Determining chemospecificity in reactions with chain transfer agent and corresponding radical via evaluation of molecular weight dependency of apparent comonomer reactivity ratios: free-radical copolymerization of vinyl acetate and dibutyl maleate

Abstract

Free-radical copolymerization of vinyl acetate (VAc) and dibutyl maleate (DBM) in deuterated chloroform (CDCl₃) initiated with 2,2′-azobis(isobutyronitrile) at 60 °C was monitored via online ¹H-NMR kinetic experiment. The reactivity ratios of the VAc (r_VAc) and DBM (r_DBM) were calculated using data obtained from two online experiments. Two, i.e. classic and new, approaches were used to collect conversion and copolymer composition data. Results showed that for a copolymerization with a relatively large difference between the reactivity ratios (r_VAc to r_DBM ratio of about 5) the reactivity ratios can be calculated by data collected only from one online ¹H-NMR experiment. In the case of copolymerization with the chloroform where copolymers with a number-average molecular weight (M_n) equal to or below 10⁴ g mol⁻¹ were synthesized, r_VAc and r_DBM were found to be 0.1135 and 0.0562 (r₁r₂ = 0.0064), respectively, [J. Polym. Res., 2014, 21, 582]. In the present work where copolymers with an M_n value of about 2 × 10⁴ g mol⁻¹ were synthesized, r_VAc and r_DBM were found to be 0.1911 and 0.0381 (r₁r₂ = 0.0073), respectively. The chemospecificity of the chloroform and corresponding trichloromethyl (CCl₃) radical in the reaction with the propagating radical and comonomers, respectively, was deduced from instantaneous copolymer composition curves. The results revealed that DBM adds preferentially onto the CCl₃ radicals derived from AIBN/CHCl₃ or AIBN/CDCl₃, indicating that copolymer composition and hence apparent reactivity ratios can be affected by the copolymer's molecular weight. Results may also be attributed to the preferential addition of the propagating radicals with a terminal DBM unit to CHCl₃ or CDCl₃.

---

Introduction

Nuclear magnetic resonance (NMR) spectroscopy is a powerful tool for polymer engineering studies to obtain both qualitative and quantitative mechanism and kinetic information from complex reacting multimonomer mixtures. ¹H-NMR spectroscopy has been demonstrated to be one of the most important and reliable techniques for studying polymer structure and copolymer composition in addition and condensation (co)polymerization reactions.^1–4 Online ¹H-NMR kinetic investigation is the best method to study polymerization kinetics and allows us to simultaneously calculate individual and overall monomer conversions as well as the comonomer mixture and copolymer chain compositions as a function of reaction progress. It is one of the advantages of this online technique relative to offline techniques and some of the other online techniques. Online ¹H-NMR kinetic experiment is among the well-accepted techniques for the kinetic study of free radical homo- and co-polymerization.^5–7

Copolymer composition is an important factor in the evaluation of copolymer characteristics.⁸ Controlling the polymer property parameters, such as copolymer composition, comonomer sequence distribution, molecular weight and distribution, as well as the kinetics of the copolymerization play the most important roles in copolymerization reactions. In order to calculate the polymer productivity and copolymer composition, comonomer reactivity ratios must be known. The method that is used most often nowadays for estimating monomer reactivity ratios is to perform copolymerization at low conversion with various initial feed compositions.⁹ Among the techniques available to determine monomer reactivity ratio at low conversions, Mayo–Lewis,¹⁰ Finemann–Ross,¹¹ inverted Finemann–Ross,¹² Kelen–Tudos,¹³ extended Kelen–Tudos,^14–16 Tidwell–Mortimer,¹⁷ and Mao–Huglin¹⁸ methods can be mentioned. Mayo–Lewis (ML), extended Kelen–Tudos (eKT) and Mao–Huglin (MH) methods can also be used for manipulation of the high conversion results.

Average copolymer composition can be affected by various factors, such as comonomer reactivity ratios¹⁹ and chemo- and regio-specificity in the initiation, transfer and termination steps.^19–22 It has been reported for the regio-selectivity of the radicals that they react with most monomers exclusively by tail β-addition, while radicals generally show a high degree of chemo-selectivity in reactions with vinyl monomers.^20,23

The effect of molecular weight (or equivalently chain length) on the instantaneous copolymer composition has been examined and proven.^24–27 When the copolymerization is performed in the presence of CTA, propagating chains are terminated by CTA and chains are initiated by CTA-derived radicals. For example, thiyl radicals generated from thiol CTA react with styrene (St) faster than acrylates.^19,27 On the other hand, the thiol reacts preferentially with propagating radicals with styryl ends owing to the chemospecificity of propagating radicals in the reaction with thiol. In such a copolymerization, therefore, the ω- and α-ends of the copolymer chains are mostly not representative of the overall copolymer composition. In other words, chains are both initiated and terminated by St, meaning that short chains are much richer in St than in the acrylates.^19,27

