3. Reactivity of esters of 5-norbornene-2,3-dicarboxylic acid in ROMP

Currently, despite the fact that ethers of 2,3-norbornene dicarboxylic acid appear to be potential material for synthesizing polymers via ROMP, the interrelation between the molecule structure and their reactivity for metathesis polymerization with full ring opening has not been stated. A few polymerization mechanisms with different catalysts (including ruthenium) are known; however, there is no detailed description of how ethers of 5-norbornene-2,3-dicarboxylic acid behave. The study of reaction activity of 5-norbornene-2,3-dicarboxylic acid ethers with different structure using an appropriate catalyst (carbene complex of ruthenium (1,3-bis- (2,4,6-trimethylphenyl)-2-imidoazolidevynilidene)dichloro(ortho-N,N-dimethylaminomethylphenylmethylene)-ruthenium—1 (Figure 2) [27] has filled this gap.

In this research, we used alkyl diesters of bicyclo[2.2.1]hept-5-en-2,3 dicarboxylic acid, obtained according to the technique given in the paper (Figure 3) [28].

Polymerization was carried out in NMR tubes, concurrently measuring the proton spectrum after a certain period using AU-program zgser.

Figure 2. Catalyst complex of ruthenium used as an initiating agent for polymerization.

Figure 3. Alkyl diesters of bicyclo [2.2.1]hept-5-en-2,3 dicarboxylic acid, used as monomers.

The monomer concentrations were determined based on decrease and growth of integrated intensities of resonances of olefinic protons of monomer—SM and polymer—SP (Figure 4)

$$\mathbf{C}\_{M} = \mathbf{C}\_{M\_0} \cdot \frac{\mathbf{S}\_M}{\mathbf{S}\_M + \mathbf{S}\_P} \tag{2}$$

$$\mathbf{C}\_{K} = \mathbf{C}\_{K\_{0}} \cdot \frac{\mathbf{S}\_{K\_{0}} \cdot \mathbf{S}\_{S}}{\mathbf{S}\_{S\_{0}} \cdot \mathbf{S}\_{K}} \tag{3}$$

Figure 4. Combining the fragments of NMR spectra 2 in the beginning of a reaction and after 20 min.

The monomer concentrations were determined based on decrease and growth of integrated intensities of resonances of olefinic protons of monomer—SM and polymer—SP (Figure 4)

CM <sup>¼</sup> CM<sup>0</sup> � SM

CK ¼ CK<sup>0</sup> �

Figure 3. Alkyl diesters of bicyclo [2.2.1]hept-5-en-2,3 dicarboxylic acid, used as monomers.

Figure 2. Catalyst complex of ruthenium used as an initiating agent for polymerization.

20 Recent Research in Polymerization

SM þ SP

SK<sup>0</sup> � SS SS<sup>0</sup> � SK (2)

(3)

where CK<sup>0</sup> and SS0—squares of integrated intensities of a catalyst and solvent, measured in the beginning of the reaction; SK and SS—current squares of integrated intensities of a catalyst and solvent during the reaction.

The AU-program multintegr was used to gauge the integrated intensities and time of the experiment. The using of low-viscosity solvents allowed obtaining high-resolution proton NMR spectra. Thus, kinetic studies should be carried out in the solution. And the set of monomer concentrations was defined to get kinetic correlations based on the spectral data. The solvent should be used as a diluent. Figure 5(a) demonstrates the curves describing the changes of concentration 2 in the course of time. According to the literature data, chloroform-d was taken as a solvent.

The molecules of chloroform-d do not react with active ruthenium and play a role of a polar medium, which stabilize 14-electron state of the active ruthenium [29]. Initially, toluene-d8 was suggested as a possible solvent, but the catalyst and monomers dissolve better in chloroform-d, which is also a widely used and more available solvent for NMR studies than toluene-d8.

Figure 5. The decrease of monomer 2 (a) and its semi-logarithmic anamorphoses (b) during polymerization with catalyst 1 with varying initial concentration of the monomer (CK<sup>0</sup> = 0.0087 mole l<sup>1</sup> , 50C).

Also, it was shown that reactivity of dimethyl ether of exo,exo-norbornene dicarboxylic acid is higher in chloroform-d [30]. Since chloroform-d boils at 60.9C in ambient conditions, the operational temperature range was limited to 50C to prevent any changes in the reactant concentration which could be caused by evaporation.

Studies [31, 32] considered the ring opening metathesis polymerization as pseudo first-order reaction as regards to the monomer concentration, which is valid for polymerization of abovementioned monomers.

