Solvent effects on free-radical copolymerization of styrene and 2-hydroxyethyl methacrylate: a DFT study

Abstract

The free-radical homopolymerization and copolymerization kinetics of styrene (ST) and 2-hydroxyethyl methacrylate (HEMA) in three different media (bulk, DMF, toluene) have been investigated by means of Density Functional Theory (DFT) calculations in combination with the Polarizable Continuum Model (PCM) and the Conductor-like Screening Model for Real Solvents (COSMO-RS). The conventional Transition State Theory (TST) is applied to calculate the rate parameters of polymerization. Calculated propagation rate constants are used to predict the monomer reactivity ratios, which are then used in the evaluation of the copolymer composition following the Mayo–Lewis equation. It is found that copolymerization reactions in bulk and toluene show similar transition geometries; whereas, DMF has a tendency to form H-bonding interactions with the polar HEMA molecules, thus decreasing the reactivity of this monomer during homopolymerization and towards ST during copolymerization. Calculations of copolymer composition further show that the amount of HEMA monomer in the ST–HEMA copolymer system decreases in the polar DMF solution. The calculated spin densities of the radical species are in agreement with the rate parameters and confirm that the copolymerization propagation rate of the ST–HEMA system is in the order: k_p(bulk) ≈ k_p(toluene) > k_p(DMF).

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Introduction

Acrylic copolymers are used as binder resins in solvent-borne automotive coatings. Copolymer composition and distribution of reactive functional groups are critical since they change the physical properties of the product. 2-Hydroxyethyl methacrylate (HEMA) is an important functional monomer used in the coatings industry. It is highly polar, so its usage in the formation of copolymer chains with styrene (ST) has gained attention since it was found that polarity and hydrophilicity of solvents affect copolymer composition and the copolymerization rate of the ST–HEMA system.¹ Free-radical copolymerization is a type of chain-growth polymerization to synthesize functional polymers.² During free-radical copolymerization chain-growth can be made possible by one of the following four propagation steps: It is important to monitor copolymer composition as a function of monomer reactivity and concentration at any time. By assuming a steady-state concentration of radicals during propagation, the relative change in the copolymer composition is derived by Mayo and Lewis:³where r₁ and r₂ are the monomer reactivity ratios for monomers 1 and 2 respectively. They can be defined by using the propagation rate constants: The Mayo–Lewis equation (eqn (5)) can be used to estimate the copolymer composition at any instant during the polymerization when the monomer reactivity ratios are known. Reactivity ratios have been determined for many important monomers and tabulated in several reference sources, such as the Polymer Handbook.⁴

The copolymer composition at any instant during polymerization can also be written in an alternative form by using the mole fraction of each monomer in the feed (f):

where F is the mole fraction of each monomer in the copolymer, r₁ = k₁₁/k₁₂, r₂ = k₂₂/k₂₁, and k_ij is the propagation rate coefficient for addition of the monomer-j to radical-i.

One of the simplest models used for copolymerization reactions is the terminal model,^3,5,6 in which it is assumed that only the terminal unit of the propagating radical influences its reactivity. In a given copolymerization system in which the terminal model is valid, only two types of radicals (i.e. corresponding to the two types of terminal unit) are considered and therefore only four different propagation reactions (i.e. corresponding to the additions of the two types of radicals to the two monomers) are characterized. A refinement of the terminal model is the penultimate model⁷ in which it is assumed that both the terminal and penultimate units of a polymer radical can affect its reactivity (a detailed description of the penultimate model is presented in the ESI†). Under the penultimate model, there are four different types of radical (–M₁M₂˙, –M₂M₂˙, –M₁M₁˙, –M₂M₁˙) and thus eight different types of reaction that need to be characterized. Fukuda et al.⁸ proposed a restricted form of the penultimate model, known as the implicit penultimate model (IPUM). In this model, it is assumed that the magnitude of the PUE on radical reactivity is independent of the coreactant and that there is thus no PUE on the selectivity of the radical. A consequence of this assumption is that the implicit PUE affects only the overall propagation rate of a copolymerization and not the composition or microstructure of the resulting polymers which can thus be fitted by the terminal model. The implicit penultimate model has been widely adopted,⁹ however the explicit penultimate model⁷ in which the PUE is allowed to affect both the reactivity and selectivity of the radical has also been used. Details of the both models have been reported in a review by Coote et. al.¹⁰