In conventional free-radical copolymerization, the comonomer reactivity ratios are generally determined at low conversion, where composition drift in the comonomer mixture can be considered to be negligible. The average chemical composition of the resulting copolymer is analyzed by various methods, such as ¹H-NMR. However, in controlled/living radical polymerization, the copolymer chain forms slowly throughout the reaction time and hence measurement of the copolymer composition at low conversion can be affected by the structure of the initiator, which may preferentially react only with one of the comonomers,^28,29 resulting in inaccurate comonomer reactivity ratio estimation by a classic approach. Therefore, to obtain reliable results, it is necessary to measure the cumulative copolymer composition at a conversion higher than about 10–15%. As a result, ML, eKT and MH methods are appropriate to calculate comonomer reactivity ratios in such situations where the effect of conversion should also be considered in the calculation of comonomer reactivity ratios.

Recently, a new approach based on the modified cumulative average copolymer composition at either low or high conversion has been introduced for the calculation of the accurate comonomer reactivity ratios in controlled/living radical copolymerization, as well as in any other living chain-growth copolymerization system.³⁰ In such conditions, the influence of possible preferential addition of one of the comonomers onto the (macro)initiator-derived (macro)radical on the copolymer composition is actually excluded (for more details, see section of “Determination of the reactivity ratios by two different approaches”).

Free-radical telomerization, i.e. free radical polymerization in the presence of a CTA, so-called telogen, is a technique to produce low to medium molecular weight functional polymers, so called telomers.³¹ Similar to controlled/living radical polymerization, the molecular weight of the telomer produced is not high enough; therefore, the influence of the preferential addition of the comonomers onto the CTA-derived radical as well as of the preferential addition of the CTA with propagating radicals on the copolymer composition cannot be ignored. In such conditions, different values for apparent reactivity ratios of the comonomers are obtained depending on the molecular weight of the synthesized copolymers. Then, the chemo-selectivity of the CTAs and corresponding radicals towards propagating radicals and comonomers, respectively, can be evaluated.

The reactivity ratios of vinyl acetate (VAc) (r_VAc) and dibutyl maleate (DBM) (r_DBM) in the free-radical copolymerization initiated by 2,2′-azobis(isobutyronitrile) (AIBN) in the presence of chloroform as a telogen were calculated from medium/high conversion data by the classic approach to be 0.1102 and 0.0421, respectively, by eKT method and 0.1135 and 0.0562, respectively, by MH method.³² Although both reactivity ratios of VAc and DBM are much less than 1, there is a relatively significant difference between the reactivity ratios of VAc and DBM. In general, for copolymerization systems with significant differences between the comonomer reactivity ratios, such as VAc/methyl acrylate,⁷ VAc/ethyl acrylate,³³ VAc/butyl acrylate³³ and VAc/butyl methacrylate,³⁴ considerable composition drifts in the comonomer mixture and copolymer are expected. Hence, for the above-mentioned systems, comonomer mixture and instantaneous copolymer compositions change considerably with the progress of the reaction and thus it is possible to calculate the monomer reactivity ratios online following these changes (for example by online ¹H-NMR kinetic experiment) during the copolymerization reaction only for one initial comonomer mixture composition.⁷

To further evaluate the accuracy of the estimated reactivity ratios in telomerization reactions, such as those reported in previous work,³² as well as to investigate the molecular weight dependency of the copolymer composition used in the estimation of apparent comonomer reactivity ratios, free-radical copolymerization of VAc and DBM initiated by AIBN in the presence of chloroform-d (CDCl₃) as a CTA is followed in the present work only for two initial comonomer mixture compositions by online ¹H-NMR kinetic experiment. Then, reactivity ratios of VAc and DBM are calculated using the classic and above-mentioned new approaches. The effect of copolymer molecular weight on the apparent comonomer reactivity ratios is then discussed. The accuracy of the estimated reactivity ratios is finally evaluated by considering the 95% joint confidence limits.

Experimental

Materials

VAc monomer (≥99%, Fluka) was dried by mixing overnight with calcium hydride, distilled under vacuum and then stored at −4 °C before use. DBM monomer (Merck, for synthesis) was dried with the procedure same as that of VAc and purified by passing through a column of basic alumina. AIBN (≥98%, Fluka) as the initiator was recrystallized from methanol. Chloroform-d (CDCl₃, ≥99%, Merck) as a solvent and CTA (telogen) were used without further purification.

Instrument

All online ¹H-NMR kinetic experiments reported in this study were performed on a Bruker Avance 400 NMR spectrometer (Bruker Instruments, Darmstadt, Germany). The sample cavity was equilibrated at 60 °C with a BVT 3000 (±0.1 °C) temperature control unit. After setting the cavity temperature at 60 °C, the sample tube with 5 mm diameter containing the reaction mixture was inserted into the sample chamber.