Figure 5(b) demonstrates that there can be seen three regions in the semi-logarithmic anamorphoses. The first region has non-linear segment of curve corresponding to the initiation stage. The second one is the straight-line segment prolongs to the extent of 70% monomer conversion (till one on the logarithmic scale, Figure 5(b)). The third region is a noticeable non-linear segment of curves, which is observed after 70% conversion. The appearance of such nonlinear segments is due to the viscosity of the reaction mixture increasing, owing to the polymer molecular weight growth. This results to the fact that the polymerization rate is limited by the diffusion of monomer molecules to the active ruthenium.

Figure 6 shows the straight-line ranges of semi-logarithmic anamorphoses of polymerization 2, catalyzed by 1. The slope of the right lines corresponds to the observed constant of polymerization ko.

Based on correlation coefficients given in Table 1, we can conclude that semi-logarithmic anamorphoses are linear in the noticed interval. Figure 6 shows the correlation of the constant ko and initial monomer concentration.

Figure 7 shows that k<sup>o</sup> linearly depends on the monomer concentration within the following range from 0.2 to 1.0 mole l<sup>1</sup> , which allows to vary the monomer concentration in this range to implement kinetic experiments.

Figure 6. Linear segments of semi-logarithmic anamorphoses of monomer 2 polymerization over catalyst 1 (CK<sup>0</sup> = 0.0087 mole l�<sup>1</sup> , 50�С, dependences are marked in accordance with Figure 5).


Table 1. Values of k<sup>o</sup> which calculated out of linear dependences on Figure 6.

Also, it was shown that reactivity of dimethyl ether of exo,exo-norbornene dicarboxylic acid is higher in chloroform-d [30]. Since chloroform-d boils at 60.9C in ambient conditions, the operational temperature range was limited to 50C to prevent any changes in the reactant

Figure 5. The decrease of monomer 2 (a) and its semi-logarithmic anamorphoses (b) during polymerization with catalyst

, 50C).

Studies [31, 32] considered the ring opening metathesis polymerization as pseudo first-order reaction as regards to the monomer concentration, which is valid for polymerization of above-

Figure 5(b) demonstrates that there can be seen three regions in the semi-logarithmic anamorphoses. The first region has non-linear segment of curve corresponding to the initiation stage. The second one is the straight-line segment prolongs to the extent of 70% monomer conversion (till one on the logarithmic scale, Figure 5(b)). The third region is a noticeable non-linear segment of curves, which is observed after 70% conversion. The appearance of such nonlinear segments is due to the viscosity of the reaction mixture increasing, owing to the polymer molecular weight growth. This results to the fact that the polymerization rate is limited by the

Figure 6 shows the straight-line ranges of semi-logarithmic anamorphoses of polymerization 2, catalyzed by 1. The slope of the right lines corresponds to the observed constant of polymer-

Based on correlation coefficients given in Table 1, we can conclude that semi-logarithmic anamorphoses are linear in the noticed interval. Figure 6 shows the correlation of the constant

Figure 7 shows that k<sup>o</sup> linearly depends on the monomer concentration within the following

, which allows to vary the monomer concentration in this range

concentration which could be caused by evaporation.

1 with varying initial concentration of the monomer (CK<sup>0</sup> = 0.0087 mole l<sup>1</sup>

diffusion of monomer molecules to the active ruthenium.

ko and initial monomer concentration.

range from 0.2 to 1.0 mole l<sup>1</sup>

to implement kinetic experiments.

mentioned monomers.

22 Recent Research in Polymerization

ization ko.

Ruthenium complex should be activated to initiate polymerization. This is carried out by the first addition of monomer, which is initiation stage as well. There exist several possible mechanisms of activation; however, based on the literature data, it is assumed that bulky olefins, including the research monomers, interact with active ruthenium on a dissociative mechanism [33]

$$K \xleftarrow{k\_1}\_{k\_{-1}} K^\* \xrightarrow{+\mathcal{M}} P^\*$$

The initiation rate equals the rate of active centers formation P\*. The active centers formation occurs in two stages. As it can be seen from Figure 8, the concentration of ruthenium complex slightly changes.

Figure 7. Correlation of the observed constant k<sup>o</sup> of monomer 2 polymerization, catalyzed by 1 with the initial monomer concentration (CK<sup>0</sup> = 0.0087 mole l�<sup>1</sup> , 50�С).

Its decrease is 1–2% from the initial catalyst concentration. Synthesized polymers at these conditions possess high molecular weight (Table 2).

