4. Reactivity-structure relationship of esters of 2,3-norbornene dicarboxylic acid

Figure 10. Semi-logarithmic correlations of polymerization 2 over catalyst 1 with varying catalyst concentration (CM<sup>0</sup> =

Figure 11. Correlation of the observed constant ko of polymerization of monomer 2, catalyzed by 1 with the initial

, 50С).

, 50С, dependences are marked in accordance with Figure 9).

0.35 molel

1

28 Recent Research in Polymerization

concentration of catalyst (CM0 = 0.35 mole l<sup>1</sup>

Based on the values of effective constants, we compared reactivity and activation parameters of polymerization of diesters exo,exo-2,3-norbornene dicarboxylic acid, which are differ by length and branched chain of ester substituent. To define the activation parameters, we used Arrhenius equation (12) and calculation results are shown in Figure 12

$$
\ln k\_{\text{e}} = \ln A - \frac{E\_{\text{a}}}{R \cdot T} \tag{12}
$$

This correlation between ln k<sup>e</sup> and 1/T for each researched ester has linear character. This proves that the interaction mechanism of ruthenium complex and corresponding ester at the different temperatures is unchanged. Table 3 presents data on effective constants and activation parameters of polymerization of diesters exo,exo-2,3-norbornene dicarboxylic acid.

Figure 12. Arrhenius correlations of polymerization of diesters exo,exo-5-norbornene-2,3-dicarboxylic acid.


Table 3. Effective constants and activation parameters of polymerization of diesters exo,exo-2,3-norbornene dicarboxylic acid.

It was expected that aliphatic radical elongation from the first to the eighth atoms of carbon would lead to gradual decrease in reactivity of esters row. However, according to Table 5, aliphatic radical elongation insignificantly affects the reactivity of esters.

On the contrary, branched substituent chain affects reactivity greatly. Constant ke of an ester with iso-butyl radical is six times lesser than constant k<sup>e</sup> of a similar ester with linear butyl radical. The steric hindrances significantly decrease the reactivity of diesters with branching aliphatic radical under interaction with active form of ruthenium complex. In study [35], the researchers attempted to make a quantitative estimation of the initiation and growth constants.

As shown in Table 5, the increase of aliphatic radical length leads to gradual increase of activation parameters. To explain changes in activation parameters, we should define the rate constant, which is dependent from monomer structure in more degree. Effective constant of polymerization includes four true constants. Constants k<sup>1</sup> and k<sup>1</sup> are determined by the structure of ruthenium complex and do not depend on the monomer structure. Nevertheless, the influence of the ester structure could be indirect. When bond Ru-N is disassociated, a 14-electron state is formed. This state is more polar than the initial 16-electron state (Scheme 4).

Scheme 4. Dissociation the Ru-N bond of catalyst.

Polar media stabilize 14-electron state and make disassociation easier. Solutions of esters, which are different in structure, may possess different dielectric permittivity and, thus, could affect constant k<sup>1</sup> and k1. However, in polymerization, solutions of esters have low concentration and the contribution of ester into the polarity of medium remains insignificant.

Esters structure would affect more constants k<sup>2</sup> and kg. First, we should understand the way monomer structure can affect constant k2. This constant defines the reaction rate, which identifies the process of monomer addition to the active form of ruthenium complex. In this process, the double bond of ester molecule occupies the vacant position in the coordination sphere of ruthenium complex (Scheme 5).

While the activation energy E<sup>a</sup> defines excess of energy, which molecules in the reaction should possess to form transition state. Pre-exponential factor A can correlate with steric factor. Both parameters define the process of reaching the top of a potential barrier and are calculated from the initial state of the system. It is unlikely that the length of aliphatic radical affected the rate and activation parameters of this reaction. It is more probable that constant k<sup>2</sup> and activation parameters are nearly equal for molecules with varying length of aliphatic radical. It is also unlikely that branching substituent can affect both the rate and activation parameters of this process.

It was expected that aliphatic radical elongation from the first to the eighth atoms of carbon would lead to gradual decrease in reactivity of esters row. However, according to Table 5,

Table 3. Effective constants and activation parameters of polymerization of diesters exo,exo-2,3-norbornene dicarboxylic

<sup>1</sup> (30С) Ea, kJ mole<sup>1</sup> A, l mole<sup>1</sup> s

1

On the contrary, branched substituent chain affects reactivity greatly. Constant ke of an ester with iso-butyl radical is six times lesser than constant k<sup>e</sup> of a similar ester with linear butyl radical. The steric hindrances significantly decrease the reactivity of diesters with branching aliphatic radical under interaction with active form of ruthenium complex. In study [35], the researchers attempted to make a quantitative estimation of the initiation and growth constants. As shown in Table 5, the increase of aliphatic radical length leads to gradual increase of activation parameters. To explain changes in activation parameters, we should define the rate constant, which is dependent from monomer structure in more degree. Effective constant of polymerization includes four true constants. Constants k<sup>1</sup> and k<sup>1</sup> are determined by the structure of ruthenium complex and do not depend on the monomer structure. Nevertheless, the influence of the ester structure could be indirect. When bond Ru-N is disassociated, a 14-electron state is formed. This state is more polar than the initial 16-electron state (Scheme 4).

aliphatic radical elongation insignificantly affects the reactivity of esters.

