Cellulose Dissolution in Mixtures of Ionic Liquids and Dimethyl Sulfoxide: A Quantitative Assessment of the Relative Importance of Temperature and Composition of the Binary Solvent

We studied the dissolution of microcrystalline cellulose (MCC) in binary mixtures of dimethyl sulfoxide (DMSO) and the ionic liquids: allylbenzyldimethylammonium acetate; 1-(2-methoxyethyl)-3-methylimidazolium acetate; 1,8-diazabicyclo [5.4.0]undec-7-ene-8-ium acetate; tetramethylguanidinium acetate. Using chemometrics, we determined the dependence of the mass fraction (in %) of dissolved cellulose (MCC-m%) on the temperature, T = 40, 60, and 80 °C, and the mole fraction of DMSO, χDMSO = 0.4, 0.6, and 0.8. We derived equations that quantified the dependence of MCC-m% on T and χDMSO. Cellulose dissolution increased as a function of increasing both variables; the contribution of χDMSO was larger than that of T in some cases. Solvent empirical polarity was qualitatively employed to rationalize the cellulose dissolution efficiency of the solvent. Using the solvatochromic probe 2,6-dichloro-4-(2,4,6-triphenylpyridinium-1-yl)phenolate (WB), we calculated the empirical polarity ET(WB) of cellobiose (a model for MCC) in ionic liquid (IL)–DMSO mixtures. The ET(WB) correlated perfectly with T (fixed χDMSO) and with χDMSO (fixed T). These results show that there is ground for using medium empirical polarity to assess cellulose dissolution efficiency. We calculated values of MCC-m% under conditions other than those employed to generate the statistical model and determined the corresponding MCC-m% experimentally. The excellent agreement between both values shows the robustness of the statistical model and the usefulness of our approach to predict cellulose dissolution, thus saving time, labor, and material.


Introduction
The need to increase the use of cellulose (Cel) from sources other than cotton, in particular from wood, has resulted in increased interest in optimizing the efficiency of solvents for the physical dissolution of Cel, i.e., without the formation of covalent bonds [1][2][3][4].
Ionic solvents, in particular ionic liquids (ILs) based on imidazole, quaternary ammonium-and phosphonium electrolytes, and salts of superbases (e.g., 1,5-diazabicyclo [4.3.0]non-5-ene (DBN) and 1,8-diazabicyclo [5.4.0]undec-7-ene (DBU)), these ILs have been employed both pure and as binary mixtures with dipolar aprotic molecular solvents [5]. A central issue in these studies was to maximize the concentration of dissolved Cel. Binary mixtures (BMs) of ILs with molecular solvents are frequently used as cellulose solvents. In addition to a better mass/heat transfer due to the lower viscosity, many dissolve more Cel than their precursor ILs [6,7]. Because of its efficiency in Cel swelling [8] Molecules 2020, 25 and high dipole moment and relative permittivity, dimethyl sulfoxide (DMSO) is most extensively employed as a co-solvent for ILs. For simplicity, we used the following definitions/acronyms in the subsequent discussion: microcrystalline cellulose (MCC) to represent Cel, mass fraction of dissolved MCC (MCC-m%; see Equation (1)), and mole fraction of dissolved MCC (MCC-χ; see Equation (2); AGU = anhydroglucose unit). For brevity, we limited our discussion to MCC-m%. As we will show below, the use of MCC-m% or MCC-χ leads to identical conclusions.
The usual procedure for optimizing the dissolution of Cel in a solvent is to change one experimental variable (or factor) at a time, e.g., temperature or composition of the BM. If needed, the first factor is fixed at its value that resulted in the maximum MCC-m%, and the other factor (e.g., BM composition) is then varied until a new maximum MCC-m% is reached [7,[9][10][11][12][13]. Although useful, this approach does not guarantee a real MCC-m% maximum for both variables. Equally important, however, this one-at-a-time approach gives no indication about the relative importance to Cel dissolution of the experimental variables. Therefore, chemometrics should be used, where both factors are varied simultaneously in a random manner [14].
The usual procedure for optimizing the dissolution of Cel in a solvent is to change one experimental variable (or factor) at a time, e.g., temperature or composition of the BM. If needed, the first factor is fixed at its value that resulted in the maximum MCC-m%, and the other factor (e.g., BM composition) is then varied until a new maximum MCC-m% is reached [7,[9][10][11][12][13]. Although useful, this approach does not guarantee a real MCC-m% maximum for both variables. Equally important, however, this one-at-a-time approach gives no indication about the relative importance to Cel dissolution of the experimental variables. Therefore, chemometrics should be used, where both factors are varied simultaneously in a random manner [14].
Many authors used solvent empirical polarity (vide infra) to qualitatively rationalize the effects of pure solvents and BMs on Cel dissolution [6,16,17]. Therefore, we used the solvatochromic probe The experimental variables studied were the dissolution temperature (T = 40, 60, and 80 • C) and the DMSO mole fraction (χ DMSO = 0.4, 0.6, and 0.8). We obtained equations that correlate MCC-m% with T and χ DMSO . These indicated that increasing the values of both factors favor MCC dissolution; the latter variable is more important in some cases.
Many authors used solvent empirical polarity (vide infra) to qualitatively rationalize the effects of pure solvents and BMs on Cel dissolution [6,16,17]. Therefore, we used the solvatochromic probe 2,6-dichloro-4-(2,4,6-triphenylpyridinium-1-yl)phenolate (WB) and cellobiose as a model for MCC and calculated the empirical polarity, E T (WB), of the disaccharide/IL-DMSO solutions. We found perfect second-order polynomial correlations between E T (WB) and T (at fixed χ DMSO ) and between E T (WB) and χ DMSO (at fixed T). Thus, there is theoretical and experimental ground for using the empirical polarity of a medium to explain its efficiency as a Cel solvent.
The generated statistical equations reproduce satisfactorily MCC dissolution data at T and χ DMSO values other than those employed to create the statistical model. This agreement shows the robustness of the chemometric approach used. Equally important, however, is that the model permits the prediction of biopolymer dissolution, saving time, labor, and material.

