Degradation Kinetics and Solvent Effects of Various Long-Chain Quaternary Ammonium Salts

Surfactants such as quaternary ammonium salts (QAS) have been in increasing demand, for emerging new applications. Recent attempts at process intensification oftheir production, have disclosed the need for a better understanding of QAS thermal stability. This work aims to determine degradation kinetics of various QASs, and theassociated solvent effects. Degradation kinetics of four methyl carbonate QASs were determined in variouspolar solvents in stainless steel batch autoclaves. 1H NMR spectrometry was employed for online analysis of the reaction mixtures. The kinetic parameters were then usedto compare the thermal stability of the four compounds in the polar solvents. Water showed not degradation, and methanol (MeOH) was the solvent that provided thesecond-best stability. Water-MeOH mixtures may provide an overall optimum. More, and longer long-chain substituents increased the degradation rate. Thermogravimetric Analysis was used to obtain the thermal stability in a solid-state, i.e. solventless environment. Isoconversional analysis showed that no reliable kinetic parameters could be determined. Nevertheless, the data did allow for a compar-ison of the thermal stability of 14 different QASs. Furthermore, the relative instability of the compounds in solid-state demonstrated the challenges of solventless QAS production.


Introduction
Surfactants serve a plethora of different use cases, in a continuously expanding market 1,2 .
These compounds are predominately applied as detergents. Cationic surfactants such as quaternary ammonium salts (QAS), are employed in more speciality-focused application, as e.g. anti-microbials 3 , and more recently in ion-exchange membranes 4,5 . These increasingly demanding appliances require highly stable compounds. Recent studies have therefore already focused on the elucidation of their thermal and alkaline stability 4,6 .
QASs are conventionally produced in batch Menshutkin 7,8 reactions, but novel production methods with dimethyl carbonate (DMC) are also being explored 9 . Their production is kinetically limited, and there is a large potential for process intensification [8][9][10][11] . In current processes, the temperature is limited by consecutive degradation reactions of the products.
This also highlights the importance of better quantification of the kinetics of this reaction for further optimisation of the process.
The scope of this research is to determine degradation kinetics of various QASs, with and without solvents. These kinetics are currently not available in literature, and they could disclose opportunities to further intensify QAS production through elevated temperature.
Comparing the thermal stability in different solvents would also elucidate their relative eligibility. By also measuring the thermal stability in solid-state, the viability of solventless production can be assessed. Lastly, the effect of different number of long-chains, their length, and various anions will be investigated.

Degradation mechanisms
According to previous studies, at least two possible degradation mechanisms can occur for QASs at elevated temperatures. Hofmann elimination has been well-known since 1958 and is considered to be the main reaction pathway 12 . The mechanism proceeds via a nucleophilic attack of the anion on the β-hydrogen, relative to the nitrogen atom. Consequently, the long chain is eliminated from the nitrogen, resulting in an alkene, a tertiary amine and a protonated anion as is illustrated by Fig. 1. It is expected that the more substituted carbon can better accommodate a positive charge in its transition state, therefore, this elimination is expected to be more favourable than the elimination of a methyl group. This also implies that more long-chain substituents make it statically more likely for elimination to occur.
However, in some cases, depending on the species, the protonated anion can perform a consecutive addition on the alkene double bond. Another proposed reaction mechanism is a nucleophilic substitution reaction on the carbon of the long-chain substituent 4 . Here, an alkane species is formed which contains the anion species of the original QAS, alongside a tertiary amine. This reaction pathway is also shown in Fig. 1. However, at most reaction conditions, it is presumed to have a less significant contribution to the degradation 4,6 .

Solvent effects
It is well-known that solvents, and their polarity greatly influence the rate of QAS production 11,[13][14][15] . It is expected that the degradation reaction is also sensitive to the used solvent and its polarity, as they can provide shielding to certain reactive sites 16 . Higher polarity is expected to better shield the sensitive β-hydrogen site from potential elimination. Water, methanol (MeOH), and iso-propanol (IPA) were selected for this work based on their polarity and their relatively good ability to sufficiently dissolve all intended QASs. Moreover, DMC was selected in order to assess the viability of methyl carbonate QAS production, with excess DMC and no (additional) solvent present. Ultimately, confluence between the solvent's added stability and the solvent effects of QAS production, would magnify the potential for process intensification.
2 Experimental Procedure