Sample preparation

Solution samples were prepared with two different monomer mixture compositions at constant initiator and overall monomer concentrations. The overall comonomers concentration, [M], to solvent concentration, [S], ratio was kept constant at 50 : 50 vol/vol. Two samples VD1 and VD2 were prepared with mole fractions of VAc equal to 0.7143 and 0.8333, respectively, in the initial comonomer mixture. The final reaction mixture prepared was then added to the NMR tube (5 mm in diameter). The solutions in the NMR tubes were then degassed with nitrogen gas (99.9% purity) to exclude oxygen from the reaction mixtures, which acts as a retardant in the free radical polymerization reactions.

Online ¹H-NMR kinetic experiments

Typically, online ¹H-NMR kinetic experiments were performed according to the following procedure. First, the sample cavity of the NMR instrument was set to the defined reaction temperature (i.e., 60 °C), and only chloroform-d (the solvent) was injected into the NMR tube. The tube containing solvent was inserted into the sample chamber and allowed to equilibrate for approximately 15 min. The magnet was then thoroughly shimmed using the chloroform-d sample. Second, the sample tube containing the reaction mixture was inserted into the sample chamber, and the start time was recorded.

The sample containing the reaction mixture was allowed to equilibrate for about 5 min. The first recorded spectrum (after the sample tube containing the reaction mixture was inserted into the cavity) was regarded as the spectrum representing zero overall monomer conversion. Although approximately 5 min had passed from insertion of the sample into the cavity to the first scan, negligible conversion had occurred because of the low overall rate of the reaction in the primary moments. To decrease the concentration of the comonomers and hence decrease the polymerization rate, and to avoid an excessive viscosity increase at higher conversions, a high amount of the chloroform-d was used.

Results and discussion

In the previous work,³² offline ¹H-NMR was used for copolymerization of VAc and DBM in order to determine the reactivity ratios of the comonomers and the overall copolymerization rate coefficient.²³ In the continuation of our previous study regarding the calculation of the reactivity ratios of VAc and MA by a new simple procedure in the conventional free-radical copolymerization⁷ and accurate calculation of the reactivity ratios of styrene and methyl methacrylate by a new general approach in the controlled radical copolymerization³⁰ by using data obtained from online ¹H-NMR kinetic experiments, reactivity ratios of VAc and DBM in the free-radical cotelomerization will be calculated through the above-mentioned new approach by data obtained only from one sample with a proper initial comonomer mixture composition.

A typical ¹H-NMR spectrum of an initial reaction mixture containing 0.7143 mole fraction of VAc at the overall monomer conversion of 45.79 mol% with the signal assignments is shown in Fig. 1.

Fig. 1 A typical ¹H-NMR spectrum recorded for the reaction mixture obtained from VAc/DBM solution copolymerization in CDCl₃ at 60 °C (overall conversion of 45.79 mol% at time 265 min) along with the peak assignment to the corresponding protons.

Signal assignments for copolymerization systems were carried out with regard to the spectra recorded for homopolymerization of both VAc and DBM and comparing them with those recorded for the copolymerization systems.³² Fig. 1 indicates clearly that the peaks in the chemical shift range of 4.4–4.65 and 4.65–5.3 ppm for VAc monomer are related to the (–CH^VAc_a) monomer and the [(–CH^VAc_b) + (–CH^VAc_k)] monomer/polymer, respectively. Additionally, the peaks of monomeric (–CH^DBM_e) and monomer/polymer [(–CH^DBM_f) + (–CH^DBM_n)] protons appear in the chemical shift ranges of 6–6.3 and 3.7–4.3, respectively. In all of the spectra for each sample, the overall integrals of peaks for protons “f” and “n” in the unreacted and reacted, respectively, DBM (Fig. 1) were adjusted to an arbitrary value of 4. The integral for the signals of other protons in the same spectrum was automatically scaled according to this value. Then all other spectra recorded at various time intervals were scaled similar to the first spectrum, so that the overall integrals of all proton signals in all the other spectra for each sample were equal to the first spectrum of each sample. Thus, the individual conversions of both VAc and DBM can be monitored as a function of reaction time.

Individual comonomer conversions of VAc and DBM as well as the overall copolymer conversion and copolymer composition were determined versus time, and corresponding curves were plotted. Individual conversions of VAc and DBM at any time were calculated via eqn (1) and (2):³²

in which x_i(t) is the individual conversion of comonomer i at time t. I_b+k(t) and I_a(t) show the intensities of the unreacted monomer and polymer methine proton peaks of the VAc units and that of the unreacted VAc monomer peak at time t, respectively. Furthermore, I_f+n(t) and I_e(t) indicate the intensities of the unreacted monomer and polymer methylene proton peaks for DBM units and methine proton peaks of the unreacted DBM monomer at time t, respectively. Overall monomer conversion (x(t)), mole fraction of comonomer i in the comonomer mixture (f_i(t)) and that in the produced copolymer chains (F̄_i(t)) at any time are related to the individual comonomer conversions by the following equations:^30,32in which is the mole fraction of comonomer i in the initial reaction mixture. F̄_i(t) is indeed the cumulative mole fraction of comonomer i incorporated into the produced copolymer chains during the reaction time t. Subscripts i and j indicate comonomers VAc and DBM, respectively.