Materials
The reagents used were purchased from Sigma-Aldrich or Merck. The MCC, Avicel PH 101 (viscosity-average degree of polymerization = 155 ± 3, Ref. [18] was purchased from FMC. Before use, the MCC was dried for 2 h at 70 • C under reduced pressure.

Synthesis of the Ionic Liquids
The DBUHAcO and TMGHAcO were synthesized according to the literature, [17] by mixing equimolar quantities of standardized solutions of the superbase (DBU and/or TMG) with acetic acid in acetonitrile (MeCN), followed by stirring for 2 h at room temperature and removal of MeCN.
The AlBzMe 2 NAcO and C 3 OMeImAcO were synthesized as given elsewhere [19][20][21]. N-Benzyl-N,N-dimethylamine was reacted with allyl bromide in MeCN. After solvent removal, the produced allylbenzyldimethy lammonium bromide was purified by suspension in cold ethyl acetate (3 times; vigorous agitation), followed by removal of the latter. The obtained bromide was transformed into the corresponding acetate by ion exchange on a macroporous resin in the acetate form (Amberlite IRN 78, 1.20 equivalent acetate ions/L resin), using methanol as eluent, followed by removal of the latter. N-Methylimidazole was reacted with 1-chloro-2-methoxyethane in MeCN under pressure (10 atm, 6 h, 85 • C), followed by removal of MeCN and purification by agitation with ethyl acetate, vide supra. The produced 1-(2-methoxyethyl)-3-methylimidazolium chloride was transformed into C 3 OMeImAcO using ion exchange, as given for AlBzMe 2 NAcO.
The synthesized ILs were dried under reduced pressure, in the presence of P 4 O 10 . We analyzed the purity of these products by 1 H NMR spectroscopy (Varian Inova model YH300 spectrometer; 300 MHz for 1 H; CDCl 3 solvent). Each IL gave the expected spectrum (See Supplementary Materials Figure S1). Figure 2 shows the equipment employed for the MCC dissolution; its parts are explained in the corresponding legend. The dissolution experiments were carried out as follows (see the flow chart of Figure 3): Known masses of the IL-DMSO BM with the desired χ DMSO (approximately 3 g) and MCC (approximately 10-30 mg) were quickly weighted into a threaded glass tube. The latter was attached to the mechanical stirrer and then introduced into a thermostated polymethacrylate water bath already set at the desired temperature (Isotemp 730 heating unit, Fisher Scientific; Aumax model N1540 digital thermometer, bath temperature constant within ±0.2 • C). The suspension was agitated at a constant speed (300 rpm, measured with a digital laser tachometer, model 2234C + , Signsmeter). The MCC dissolution was judged visually, without opening the glass tube, under 12× magnifying glass provided with an LED light. The final decision (on MCC dissolution) was reached with the aid of a microscope (Nikon, Tokyo, Japan, Eclipse 2000 microscope with cross polarization). Complete cellulose dissolution was evidenced by observing a clear (i.e., dark) view, see Figure 4A. If complete dissolution was not observed after 2 h of agitation ( Figure 4B), the suspension was agitated further for an additional hour. We considered that MCC maximum dissolution was reached when the biopolymer remained undissolved after 3 h from the last solid addition. for an additional hour. We considered that MCC maximum dissolution was reached when the biopolymer remained undissolved after 3 h from the last solid addition.

