TBHP 70% (Merck) was extracted from the aqueous solution with toluene and its concentration was measured as described below. Commercial polyisoprene (M_n = 441,000 D, M_w = 704,000 D) was purified as described below prior to epoxidation reactions. All other chemicals were commercial grade and used as received.

The catalytic precursor MoO₂(acac)₂ was synthetized according to the classical method [29] : ten grams of the corresponding oxide were refluxed with 50 mL of 2,4-pentanodione for 18 h. The mixture was filtered, and the solution was added to 150 mL of petroleum ether, which was chilled for 1 h in an ice bath. An orange-yellow powder was formed, which was filtered and washed several times with petroleum ether. For catalytic reactions, the appropriate amount of catalyst was dissolved in toluene, under argon.

Commercial polyisoprene, 20 g, was dissolved in 200 mL of THF, under stirring. The solution was filtrated to eliminate some unsolved microgels that could be present. The solution was then added dropwise to 2 L of 95% ethanol, inducing the precipitation of the polymer. The polymer was pressed and dried in a vacuum oven until constant weight. It was then characterized by ¹H and ¹³C NMR and IR. The spectra were in accordance with the literature [16] [17] [18]. ¹H NMR showed that the polyisoprene had the following composition: 10% 3.4; 20% 1.4 trans and 70% 1,4 cis.

TBHP was supplied in aqueous solution. In order to use it in toluene solutions, it must be previously extracted. In an extraction funnel, 50 mL of commercial aqueous solution of TBHP 70% and 85 mL of toluene were vigorously shaken. The bottom aqueous phase was discarded, and the upper organic phase stored in a closed flask. Its concentration was measured by ¹H NMR after the determination of the density of the solution, by the following method. The TBHP/toluene (mole/mole) ratio, R, can be obtained by ¹H NMR by normalizing the area of their methyl peaks, Equation (1), where A is the area of the peaks and n the number of moles.

R = A T B H P 9 A toluene 3 = n TBHP n toluene (1)

The density of the solution, its mass divided by its volume, can be calculated in terms of molar masses, Equation (2), where ρ is the density of the solution, M ¯ the molar mass and V the solution volume.

ρ = n TBHP M ¯ TBHP + n toluene M ¯ toluene V (2)

Replacing Equation (1) into Equation (2), the solution density can be obtained as function of the molar ratio, Equation (3).

ρ = n TBHP M ¯ TBHP + n TBHP R M ¯ toluene V = n TBHP ( R M ¯ TBHP + M ¯ toluene R ) V (3)

Therefore, the number of mols of TBHP in one mL of solution, can be calculated by Equation (4).

n TBHP = R ρ R M ¯ TBHP + M ¯ toluene . (4)

Blank tests, either in the absence of catalyst or TBHP were performed, and samples showed no modification on both ¹H NMR and IR spectra. The catalytic reactions were performed starting from a stock solution of polyisoprene 5% (w/V) in toluene, using samples of 20 mL, under argon. Since after the polymerization reaction one double bond from each isoprene monomer remains, the starting number of double bonds was always 1 g/68 g∙mol⁻¹ (=0.0147 mol). To polymer solutions, the necessary amount of catalyst in toluene was added. In an ice bath, TPHP was slowly added and the system was heated in a thermostatic bath, previously regulated to the reaction temperature. The reactions were conducted for predetermined times under argon and magnetic stirring and then quenched with Na₂SO₃. The products were then precipitated in ethanol containing 2,6-di-tert-butyl-4-methylphenol (BHT). After pressing and drying in a vacuum oven until constant weight, the samples were characterized by ¹H and ¹³C NMR and IR.

The amount of epoxide was calculated using ¹H NMR, from the ratio of the areas (A) of the hydrogens from oxirane rings (at 2.7 ppm) and the starting area of double bonds (at 4.7 and 5.2 ppm), as already described [30], using Equation (5).

Epoxide ( mol % ) = A 2 .7ppm A 2 .7ppm + A 4 .7ppm 2 + A 5 .2ppm × 100 . (5)

To investigate the influence of the reaction conditions on the degree of epoxidation, it was used fractional factorial experimental design with two levels for each experimental variable. The experimental variables were catalyst ([Mo]) and oxidizing agent ([TBHP]) concentrations, calculated over molar concentration of polymer double bonds, reaction temperature and time. Since there were four experimental variables to investigate, a full two levels factorial experimental design would require a total of sixteen experiments. To minimize experimental cost, we use a half factorial design of eight experiments.

The experimental conditions have been chosen from a previous work in which VO(acac)₂ was employed as the catalyst [9] The best reaction conditions with that catalyst were obtained using 150% of TBHP, 1% of VO(acac)₂ and toluene as solvent, under reflux and magnetic stirring for one hour. However, using these conditions with MoO₂(acac)₂, high degree of epoxidation was obtained, and undesirable polymer reticulation occurred, making it unfeasible to quantify and characterize the products. Other preliminary tests were done in milder conditions, which proved to be more suitable for this catalytic system. The higher and lower values of the experimental variables are shown in Table 1.