Based on Figure 8 and Table 2, we can conclude that the formation of active centers is slower than the growth of polymer chain. The research [34] also confirmed this, stating that for polymerization of exo-exo-5,6-bi(methoxycarbonyl)-7-oxabicyclo[2.2.1]hept-2-ene over Grubbs catalyst of the first generation the correlation of constants is ki/k<sup>g</sup> = 0.23. Moreover, the study [29] suggests that the correlation ki/k<sup>g</sup> is even lesser and equals 0.03 for catalyst with Nchelating ligand. In addition, based on the data presented, we can assume that disassociating of nitrogen defined by constant k<sup>1</sup> is limiting in the initiation reaction. Notably that the monomer molecule does not interact during initiation, that is why the formation rate of the active ruthenium complex K\* only depends on the temperature and initial concentration of ruthenium complex. Thus, the structure of the monomer molecule can affect the second stage of initiation defined by constant k<sup>2</sup> and the stage of polymer chain growth defined by constant k<sup>g</sup> (it is suggested that constants of different stages of polymerization are equal k<sup>1</sup> <sup>g</sup> ¼ k 2 <sup>g</sup> ¼ … ¼ kg)

$$\begin{aligned} P^\* + M & \xrightarrow{k\_{\mathfrak{g}}^1} P^\*M\\ P^\*M + M & \xrightarrow{k\_{\mathfrak{g}}^2} P^\*M\_2\\ \cdots\\ P^\*M\_n + M & \xrightarrow{k\_{\mathfrak{g}}} P^\*M\_{n+1} \end{aligned}$$

Figure 8. Ruthenium complex decrease during polymerization of monomer 2 with different initial concentration of catalyst 1 (CM<sup>0</sup> = 0.35 mole l�<sup>1</sup> , 50�С).


Table 2. Average molecular weight of the obtained polymers depending on the number of initial reagents.

Kinetics of monomer consumption is complicated (Figures 5(a) and 9).

Its decrease is 1–2% from the initial catalyst concentration. Synthesized polymers at these

Figure 7. Correlation of the observed constant k<sup>o</sup> of monomer 2 polymerization, catalyzed by 1 with the initial monomer

Based on Figure 8 and Table 2, we can conclude that the formation of active centers is slower than the growth of polymer chain. The research [34] also confirmed this, stating that for polymerization of exo-exo-5,6-bi(methoxycarbonyl)-7-oxabicyclo[2.2.1]hept-2-ene over Grubbs catalyst of the first generation the correlation of constants is ki/k<sup>g</sup> = 0.23. Moreover, the study [29] suggests that the correlation ki/k<sup>g</sup> is even lesser and equals 0.03 for catalyst with Nchelating ligand. In addition, based on the data presented, we can assume that disassociating of nitrogen defined by constant k<sup>1</sup> is limiting in the initiation reaction. Notably that the monomer molecule does not interact during initiation, that is why the formation rate of the active ruthenium complex K\* only depends on the temperature and initial concentration of ruthenium complex. Thus, the structure of the monomer molecule can affect the second stage of initiation defined by constant k<sup>2</sup> and the stage of polymer chain growth defined by constant k<sup>g</sup>

> <sup>g</sup> ¼ k 2

<sup>g</sup> ¼ … ¼ kg)

(it is suggested that constants of different stages of polymerization are equal k<sup>1</sup>

P∗

P∗

<sup>P</sup><sup>∗</sup> <sup>þ</sup> <sup>M</sup>! k1 g P∗ M

<sup>M</sup> <sup>þ</sup> <sup>M</sup>! k2 g

<sup>M</sup><sup>n</sup> <sup>þ</sup> <sup>M</sup>! kg

…

P<sup>∗</sup>M<sup>2</sup>

<sup>P</sup><sup>∗</sup>M<sup>n</sup>þ<sup>1</sup>

conditions possess high molecular weight (Table 2).