Calculation of the Empirical Solution Polarity, ET(WB)
We used Equation (3) to calculate the solution empirical polarity using WB as a solvatochromic probe [22]: for an additional hour. We considered that MCC maximum dissolution was reached when the biopolymer remained undissolved after 3 h from the last solid addition.

Calculation of the Empirical Solution Polarity, ET(WB)
We used Equation (3) to calculate the solution empirical polarity using WB as a solvatochromic probe [22]: for an additional hour. We considered that MCC maximum dissolution was reached when the biopolymer remained undissolved after 3 h from the last solid addition.

Calculation of the Empirical Solution Polarity, ET(WB)
We used Equation (3) to calculate the solution empirical polarity using WB as a solvatochromic probe [22]:

Calculation of the Empirical Solution Polarity, E T (WB)
We used Equation (3) to calculate the solution empirical polarity using WB as a solvatochromic probe [22]: where λ max is the wavelength of the solvatochromic peak, and E T (WB) is the corresponding empirical polarity. Solutions of MCC in IL-DMSO scatter visible light, especially at high biopolymer concentrations. Therefore, we used cellobiose (CB) as a model for Cel [19,23,24] and prepared solutions that contained CB concentration (CB-m%) equivalent to (MCC-m%). We pipetted 50 µL of the WB stock solution in acetone (1 × 10 −3 mol L −1 ) into glass vials and removed the solvent under reduced pressure in the presence of P 4 O 10 . To each vial we added 1 mL of the appropriate CB-m%/IL-DMSO solution, dissolved the solid probe (vortex agitation), and transferred the resulting clear solution to a 1 cm path length semi-micro quartz cell with a PTFE stopper. We recorded each spectrum twice at a resolution of 0.2 nm, at 30, 40, 50, and 60 • C using a Shimadzu UV-2550 UV-Vis spectrophotometer provided with a digital thermometer (model 4000A, Yellow Springs Instruments, Yero Springs, OH, USA). We calculated the value of λ max from the first derivative of the spectrum. The value of E T (WB) at 80 • C was calculated by extrapolation of the E T (WB) versus T curve.

Statistical Design of the Cellulose Dissolution Experiment
Design of experiments (DOE) [25,26] is a systematic method to determine the relationship between experimental variables or factors affecting the output of a process. This method is used to find cause-and-effect relationships [14]. To perform DOE, we used the Statistica Software (version 13.0, Dell, Austin, TX, USA). The order of design points was randomized to reduce the effect of unpredicted variables (vide infra); the total number of experiments for each MCC/IL-DMSO was 16. A quadratic model was fitted to the dissolution data, see Section 3 (Results and Discussion). Response surfaces (vide infra) were generated by the response surface methodology (RSM) as implemented in the Statistica software.