Chemicals and Synthesis
The required chemicals were obtained from various vendors. Some QASs were not commercially available, and were synthesised. All used reactants and QASs, their source and their purity have been listed in Table 1. Besides these chemicals, all required solvents were obtained in Technical Grade from VWR Chemicals. Lastly, 1,4-Difluorobenzene (F 2 Bz) was used as an internal standard and purchased from Sigma Aldrich with over 99% purity.
The synthesis of the QASs as shown in Table 1, was carried out in either 40 mL stainless steel batch autoclaves or a plug-flow reactor. The plug-flow reactor has been thoroughly described in earlier work 11 . The batch reactors were loaded with the respective reactants and MeOH as a solvent, and placed in a pre-heated oven. In order to ensure full conversion of the tertiary amine, all experiments were performed in excess MeI or DMC. The tertiary amine to MeI/DMC to MeOH molar ratio was 1:5:10. As BnCl is difficult to separate from the final mixture, this reactant was used in equimolar amounts compared to the tertiary amine. For all products, the method, reaction time, and temperature have been tabulated in Table 2.
To prevent consecutive degradation of the QAS, the reaction temperature was limited to a maximum of 120 • C. Note that this resulted in very long reaction times in some cases, as the reactivity of tertiary amines with an increasing amount of long-chain substituents severely diminishes. After the synthesis, all remaining excess reactant and MeOH was evaporated with a rotary evaporator or a vacuum oven. Thereafter, the purity was verified by means of 1 H NMR spectroscopy (Table 1).

Reaction Kinetics in a Batch Autoclave
The degradation reaction required relatively high temperatures of around 200 • C, for reaction times of no more than a single workday. Small volume (2.5 mL) Swagelok stainless steel autoclaves were devised to perform the kinetic experiments. These self-made reactors were low-cost, allowed for elevated temperatures and pressures, and were convenient to make in numbers. Moreover, their small volume meant that not a large amount of chemicals was required.
For each experiment, a new stock solution was made. This solution consisted of the concerning solvent, 0.2 M of QAS, and a known amount of F 2 Bz as an internal standard.
The 0.2 M was the maximum concentration that would dissolve for all solvent-QAS combinations. The internal standard was added to account for potential solvent evaporation.
The reactors were flushed with the solvent, the stock solution, and then filled with the stock solution. A minimum amount of headspace was ensured, to limit the formation of a vapour phase. Thereafter, the autoclaves were locked, airtight. For each solvent-QAS combination, a time series was measured at five different temperatures. One time series consisted of five samples, taken after different reaction times, and the stock solution. At t = 0, five autoclaves were placed in a pre-heated oil bath. One-by-one they were later removed at regular, pre-determined time intervals, and immediately quenched in an ice bath.
All QASs from Table 1 were initially supposed to be analysed according to this method.
However, upon testing, only the four methyl carbonate QASs showed sufficient degradation.
The other compounds were too stable at temperatures up to ca. 250 • C, and these were thus excluded from this part of the experiments.

1 H NMR Spectroscopy
After the reaction mixtures were quenched, a sample was added to a NMR tube, and a small amount of deuterated chloroform was added. If any signs of immiscibility were observed, further addition of the respective solvent ensured a single phase. The vials were analysed in a Bruker-400 400 MH NMR spectrometer, programmed to take 32 scans with a recycle delay of 2 s.  Nevertheless, it is expected that these second and third degradation reaction rates are significantly lower the the first. This assumption, and its implications will be further discussed in Section 4.1.

Thermogravimetric Analysis
Thermogravimetric Analysis (TGA) was performed to assess the thermal stability of the QASs in solid-state. This would mimic the conditions of a solventless production process.
Also, the TGA allowed for measuring the compounds that had proven to be too stable in dissolved state. This concerns all non methyl carbonate QASs. The TGA measurements were carried out in a TA Instruments Q500. Inert and empty, platinum pans were tared by the TGA. Subsequently, the pans loaded on a 0.1 mg accuracy balance with approximately 15 ±1 mg of pure QAS sample. In the TGA, the sample was subjected to temperature gradient ranging from 30 • C to 300 • C at heating rates of 2, 5, 10, 20 • C min −1 under an inert nitrogen atmosphere. Prior to the temperature ramp, a half hour isothermal step at 30 • C was programmed. This reaffirmed the purity of the sample, as any water that it may have been attracted due to its hygroscopic nature, will be removed by the nitrogen purge.
After that, every 0.25 s the temperature and mass of the sample were recorded.