From the x_VAc(t) and x_DBM(t) values obtained by online ¹H-NMR kinetic experiments, it is possible to calculate x(t), f_i(t) and F̄_i(t) as a function of time via eqn (3)–(5). The results of the calculation are given in Table S1 of the ESI.† The corresponding curves for individual and overall conversion of the copolymerization system of VAc and DBM are shown in Fig. 2 and 3. The reaction temperature in the experiments was set at 60 °C. Fig. 2 and 3 reveal that both comonomers copolymerize and DBM incorporates into the copolymer at a higher rate than VAc. This event occurs only when the mole fraction of VAc in the initial feed is higher than that of DBM.³² It was deduced that in the earlier stages of copolymerization, due to the almost alternating structure of the produced chains, a lower amount of DBM in the initial feed leads to faster incorporation of DBM into the copolymer chains. Therefore, significant drift in the comonomer mixture composition with the reaction progress is expected. After that, the ability and tendency of the VAc comonomer for homopolymerization in the absence of DBM comonomer results in the formation of VAc homopolymer chains with a higher rate constant (k_p,VAc > k_p,copolymer > k_p,DBM where k_p indicate propagation rate coefficient), from which the overall rate of polymerization and F̄_VAc increase.³² In approval of the aforementioned statement, the overall conversion of comonomers versus time in two different mole fractions of VAc in the initial feed (both higher that 0.5) (Fig. 3) clearly show that the higher the amount of VAc content in the initial feed, the higher the conversion rate will be. In these experiments, DBM always preferentially incorporates into the copolymer chain at a higher rate. The final molar conversion of DBM monomer was recorded to be about 67 and 89% for 0.714 and 0.833, respectively, mole fractions of VAc in the initial reactions mixture, while that of VAc monomer doesn't exceed the 50% at the same time for both experiments.

Fig. 2 Individual and overall conversions of VAc and DBM as a function of reaction time for the free-radical solution copolymerization of the experiment VD2 containing 0.8333 mole fraction of VAc ([VAc]₀ : [DBM]₀ = 5 : 1) in the initial comonomer mixture at 60 °C.

Fig. 3 Overall comonomer conversion as a function of reaction time in experiments VD1 ([VAc]₀ : [DBM]₀ = 2.5 : 1) and VD2 ([VAc]₀ : [DBM]₀ = 5 : 1) at 60 °C.

Online ¹H-NMR spectra recorded for sample VD2 versus the reaction time are shown in Fig. 4. It is clear from this figure that with the progress of the polymerization reaction, the intensities of the peaks related to the protons of comonomers incorporated into the copolymer chains are increasing. So, the progress of the reaction can be followed with time by following the decreasing intensities of the comonomeric areas and the increase in regions related to copolymer protons. As a consequence, it is possible to investigate the kinetics of the VAc/DBM copolymerization reaction. It should be noted that isothermal conditions were established during the course of the reaction due to low rate of the copolymerization reaction and the high amount of solvent used.

Fig. 4 Progress of the free-radical solution copolymerization reaction of VAc and DBM as a function of time for experiment VD2 containing 0.8333 mole fraction of VAc in the initial feed.

Determination of the reactivity ratios by two different approaches

As mentioned before, calculation of the reactivity ratios of any comonomer by using a classic approach requires preparation of samples with different mole fraction of comonomers in the initial feed. On the other hand, following the reaction progress and comonomer mixture compositions as a function of reaction time by online ¹H-NMR kinetic experiments only for one sample with a proper initial comonomer mixture composition allows us to collect adequate data for calculation of the comonomer reactivity ratios by a new approach introduced in the literature.^7,21 According to this approach, copolymer composition for at least two different overall conversions (x(t) and x(t′) in which t′ > t and t ≠ 0) for any initial comonomer mixture composition is determined. The copolymer chain grown during time t is considered in fact to be the macroinitiator terminated with one of the comonomers under study, which will further grow during the time interval Δt′ = t′ − t from a comonomer mixture with composition of f(t) at any time t. Thus, accurate cumulative average copolymer composition (F̄(Δt′) as well as the individual (x_VAc(Δt′) and x_DBM(Δt′)) and overall (x(Δt′)) comonomer conversions for a copolymer produced during Δt′ can be calculated at either low or high conversion. Initial comonomer mixture composition for the copolymer formed during this time interval (Δt′) is considered in fact to be the composition of the comonomer mixture at time t (i.e. f(t), which is defined as the molar ratio of comonomer i to comonomer j in the comonomer mixture). Therefore, the new approach uses data obtained from online ¹H-NMR spectra during any time intervals to calculate the reactivity ratios of the comonomers.⁷ These data can be obtained via the following equations:^28,30

x(Δt′) = f_VAc(t)x_VAc(Δt′) + f_DBM(t)x_DBM(Δt′) (10)

where

Δt′ = t′ − t and t′ > t (11)

in which t is any time during the reaction and t′ is also any time after time t. f(t) and F̄(Δt′) indicate the molar ratio of VAc to DBM in the reaction mixture at time t and that in the copolymer produced during the time interval Δt′. x_VAc(Δt′), x_DBM(Δt′) and x(Δt′) indicate individual conversions of VAc and DBM and corresponding overall conversion, respectively, during the same time interval Δt′. Data obtained by eqn (6)–(10) are given in Table S2 of the ESI† for both experiments VD1 and VD2.