Coote et al. in their study of the addition of gamma-substituted propyl radicals to alkenes have demonstrated computationally that the magnitude of the penultimate unit effect is strongly dependent on the reacting alkene.^11,12 The same group has studied the effect of substituents (X = H, F, or CN) on the addition of 1-Y,3-X-disubstituted propyl radicals (Y = F or CN) to ethylene and found out that the explicit rather than implicit penultimate model should provide a more physically realistic description of copolymerization kinetics.¹³ Finally it was shown for para-substituted styrenes that the explicit penultimate model provides a more physically realistic description of copolymerization kinetics than the implicit penultimate model.¹⁴ The same group, in their study of the penultimate effect for the ATRP activation step has identified significant penultimate effects in the equilibrium constants between active and dormant species.¹⁵ In the radical ring-opening copolymerization of 2-methylene 1,3-dioxepane and methyl methacrylate, Davis et al. claimed that the terminal and penultimate unit models for copolymerization could not adequately describe the experimental results.¹⁶

The effect of solvent on the free-radical copolymerization has been the subject of many investigations since the first demonstration of solvent effects on the radical polymerization of methyl methacrylate and styrene.¹⁷ Among several explanations of solvent effects in radical copolymerization, the ‘bootstrap’ model as suggested by Harwood¹⁸ proposes that the solvent does not affect the reactivity of the growing chain radical, but it affects the partitioning of the monomer between the free solvent and the growing chain radicals. As a result, by changing the monomer concentration in the feed (appears as the mole fraction of the monomer in the above copolymer equation), the solvent modifies the copolymer composition. Later, Klumperman and O'Driscoll¹⁹ proposed a partition coefficient (k) as the ratio between the monomer concentration in the vicinity of the growing chain radicals (local concentration) and in the solution (global concentration), thus quantifying the partitioning phenomena described by Harwood.

Experimental studies of solvent effects on copolymerization kinetics involve measuring propagation rate coefficients via the pulsed laser polymerization (PLP) technique.^20–27 Solvent effects on the propagation of methacrylic acid (MAA) are studied via PLP and specific monomer–solvent interactions are investigated using FTIR spectroscopy.²⁸ Propagation rate constants of acrylic acid (AA) and MAA in water are significantly influenced by organic solvents and changing monomer concentrations.²⁹ Also, benzyl alcohol and N-methyl pyrrolidinone (NMP) as solvents influence MMA and ST homopolymerizations by changing the activation energies and preexponential factors.³⁰ Beuermann et al. studied the radical polymerization of AA and MAA in aqueous solutions in several studies^31–35 and observed an increase in k_p with dilution of monomer concentration. Upon formation of dimers in the water phase, acrylamide (AAm) and N-isopropyl acrylamide (NIPAM) aqueous phase monomer concentrations and apparent k_p values in water decrease as in the polymerizations of AA, MAA and acrylates.^36,37 Quantum-chemical calculations with the incorporation of solvation methods offer a fast and reliable approach to investigate the solvent effects on the kinetics of complicated systems.^38–40 Since experimental determination of reactivity ratios and kinetic parameters can sometimes be challenging particularly for complex systems, the results of quantum-chemical calculations can be useful in describing solvent effects on the copolymerization kinetics of many systems.

It is important to note that there have been several studies^41–45 including our recent work^46–49 on the theoretical modeling of free-radical polymerization and copolymerization kinetics by means of quantum-chemical approaches; however, the vast majority of these theoretical studies focus on the evaluation of kinetic parameters without incorporating solvent effects. Among few theoretical studies including solvent effects is the work by Thickett and Gilbert⁵⁰ where a simple Polarizable Continuum Model (PCM)^51,52 was used to model the AA propagation kinetics; though, the method used in this study turned out to be insufficient for a quantitative description of the reaction rate. In a more recent study by Coote et al.,⁵³ the use of Conductor-like Screening Model (COSMO)^54–57 resulted in a better agreement between theory and experimental rate parameters; yet, the systems under investigation (vinyl chloride and acrylonitrile) showed minor solvent dependence. In other systems, such as ethyl α-hydroxymethacrylate (EHMA) that exhibit strong molecular interactions through H-bonding, the application of continuum solvation methods was insufficient for a quantitative description of the propagation rate coefficients presumably due to the neglect of H-bonding interactions in the continuum solvent models.⁵⁸ In a recent study by some of us, propagation rates of AA and MAA in bulk and in water are reproduced qualitatively; the rate acceleration in solution is reproduced by using both implicit/explicit solvation models and COSMO-RS calculations.⁵⁹ Also, for methyl acrylate (MA) and vinyl acetate (VA) propagations, the calculated reaction barriers reproduced the experimental findings to within 4 kJ mol⁻¹ by correcting gas phase calculations to the solution phase using free energies of solvation computed by COSMO-RS.⁶⁰ Therefore, in particular, for systems that show strong solvent dependence through specific interactions with solvent, the propagating radical and/or monomers, the inclusion of explicit solvent molecules in the calculations should provide reliable rate parameters, as in one of our recent studies where explicit solvent plays an important role in the tacticity of the propagating chain and the rate of polymerization.⁴⁹