Fitting the Batch Kinetics
The batch reactions were assumed to occur according to first-order kinetics. Hofmann elimination is known to be a second-order reaction, yet it is stated in literature that its conversion is independent of the initial concentration 4 . The assumption will later be validated. The QAS concentrations that were computed from the 1 H NMR spectral data were thus fitted in accordance with Eq. 1 and 2. A linear plot of −ln(C) − ln(C 0 ) vs. t (Eq. 2) would confirm the first-order assumption, and allow for fitting k as its slope.

Isoconversional Method
The isoconverional method enables the ability to ascertain the mechanisms of the reaction, without making prior assumptions about a model. In this model, the reaction rate is represented by a temperature dependent part and a conversion dependent part (Eq. 3).
At a constant conversion, the equation can be rewritten to obtain Eq. 4. As the remaining variables, t and T , are correlated through a fixed heating rate applied by the TGA, i.e.
β. Resulting isoconversional methods can be either differential or integral, each with its advantages and disadvantages. In this study, the Kissinger-Akahira-Sunose method was selected, as depicted in Eq. 5 17 . Compared to other methods, this method has shown to have superior accuracy for determining activation energies 18 .
Analysis of the behaviour of E α vs. α can then provide information about the actual degradation mechanism and the relating model. Significant variation of this relation would imply a complex process, with potentially multiple kinetic or physical steps involved 17 . In contrast, relative independence of these variables indicates a more straightforward reaction.
Such reaction could be modelled with general Arrhenius correlations, e.g. for first order shown in Eq. 6.
4 Results and Discussion

Degradation Kinetics
Analysis of the 1 H NMR data that was collected from the degradation reaction experiments, resulted in concentration profiles for all methyl carbonate QASs. DTMA-MC represented a typical profile as depicted in Fig. 3a. First-order kinetics were assumed for the subsequent fits. The required linearity that clearly followed, confirmed this assumption and the reaction rate constants were computed (Fig. 3b). This is in accordance with   The Arrhenius parameters were used to interpolate and extrapolate reaction rate constants at 120 and 200 • C, respectively (Fig. 5). These values allow for a comparison of the QASs' thermal stability at a more or less average investigated temperature, as well as at a more conventional synthesis temperature. The relative degradation rates at 200 • C are particularly useful for identifying process intensification opportunities.
All QASs have clearly proven to be most stable in MeOH. Overall, IPA provides more stability than DMC, with the noteworthy exception of DTMA-MC. The slight demixing that was described earlier may have somewhat suppressed the reaction. Generally, these observations illustrate that MeOH would be most eligible as a solvent for synthesis of these compounds. Moreover, solventless production with excess DMC poses a significant drawback, as the product's stability is greatly diminished. Fig. 5 also shows that more long-chain side-chains cause a relative increase of the degradation rate. This is a well-known effect, as it provides more β-hydrogen sites where a potential Hofmann elimination can occur.
Finally, comparing the reaction rates of TDMA-MC and TBMA-MC demonstrates the overall increased stability that shorter chains provide. This is in line with findings by Friedli et al.
in 1990 19 . The described trends apply both at 120 and 200 • C. It is peculiar that the effect of chain length (TDMA-MC vs. TBMA-MC) seems to be reversed at 200 • C in DMC. No viable explanation was found for this remarkable observation. As mentioned in Section 2.3, the measurements in DMC posed the additional intricacy of secondary (DDMA-MC), and tertiary (TDMA-MC and TBMA-MC) degradation reactions.
It was the expectation that these were slower, which is confirmed by Fig. 5. In all cases, less long-chain substituents results in a lower degradation rate. Moreover, the additional degradation reactions can only occur after the initial degradation and the consecutive re-alkylation have occurred. This will result in lower concentrations of secondary QASs and even lower concentrations of tertiary QASs. Overall, these unaccounted resulting reaction rates will be profoundly slower. The progression from DTMA-MC to DDMA-MC to TDMA-MC, with around a factor 2 increase in degradation rate seems plausible. Still, a slight overestimation the DDMA-MC and TDMA-MC degradation rate in DMC can not be precluded. For TBMA-MC in DMC, it seems that the reaction rate is probably overestimated.

