Toward an understanding of the effects of nanocellulose during the free-radical polymerization reactions. Kinetic aspects of suspension-free radical polymerization of methyl methacrylate (MMA) in the presence and absence of nanocellulose

Abstract

The aim of the present study is to examine the evolution of monomer conversion during suspension free radical polymerization of methyl methacrylate (MMA) at 80 °C, both in the presence and absence of nanocellulose obtained via TEMPO oxidation. The main focus of this work is on the kinetic aspects of MMA polymerization, particularly the diffusive step of the termination reaction and its impact on polymeric radicals. Experimental conversion evolutions are tracked using gravimetry. In addition, we employed an existing mathematical model to describe the effects of nanocellulose during polymerization, using the Einstein diffusion equation, geometric considerations and an approach that accounts for termination between short and long polymeric radicals. This model explains the evolution of monomer conversion regarding the effects produced by nanocellulose during the free radical polymerization reactions, focusing on factors that affect the diffusive termination step as difficulties for the short polymeric radicals reacting with the long radicals and the decrease of the segmental mobility. Our experimental results exhibit a premature autoacceleration with the presence of nanocellulose during polymerization reactions. Based on the adjustments made to the model, the theoretical results suggest that this reaction behavior is due to the impact of nanocellulose on the termination stage, which hinders a successful termination collision between short and long polymeric radicals while decreasing the segmental mobility of long radicals. Therefore, at higher nanocellulose content, the termination coefficient is reduced further.

Appendix

Experimental results

Table 1 shows the monomer conversion calculated with Eq. 1 corresponding to the reaction with and without nanocellulose. The monomer conversions were calculated with experimental data and the model results were graphed in Fig. 3 to analyze their tendency and causes.

Table 1 Experimental monomer conversion at 80 °C using 0.5 w_t0% of BPO and the weight fraction percentage of nanocellulose (NC) indicated. All percentages are based on the monomer

The results of Table 1 are the values obtained (truncated to two decimal places), with differences in the range of 1e-4. Therefore, the experiments presented good reproducibility.

Main kinetic equations

$$\frac{d\left[{I}_{2}\right]}{dt}=-{k}_{d}\left[{I}_{2}\right]- \frac{\left[{I}_{2}\right]}{V} \frac{dV}{dt}$$

(11)

$$\frac{d\left[C\right]}{dt}={k}_{d}\left[{I}_{2}\right]-{k}_{ti}\left[C\right]-{k}_{dd}\left[C\right]-\frac{\left[C\right]}{V} \frac{dV}{dt}$$

(12)

$$\frac{d\left[{R}^{*}\right]}{dt}={2k}_{dd}\left[C\right]-{k}_{i}\left[{R}^{*}\right][M]-\frac{\left[{R}^{*}\right]}{V} \frac{dV}{dt}$$

(13)

$$\frac{d[M]}{dt}=-{k}_{p}\left[M\right]\left[{\lambda }_{0}\right]-\frac{\left[M\right]}{V} \frac{dV}{dt}={-R}_{p}$$

(14)

The differential Equation for moments 0, 1 and 2 of “live” chains (λ) are:

$$\frac{d{\lambda }_{0}}{dt}={k}_{i}\left[M\right]\left[{R}^{*}\right]-{k}_{t}{ {{\lambda }_{0}}^{2}}-\frac{{\lambda }_{0}}{V}\frac{dV}{dt}$$

(15)

$$\begin {aligned}\frac{d{\lambda }_{1}}{dt}=&{k}_{i}\left[M\right]\left[{R}^{*}\right]+{k}_{p}\left[M\right]{\lambda }_{0}-{{k}_{trm}\left[M\right]\lambda }_{1}\\&+ {{k}_{trm}\left[M\right]\lambda }_{0}-{k}_{t}{{\lambda }_{0}\lambda }_{1}-\frac{{\lambda }_{1}}{V}\frac{dV}{dt}\end {aligned}$$

