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A quantum chemistry study of the free-radical copolymerization propagation kinetics of styrene and 2-hydroxyethyl acrylate.


Several works focused on the study of acrylic copolymers, widely used as resins for coatings, appeared recently in the literature. In particular, the free radical copolymerization kinetics was investigated to get a good understanding of the mechanism of copolymer chain-growth (1-7). Copolymers based on 2-hydroxyethyl acry-late (HEA) were reported by copolymerization with ethers, acrylates, or methacrylates (8-13). Notably, HEA is a functional monomer whose copolymers are also useful as biomaterials (14-17). In fact, even if acrylates are generally more toxic than methacrylates (18), (19), poly-HEA (PHEA) based materials are used as cell-culturing media and are applicable for in vitro experiments (20).

Despite of the PHEA potentials, a few studies on the kinetics of copolymerization involving HEA have been reported. The direct synthesis of PHEA is made through atom transfer radical polymerization as controlled free radical polymerization method (21), whereas Bian and Cunningham proposed the nitroxide-mediated living radical polymerization of HEA (22). Jansen et al. investigated the copolymerization of HEA and 2-hydroxyethyl methac-rylate using the real-time Fourier transform infrared spectroscopy (10). With the same technique, it was found that the copolymerization of HEA and n-butyl acrylate, by the use of a nitroxide mediator, leads to an acceleration of HEA conversion and polymerization rate, thanks to hydrogen bonding interactions between the hydroxyl group of HEA monomer and the nitroxide (9). Moreover, the influence of the solvent on the apparent reactivity ratios in free radical copolymerization between HEA and itaconic acid was also studied (23). With particular reference to the HEA/styrene (ST) system, solution copolymerizations were carried out in benzene at 60[degrees]C (24), whereas proton nuclear magnetic resonance and gel permeation chromatography were used to study HEA/ST free radical copolymerization mediated by 2,2,6,6-tetra-methyl-1-piperidinyloxy (TEMPO) at 125 [degrees] C (25). Finally, Monte Carlo simulations were used to predict molecular weight distribution and composition of HEA/ST copolymers (26).

The limited number of investigations on HEA reactivity in free radical polymerization processes is partly due to the fact that HEA polymerization leads to high molecular weight products through crosslinking and transfer to polymer reactions. As a matter of fact in recent years, it was well established that the main issue in acrylate kinetics is the occurrence of secondary reactions, such as chain transfer and the formation of midchain radicals (MCRs) (27-29). The experimental evaluation of kinetic parameters for these reactions is very complicated to achieve due to the reactivity differences between secondary and tertiary carbon radicals (30). However, improvements have been recently made for several polymerization systems applying the pulsed laser polymerization (PLP) technique (28), (30-32). Although previous mentioned studies on this topic did not refer directly to HEA, the same reaction patterns might occur even for this monomer. Therefore, the resulting complexity of the operative kinetic scheme is the main cause of difficulties in the experimental analysis (33), (34).

To overcome such problems, and with the aim of supporting and enriching the experimental efforts, theoretical predictions of kinetics based on quantum mechanics methods could represent an effective tool (35-45). This is especially promising since the potential of density functional theory (DFT) to investigate free radical copolymer-ization kinetics was already shown in the literature (6), (7), (40), (46). In this work, a DFT based computational approach is applied to study the reactivity of HEA in free radical homopolymerization and copolymerization with ST. In particular, the monomer reactivity ratios, [r.sub.UEA] and [r.sub.ST], are evaluated at 50 [degrees] C and 125 [degrees] C and compared with those proposed in literature (8), (25). Finally, the evolution of the copolymer composition is investigated according to the terminal model (47).


The selected computational approach adopted is based on DFT. In particular, the Becke 3 parameter and Lee-Yang-Parr functional (B3LYP) were used in the DFT calculations to evaluate exchange and correlation energies (48), (49). All quantum chemical calculations of reactants and products were performed with a spin multiplicity of 2 using an unrestricted wave function (UB3LYP). B3LYP methods provide excellent low-cost performance, as demonstrated in previous works reported in the literature (6), (7), (39), (45), (50-52). The all electron 6-31 basis set with added polarization functions (6-31G(d,p)) was used as basis set. All geometries were fully optimized with the Berny algorithm and were followed by frequency calculations. The geometry of each molecular structure was considered stable only after calculating vibrational frequencies and force constants and if no imaginary vibrational frequency was found. Transition state structures are located adopting the synchronous transit-guided quasi Newton method and are characterized by a single imaginary vibrational frequency [53]. The corresponding kinetic constants were determined through the classical transition state theory as:


where [k.sub.b] and h are Boltzmann and Plank constant, respectively, T is the temperature, [E.sub.a] is the activation energy of the process, and Q represents the product of the partition functions ([q.sup.vib] [q.sup.rot] [q.sup.(rot, int)]) for transition states ([not equal to]) and reactants (R). In particular, [q.sup.vib] and [q.sup.rot] are the vibrational and rotational partition functions, respectively, calculated according to Eqs. 2 and 3.