In this regard, we have performed quantum-chemical calculations to monitor solvent effects on the free-radical copolymer composition and propagation rate coefficient of ST with HEMA; polar aprotic N,N-dimethylformamide (DMF), and nonpolar toluene are used as solvents in the calculations. The choice of these solvents depends on the experimental findings that both of these solvents have an impact on the copolymer composition (and monomer reactivity ratios) of the ST–HEMA system.⁶¹

Methodology

The rate of a free-radical polymerization reaction is expressed aswhere k_p, k_d and k_t are the rate coefficients for the propagation, initiator decomposition and termination steps. f is the intiator efficiency, [M] and [I] are the concentrations of the monomer and initiator, respectively.⁶² In this study, the effect of solvent on the homopolymerization of HEMA and ST, and on the copolymerization of ST–HEMA copolymer system have been investigated; the propagation steps have been modeled and their k_p values have been used to represent the homo- and copolymerization reactions.

The conventional transition state theory (TST) is used to calculate the rate constants. The rate constant of a bimolecular reaction A + B → C is expressed⁶³ in terms of the molecular Gibbs free energy difference between the activated complex and the reactants (with inclusion of zero point vibrational energies):

where R represents the universal gas constant and k is the transmission coefficient which is assumed to be about 1 and p^θ is the standard pressure of 10⁵ Pa (1 bar).⁶⁴

To achieve the above-mentioned goal, the stationary points corresponding to the 3D structures along the reaction paths depicted in Scheme 1 have been located using M06-2X/6-31+G(d,p) since this methodology⁶⁶ is recommended for thermochemistry, kinetics, and noncovalent interactions. A detailed conformation search has been carried out in each case and the structures corresponding to the global minima have been considered later for the evaluation of the energetics and kinetics. The structures of the most stable conformations of the reactants have been considered in generating the transition state structures; this is followed by a full conformer search around the critical bond, a 30 degree rotation followed by optimization. The above mentioned procedure has been carried out both in bulk and in solution. Geometries in solution have been located using the Polarizable Continuum Model (PCM)^51,52 and solvation effects have been included with the COSMO-RS^54–57 methodology. In PCM calculations the dielectric of the medium in toluene has been taken as 2.4 whereas in DMF this has a value of 37.2. On the other hand, for the copolymerization in bulk where ST acts as a monomer, the medium has a dielectric of 2.4 – similar to toluene; when HEMA acts as a monomer, the bulk has been treated as a medium similar to HEMA with a dielectric of 7.6. (Note that HEMA has a dielectric constant of 7.6 similar to that of THF.) Consequently, for the homopolymerization of HEMA in bulk, the dielectric of the medium has been taken as 7.6 and, for the ST homopolymerization it has been considered as 2.4.

Scheme 1 Reaction paths followed in this study.

The Gaussian 09 program package⁶⁵ has been used for geometry optimization, whereas single point COSMO calculations have been performed using the ADF (Amsterdam Density Functional Theory)⁶⁶ package. Single point COSMO calculations in ADF using the BP/TZP level are performed to generate the cavity and surface charge densities in conducting medium. For the COSMO-RS calculations in bulk, the medium is considered to consist of the monomers themselves (i.e. ST if HEMA radical attacks ST or HEMA if ST radical attacks HEMA); the monomer concentration is assumed to be higher than that of the radical concentration during propagation in these calculations, the solute is embedded in a molecule shaped cavity and its surface is polarized by the solvent molecules. Thus we assumed that during the polymerization reactions in bulk, the radical species are in contact with the monomers to which they are supposed to attack and the polarization of the surface of the solute is affected by the molecules which are closer to it.

The attack of a syn HEMA radical on a HEMA monomer during the propagation step is depicted in Scheme 2. Radical species can attack the monomer from two directions. Overall there are 4 possible ways for a syn HEMA radical to attack a HEMA monomer. Similarly there are four other possibilities for the attack of an anti-radical: overall 8 different transition state structures for the propagation step of HEMA during homopolymerization have been located (Fig. S1, Table S1, ESI†). Note that in all media the structures corresponding to global minima have been considered (Fig. 1) for further kinetic investigations.

Scheme 2 Radical (syn) addition to HEMA (s-cis and s-trans).

Fig. 1 Propagation transition states of HEMA (M06-2X/6-31+G(d,p)).