(16)

$$\begin {aligned}\frac{d{\lambda }_{2}}{dt}=&{k}_{i}\left[M\right]\left[{R}^{*}\right]+2{k}_{p}\left[M\right]{\lambda }_{1}+{k}_{p}\left[M\right]{\lambda }_{0}- {k}_{trm}\left[M\right]{\lambda }_{2}\\&+{k}_{trm}\left[M\right]{\lambda }_{0}-{k}_{t}{{\lambda }_{0}\lambda }_{2}-\frac{{\lambda }_{2}}{V}\frac{dV}{dt}\end {aligned}$$

(17)

Assuming the quasi-steady state approach to Eqs. 15, 16 and 17, Eqs. 18, 19 and 20 are obtained, respectively.

$${\lambda }_{0}={\left(\frac{{2k}_{dd}\left[C\right]{ }-\frac{\left[{R}^{*}\right]}{V}\frac{dV}{dt}}{{k}_{t}}\right)}^{1/2}$$

(18)

$${\lambda }_{1}=\frac{{k}_{i}\left[M\right]\left[{R}^{*}\right]+{\lambda }_{0}({k}_{p}\left[M\right]+{k}_{trm}\left[M\right])}{{k}_{t}{\lambda }_{0}+{k}_{trm}\left[M\right]+\frac{1}{V}\frac{dV}{dt}}$$

(19)

$${\lambda }_{2}=\frac{{k}_{i}\left[M\right]\left[{R}^{*}\right]+{\lambda }_{0}({k}_{p}\left[M\right]+ {k}_{trm}\left[M\right])+2{k}_{p}\left[M\right]{\lambda }_{1}}{{k}_{t}{\lambda }_{0}+{k}_{trm}\left[M\right]+\frac{1}{V}\frac{dV}{dt}}$$

(20)

The differential Equation for moments 0, 1 and 2 of “dead” chains (μ) are:

$$\frac{{d\mu }_{0}}{dt}={k}_{trm}\left[M\right]{\lambda }_{0}+{k}_{t}{\lambda }_{0}{\lambda }_{0}-\frac{\left[{\mu }_{0}\right]}{V} \frac{dV}{dt}$$

(21)

$$\frac{{d\mu }_{1}}{dt}={k}_{trm}\left[M\right]{\lambda }_{1}+{k}_{t}{\lambda }_{1}{\lambda }_{0}-\frac{\left[{\mu }_{1}\right]}{V} \frac{dV}{dt}$$

(22)

$$\frac{{d\mu }_{2}}{dt}={{k}_{trm}[M]\lambda }_{2}+{k}_{t}{{\lambda }_{2}\lambda }_{0}-\frac{\left[{\mu }_{2}\right]}{V} \frac{dV}{dt}$$

(23)

Considering the quasi-steady state approach (QSSA):

$${k}_{i}\left[R^{*}\right][M]={2k}_{dd}\left[C\right]-\frac{\left[{R}^{*}\right]}{V} \frac{dV}{dt}$$

(24)

M_n and M_w are calculated by applying the method of moments.

$${M}_{n}={M}_{M}*\frac{{\mu }_{1}+{\lambda }_{1}}{{\lambda }_{0 }{+\mu }_{0}}$$

(25)

$${M}_{w}={M}_{M}*\frac{{\mu }_{2}+{\lambda }_{2}}{{\lambda }_{1 }{+\mu }_{1}}$$

(26)

where I₂ is the initiator, C is a pseudo-complex formed by two contiguous molecules of primary radicals R* (initiator fragments), k_d, k_ti, k_dd, k_i, k_p, k_t,k_trm are the rate coefficients for initiator decomposition, recombination between initiator fragments, diffusion of initiator fragments, initiation, propagation, termination and chain transfer to monomer, respectively. M refers to monomer, and M_M to its molecular weight.

R_p is the rate of polymerization. In Eq. (14) consumption of monomer by the chain transfer to monomer has been neglected The term dV/dt represents the volume contraction of the reaction mixture resulting from the different densities of monomer (ρ_mon) and polymer (ρ_pol) and is given by

$$\frac{dV}{dt}={R}_{p}{M}_{M}V\left(\frac{1}{{\rho }_{pol}}-\frac{1}{{\rho }_{mon}}\right)$$

(27)

Residual plot

Fig. 8

e_rr corresponding to the polymerizations carried out in Fig. 3A-C