapolation from the trace produced after complete polymerization (no change in the heat produced during the reaction). The total amount of heat released during non-isothermal experiments of PEGMEMA was in the vicinity of 177 J g−1, which multiplied by its average molecular weight leads to 53 kJ mol−1, whereas in non-isothermal polymerization of PEGMA it was around 154 J g−1, which multiplied by its average molecular weight results in 55.4 kJ mol−1. Both values were very close to what is proposed in literature for the standard heat of polymerization of a methacrylate double bond, i.e. 54.9 kJ mol−1 .
After the end of the polymerization the pans were weighted again and a negligible loss of monomer (less than 0.1 mg) was observed only in a few experiments.
When performing kinetic computations on thermal analysis data, one question that arises is whether experiments will be performed under isothermal or non-isothermal conditions. According to the ICTAC report, isothermal experiments are carried out in a limited temperature range . According also to our previous experience on such experiments  when polymerization is carried out at low temperatures, it may be difficult to reach complete conversion over a reasonable time period (sometimes it may last for a lot of hours). In contrast, in polymerizations at high temperatures, the heat-up time becomes comparable to the characteristic time of the process, which means a significant extent of conversion is reached before the isothermal regime sets in . Usually, inhibitors included in the monomer molecules, if not removed, play the role of permitting the reaction to be recorded even when it is carried out at high temperatures. Nevertheless, it has been suggested that the best practice would be to perform at least one isothermal run in addition to a series of constant heating rates runs . The isothermal run would be of assistance in selecting a proper reaction model. In fact, a combination of non-isothermal and isothermal experiments would be the best way to properly establish kinetic models . A truly good model should simultaneously fit both types of runs with the same kinetic parameters.
From an inspection of the curves presented in Fig. 1, the typical behaviour of a radical polymerization system with diffusion-controlled phenomena affecting reaction rate was observed in all experiments. A typical radical polymerization mechanism includes mainly three steps: decomposition of the initiator to primary radicals, reaction of these radicals with monomer molecules to initiate polymerization, propagation of the macro-radicals by reacting with several monomer molecules and termination of two macro-radicals to form the final polymer. At the initial polymerization stage, purely chemical kinetics controls the reaction. As polymerization proceeds, the reaction rate significantly increases with time accompanied by an increase in monomer conversion. This is the well-known auto-acceleration or gel-effect phenomenon and is attributed to the effect of diffusion-controlled phenomena on the termination reaction and the reduced mobility of live macro-radicals in order to find one another and react. Therefore, their concentration increases locally, leading to increased polymerization rates . Afterwards, the reaction rate falls significantly and at very high conversions, beyond 80–90%, it tends asymptotically to zero. Polymerization almost stops before the full consumption of the monomer. At this point the glass transition temperature, Tg of the monomer-polymer mixture approaches reaction temperature, thus a glassy state appears and it corresponds to the well-known glass effect. This is attributed to the effect of diffusion-controlled phenomena on the propagation reaction and the reduced mobility of monomer molecules to find a macro-radical and react .
Simple free-radical polymerization kinetics using mechanistic modelling
Isothermal polymerization with isoconversional methods
As it can be seen, the value estimated at 5% conversion is the same (i.e. 94.4 kJ mol−1) with that estimated previously using the − ln(1 − X) versus t plots. This was expected since these plots were created by taking the 1–9% conversion interval. Effective activation energy decreased with conversion from 95 to almost 84 kJ mol−1 until about 30% conversion, where afterwards it almost reaches a plateau at this value. The kinetics at the initial stages of polymerization (i.e. at conversions less than 30%) occurs in the kinetic mode, as normally is the case of all polymerization reactions . It is frequently found that the largest value of the activation energy is estimated at conversion tending to zero. This, according to Vyazovkin , is because the activation energy of initiation, Ei, is typically larger than that of propagation, Ep and termination, Et reactions. Therefore, at the initial stages Ei dominates the overall activation energy. Afterwards, a steady-state regime becomes operative where E drops to the value estimated using Eq. (3), i.e. Eeff = Ep + (Ed − Et)/2. Using the values of Ep, Ed and Et calculated for PHEMA, i.e. 21.9, 143 and 5.6 kJ mol−1, respectively , Eff is estimated at 90.6 kJ mol−1. The steady-state value of nearly 84 kJ mol−1 reached here is slightly lower attributed to the bulkier monomer of PEGMA compared to HEMA. As polymerization progresses further at high monomer conversions, the rate control changes from a kinetic to diffusion regime as reflected by an increase in the activation energy. The increasing character of the dependence indicates that the rate is limited by the mobility of large molecules or long segments of the polymer chains .
This equation actually consist the differential method of Friedman, where EX can be estimated from the slope of the linear curves obtained after plotting the left-hand side of Eq. (8) versus 1/T.