Methyl 0.11 <sup>82</sup> <sup>2</sup> 1012 Propyl 0.10 <sup>89</sup> <sup>2</sup> 1013 Butyl 0.08 <sup>92</sup> <sup>7</sup> 1013 Iso-butyl 0.01 <sup>72</sup> <sup>6</sup> 109 Pentyl 0.21 <sup>105</sup> <sup>2</sup> 1016 Octyl 0.17 <sup>121</sup> <sup>2</sup> 1018

Substituent ke, l mole<sup>1</sup> s

30 Recent Research in Polymerization

acid.

Scheme 4. Dissociation the Ru-N bond of catalyst.

It is necessary to mention that the influence of the previous monomer unit may affect rate and activation parameters of monomer addition reaction to one of the active forms of ruthenium. However, this factor is absent on this stage of the reaction.

Having analyzed the experimental data, we concluded that the structure of monomer is more likely to affect the growth reaction of polymer chain with constant kg.

It is known from literature data that esters of 5-norbornene-2,3-dicarboxylic acid can chelate the active forms of ruthenium complex with carbonyl oxygen of ester group, thus, forming hexatomic intramolecular complex [36]. Therefore, two active forms of ruthenium complex can take part in the polymer chain-growth reaction (Figure 13).

RudO bond strength depends on donor properties of carbonyl oxygen. In esters row, the donor properties of oxygen will enhance as there will increase inductive effect of growing radical. At the same time, RudO bond strength will increase. Reinforcement of RudO bond decreases mobility of ester fragment and makes its intramolecular complex more rigid.

Scheme 5. Coordination of the monomer's molecule with ruthenium complex.

Figure 13. Non-chelated (а) and chelated (b) active forms of ruthenium complex.

When transition state is formed, monomer molecules occupy the position of oxygen in coordination sphere of ruthenium, what is accompanied by destruction of intramolecular complex (Scheme 6).

To degrade RudO bond, it is necessary to spend some energy. Lengthening of aliphatic radical, which promotes improvement of donor properties of carbonyl oxygen and intensification of RudO bond, increases the amount of energy needed to degrade RudO bond. That is why activation energy rises as the length of aliphatic radical increases. If the activation energy corresponds to the excessive energy that reacting molecules should possess to pass the potential barrier, then pre-exponential multiplier defines peculiarities of interaction of these molecules. Pre-exponential multiplier can correlate with the change of activation entropy, which depends on changes in the number of freedom degrees of the reacting molecules. Ruthenium and the previous monomer unit can form a ring with lesser number of freedom degrees than the complex they form of non-ring structure. Besides the rigidness of intramolecular complex depends on RudO bond strength (the more strength RudO bond, the more stable is intramolecular complex). Therefore, the increase of pre-exponential multiplier defined by the growth of aliphatic radical is explained by the increase in the number of freedom degrees, which appear when intramolecular complex degrades during the formation of transition state.

To form RudO bond, carbonyl oxygen and ruthenium should be positioned in a certain way. When RudO if formed, the molecule geometry is changed. Steric factor is one of the

Scheme 6. The destruction of the intramolecular complex with the addition of a new monomer's molecule.

hindrances making the formation of intramolecular complex harder. In the case of ester with branched substituent, bulky iso-butyl radicals cannot set near each other properly for carbonyl oxygen to form strength bond with ruthenium due to steric hindrances. This reduces the activation energy and pre-exponential multiplier. In addition, iso-butyl fragments of the previous monomer unit hinder the monomer placement in the coordination sphere of ruthenium, which cuts reactivity of this ester.

Figure 14 demonstrates Arrhenius correlations of constant k<sup>e</sup> in three 3-dimensional isomers of dimethyl ester of 5-norbornene-2,3-dicarboxyl acid. The correlations are linear in the range of temperatures, which proves that the interaction mechanism of ruthenium complex and the corresponding ester is permanent.

Based on the correlations in Figure 14, we calculated effective constants and activation parameters of polymerization. The results are in Table 4.

Table 4 shows that the orientation of ester substituents to the norbornene ring affects both reactivity and activation parameters of polymerization.