It should be noted that data obtained for each sample are sufficient to calculate the monomer reactivity ratios. However, it is preferable to combine the data for two samples and then calculate the more reliable reactivity ratios of VAc and DBM. The results of the calculation of the comonomer reactivity ratios by different methods including extended Kelen–Tudos (eKT) and Mao–Huglin (MH) methods are given in Table 1. In this table, the term “classic approach 1” refers to the conventional approach reported in the previous work²³ that can be used to calculate reactivity ratios by the different methods, such as eKT and MH methods, while the term “classic approach 2” refers to an approach similar to “classic approach 1” except that data collected from only two online ¹H-NMR kinetic experiments are used in the calculations. In addition, the term “new approach” refers to the recently introduced procedure in the calculation of reactivity ratios by using only one online ¹H-NMR kinetic experiment.⁷ This procedure is based on following the comonomer mixture and copolymer compositions at different reaction time intervals (see eqn (6)–(11)), from which enough data for calculation of reactivity ratios can be obtained for a copolymerization system with a large difference between the comonomer reactivity ratios.⁷

Table 1 Reactivity ratios of VAc and DBM reported in the literature together with the results obtained in this work in chloroform solvent at 60 °C

Terminal unit model (TUM)
rVAc	rDBM	Approach/method used	Reference
0.1102	0.0421	Classic approach 1/eKT	32
0.1135	0.0562	Classic approach 1/MH	32
0.1787 ± 0.0089	0.0062 ± 0.1185	Classic approach 2/eKT	This work
0.1792 ± 0.0090	−0.0081 ± 0.1165	Classic approach 2/MH	This work
0.1911 ± 0.0045	0.0381 ± 0.0788	New approach/MH	This work
0.1901 ± 0.0045	0.0151 ± 0.0755	New approach/eKT	This work

---

Simplified penultimate unit model (PUM)
rVAc/r′VAc	rDBM/r′DBM	Approach/method used	Reference
0.1612 ± 0.0450/0.1954 ± 0.0486	0/0	Classic approach 2/MH	This work
0.1812 ± 0.0205/0.1890 ± 0.0247	0/0	New approach/MH	This work

---

A simplified penultimate unit model (PUM) was also used to calculate the ultimate (r_VAc) and penultimate (r′_VAc) reactivity ratios of VAc by assuming r_DBM = r′_DBM = 0 (Table 1). There is no significant difference between the ultimate and penultimate reactivity ratios of VAc, suggesting that copolymer composition, microstructure and drifts in the comonomer mixture and copolymer compositions of the VAc/DBM copolymerization system can be described well by the terminal unit model (TUM).

In the previous work,²³ free-radical copolymerization of VAc and DBM was performed with a procedure the same as that in the present work; however, chloroform was used instead of deuterated chloroform. GPC results showed that number-average molecular weight of the copolymers formed in the free-radical copolymerization of VAc and DBM with CHCl₃ as a CTA (M_n = 10 350 g mol⁻¹ with PDI = 2.36 for f^o_VAc = 0.5)³² is much lower than that with CDCl₃ as a CTA in the present work (M_n = 20 595 and 19 856 g mol⁻¹ with PDI = 1.95 and 2.06 for f^o_VAc values of 0.714 and 0.833, respectively). It can be attributed to the different transfer constants to the solvent where the chain transfer ability of deuterated chloroform has been reported to be lower than that of chloroform.³¹ The higher the molecular weight is, the lower the influence of the chemospecificity in reactions with CTA and/or corresponding radical on the copolymer composition will be (Scheme 1). Hence, different reactivity ratios are expected, as can be seen in Table 1. One can expect that the copolymer compositions obtained in the present work are more accurate than those obtained in the previous work,³² which will be discussed in the next section based on the 95% joint confidence limits.

Scheme 1 A schematic representation of the effect of molecular weight on the copolymer composition (F_A) where one of the comonomers (A in the present case) adds preferentially onto the initiator/CTA-derived trichloromethyl radicals.

