Kinetic depression in water-lean solvents

https://doi.org/10.1016/j.seppur.2020.118193

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In general, most kinetic data available for alkanolamine reaction with CO₂ shows that this reaction becomes slower with the addition of organic diluents. This holds equally for primary, secondary and ternary amines.

Adopting the zwitterion mechanism as a framework, this result can be broken down into two correlated phenomena: a decrease in k₂ and a simultaneous decrease in k_b/k₋₁. The interpretation of these effects inside this framework is that the zwitterion species is particularly unstable in water-lean solvents, which would have the effect of slowing down the direct reaction to form zwitterion (k₂ decreases) and speeding up the reverse reaction (k₋₁ increases, k_b/k₋₁ decreases). Some authors have argued that, due to the low polarities of organic diluents, electrolytic species become inherently less stable in water-lean solvents than they are in aqueous ones [38], [39].

Another way that this phenomenon is felt, still in the zwitterion framework, is that the apparent reaction order with respect to the amine itself is reduced when shifting to water-lean solvents. For example, Usubharatana and Tontiwachwuthikul [132] report a reaction order approaching 1.09 for MEA in water, 1.61 in methanol/water 1/1 in mass basis, and 1.73 in pure methanol. These fractionary reaction orders are perfectly consistent with the mathematical formulation of the CO₂ rate of conversion following the zwitterion mechanism.

If one adopts the termolecular framework, the corresponding conclusion would be that the formation of the three-molecular complex leading to carbamate formation is destabilized by the removal of water from the solvent, causing an overall slowing down of reaction rates. The shifting of reaction order means that the solvent itself is less apt to act as base in the termolecular reaction. Thus, in aqueous MEA, water is able to take part in the deprotonation of the termolecule and the apparent overall reaction order with respect to MEA approaches unity. On the other hand, when considering MEA + methanol, the reactivity of the solvent relies heavily on MEA itself acting as a base, meaning its reaction order increases to 1.73. The determining factor on whether a diluent takes part in the reaction or not is better explained by its autoprotolysis constant, which expresses its potential to donate/receive electrons.

Sada et al. [39] were the first to connect this depression of reaction rates and increase of reaction order with the Hildebrand solubility parameter (δ), a parameter which, as they helpfully pointed out afterwards [58], seems to correlate pretty well to the reciprocal of the dielectric permittivity (ε). A number of publications followed swift, in which more amines and diluents were screened, each time ending with a log(k₂) vs. 1/ε plot to reinforce the initial observations of Sada et al. [39]. Among these publications, we must note the meticulous work carried by the researchers of Pusan National University, who have screened the kinetics of a large array of amines in diverse organic diluents [126], [127], [133], [134], [135]. Dinda et al. [136], [137] have validated this relationship even for aniline, an organic amine, in solvents such as chloroform, toluene, methyl ethyl ketone and acetonitrile.

“Fig. 6. Kinetic rates and reaction order of AMP at 25 °C and concentrations between 1 and 3 mol∙l⁻¹ in water-free solvents containing methanol, ethanol, 1-propanol, 1-butanol, ethylene glycol, propylene glycol and propylene carbonate. Viewed from the dielectric permittivity perspective. Adapted from Son et al. [135].”

“Fig. 7. Kinetic rates and reaction order of AMP at 25 °C and concentrations between 1 and 3 mol∙l⁻¹ in water-free solvents containing methanol, ethanol, 1-propanol, 1-butanol, ethylene glycol, propylene glycol and propylene carbonate. Viewed from the autoprotolysis constant perspective. Adapted from Son et al. [135]. Autoprotolysis constants obtained in Izutsu [138] and Kundu and Das [139].”

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In Fig. 6, Fig. 7, we see that the apparent trend between ε and pK_S means that both the zwitterion and termolecular explanation for fractionary orders of reaction are consistent with the data available for reaction rates in water-lean solvents. Sadly, the biggest outlier in Fig. 6 is also an outlier in Fig. 7 (propylene carbonate, ε = 65, pK_S = 29.2). We might mention that there are suspicions that propylene carbonate is reactive with AMP itself [32]. Minus this exception, it seems as if there are observable trends between reaction rates, orders, dielectric permittivities and autoprotolysis constants.