where [v.sub.i] are the vibrational frequencies, [I.sub.x], [I.sub.y], [I.sub.z] are the rotational constants, and [sigma] is the rotational symmetry number. Moreover, [q.sup.(rot, int)] is the internal rotation partition function. In fact, previous works showed that the computational accuracy is improved by treating the low-vibralional frequencies, indicative of a small energy barrier for the relative motion of a partion of the molecule with respect to the other one, as internal rotations [35, 36, 54, 55]. More in detail, for internal motions corresponding to the lower vibrational frequencies, the potential energy was calculated, as a function of the rotational angle, at the B3LYP/6-31G(d) level of theory, and it was then interpolated using cubic splines. As reported in the literature [51], the calculated potential energy, V ([empty set]), was used to solve the rotational ID Schrodinger equation:

- [h.sup.2] / 2 [I.sub.m] x [a.sub.2] [PHI] / a [[empty set].sup.2] + V ([empty set]) x [PHI] ([empty set]) = [epsilon] x [PHI] ([epsilon])

where h is the ratio between the Planck constant and 2 [pi], [PHI] is the energy levels associated with each vibrational frequency, [PHI] is the rotational angle, and [I.sub.m] is the reduced moment of inertia of a part of the molecule with respect to the other one calculated either as (56):

[I.sub.m] = [I.sub.1] x [I.sub.2] / [I.sub.1] + [I.sub.2]

where [I.sub.1] and [I.sub.2] are the moments of inertia of the two rotating moieties. The internal rotation partition function was then calculated according to Eq. 6.


where zk is the calculated eigenvalue, [g.sub.k] is the degeneracy of rotational energy level [[epsilon].sub.k], and [[sigma]] is the symmetry number of the internal rotation.

All quantum chemistry calculations are performed with the Gaussian 03 suite of programs and all pictures are drawn with PyMol 1.3 [57, 58].


As mentioned in the Introduction section, there are few reported studies on HEA/ST free radical copolymerization; moreover, data reported in the literature are quite scattered. According to the Q-e scheme proposed by Alfrey and Price [59], the monomer reactivity ratios are estimated as [r.sub.HEA] = 0.31 and [r.sub.ST] = 0.36 [26]. Chow measured the same parameters by solution polymerization of HEA with ST in benzene at 60 [degrees] C obtaining values of [r.sub.HEA] = 0-34 and [r.sub.ST] = 0.38 [24]. Later, Penlidis and coworkers proposed a series of observations about the HEA/ST polymerization, examining reactivity ratios and full conversion kinetics as a function of experimental variables such as feed composition, temperature, and initiation concentration. Copolymer composition data at 50 [degrees] C were proposed and reactivity ratios of [r.sub.HEA] = 0.20 and [r.sub.ST] = 0.46 were determined. The work emphasized all the difficulties related to the experimental investigation of HEA/ST system, showing in particular the variability in the reactivity ratio values probably due to the polarity change in the copolymer and monomer mixture, depending on the initial comonomer feed composition [8]. Recently, the living free-radical copolymerizations of ST with a series of polar monomers, including HEA, mediated by TEMPO and initiated by benzoyl peroxide at 125 [degrees] C were studied [25]. Monomer reactivity ratios of [r.sub.HEA] = 0.43 and [r.sub.ST] = 0.28 were found, but limits in controlling the process during the polymerization are highlighted even in this work.

HEA* + HEA* [right arrow] [k.sub.HEA - HEA] HEA - HEA*

HEA* + ST [right arrow] [k.sub.HEA - ST] HEA - ST*

ST* + ST [right arrow] [k.sub.pST - ST] SY - ST*

ST* + HEA [right arrow] [k.sub.ST - HEA] ST - HEA

SCHEME 1. Elementary reactions involved in the determination of the monomer reactivity ratios.

With the aim to compare our results with the copolymer composition data available in literature [8, 25], the HEA/ST copolymerization was studied by the computational method at 50 [degrees] C and 125 [degrees] C. To obtain rHEA and rST values, the elementary reactions in Scheme 1 were simulated. Monomer reactivity ratios were determined as defined in Eqs. 7 and 8.

[r.sub.HEA] = [k.sub.HEA] HEA / [k.sub.HEA] - ST [r.sub.ST] = [k.sub.ST] - ST / [k.sub.ST] - HEA The Arrhenius kinetic parameters obtained by the simulations at the two temperatures are collected in Table 1 and the corresponding values of monomer reactivity ratio are summarized in Table 2. Finally, the transition state geometries for the reactions reported in Scheme 1 are shown in Fig. 1.
TABLE 1. Arrhenius kinetic parameters for HEA/ST theoretically
determined at 50 [degrees] C and 125 [degrees] C.