In DMF, explicit solvent molecules have been included and the supermolecules are optimized in solution using the PCM methodology (implicit–explicit solvation model). The calculated free energy of solvation was corrected using the term RT ln(24.46) in order to take into account the unit transformation from 1 mol L⁻¹ (g) to 1 mol L⁻¹ (solution).⁶⁷ Contribution of the solvent to the Gibbs free energy computed by COSMO-RS and thermal corrections from the methodology with which the structures are optimized is finally added to the electronic energy. (A sample calculation is displayed in Table S2 in the ESI.†)

The mole fraction of monomer-1 in the copolymer (F₁) depends only on monomer mole fractions (f₁ and f₂, with f₁ + f₂ = 1) and the monomer reactivity ratios can be calculated using the Mayo–Lewis equation³ (eqn (5)).

In the copolymerization reactions two alternatives have been considered: a HEMA radical attacking a ST monomer and a ST radical attacking a HEMA monomer. The effect of polar, nonpolar media as well as the copolymer composition on the copolymerization kinetics is investigated. After the calculation of homo- and copolymerization rate constants, the monomer reactivity ratios and copolymer compositions are estimated using eqn (6) and (7). Spin density calculations have also been used to rationalize our findings.

In this study, the terminal rather than the penultimate model has been used to understand qualitatively the role of the solvent on the copolymerization kinetics of the ST–HEMA system. The presence of explicit solvent molecules together with the increasing number of alternatives for the transition structures would render the calculations with the penultimate model too cumbersome to be of practical usage.

Results and discussion

3D structures

The most stable transition state structures for the homopropagation of HEMA in bulk, toluene, and DMF are depicted in Fig. 1. In bulk and in toluene, intramolecular H-bonding interactions to form 7-membered rings between the hydroxyl proton and carbonyl oxygen have been observed in both moieties of the transition structures; these structures resemble each other. The transition structure in toluene has a lower dipole moment (8.345 D) as compared to the one in bulk (9.152 D) and also the charge separation between the carbonyl oxygen and the methyl proton in HEMA in toluene stabilizes this transition state more than the one in the bulk. The intramolecular interactions are ruptured with the inclusion of explicit DMF molecules in the system: the hydroxyl proton prefers to form H-bonds with the amide oxygen of the solvent. A weak interaction between the carbonyl oxygen and the amide proton stabilizes this structure as well.

In the case of styrene (Fig. 2), the transition state structures are similar in bulk and in solution: the two aromatic rings are close to each other due to C–H⋯π interactions, known to be important non-covalent interactions between benzene and heterocycles, especially in biomolecular systems or between 2 benzene rings.^68,69 The critical bond distance in bulk (d = 2.260 Å) is longer as compared to the one in DMF (d = 2.255 Å), thus an early transition state, and faster propagation is expected in bulk. In DMF, as the polarity of the medium increases, the critical bond distance shortens. In bulk medium, the reactants combine easily to yield a transition structure, however in polar medium the forming critical bond is screened by the continuum: as the polarity of the solvent increases, reactants are more shielded by the solvent and transition structures form later.

Fig. 2 Propagation transition states of ST (M06-2X/6-31+G(d,p)).

For copolymerization reactions, both cases where ST radical attacks to a HEMA monomer and HEMA radical attacks to a ST monomer have been considered. The most stable copolymerization transition states are depicted in Fig. 3. In bulk and in toluene the transition structures are similar, whereas in DMF, the intramolecular H-bonds are replaced by interactions with solvent molecules. In DMF, the number of intermolecular H-bonding interactions increases because of the explicit solvent molecules in the vicinity, thereby decreasing the disorder in the system. Thus, the entropy of activation decreases and slower propagation is anticipated in DMF.

Fig. 3 Copolymerization transition states of the ST–HEMA copolymer system (M06-2X/6-31+G(d,p)).