*Molar proportion to double bonds present in polymer.

The experimental variables, z_i, were normalized within the [−1, +1] interval according to Equation (6), where z_i denotes the actual variable values, the subscripts max and min stand for the maximum and minimum values used in the experimental design and xi is the normalized variable value. This normalization is useful when comparing variables with different sizes, such as catalyst concentration, that varies from 0.1 to 0.5 mol%, and temperature, that varies from 60˚C to 80˚C, all variables would be in the [−1, +1] range [28]. The experimental matrix of the half factorial experimental design is presented in Table 2.

x i = 2 z i − ( z max + z min ) z max − z min (6)

The product degree of epoxidations were related to the reaction conditions using Equation (7), where y is this physical-chemical property, x_i and x_j are normalized reaction conditions, n is the number of independent variables, a₀ is the independent parameter, and a_i and a_ij are model parameters related to the linear and the interaction of two variables effects.

y = a 0 + ∑ i = 1 n a i x i + ∑ i = 1 n − 1 ∑ j = i + 1 n a i j x i x j (7)

The estimation of parameters from Equation (7) was performed using least squares regression, using the software Statistica 8.0 (StatSoft). Statistical Student’s t-test was performed to evaluate parameter significance. The parameter was removed from the Equation (7) model when its confidence was lower than 95%.

According to the literature [25], the peaks presented in Table 3 are relevant for calculations involving the epoxidation of polyisoprene.

Since selectivity in epoxidation is favored by the electronic environment of the double bonds [31], 1,4 double bonds are preferentially epoxidized, maintaining the area of the 3,4 units (1’ and 2’) constant. After epoxidation, a new sign is also observed at 1.3 ppm due to methyl groups near oxyrane rings (5’’). As epoxidation degrees increase, the area of peaks attributed to 1,4 double bonds (3) decreases, while the area of a new peak at 2.7 ppm (3’’) increases proportionally. Small peaks that could be attributed to ring opening or chain breaking, such as alcohols, ethers or acids were observed in some cases.

*Molar proportion to double bonds present in polymer.

Epoxide rings can also be observed by ¹³C NMR. According to the literature [32], the new peaks are attributed as shown in Table 4.

The selectivity of the reaction can again be stated as no peaks that could be attributed to carbonylic or hydroxyl-bonded carbons were seen.

The bands that could be attributed are: 830 cm⁻¹ (cis-1,4 C=C-H deformation), 1648 cm⁻¹ (C=C stretching), 1384 cm⁻¹ (CH₃ deformation), 1455 cm⁻¹ (CH₂ deformation) and 881 cm⁻¹ (oxyrane ring). This last one increases as epoxidation degrees increase, as well as the band at 830 cm⁻¹ decreases. Very weak bands due to the formation of carbonylic and hydroxyl-bonded carbons could be seen for some reactions.

The results obtained in the epoxidation of polyisoprene are presented in Table 5,

^aDetermined by ¹H NMR, Equation (5).

where the degree of epoxidation was calculated from ¹H NMR analysis according to Equation (5).

The degree of epoxidation was related to the reaction conditions according to Equation (7), whose parameters are presented in Table 6. Since it was done a half factorial experimental design, only two independent interaction effects between two variables (a_ij) would be quantifiable. Furthermore, these two effects could be confused with interaction effect between other two variables. However, with the experimental data available none of the interaction effects were statistically significant, leaving a better model with solely the linear effects (a_i). All linear effects were statistically significant, indicating that all reaction conditions variables influence the degree of epoxidation.

It can be observed that the empirical model of Equation (7), Table 6 gives a good adjustment of the epoxidation degree as function of reaction conditions. As shown in Figure 2, the experimental data as function of the calculated values are very close to and well distributed around the line y = x.

The parameter a₀ (Equation (7), Table 6) gives the average value of the

epoxidation degree, while the a₁, a₂, a₃ and a₄ are the linear effects of the temperature, oxidant (TBHP) concentration, catalyst (Mo) concentration and reaction time, respectively. These parameters are all significant, meaning that all variables influence the epoxidation degree. The positive values of the parameters indicate that and when one of these variables increases the degree of epoxidation will increase. The parameter value quantifies the growth of the epoxidation degree value with the increment of the dimensionless reaction variable. The parameters a₂ and a₃ present the same value, indicating that the oxidant and the catalyst concentration have the same influence over the epoxidation degree. However, it is noteworthy that the parameters were obtained from the normalized reaction variables; therefore, in the regular scale, increasing catalyst concentration in 0.2 mol% gives the same effect as increasing the oxidant concentration in 10 mol%. The effect of the reaction variables over the degree of epoxidation can be better observed in Figure 3. More specifically, the results indicate that, when the reaction temperature increases 10˚C, the epoxidation degree will raise 9.25%, while the degree of epoxidation will increase 6.25% if either the oxidant concentration varies 10 mol% or the catalyst concentration varies 0.2 mol%. For the reaction time, an increase in 2 h will generate an increment of 10.75% in the epoxidation degree.