According to this method, the effective activation energy can be estimated from a plot of ln(β/T2) versus 1/T.
Furthermore, results from the differential non-isothermal variation of activation energy are compared to corresponding from isothermal data in Fig. 3. Similar values to those obtained from isothermal experiments were calculated. For PEGMA, in isothermal polymerizations, Eff varied from 95 to 80 kJ mol−1, whereas in non-isothermal it starts from 90 kJ mol−1 decreases to 70 kJ mol−1 and then increases again to 95 kJ mol−1. Data from non-isothermal experiments were lower than the corresponding from isothermal, at conversions less than 70%, whereas they are larger at higher. This could be a result of the higher mobility of the monomer molecules and macro-radicals inside the polymerizing mixture due to the increased reaction temperatures in non-isothermal experiments compared to the isothermal. In addition in both experiments a clear tendency to decrease at the initial conversions was observed, which is a result of the effect of diffusion-controlled phenomena.
Effect of the monomer chemical structure on radical polymerization kinetics
Concerning the effect of diffusion-controlled phenomena on the variation of the effective activation energy, one can expect the EX dependence to decrease when the polymerization rate becomes limited by the diffusion of small molecules such as a monomer or a short segment of a polymer chain. An increasing dependence is expected when the process becomes determined by the diffusion of large molecules, such as the macromolecular chains . Note that diffusion-control becomes operative long before the reaction system vitrifies. According to Vyazovkin , it is important to realize that the primary cause of a change from kinetic to diffusion control is an increase in the mixture viscosity that may or may not lead to vitrification. In Fig. 8, a sharp decrease in EX was observed for PEGMEMA at X < 0.3. Thus in this region for this system viscosity undergoes a significant decrease and a plateau is reached at low Ex values approximately equal to 50 kJ mol−1. A similar decrease to comparable values has been also reported in literature for an epoxy-amine system . Note that no significant decrease in EX was observed in the same region for the isothermal case. This is because the effect is associated exclusively with a decrease in the viscosity, which under isotherm conditions it can only increase. Using the oligomer with the hydroxyl groups, i.e. PEGMA, this decrease of EX stops at 20% conversion, and a subsequent increase is observed. This secondary increase in PEGMA can be associated with specific interactions, since in the polymer, both OH···OH and C=O···HO types of hydrogen bonds can occur. Not only the dimer structure (OH···OH), but also the aggregate structure (···OH···OH···OH···) have been found in many systems, including liquid alcohols and solid polymers . It has been found that 53.7% of the OH group on the PHEMA side chain terminal contributes to the OH···OH type of hydrogen-bond, while the remaining 47.3% are engaged in the OH···O=C type of hydrogen bond, at ambient temperature . The formation of these bonds results in increasing activation energy during polymerization. No such phenomena appear in monomers without hydroxyl groups, such as PEGMEMA. So, that an increase in the activation energy was not observed.
The radical polymerization kinetics of two oligomers, namely PEGMA and PEGEMA having a polymerizable methacrylate moiety connected to a short polyethylene glycol chain was investigated. Experimental polymerization rate and conversion data were measured using DSC under non-isothermal, or isothermal conditions at different constant heating rates or reactions temperatures, respectively. Isoconversional techniques were employed to estimate the variation of the effective activation energy as a function of monomer conversion. It was found that isothermal and non-isothermal experiments results in similar trends of the activation energy, whereas by comparison of differential to integral isoconversional methods it can be postulated that in non-isothermal polymerization experiments it is not recommended using integral methods. From comparison of the two oligomer molecules employed in the polymerization experiments, it was clear that the presence of the terminal hydroxyl group in PEGMA compared to the methoxy group in PEGMEMA leads to different conversion time profiles and activation energies. In particular, monomer–monomer association through hydroxyl groups results in initially lower activation energy of PEGMA. As polymerization proceeds, the existence of aggregated hydroxyl structures (···OH···OH···OH···) in the PEGMA macromolecular chain result in higher activation energies and a more abrupt increase in the conversion time curve.
- 2.Achilias DS, Verros GD. Modeling of diffusion-controlled reactions in free radical solution and bulk polymerization: model validation by DSC experiments. J Appl Polym Sci. 2010;116:1842–56.Google Scholar
- 12.Üzgün S, Akdemir O, Hasenpusch G, Maucksch C, Golas MM, Sander B, Stark H, Imker R, Lutz J-F, Rudolph C. Characterization of tailor-made copolymers of oligo(ethylene glycol) methyl ether methacrylate and N,N-dimethylaminoethyl methacrylate as nonviral gene transfer agents: influence of macromolecular structure on gene vector particle properties and transfection efficiency. Biomacromolecules. 2010;11(1):39–50. https://doi.org/10.1021/bm9008759.CrossRefGoogle Scholar