Kinetics

The transition structures for homopolymerization and copolymerization look very much alike in bulk and in toluene. In DMF, explicit solvent molecules provide more ordered structures, except in the case of ST–HEMA(R)–DMF. In this transition structure, the unbridged DMF molecule increases the disorder, thereby having a higher pre-exponential factor. In solution if the reactants are more stabilized than the transition state, the Gibbs free energy of activation increases, however, if the reverse happens, the barrier decreases and accelerates the propagation reaction (Fig. 4). For example in DMF, all the propagation rate constants decrease as compared to the ones in bulk and toluene; in cases where HEMA is present, intramolecular H-bonding interactions are disturbed, and intermolecular H-bonds stabilize the species. In the homopolymerization of HEMA, DMF stabilizes the reactants by 3.74 kcal mol⁻¹, and the transition state by 3.29 kcal mol⁻¹, the reactants are stabilized more than the transition structure as displayed by the Gibbs free energy profile (Fig. 4b). The rate deceleration in DMF compared to toluene can be attributed to the relative stabilization of the reactants in the two media: in toluene, HEMA and HEMA(R) are destabilized by 2.18 and 2.17 kcal mol⁻¹, whereas in DMF due to the stabilizing H-bonding interactions HEMA and HEMA(R) are stabilized by 1.73 and 2.00 kcal mol⁻¹ respectively. For ST and ST(R) the stabilization energies are 0.06 kcal mol⁻¹ and 0.09 kcal mol⁻¹ in toluene and 1.72 kcal mol⁻¹ and 1.45 kcal mol⁻¹ in DMF, respectively, these small differences are reflected in the values of the rate constants. Furthermore, in the homopolymerization of HEMA, toluene destabilizes the reactants by 4.35 kcal mol⁻¹, while it destabilizes the transition state by 3.55 kcal mol⁻¹ indicating that in a nonpolar medium, the activation energy barrier is lower due to the larger destabilization of the reactants. In cases where H-bonds are not present (ST–ST–DMF) the dielectric of the polar medium decelerates the reaction. (Activation barriers and stabilization energies for the gas phase geometries are provided in Table S3, ESI.†)

Fig. 4 Gibbs free energy profiles for the propagation reactions when (a) there is no solvent in the medium, (b) when the reactants are stabilized and, (c) when the transition state is stabilized by solvent molecules (R: reactant, R–S: reactant–solvent complex and P: product).

As displayed in Table 1, ordered transition structures have low pre-exponential factors and entropies of activation due to stronger inter- or intramolecular interactions. Note that in the homopolymerization of ST, the pre-exponential factors are higher as compared to the ones in homopolymerization of HEMA: this can be attributed to the weak interactions between the ST rings increasing the disorder of the system as opposed to HEMA–HEMA(R) where the transition structures are more ordered due to the presence of intramolecular H-bonding interactions.

Table 1 Activation energy barriers E_a (kcal mol⁻¹), Gibbs free energies of activation ΔG^# (kcal mol⁻¹), propagation rate constants k_p (L mol⁻¹ s⁻¹), pre-exponential factors A (L mol⁻¹ s⁻¹) monomer reactivity ratios in bulk, DMF, and toluene and relative propagation rate constants for homopolymerization of HEMA and ST (experimental values⁶¹ are in parenthesis) at 298.15 K (M06-2X/6-31+G(d,p))

	HEMA–HEMA	ST–ST	HEMA–ST(R)	ST–HEMA(R)
a k p DMF (HEMA–HEMA): 3763 L mol^−1 s^−1. b k p DMF (ST–ST): 691 L mol^−1 s^−1.
Bulk
E a	2.91	4.44	3.25	1.04
ΔG^#	14.04	14.43	12.63	13.79
k p	7.81 × 10^00	4.05 × 10^00	8.46 × 10^01	1.19 × 10^01
A	1064	7291	20 595	69
k p Bulk/kp DMF	2.1 (1.7)	4.7 (1.3)
r HEMA	0.65 (0.49)
r ST	0.05 (0.27)
DMF
E a	1.89	4.96	3.37	2.11
ΔG^#	14.47	15.35	14.35	13.79
k p	3.78 × 10^00	8.59 × 10^−01	4.63 × 10^00	1.18 × 10^01
A	91	3759	1370	418
k p DMF/kp DMF	1.0 (1.0)^a	1.0 (1.0)^b
r HEMA	0.32 (0.53)
r ST	0.19 (0.45)
Toluene
E a	0.69	4.44	3.13	1.04
ΔG^#	13.23	14.49	12.55	13.83
k p	3.06 × 10^01	3.66 × 10^00	9.63 × 10^01	1.10 × 10^01
A	97	6591	18 963	64
k p Toluene/kp DMF	8.1 (1.7)	4.3 (1.3)
r HEMA	2.77 (1.09)
r ST	0.04 (0.23)

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The monomer reactivity ratios are in good qualitative agreement with the experimental values, except for r_HEMA in toluene. In toluene, r_HEMA is greater than 1, indicating that in a nonpolar medium, homopolymerization of HEMA is preferred over copolymerization as mentioned earlier. The deviation from experiment in toluene may be due to the overestimation of the homopolymerization rate constant due to the presence of regular intramolecular interactions which in reality may be somewhat ruptured. On the other hand, r_ST values indicate that for ST, copolymerization reactions are faster than homopolymerization in all media.