, 50�С).

concentration (CK<sup>0</sup> = 0.0087 mole l�<sup>1</sup>

24 Recent Research in Polymerization

In polymerization, a monomer is used during initiation and growth of the polymer chain

$$-\frac{d\mathbf{C\_M}}{dt} = k\_2 \cdot \mathbf{C\_{K^\*}} \cdot \mathbf{C\_M} + k\_\mathbf{g} \cdot \mathbf{C\_{P^\*}} \cdot \mathbf{C\_M} \tag{4}$$

The concentration of active ruthenium complex CK\* and concentration of active chains CP\* are low, with CP\* due to the absence of reactions of termination [5, 6] and transfer [22] of the chain constantly increases during the reaction. Since k<sup>1</sup> is much lesser than constants k�<sup>1</sup> and k2, it is possible to apply the principle of quasistationary for concentration of the active form CK\*:

Figure 9. Monomer 2 consumption in the polymerization reaction over varying initial catalyst concentration CM0 = 0.35 mole l�<sup>1</sup> , 50�С).

$$\frac{d\mathbb{C}\_{\mathbf{K}^\*}}{dt} = k\_1 \cdot \mathbb{C}\_{\mathbf{K}} - k\_{-1} \cdot \mathbb{C}\_{\mathbf{K}^\*} - k\_2 \cdot \mathbb{C}\_{\mathbf{K}^\*} \cdot \mathbb{C}\_{\mathbf{M}} = 0 \tag{5}$$

$$\mathbf{C}\_{\mathbf{K}^\*} = \frac{k\_1 \cdot \mathbf{C}\_{\mathbf{K}}}{k\_{-1} - k\_2 \cdot \mathbf{C}\_{\mathbf{M}}} \tag{6}$$

The second stage of the initiation reaction can be viewed as pseudo first-order one proceeding with effective constant k<sup>2</sup><sup>e</sup> ¼ k<sup>2</sup> � CM0 . This assumption is fair as CK0 ≪ CM0 and CK0 ≫ CK<sup>∗</sup> . Taking into consideration that the catalyst concentration slightly changes during the reaction, it could be considered that C<sup>K</sup> ffi CK0 . Then, changes in the concentration of active chains over time are defined by the following equation:

$$\frac{d\mathbb{C}\_{\rm P}}{dt} = \frac{k\_1 \cdot \mathbb{C}\_{\rm K\_0}}{k\_{-1} - k\_2 \cdot \mathbb{C}\_{\rm M\_0}} \cdot k\_2 \cdot \mathbb{C}\_{\rm M\_0} \tag{7}$$

After integrating we get:

$$\mathbf{C}\_{\mathbf{P}^\*} = \frac{\frac{k\_1}{k\_{-1}} \cdot k\_2 \cdot \mathbf{C}\_{\mathbf{K}\_0} \cdot \mathbf{C}\_{\mathbf{M}\_0}}{1 + \frac{k\_2}{k\_{-1}} \cdot \mathbf{C}\_{\mathbf{M}\_0}} \cdot t \tag{8}$$

The amount of active chains is equal to the decreasing of the monomer, which is forming these chains. Knowing the active chains' concentration from Eq. (8), the change in monomer concentration in time can be described by Eq. (9):

$$-\frac{d\mathbb{C}\_{\mathsf{M}}}{dt} = \frac{\frac{k\_{\mathsf{l}}}{k\_{-\mathsf{l}}} \cdot k\_{2} \cdot \mathbb{C}\_{\mathsf{K}\_{0}} \cdot \mathbb{C}\_{\mathsf{M}\_{0}}}{1 + \frac{k\_{2}}{k\_{-\mathsf{l}}} \cdot \mathbb{C}\_{\mathsf{M}\_{0}}} + \frac{\frac{k\_{\mathsf{l}}}{k\_{-\mathsf{l}}} \cdot k\_{2} \cdot \mathbb{C}\_{\mathsf{K}\_{0}} \cdot \mathbb{C}\_{\mathsf{M}\_{0}}}{1 + \frac{k\_{2}}{k\_{-\mathsf{l}}} \cdot \mathbb{C}\_{\mathsf{M}\_{0}}} k\_{\mathsf{g}} \cdot \mathbb{C}\_{\mathsf{M}} \cdot t \tag{9}$$

To simplify the equation and implement semi-logarithmic coordinates for defining the rate constant, we can ignore the first component of the right side of the equation, since it contributes less if compared with the second component. This assumption is fair for the later stages of polymerization. The formula k1 <sup>k</sup>�<sup>1</sup> �k2�CK0 �CM0 <sup>1</sup><sup>þ</sup> <sup>k</sup><sup>2</sup> <sup>k</sup>�<sup>1</sup> �CM0 � t can be expressed as the following product CK0 � f , where f is the effectiveness of initiation equal to <sup>C</sup>P<sup>∗</sup> CK0 ¼ k1 <sup>k</sup>�<sup>1</sup> �k2�CM0 �t <sup>1</sup><sup>þ</sup> <sup>k</sup><sup>2</sup> <sup>k</sup>�<sup>1</sup> �CM0 . Then, we can put it down the following way:

$$-\frac{d\mathbb{C}\_{\mathsf{M}}}{\mathbb{C}\_{\mathsf{M}}} = k\_{\mathsf{g}} \cdot \mathbb{C}\_{\mathsf{K}\_{0}} \cdot f \cdot dt \tag{10}$$

After integrating, we would acquire:

dCK<sup>∗</sup>

time are defined by the following equation:

After integrating we get:

mole l�<sup>1</sup>

, 50�С).