                                T = 50 degrees C
                  [Log.sub.10]  [E.sub.a]  [k.sub.i-j]  [Log.sub.10]
                  (A)                                   (A)

HEA* + HEA                8.04       6.03        9,221          8.35
[right arrow]

HEA* + ST [right          8.27       5.10       65,491          8.62

ST* + ST [right           8.43       8.28          672          8.47

ST* + HEA [right          7.67       6.40        2,167          7.97

                  T = 125 degrees C

                  [E.sub.a]  [k.sub.i-j]
HEA* + HEA             6.03      110,326
[right arrow]

HEA* + ST [right       5.10      664,618

ST* + ST [right        8.28        8,314

ST* + HEA [right       6.40       28,560

Activation energies ([E.sub.a]) in kcal [mol.sup.-1], A and
[k.sub.i -j] in L [mol.sup.-1] [s.sup.-1]. [k.sub.i -j] = A * exp
TABLE 2. Monomer reactivity ratios for copolymerization
of 2-hydroxyethyl acrylate (HEA) and styrene (ST).

             T = 50 [degrees] C  f = 125 [degrees] C

[r.sub.HEA]                0.14                 0.17
[r.sub.ST]                 0.31                 0.29

The values of the [k.sub.ST] - ST rate coefficient in Table 1 are in reasonable agreement with those proposed in the literature for the ST homopolymerization and measured by PLP (237 and 2318 [Lmol.sub.-1] [s.sub.-1] at 50 [degrees] C and 125 [degrees] C, respectively) [60]. In particular, the Arrhenius pre-expo-nential for this elementary reaction differs slightly from that published in an our previous work [6] due to the modification introduced in its evaluation, as illustrated in the Computational Details section. No check is possible for the other kinetic constants due to the lack of experimental data. On the other hand, another interesting remark can be done comparing the rate coefficient values to the transition state geometries [7]. The calculated values exhibit the following ranking: [k.sub.HEA-ST] > [k.sub.HEA-HEA] > [k.sub.ST-HEA] > [k.sub.ST-ST] This trend in reactivity is reflected by the values of the distance (d) between the two carbon atoms involved in each radical-monomer reaction, shown in Fig. 1. In fact, d decreases as the corresponding rate coefficients ([d.sub.HEA-ST] < [d.sub.HEA-HEA] < [d.sub.ST-HEA] < [d.sub.ST-ST]): larger distances indicate higher reactivities, as the radical and the monomer react dissipating less energy to approach each other.

Moving to the analysis of the monomer reactivity ratios, they exhibit a weak dependence on temperature. Moreover, to understand the reliability of these parameters, a plot of HEA mole fraction in the copolymer (F1) as a function of HEA mole fraction in the monomer phase ([f.sub.1]) at the two investigated temperatures is reported in Figs. 2 (50 [degrees] C) and 3 (125 [degrees] C), respectively. In each figure, experimental values of copolymer composition from the literature (Ref. 8 at 50 [degrees] C and Ref. 25 at 125 [degrees] C) are compared with the prediction of the Mayo-Lewis terminal copolymerization model (Eq. 9) calculated using the monomer reactivity ratios evaluated by our computational method [47],

The results in Figs. 2 and 3 confirm the reliability of the calculated values of reactivity ratios: the terminal model reproduces the experimental data at both temperatures. Even though the prediction is less accurate at 125 [degrees] C with HEA mole fraction in the monomer phase larger than 0.5, such result is quite satisfactory. Moreover, considering that chain transfer to polymer and formation of MCRs cause the main problem in the acrylate polymerization as mentioned in the Introduction section, some deviation between experimental and calculated composition data were predictable. In fact, the calculations performed are not affected by the side reactions and yield data for the hypothetical case in which all the side reactions could be switched off. Despite of this simplification, the proposed approach is able to reproduce with reasonable agreement the real system.

[F.sub.1] = [r.sub.1] [[f.sup.2].sub.1] / [r.sub.1] [[f.sup.2].sub.1] + 2 [f.sup.1] [f.sup.2] + [r.sub.2] [[f.sup.2].sub.2]


A computational study on the free-radical copolymerization propagation kinetics of HEA and ST was proposed. HEA/ST copolymerization was investigated at 50 [degrees] C and 125 [degrees] C, and relative kinetic parameters were determined adopting DFT. In particular, simulations at 50 [degrees] C led to monomer reactivity ratios of [r.sub.HEA] = 0.14 and [r.sub.ST] = 0.31, whereas calculation performed at 125 [degrees] C gave values of [r.sub.HEA] = 0.17 and [r.sub.ST] = 0.29. Moreover, taking as reference experimental data proposed in previous works, the copolymer composition as a function of monomer composition was investigated, at the same temperatures indicated above. In both cases, the prediction by the terminal copolymerization model, obtained using computational parameters, well described the composition trend showed in literature, confirming the potentiality of the computational approach proposed. It can also provide useful information for the lack of experimental data relative to composition-averaged copolymerization propagation rate coefficient, even extending the set of computational data here proposed with the determination of kinetic parameters necessary to study the presence of a possible penultimate unit effect [61].





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Correspondence to: Davide Moscatelli; e-mail: DOI 10.1002/pen.22045

Published online in Wiley Online Library ( [c] 2011 Society of Plastics Engineers

Marco Dossi, Giuseppe Storti, Davide Moscatelli Dipartimento di Chimica, Materiali e Ingegneria Chimica "Giulio Natta", Politecnico di Milano, 20131 Milano, Italy
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