The propagation rate constants for the homopolymerization reactions reveal the fact that even though the calculated values are not in quantitative agreement with experiment, they depict the experimental trend qualitatively pretty well (Table 1). In both cases (ST and HEMA), polymerization in polar medium is slower compared to bulk and nonpolar medium. In ST–ST case, rate constants in bulk and toluene increase almost to the same extent as compared to the one in DMF. In toluene, for the HEMA–HEMA homopolymerization, the deviation from experiment maybe attributed to the overestimation of the propagation rate constant in this medium as mentioned earlier. The discrepancies between experimental and calculated values may also be due to the simplicity of the models used. A thorough conformer search in a longer polymeric chain followed by inclusion of the penultimate effects might lead to quantitative agreement with experimental values.

The calculated and experimental monomer reactivity ratios in Table 1 have been used in the Mayo–Lewis equation to deduce the copolymer composition data for the ST–HEMA copolymer system (Fig. 5). In DMF, the HEMA monomer fraction in the copolymer is lower than the one in toluene since in DMF, HEMA interacts with the solvent and the local monomer concentration around the ST radical decreases. As the HEMA fraction in solution increases, the local HEMA monomer concentration around radical species increases and the mole fraction in the copolymer increases. The mole fractions of HEMA in the copolymer (F_HEMA) increases and become closer to the experimental values as the f_HEMA increases. In toluene, the higher deviation from experiment may be attributed to the higher monomer reactivity ratio (r_HEMA) in this medium as compared to the ones in bulk and DMF.

Fig. 5 Copolymer composition data for ST–HEMA system, mole fraction of HEMA in the copolymer (F_HEMA) as a function of HEMA mole fraction in solution (f_HEMA) (M06-2X/6-31+G(d,p)).

Mulliken atomic spin densities of the radical carbon atoms of HEMA and ST radicals are given in Table 2. The radicals have the lowest spin densities in DMF, thus the lowest rate constants in polar medium (Table 1) can be attributed to the lower reactivity of the radical species in this medium. The spin densities are higher in bulk and toluene where the calculated values for propagation rate constants are higher. In all media, the ST radical bears the highest spin density, in bulk and in toluene the copolymerization reaction where the ST radical attacks the HEMA monomer (HEMA–ST(R)) is favored over the attack of the HEMA radical on the styrene monomer (HEMA(R)–ST) (Table 1). However in DMF due to the presence of explicit solvent molecules around HEMA, the attack by the ST radicals is inhibited. On the other hand, HEMA will easily attack the free ST monomers as demonstrated by the calculations.

Table 2 Mulliken atomic spin densities (M06-2X/6-31+G(d,p)) for the radical carbon atoms of HEMA and ST radicals

	Bulk	DMF	Toluene
a In the presence of explicit DMF.
	0.815	0.802^a	0.825
	0.885	0.882	0.885

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Conclusion

By performing quantum-mechanical calculations on the solvent effects of ST–HEMA homo- and copolymerization kinetics, we find that noncovalent interactions like H-bonding within the monomers or with the solvent are key to understanding the solvent dependence of polymerization reactions. The intramolecular H-bonding interactions within HEMA molecules in bulk and nonpolar media are replaced with intermolecular H-bonding interactions between HEMA and polar solvent (DMF). Interestingly, this gives rise to a pronounced rate reduction in the polymerization of ST–HEMA system in the DMF solution. Variations in the propagation rate in different media affect the monomer reactivity ratios, which in turn affect the copolymer composition. In agreement with the pronounced rate reduction of the ST–HEMA system in DMF, the HEMA fraction in the copolymer is found to be low in this media as compared to the other cases (bulk and toluene environment). Spin density calculations of the radical species further support the calculated and measured rate parameters.

In summary, the change in the polymerization environment (bulk, nonpolar, polar) does affect the free-radical polymerization kinetics of ST–HEMA system; this effect is more pronounced when there are specific interactions like H-bonding between the monomers and solvents. This study qualitatively describes the solvent dependence of free-radical polymerization kinetics of ST–HEMA system through a combination of quantum-mechanical tools with the incorporation of solvation methods and we believe it provides a fast and reliable method for the study of solvent effects in the free-radical homo- and copolymerization kinetics. Longer polymeric chains where penultimate effects are considered may reproduce quantitatively the experimental findings provided that the conformational space for all the possible modes of attack is carefully explored.

Acknowledgements

The computational resources used in this work were provided by the National Center for High Performance Computing of Turkey (UHEM) under the grant number 1002212012, the TUBITAK ULAKBIM High Performance Computing Center, the project DPT-2009K120520. We gratefully acknowledge the Boğaziçi University research Grants under the project number 12B05P6.