As mentioned before, individual monomer conversions versus time data may be used to determine changes in the comonomer mixture composition as a function of the overall monomer conversion. Using the Meyer–Lowry equation³⁵ and reactivity ratios of the MH method in the new approach, theoretical mole fraction of DBM in the comonomer mixture (f_DBM(t)) as a function of the overall monomer conversion were calculated and compared with the corresponding experimental data (Fig. 5). It is clear from this figure that for DBM mole fractions in the initial feed under study, incorporation of DBM into the copolymer chains is more favored than that of VAc. Drift in the comonomer mixture composition with conversion is significant, indicating that following two reactions under study allows us to collect enough data for estimation of the reactivity ratios.³²

Fig. 5 Comonomer mixture composition as a function of overall comonomer conversion for various mole fractions of DBM in the initial feed (symbols show the experimental data and continuous lines indicate the theoretical data calculated by using reactivity ratios of the new approach via the MH method).

Fig. 6 indicates the theoretical (calculated by using the Meyer–Lowry equation along with the material balance equation introduced in the literature,³⁵ where reactivity ratios of the MH method in the new approach were used) and experimental values obtained for cumulative copolymer composition versus overall conversion.

Fig. 6 Dependency of cumulative copolymer composition as a function of overall monomer conversions on various monomer molar ratios of VAc to DBM (mole fraction of DBM) in the initial reaction mixture (symbols show the experimental data and continuous lines indicate the theoretical data calculated by using the reactivity ratios of the new approach via the MH method).

The basic equation for instantaneous copolymer composition is defined as follows:

The theoretical instantaneous copolymer composition curve obtained from the differential copolymer composition equation of Mayo–Lewis (eqn (12)) by using monomer reactivity ratios obtained in the previous³² and present works are shown in Fig. 7. For reactivity ratios obtained by the new approach via the MH method, copolymerization of the VAc/DBM system shows an unstable azeotropic point equals to f^o_VAc = 0.5432. This means that the copolymer composition will drift away from the azeotropic composition with conversion. Furthermore, small monomer concentration fluctuations will cause the operating point to move away from the azeotrope point.

Fig. 7 Theoretical variation of the instantaneous copolymer composition (F_VAc) as a function of the mole fraction of VAc in the initial feed (f^o_VAc) for VAc/DBM copolymerization (theoretical values were calculated from the copolymer composition equation (eqn (12)) by using the reactivity ratios of various approaches).

The results observed in Fig. 7 can be attributed to the preferential addition of DBM onto the trichloromethyl (CCl₃) radicals derived from a reaction between the AIBN-derived 2-cyano-2-propyl radicals and CTA (CHCl₃ or CDCl₃) (Scheme 1) and/or to the preferential addition of the propagating radicals with terminal DBM unit to the CTA. In other words, there is no higher tendency for VAc monomer and corresponding radical to react with CCl₃ radicals and CTA. Therefore, results observed in Fig. 7 may be attributed to this fact that radicals generated from DBM comonomer are more stable than those from VAc comonomer.^36,37 It can be attributed to the resonance of the carbon-centered radical with the carbonyl group in the DBM. DBM monomer has been reported to be unable to homopolymerize while it can copolymerize easily with comonomers such as VAc and styrene.^32,36 Once the DBM adds to the primary CCl₃ radicals, electron-rich VAc then adds preferentially to the DBM-derived stable radicals followed by addition of electron-deficient DBM to the VAc-derived unstable radicals. In other words, the VAc/DBM system has a tendency towards alternating copolymerization with a r_VAcr_DBM value close to zero (Table 1). Consequently, performing copolymerization reactions with at least two different conditions leading to the low/medium and high molecular weight copolymers is introduced in the present work as a strategy to exactly determine a comonomer that adds preferentially to the initiator/CTA-derived radicals and/or a propagating radical that adds preferentially to the CTA.

In the previous³² and present works where CHCl₃ and CDCl₃, respectively, were used as CTAs, 2-cyano-2-propyl radicals are generated from AIBN and then react with above-mentioned CTAs, producing CCl₃ radicals^31,38 (Scheme 1) with a possible different reactivity towards comonomers (VAc and DBM in the present study) in the free-radical copolymerization. To our knowledge, there are no reports on the absolute rate constant (k₁) for the addition of carbon-centered radicals to DBM; however, owing to its structure, the k₁ value of the DBM is expected to be almost similar to that of the methyl acrylate (MA). A similar trend for carbon-centered radicals with a halo- (chloro- in the present case) or cyano-heteroatom substituent is expected.²³ For example, k₁ values for the addition of 2-cyano-2-propyl radicals to VAc and MA at 315 K have been reported to be 41 and 370 L mol⁻¹ s⁻¹, respectively,³⁹ indicating that the MA (and hence DBM) is more reactive than the VAc.^23,39

Addition of the CCl₃ radicals to various vinyl C=C bonds of the CH₂=CHX (X indicates substituent) monomers has been investigated in the literature.^{20,23,40–44} k₁ values for the addition of the CCl₃ radicals to VAc and MA at 30 and 22 °C, respectively, have been reported to be 1120 (ref. 40) and 29 000 (ref. 44) L mol⁻¹ s⁻¹, respectively, indicating again that the MA (and hence DBM) is more reactive than the VAc. Based on the results in Fig. 7, a similar trend was observed in the present work where electron-deficient DBM adds onto the CCl₃ radicals faster than electron-rich VAc, meaning that CCl₃ radicals possess some electrophilic character.