Design of the Cellulose Dissolution Experiments
As shown in Section 2, we used one cellulose sample (MCC) and carried out the dissolution experiment at a fixed stirring rate. Therefore, the only experimental variables were T and χ DMSO . Each variable had three values or levels. According to DOE, the minimum number of experiments is 9 (i.e., equal to the number of levels (number of variables) = 3 2 ). In order to increase the robustness of the model, we repeated the central point (T = 60 • C and χ DMSO = 0.6) three more times and repeated the minimum and maximum levels (T = 40, 80 • C; χ DMSO = 0.4, 0.8) one more time, giving 16 experiments for each IL-DMSO BM (9 + 3 + (2 × 2)).
It is customary to denote the low, intermediate, and high values of factor levels by −1, 0, and +1, respectively. For example, we designated 40, 60, and 80 • C by −1, 0, and 1. Table S1 shows the randomized order of experiments using this designation as generated by the software employed. Table 1 shows the experimentally determined dependence of MCC-m% and MCC-χ on T and χ DMSO . In Table 1, we list in footer ( d ) the empirical polarity E T (WB) of the mixtures (CB + IL + DMSO) at different temperatures and DMSO mole fractions.
As there were two experimental variables, we expected that a quadratic model should fit our data [14] as given by Equation (4) for the present case: MCC-m% or χ MCC = Constant + a 1 T + a 2 χ DMSO + a 3 T 2 + a 4 (χ DMSO ) 2 + a 5 (Tx χ DMSO ) (4) where a 1 , a 2 , etc., are regression coefficients. Note that whereas the terms in T and χ DMSO are related directly to the variables studied, the quadratic and "cross" terms (i.e., T 2 , (DMSO) 2 , and Tx χ DMSO ) are required for a better statistical fit of the model to the data. In other words, the term a 4 (χ DMSO ) 2 does not necessarily mean that Cel dissolution occurs by the dimer of DMSO.
Based on this quadratic model, we constructed the corresponding Pareto charts for the four IL-DMSO BMs [27]. In Figure 5, the bars extending past the vertical (red) line indicate values reaching statistical significance (p = 0.05). Thus, both experimental variables were statistically relevant to Cel dissolution; both have comparable relevance, in agreement with previously published data on cellulose dissolution (vide supra). Table 1. Dependence of the dissolution of microcrystalline cellulose (MCC) in IL/DMSO binary mixtures on the molecular structure of the IL, the temperature, and the mole fraction of DMSO in the starting binary solvent a .  We used the data in Table 1 to generate two important pieces of information, namely, the response surfaces [28] and regression equations that correlate cellulose dissolution with the experimental variables. Figure 6 shows the responses of MCC dissolution to T and χ DMSO for the investigated IL-DMSO BMs. All of the color-coded response surfaces show that Cel dissolution increased as a function of increasing the temperature, and their maximum values (at the same T) were approximately 0.6 (χ DMSO ). The response surfaces of Figure 6 are in agreement with the abovementioned data on the efficiency of Cel dissolution in IL-DMSO BMs, namely, as a function of increasing T. The Cel-m% shows a "bell-shaped" curve (increase → maximum → decrease) as a function of increasing the concentration of DMSO in the BM. This (bell-shaped) behavior is related to competition for the solvation of the AGU hydroxyl groups by ions of the IL versus DMSO. Thus, the initial dilution of the IL with DMSO increased the dissociation of the ionic solvent, leading to efficient IL-Cel interactions (both hydrogen-bonding and hydrophobic interactions) and enhanced biopolymer dissolution. The competition between both solvent components for the hydroxyl groups of the AGU increased, however, on further dilution with DMSO, leading to a decrease in MCC-m%. The reason is that DMSO, unlike the IL, causes swelling but not dissolution of cellulose [29][30][31].
Molecules 2020, 25, x; doi: FOR PEER REVIEW www.mdpi.com/journal/molecules not necessarily mean that Cel dissolution occurs by the dimer of DMSO.
Based on this quadratic model, we constructed the corresponding Pareto charts for the four IL-DMSO BMs [27]. In Figure 5, the bars extending past the vertical (red) line indicate values reaching statistical significance (p = 0.05). Thus, both experimental variables were statistically relevant to Cel dissolution; both have comparable relevance, in agreement with previously published data on cellulose dissolution (vide supra). We used the data in Table 1 to generate two important pieces of information, namely, the response surfaces [28] and regression equations that correlate cellulose dissolution with the experimental variables. Figure 6 shows the responses of MCC dissolution to T and χDMSO for the investigated IL-DMSO BMs. All of the color-coded response surfaces show that Cel dissolution increased as a function of increasing the temperature, and their maximum values (at the same T) were approximately 0.6 (χDMSO). The response surfaces of Figure 6 are in agreement with the abovementioned data on the efficiency of Cel dissolution in IL-DMSO BMs, namely, as a function of increasing T. The Cel-m% shows a "bell-shaped" curve (increase → maximum → decrease) as a function of increasing the concentration of DMSO in the BM. This (bell-shaped) behavior is related to competition for the solvation of the AGU hydroxyl groups by ions of the IL versus DMSO. Thus, the initial dilution of the IL with DMSO increased the dissociation of the ionic solvent, leading to efficient IL-Cel interactions (both hydrogen-bonding and hydrophobic interactions) and enhanced biopolymer dissolution. The competition between both solvent components for the hydroxyl groups of the AGU increased, however, on further dilution with DMSO, leading to a decrease in MCC-m%. The reason is that DMSO, unlike the IL, causes swelling but not dissolution of cellulose [29][30][31].  Additionally, we calculated the regression equations, shown in Table 2, that quantify, for the first time, this dependence.   Additionally, we calculated the regression equations, shown in Table 2, that quantify, for the first time, this dependence. Table 2. Regression equations for the dependence of the concentration of dissolved cellulose on the temperature (T) and the mole fraction of DMSO (χ DMSO ).