We have carried out a statistic analysis on the data presented in Fig. 6. The Pearson correlation coefficients between ε and ln(k₂), ln(k_b/k₋₁) and ln(N) are respectively R(ε,ln(k₂)) = 0.8005, R(ε,ln(k_b/k₋₁)) = 0.7935 and R(ε, ln(N)) =  − 0.7869. However, when the data points corresponding to propylene carbonate are removed, these increase to R(ε,ln(k₂)) = 0.9874, R(ε,ln(k_b/k₋₁)) = 0.9609 and R(ε, ln(N)) =  − 0.9408. Those are fairly good indications of pattern behavior, notwithstanding the relatively small size of the available dataset. A similar analysis can be performed on the data shown in Fig. 7, resulting in that the correlation coefficients are respectively R(pK_S,ln(k₂)) =  − 0.4908, R(pK_S,ln(k_b/k₋₁)) =  − 0.4902 and R(pK_S,ln(N)) = 0.4972, while removal of the data points corresponding to propylene carbonate increases those values to R(pK_S,ln(k₂)) =  − 0.7979, R(pK_S,ln(k_b/k₋₁)) =  − 0.8434 and R(pK_S,ln(N)) = 0.8911. Therefore, it looks as if the dielectric permittivity correlation has a statistical edge over the autoprotolysis constant correlation.

Though a similar behavior is observed in nonaqueous solvents containing tertiary amines, we have not encountered any publication that reports reaction orders different than unity regarding the amine itself [37], [126], [127].

To compare both mechanisms, we have attempted to interpret a set of kinetic data employing the termolecular approach instead of the zwitterion approach. We have treated the data obtained by Park et al. [134] for mixtures between DEA and a row of different diluents (water, methanol, ethanol, 1-propanol, 1-butanol, ethylene glycol, propylene glycol and propylene carbonate). Their observations are presented in the form of the overall kinetic coefficient k_ov, which in the case of the zwitterion mechanism is defined as below. The choice of disregarding the reaction between CO₂ and free hydroxide anions came from the authors themselves.kov=Am1k2+k-1k2·kb·1Am

Having presented their data in terms of k_ov, the kinetic rates k₂ and k_b/k₋₁ can be calculated by the authors by following a simple linear regression.Amkov=1k2+k-1k2·kb·1Am

Conversely, if one employed the termolecular mechanism equation for reaction rates, the linear regression required for obtaining the kinetic coefficients would be the one shown below.kovAm2=kAm+kD·DAm

“Fig. 8. Termolecular mechanism kinetic coefficients for DEA at 25 °C and concentrations between 1 and 3 mol∙l⁻¹ in water-free solvents containing methanol, ethanol, 1-propanol, 1-butanol, ethylene glycol and propylene glycol. Regressed from data obtained by Park et al. [134]. Demonstration of their behavior with shifting dielectric permittivities.”

“As one can see in Fig. 8, though the behavior of the kinetic coefficient k_Am seems to be correlated to the dielectric permittivity of the diluent, the behavior of k_D appears to be more erratic. Since, as we have seen before, ε and kP_S follow a similar trend, Fig. 8 does not look much different once it is plotted in terms of the autoprotolysis constant. For effect of comparison, the same data was regressed in terms of the zwitterion mechanism kinetic coefficients, and the results are presented in Fig. 9. Naturally, these results are the same as the ones calculated by Park et al. [134] themselves. Though there are variations from the trend, the appearance of a regular behavior in Fig. 9 is certainly stronger than in Fig. 8. A more thorough statistical approach to these visual observations is shown on Table 5. One can see that the regression of the kinetic coefficients k_Am and k_D, for the termolecular mechanism, and k₂ and k_b/k₋₁, for the zwitterion mechanism, is carried out with fairly good values for the Pearson correlation coefficients. In general, both approaches seem to produce a reliable parametrization of the kinetic data (with the caveat that we are considering that k_b and k₋₁ are always lumped together in k_b/k₋₁, meaning that both mechanisms result in the same number of parameters). However, when one tries to correlate the kinetic coefficients with properties of the pure diluents such as their dielectric permittivity ε or autoprotolysis constant pK_S, the best Pearson coefficients are observed for the zwitterion kinetic constants and the dielectric permittivities. Interestingly thus, it seems that the approach initially adopted by Sada et al. [39] and then by the researchers of the Pusan National University [126], [127], [133], [134], [135] turns out to be the most adequate one for this particular case of water-lean solvents containing DEA (see Table 5).”

“Fig. 9. Zwitterion mechanism kinetic coefficients for DEA at 25 °C and concentrations between 1 and 3 mol∙l⁻¹ in water-free solvents containing methanol, ethanol, 1-propanol, 1-butanol, ethylene glycol and propylene glycol. Regressed from data obtained by Park et al. [134]. Demonstration of their behavior with shifting dielectric permittivities.”

Table 5. Kinetic coefficients and statistical parameters R (Pearson correlation coefficients) for treatment of the data from solvents containing DEA by Park et al. [134]. Both k_Am amd k_D are given in m⁶∙kmol⁻²∙s⁻¹, k₂ is given in m³∙kmol⁻¹∙s⁻¹, and k_b/k₋₁ is given in m³∙kmol⁻¹.