There are no reports on the addition of the VAc- and DBM (or MA)-radicals to CHCl₃ or CDCl₃; however, the absolute rate constant for addition of the VAc radical to bromotrichloromethane (CBrCl₃), leading to dead VAc–Br and a CCl₃ radical, has been reported to be 2740 L mol⁻¹ s⁻¹.⁴⁰ More experimental data is needed to exactly evaluate the possible preferential reaction of CTA (CHCl₃ or CDCl₃ in the present study) with one of the propagating radicals with terminal VAc and DBM units. Although the chemospecificity of CTA with propagating radicals has not been considered in Scheme 1, based on the results given in Fig. 7 and those observed for the preferential reaction of the thiol (RSH) with the propagating radicals with the St unit in comparison with those with the acrylate unit,^19,27 one may expect that CHCl₃ or CDCl₃ may react preferentially with propagating radicals with a terminal DBM unit.

Comonomer reactivity ratios obtained by all methods were used in the Meyer–Lowry equation to plot the theoretical estimation of comonomer mixture and copolymer composition. The best fitting between the theoretical and experimental values was obtained for reactivity ratio values of the MH method calculated by the new approach in the present work (Fig. 6 and 7), indicating the accuracy of the reactivity ratios obtained by the new approach with corresponding copolymer composition data obtained from high molecular weight copolymers produced during two online ¹H-NMR kinetic experiments.

Joint confidence limits

95% joint confidence limits is a more adequate idea to evaluate the accuracy of the calculated reactivity ratios e. The correct values are deduced to lie within the confidence area, thus giving an idea of the suitability of the model used. The smaller the experimental error and better the experimental design is, the smaller the area of uncertainty will be. The 95% joint confidence limits for the reactivity ratios of VAc/DBM system are shown in Fig. 8. As can be seen in this figure, the MH method gives the most accurate estimates with most accurate estimates in the new approach. So the reactivity ratios calculated by the MH method via the new approach were used in evaluation of the theoretical drifts in the comonomer mixture and copolymer compositions.

Fig. 8 95% joint confidence limits for the reactivity ratio data determined by the eKT and MH methods via classic approach 2 and the new approach in the copolymerization of VAc and DBM.

Conclusion

Free radical solution copolymerization of VAc and DBM in the presence of CDCl₃ as a solvent and CTA using AIBN as the initiator was successfully followed at 60 °C via online ¹H-NMR kinetic experiment. The reactivity ratios of VAc and DBM were calculated via two different approaches by data collected from two kinetic experiments via online monitoring of the reaction progress up to the medium overall monomer conversions. To consider the conversion effect, eKT and MH methods were used in the calculation of the reactivity ratios. The 95% joint confidence limits as well as good agreement between the theoretical and experimental drifts in the comonomer mixture and copolymer compositions with conversion confirmed that MH estimates are more reliable and accurate. Moreover, among the two approaches used, the new approach resulted in the most accurate estimation of the reactivity ratios. It was concluded from the results that the new approach can be used with a high accuracy for calculation of reactivity ratios with r_VAc to r_DBM ratios of about 5 where the drift in the comonomer mixture composition is significant but isn't very high. It was also found that copolymer composition and hence reactivity ratios can be affected by the copolymer's molecular weight. Therefore, performing copolymerization with at least two different conditions, one leading to low/medium molecular weight copolymers and another leading to high molecular weight copolymers, collecting corresponding data and calculating apparent comonomer reactivity ratios can be considered as a strategy to determine a comonomer that adds preferentially to initiator/CTA-derived radicals as well as to evaluate preferential addition of one of the propagating radicals to CTA. Then, more accurate reactivity ratios can be deduced from the experimental data.