26 Recent Research in Polymerization

dCP<sup>∗</sup>

CP<sup>∗</sup> ¼

dt <sup>¼</sup> <sup>k</sup><sup>1</sup> � <sup>C</sup>K0

k1

k�<sup>1</sup> � k<sup>2</sup> � CM0

<sup>k</sup>�<sup>1</sup> � <sup>k</sup><sup>2</sup> � <sup>C</sup>K0 � <sup>C</sup>M0 <sup>1</sup> <sup>þ</sup> <sup>k</sup><sup>2</sup>

<sup>k</sup>�<sup>1</sup> � <sup>C</sup>M0

dt <sup>¼</sup> <sup>k</sup><sup>1</sup> � <sup>C</sup><sup>K</sup> � <sup>k</sup>�<sup>1</sup> � <sup>C</sup>K<sup>∗</sup> � <sup>k</sup><sup>2</sup> � <sup>C</sup>K<sup>∗</sup> � <sup>C</sup><sup>M</sup> <sup>¼</sup> <sup>0</sup> (5)

� k<sup>2</sup> � CM0 (7)

� t (8)

(6)

<sup>C</sup>K<sup>∗</sup> <sup>¼</sup> <sup>k</sup><sup>1</sup> � <sup>C</sup><sup>K</sup>

Figure 9. Monomer 2 consumption in the polymerization reaction over varying initial catalyst concentration CM0 = 0.35

The second stage of the initiation reaction can be viewed as pseudo first-order one proceeding with effective constant k<sup>2</sup><sup>e</sup> ¼ k<sup>2</sup> � CM0 . This assumption is fair as CK0 ≪ CM0 and CK0 ≫ CK<sup>∗</sup> . Taking into consideration that the catalyst concentration slightly changes during the reaction, it could be considered that C<sup>K</sup> ffi CK0 . Then, changes in the concentration of active chains over

k�<sup>1</sup> � k<sup>2</sup> � C<sup>M</sup>

$$\ln \frac{\mathbb{C}\_{\text{M}\_0}}{\mathbb{C}\_{\text{M}}} = k\_{\text{g}} \cdot \mathbb{C}\_{\text{K}\_0} \cdot f \cdot t \tag{11}$$

Taking into consideration that f for each monomer differs only by the value of k<sup>2</sup> constant, which depends on the structure of monomer, it is possible to compare reaction capacity and values of activation parameters using product f�kg.

The chain growth rate constant of polymer k<sup>g</sup> times the effectiveness of initiation f corresponds the tangent of the slope in the straight-line segment of semi-logarithmic correlation, which equals the product of the observed constant k<sup>o</sup> times the initial catalyst concentration CK0 (Figure 10).

Correlations in Figures 7 and 11 demonstrate that the observed constant of polymerization k<sup>o</sup> linearly depends on both the initial concentration of monomer and the initial catalyst concentration.

Linear correlation of k<sup>o</sup> from CK0 is observed because Eq. (1) takes the initial concentration of catalyst into consideration. In turn, k<sup>o</sup> linearly depends on CM0 since Eq. (11) includes parameter f, which depends on the initial concentration of monomer. Based on the data presented, we can conclude that it is possible to use the effective constant <sup>k</sup><sup>e</sup> <sup>¼</sup> <sup>k</sup><sup>o</sup> CK0 �CM0 to compare reaction capacity of the ethers under study. The dimensionality of constant k<sup>e</sup> correspond the dimensionality of second-order constant since the concentration of monomer is included in numerator

Figure 10. Semi-logarithmic correlations of polymerization 2 over catalyst 1 with varying catalyst concentration (CM<sup>0</sup> = 0.35 molel 1 , 50С, dependences are marked in accordance with Figure 9).

Figure 11. Correlation of the observed constant ko of polymerization of monomer 2, catalyzed by 1 with the initial concentration of catalyst (CM0 = 0.35 mole l<sup>1</sup> , 50С).

and denominator of the equation of the initiation effectiveness. Since constant k<sup>o</sup> depends on the initial concentration of catalyst linearly, we can use the noticed range of concentration to estimate reactivity of esters.