When transition state is formed, monomer molecules occupy the position of oxygen in coordination sphere of ruthenium, what is accompanied by destruction of intramolecular complex

Figure 13. Non-chelated (а) and chelated (b) active forms of ruthenium complex.

To degrade RudO bond, it is necessary to spend some energy. Lengthening of aliphatic radical, which promotes improvement of donor properties of carbonyl oxygen and intensification of RudO bond, increases the amount of energy needed to degrade RudO bond. That is why activation energy rises as the length of aliphatic radical increases. If the activation energy corresponds to the excessive energy that reacting molecules should possess to pass the potential barrier, then pre-exponential multiplier defines peculiarities of interaction of these molecules. Pre-exponential multiplier can correlate with the change of activation entropy, which depends on changes in the number of freedom degrees of the reacting molecules. Ruthenium and the previous monomer unit can form a ring with lesser number of freedom degrees than the complex they form of non-ring structure. Besides the rigidness of intramolecular complex depends on RudO bond strength (the more strength RudO bond, the more stable is intramolecular complex). Therefore, the increase of pre-exponential multiplier defined by the growth of aliphatic radical is explained by the increase in the number of freedom degrees, which appear when intramolecular complex degrades during the formation of transition state.

To form RudO bond, carbonyl oxygen and ruthenium should be positioned in a certain way. When RudO if formed, the molecule geometry is changed. Steric factor is one of the

Scheme 6. The destruction of the intramolecular complex with the addition of a new monomer's molecule.

(Scheme 6).

32 Recent Research in Polymerization

The presence of substituent in endo-position reduces reaction capacity of ester. This corresponds with the data shown in other studies [34, 37–40], which estimated reaction capacity of endo- and exo-isomers of dicyclopentadiene and 2,3-dicarbomethoxy-5-norbornene. In the research of Delaude at al. [40] measured the initiation constants for monomers 2, 3, and 4 over [RuCl2(pcymene)]2 complex activated with trimethylsilyldiazomethane; their values at 25С were 0.040,

Figure 14. Arrhenius correlations of polymerization of three-dimensional isomers of dimethyl ester 5-norbornene-2,3 dicarboxylic acid.


Table 4. Effective constants and activation parameters of polymerization of three-dimensional isomers of dimethyl ester 2,3-norbornene dicarboxylic acid.

0.025, and 0.05 l mole<sup>1</sup> s <sup>1</sup> for 2, 3, and 4, respectively. At the same time, the constant of chain growth remains the same for all monomers and is within the range of 0.003–0.006 l mole<sup>1</sup> s 1 . The initiation stage of monomer 2 catalyzed by 1 is much slower than the chain growth stage. If we compare the constant of initiation and growth of monomer 2 catalyzed by 1 and [RuCl2(pcymene)]2, then we would notice that initiation catalyzed by 1 is slower than chain growth in distinction from [RuCl2(p-cymene)]2, which affects initiation in a way that it is 10-fold faster than the growth of polymer chain. Comparison of constants defining polymerization initiated by these complexes is not adequate since these complexes have different structure and may have different activation mechanisms. However, in both the cases, ester groups in endo-position are located not far enough from the double bond of norbornene ring and sterically hinder the monomer attack by double bond of ruthenium. This would affect the polymerization rate of these esters both in the case of initiation by complex 1 and in the case of initiation by [RuCl2(pcymene)]2. In the first case, the steric factor would affect both constants k<sup>2</sup> and kg.

Each monomer is determined by its own set of activation parameters different from others. To explain the way the activation parameters change, we compiled a set of monomers in ascending order to form RudO bond and intramolecular complex. Exo,endo-isomer is more prone to form RudO bond since its ester substituents are located on different sides in relation to the norbornene ring and do not hinder each other during the formation of intramolecular complex. RudO bond is more strength, and intramolecular complex is more rigid in comparison with other isomers. That is why high activation energy and pre-exponential multiplier are typical for exo,endo-isomer. Exo,exo-isomer is the second on the capability to form RudO bond. This ester is inferior to exo,endo-isomer, since its ester substituents are located on one side in relation to norbornene ring. This sterically hinders their mutual distribution necessary for the formation of RudO bond. RudO bond has less strength, and intramolecular complex is more flexible. That is why if compared with exo,endo-isomer, exo,exo-isomer is defined by lower activation energy and pre-exponential multiplier.

Endo,endo-isomer is the third on the ability to form RudO bond. Because of the way ester substituents are located inside norbornene ring, this ester cannot form strong RudO bond. Ester group in endo-position cannot properly distribute in the coordination sphere of ruthenium to form intramolecular complex. That is why this molecule possesses low activation energy and pre-exponential multiplier.

In the paper [41], the authors estimated reactivity of these esters using the observed polymerization constant k<sup>o</sup> as the criterion for comparing reaction capacity of monomers.