References

1. A. S. Brar and A. Yadav, J. Polym. Sci., Part A: Polym. Chem., 2001, 39, 4051–4060.
2. P. Lewinski, S. Sosnowski, S. Kazmierski and S. Penczek, Polym. Chem., 2015, 6, 4353–4357.
3. M. Pocci, S. Alfei, F. Lucchesini, S. Castellaro and V. Bertini, Polym. Chem., 2013, 4, 740–751.
4. B. S. Beckingham, G. E. Sanoja and N. A. Lynd, Macromolecules, 2015, 48, 6922–6930.
5. L. Baener, C. Barner-Kowollik and T. P. Davis, J. Polym. Sci., Part A: Polym. Chem., 2002, 40, 1064–1074.
6. D. M. Haddleton, S. Perrier and S. A. F. Bon, Macromolecules, 2000, 33, 8246–8251.
7. M. Abdollahi and M. Sharifpour, Polymer, 2007, 48, 25–30.
8. I. Erol, O. Sen, A. Dedelioglu and C. Cifci, J. Appl. Polym. Sci., 2009, 114, 3351–3359.
9. G. Alfery and J. Goldfinger, J. Chem. Phys., 1944, 12, 205.
10. F. P. Mayo and F. M. Lewis, J. Am. Chem. Soc., 1944, 66, 1594–1601.
11. M. Finemann and S. D. Ross, J. Polym. Sci., 1950, 5, 259–262.
12. M. Finemann and S. D. Ross, J. Polym. Sci., Part A: Gen. Pap., 1964, 2, 1687–1698.
13. T. Kelen and F. Tudos, J. Macromol. Sci., Chem., 1975, 9, 1–27.
14. T. Kelen, F. Tudos, T. Foldes-Berezsnich and B. Turcsanyi, J. Macromol. Sci., Chem., 1976, 10, 1513–1540.
15. T. Kelen, F. Tudous, B. Turcsányi and J. P. Kennedy, J. Polym. Sci., Polym. Chem. Ed., 1977, 15, 3047–3074.
16. F. Tudos and T. Kelen, J. Macromol. Sci., Chem., 1981, 16, 1283–1297.
17. P. W. Tidwell and G. A. Mortimer, J. Polym. Sci., Part A: Gen. Pap., 1965, 3, 369–387.
18. R. Mao and M. B. Huglin, Polymer, 1993, 34, 1709–1715.
19. G. Moad and D. H. Solomon, The Chemistry of Radical Polymerization, Elsevier, 2nd edn, 2006, pp. 381–384.
20. A. V. Sokolov, Int. J. Quantum Chem., 2002, 88, 358–369.
21. W. H. Stockmayer, J. Chem. Phys., 1945, 13, 199–207.
22. T. Fueno and J. Furukawa, J. Polym. Sci., Part A: Gen. Pap., 1964, 2, 3681–3695.
23. G. Moad and D. H. Solomon, The Chemistry of Radical Polymerization, Elsevier, 2nd edn, 2006, pp. 111–117.
24. M. N. Galbraith, G. Moad, D. H. Solomon and T. H. Spurring, Macromolecules, 1987, 20, 675–679.
25. K. F. O'Driscoll, J. Coat. Technol., 1983, 55, 57.
26. F. M. Mirabella Jr, Polymer, 1977, 18, 705–711.
27. T. H. Spurling, M. Deady, J. Krstina and G. Moad, Makromol. Chem., Macromol. Symp., 1991, 51, 127–146.
28. M. A. Semsarzadeh and M. Abdollahi, Polymer, 2008, 49, 3060–3069.
29. H. Jianying, C. Jiayan, Z. Jiaming, C. Yihong, D. Lizong and Z. Yousi, J. Appl. Polym. Sci., 2006, 100, 3531–3535.
30. M. Abdollahi, J. Appl. Polym. Sci., 2011, 122, 1341–1349.
31. M. A. Semsrzadeh and M. Abdollahi, J. Appl. Polym. Sci., 2008, 110, 1784–1796.
32. S. S. Rahdar, E. Ahmadi, M. Abdollahi and M. Hemmati, J. Polym. Res., 2014, 21, 582.
33. A. S. Brar and S. Charan, J. Polym. Sci., Part A: Polym. Chem., 1995, 33, 109–116.
34. A. S. Brar and S. Charan, J. Appl. Polym. Sci., 1994, 51, 669–674.
35. V. E. Meyer and G. G. Lowry, J. Polym. Sci., Part A: Polym. Chem., 1965, 3, 2843–2851.
36. T. Sato, T. Kitajima, M. Seno and Y. Hayashi, J. Polym. Sci., Part A: Polym. Chem., 1998, 36, 1449–1455.
37. J. Olvera-Mancilla, S. López-Morales, J. Palacios-Alquisira, D. Morales-Morales, R. Le Lagadec and L. Alexandrova, Polymer, 2014, 55, 1656–1665.
38. M. Destarac, B. Pees and B. Boutevin, Macromol. Chem. Phys., 2000, 201, 1189–1199.
39. H. Fischer and L. Radom, Angew. Chem., Int. Ed., 2001, 40, 1340–1371.
40. H. W. Melville, J. C. Robb and R. C. Tutton, Discuss. Faraday Soc., 1953, 14, 150–160.
41. M. S. Kharasch, E. Simon and W. Nudenberg, J. Org. Chem., 1953, 18, 328–336.
42. M. S. Kharasch and M. Sage, J. Org. Chem., 1949, 14, 537–542.
43. A. V. Sokolov, Russ. Chem. Bull., 1993, 42, 640–643.
44. R. G. Gasanov and T. T. Vasil'eva, Bull. Acad. Sci. USSR, Div. Chem. Sci., 1989, 38, 719–722.

---

Footnote

† Electronic supplementary information (ESI) available: The experimental data obtained from ¹H-NMR spectra can be seen as a separate DOC file. See DOI: 10.1039/c6ra21888a

---