References

1. K. Liang, M. Dossi, D. Moscatelli and R. A. Hutchinson, Macromolecules, 2009, 42, 7736–7744.
2. J. R. Fried, Polymer Science & Technology, Prentice Hall, NJ, 2003.
3. F. R. Mayo and F. M. Lewis, J. Am. Chem. Soc., 1944, 66, 1594–1601.
4. J. Brandrup and E. H. Immergut, Polymer Handbook, John Wiley & Sons, New York, 1989.
5. E. Jenkel, Z. Phys. Chem., Abt. A, 1942, 24, 190.
6. J. Turner Alfrey and G. Goldfinger, J. Chem. Phys., 1944, 12, 205–209.
7. E. Merz, T. Alfrey and G. Goldfinger, J. Polym. Sci., 1946, 1, 75–82.
8. T. Fukuda, Y. D. Ma and H. Inagaki, Macromolecules, 1985, 18, 17–26.
9. T. Fukuda, K. Kubo and Y. D. Ma, Prog. Polym. Sci., 1992, 17, 875–916.
10. M. L. Coote and T. P. Davis, Prog. Polym. Sci., 1999, 24, 1217–1251.
11. M. L. Coote, T. P. Davis and L. Radom, Macromolecules, 1999, 32, 5270–5276.
12. M. L. Coote, T. P. Davis and L. Radom, THEOCHEM, 1999, 461, 91–96.
13. M. L. Coote, T. P. Davis and L. Radom, Macromolecules, 1999, 32, 2935–2940.
14. M. L. Coote and T. P. Davis, Macromolecules, 1999, 32, 3626–3636.
15. C. Y. Lin, M. L. Coote, A. Petit, P. Richard, R. Poli and K. Matyjaszewski, Macromolecules, 2007, 40, 5985–5994.
16. G. E. Roberts, M. L. Coote, J. P. A. Heuts, L. M. Morris and T. P. Davis, Macromolecules, 1999, 32, 1332–1340.
17. T. Ito and T. Otsu, J. Macromol. Sci., Chem., 1969, 3, 197.
18. H. J. Harwood, Makromol. Chem., Macromol. Symp., 1987, 10, 331–354.
19. B. Klumperman and K. F. O'Driscoll, Polymer, 1993, 34, 1032–1037.
20. K. F. O'Driscoll, M. L. Monteiro and B. Klumperman, J. Polym. Sci., Part A: Polym. Chem., 1997, 35, 515–520.
21. S. Beuermann and M. Buback, Prog. Polym. Sci., 2002, 27, 191–254.
22. L. H. Yee, M. L. Coote, R. P. Chaplin and T. P. Davis, J. Polym. Sci., Part A: Polym. Chem., 2000, 38, 2192–2200.
23. R. A. Hutchinson, D. A. Paquet, J. H. Mcminn and R. E. Fuller, Macromolecules, 1995, 28, 4023–4028.
24. M. Buback, R. G. Gilbert, R. A. Hutchinson, B. Klumperman, F. D. Kuchta, B. G. Manders, K. F. O'Driscoll, G. T. Russell and J. Schweer, Macromol. Chem. Phys., 1995, 196, 3267–3280.
25. J. Sarnecki and J. Schweer, Macromolecules, 1995, 28, 4080–4088.
26. U. Bergert, S. Beuermann, M. Buback, C. H. Kurz, G. T. Russell and C. Schmaltz, Macromol. Rapid Commun., 1995, 16, 425–434.
27. M. L. Coote and T. P. Davis, Eur. Polym. J., 2000, 36, 2423–2427.
28. S. Beuermann, D. A. Paquet, J. H. McMinn and R. A. Hutchinson, Macromolecules, 1997, 30, 194–197.
29. F. D. Kuchta, A. M. van Herk and A. L. German, Macromolecules, 2000, 33, 3641–3649.
30. M. D. Zammit, T. P. Davis, G. D. Willett and K. F. O'Driscoll, J. Polym. Sci., Part A: Polym. Chem., 1997, 35, 2311–2321.
31. S. Beuermann, M. Buback, P. Hesse, S. Kukuckova and I. Lacik, Macromol. Symp., 2007, 248, 23–32.
32. S. Beuermann, M. Buback, P. Hesse, S. Kukuckova and I. Lacik, Macromol. Symp., 2007, 248, 41–49.
33. S. Beuermann, M. Buback, P. Hesse and I. Lacik, Macromolecules, 2006, 39, 184–193.
34. I. Lacik, S. Beuermann and M. Buback, Macromolecules, 2001, 34, 6224–6228.
35. I. Lacik, S. Beuermann and M. Buback, Macromolecules, 2003, 36, 9355–9363.
36. F. Ganachaud, R. Balic, M. J. Monteiro and R. G. Gilbert, Macromolecules, 2000, 33, 8589–8596.