Solvent Effects
The remarkable observation of water's elimination of the degradation reaction inspired further investigation. Dekel et al. have also described water's profound stabilising effect 20 . It is generally known that polar (protic) solvents, such as water, MeOH, and IPA can provide shielding to certain reactive sites 16 . The fact water transcends MeOH and IPA in this regard is perhaps due to its higher dielectric constant. The dielectric constants for water, MeOH, and IPA at 25 • C are 79, 33, and 11, respectively 14 . Water's smaller molecular size may also contribute, as it could allow the molecule to better shield the concerning site.
Water was now added to the earlier investigated mixtures in small amounts to form binary solvent mixtures. DMC was excluded from these measurements, as it can be hydrolysed in water-based systems to form carbon dioxide and MeOH 21 . Water caused too many miscibility complications for TDMA-MC and TBMA-MC, so these QASs were also not included. For  In MeOH there appears to be a distinct effect of the addition of water, in increasing amount. In IPA the effect is certainly less pronounced, and in DDMA the 10:1 ratio caused higher conversions even. While higher proportions of water may contribute further, in these amounts the effect was considered negligible. The effect of water in MeOH definitely shows potential for further increased thermal stability of QASs. Further research could also unveil if the effect persists for more QASs and similar compounds. There may be an optimum ratio involved (varying per QAS), depending on the solubility and the influence on the formation reaction rate.

Thermogravimetric Analysis and Isoconversional Plots
The TGA experiments resulted in mass loss profiles vs. temperature for all 14 QASs. In Fig.   7 a typical plot is shown of BzDDMA-Cl for 2, 5, 10, and 20 K min −1 . Most compounds followed a similar trajectory, although some showed some slight slope transitions, indicating more complex (kinetic) behaviour. Subsequently, the TGA data was used to perform the isoconversional analysis. The resulting E a vs. α plots provided further insight into the degradation mechanism, and they are shown in Fig. 8. They have been divided into di-and trimethyl QASs (Fig. 8a) and monomethyl QASs (Fig. 8b). Stable (i.e. independent) activation energies with an increase in conversion would signal simple first-order kinetics. A generally accepted deviation of up to 10% from low to high can be still be considered independent 17  and that at a certain progression in the reaction its evaporation limits the measured weight loss. In other words, from a certain α, evaporation was measured, rather than degradation.
This appears as a resistance, and translates to a runaway of the activation energies.
Based on these observations, it is concluded that the QASs are generally prone to complex degradation mechanisms. The expected first-order kinetic fitting is therefore not possible here. Further kinetic analysis is required to obtain the desired kinetic parameters. Differen-tial Thermal Analysis plots, deconvolution, and Master Plots are two approaches that could provide the required insight 17,22,23 . However, this is beyond the scope of this work.

Solid-State Thermal Stability
In the previous section it was concluded that no reliable kinetic constants could be computed.
Still, the thermogravimetric data does provide insight into the (relative) thermal stability of the measured compounds. In Table 4

Conclusions
The degradation reaction's kinetic parameters have been successfully determined for four methyl carbonate QASs in MeOH, IPA, and DMC. Water showed no observable degradation, and in term of thermal stability it was found that MeOH > IPA > DMC. As expected, more long-chain substituents and longer chains resulted in lower thermal stability. Binary solvent mixtures were also investigated, and small additions of water to MeOH (10:1 and 5:1 ratio) further enhanced the QAS stability. This effect was not observed in IPA. It can be concluded that MeOH is most suitable for stabilising the methyl carbonate QASs during their production, and that an optimum MeOH:water ratio could be beneficial to further explore.
In solid-state, 14 QASs were evaluated. Isoconversional analysis proved that their kinetic and physical behaviour was too complex to determine Arrhenius parameters. Nevertheless, the isoconversional method did provide average, model-less E a values. Furthermore, the thermogravimetric data allowed for the computation of average T 50% values, which indicated at which temperature 50% of the compound had degraded. Together, these to parameters provided a comparison of the relative thermal stability of the compounds. This showed that different anions provided various degrees of stability (Br − > Cl − > NO − 3 > I − > MC − ).
In accordance with the findings in dissolved state, solid-state thermal stability showed to decrease with more, and longer long-chain substituents. Finally, degradation rates have proven to be orders of magnitude faster in absence of a solvent.