37. S. A. Seabrook, M. P. Tonge and R. G. Gilbert, J. Polym. Sci., Part A: Polym. Chem., 2005, 43, 1357–1368.
38. K. J. Laidler and M. C. King, J. Phys. Chem., 1983, 87, 2657–2664.
39. D. G. Truhlar, W. L. Hase and J. T. Hynes, J. Phys. Chem., 1983, 87, 2664–2682.
40. D. G. Truhlar, B. C. Garrett and S. J. Klippenstein, J. Phys. Chem., 1996, 100, 12771–12800.
41. M. Dossi, G. Storti and D. Moscatelli, Polym. Eng. Sci., 2011, 51, 2109–2114.
42. M. Dossi, K. Liang, R. A. Hutchinson and D. Moscatelli, J. Phys. Chem. B, 2010, 114, 4213–4222.
43. M. L. Coote, Macromol. Theory Simul., 2009, 18, 388–400.
44. V. Van Speybroeck, K. Van Cauter, B. Coussens and M. Waroquier, ChemPhysChem, 2005, 6, 180–189.
45. P. Cieplak and A. Kaim, J. Polym. Sci., Part A: Polym. Chem., 2004, 42, 1557–1565.
46. B. Dogan, S. Catak, V. Van Speybroeck, M. Waroquier and V. Aviyente, Polymer, 2012, 53, 3211–3219.
47. T. Furuncuoglu, I. Ugur, I. Degirmenci and V. Aviyente, Macromolecules, 2010, 43, 1823–1835.
48. I. Degirmenci, V. Aviyente, V. Van Speybroeck and M. Waroquier, Macromolecules, 2009, 42, 3033–3041.
49. T. F. Ozaltin, I. Degirmenci, V. Aviyente, C. Atilgan, B. De Sterck, V. Van Speybroeck and M. Waroquier, Polymer, 2011, 52, 5503–5512.
50. S. C. Thickett and R. G. Gilbert, Polymer, 2004, 45, 6993–6999.
51. S. Miertus, E. Scrocco and J. Tomasi, Chem. Phys., 1981, 55, 117–129.
52. S. Miertus and J. Tomasi, Chem. Phys., 1982, 65, 239–245.
53. E. I. Izgorodina and M. L. Coote, Chem. Phys., 2006, 324, 96–110.
54. A. Klamt and G. Schuurmann, J. Chem. Soc., Perkin Trans. 2, 1993, 799–805.
55. A. Klamt, J. Phys. Chem., 1995, 99, 2224–2235.
56. A. Klamt, COSMO-RS: from quantum chemistry to fluid phase thermodynamics and drug design, Elsevier, Amsterdam, Oxford, 2005.
57. A. Klamt, V. Jonas, T. Burger and J. C. W. Lohrenz, J. Phys. Chem. A, 1998, 102, 5074–5085.
58. I. Degirmenci, D. Avci, V. Aviyente, K. Van Cauter, V. Van Speybroeck and M. Waroquier, Macromolecules, 2007, 40, 9590–9602.
59. T. Alfrey, Abstr. Pap., Jt. Conf. – Chem. Inst. Can. Am. Chem. Soc., 1976, 36.
60. C. Y. Lin, E. I. Izgorodina and M. L. Coote, Macromolecules, 2010, 43, 553–560.
61. K. Liang and R. A. Hutchinson, Macromolecules, 2010, 43, 6311–6320.
62. K. Matyjaszewski and T. P. Davis, Handbook of radical polymerization, Wiley-Interscience, Hoboken, Chichester, 2002.
63. D. A. McQuarrie and J. D. Simon, Physical chemistry: a molecular approach, University Science Books, Sausalito, Calif., 1997.
64. P. W. Atkins and J. De Paula, Atkins' physical chemistry, Oxford University Press, Oxford, New York, 2006.
65. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, N. J. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, Ö. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski and D. J. Fox, R. A. Gaussian 09, Gaussian Inc., Wallingford CT, 2009.
66. J. N. Louwen, C. Pye and E. V. Lenthe, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands, 2008.
67. M. D. Liptak, K. C. Gross, P. G. Seybold, S. Feldgus and G. C. Shields, J. Am. Chem. Soc., 2002, 124, 6421–6427.
68. T. Alfrey, F. J. Honn and H. Mark, J. Polym. Sci., 1946, 1, 102–120.
69. T. Alfrey and C. C. Price, J. Polym. Sci., 1947, 2, 101–106.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c3nj00820g

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