Entry
Ionic Regarding Table 2, we have the following comments: 1.
In order to compare the regression coefficients directly, the values of T and χ DMSO were reduced, so that they varied between 0 and 1, before being subjected to the regression analysis; 2.
The magnitudes of the regression coefficients indicate the susceptibility/response of the phenomenon studied (i.e., Cel dissolution) to the experimental variables. In addition to expressing the concentration of dissolved Cel as MCC-m%, we also report our data as MCC-χ. The latter scale is more fundamental because differences in the molar masses of mixture components (Cel, CB, IL, co-solvent) do not affect the numerical value of the component. Additionally, the mole fraction scale permits calculation of the number of IL and DMSO molecules required to dissolve Cel. For example, maximum MCC dissolution was observed at 80 • C and χ DMSO approximately 0.6 ( Figure 6). Under these conditions, the molar ratios IL:DMSO per AGU were: AlBzMe 2 NAcO, 3.1:4.7; C 3 OMeImAcO, 1.7:2.5; DBUHAcO, 5.4:8.1, TMGHAcO, 9.7:14.9. Thus, the most efficient solvent system was that based on imidazole because it required smaller numbers of IL and DMSO molecules to dissolve Cel. We recommend that the mole fraction scale should be employed to compare the efficiency of different Cel solvents; 3.
As argued above, we concentrated on the regression coefficient of the second (T) and the fourth (χ DMSO ) terms of the equations listed in Table 2. These showed that both variables had comparable effects on MCC dissolution, at least in the range studied, in agreement with Pareto's chart ( Figure 5) and the abovementioned data in the literature where only one variable at a time was changed. Although the two concentration scales (i.e., MCC-m% and MCC-χ) resulted in different values of regression coefficients, the trends were qualitatively similar; 4.
The excellent calculated correlation coefficients (R 2 ) were satisfactory and show the importance of using dedicated dissolution equipment and a consistent dissolution protocol, and both ensure reproducible results as argued elsewhere [15]; 5.
Regarding the aprotic ILs, C 3 OMeImAcO showed a larger decrease of MCC-m% than AlBzMe 2 AcO as a function of increasing χ DMSO , from 0.6 to 0.8. As discussed elsewhere [21], the oxygen atom of the C 3 Omoiety is a Lewis base, capable of forming intramolecular hydrogen bonds with C2-H of the imidazolium ring, in addition to intermolecular bonds with the hydroxyl groups of the AGU. It is possible that the efficiency of intermolecular hydrogen bonding is impaired at higher T due to the concomitant large increase of entropy; 6.
To test the robustness of these correlations, we calculated MCC-m% under conditions other than those employed to generate the statistical models, and also determined the concentration of dissolved MCC experimentally. Table 3 shows the excellent agreement between the predicted and experimental values with the difference ranging between 0.7% and 6.2%. Entry 4 is interesting because the temperature employed was outside the T range investigated. 7.
Many authors used solvatochromic parameters to assess the efficiency of Cel solvents. In this regard we note: − We used E T (WB) because values of λ max of the corresponding solvatochromic peak showed a much larger dependence on the experimental conditions than other probes employed for calculation of, for example, Lewis basicity (SB; S = solvent). Consider the following values of ∆λ max of WB that we observed for CB/TMGHAcO-DMSO on changing χ DMSO from 0.4 → 0.8: 10 nm (T = 40 • C) and 16.7 nm (T = 60 • C). The corresponding ∆λ max for N,N-dimethyl-4-nitroaniline (one of the homomorphic pair employed to calculate SB) were 0.1 nm (T = 40 • C) and 0.6 nm (T = 60 • C). In the present case, therefore, WB is much more sensitive to changes in the experimental variables than other solvatochromic probes that are used to calculate specific Cel-solvent interactions. Note that empirical solvent polarity is related to the parameters that describe the specific solute-solvent interactions by Equation (5) [22][23][24][25][26][27][28][29][30][31][32]: where SB is as defined before; SA, SD, and SP refer to Lewis acidity, dipolarity, and polarizability, respectively. That is, the dependence of E T (probe) on the experimental variables reflects collectively the dependence (on the same variables) of hydrogen bonding (as given by SA and SB) and the hydrophobic interactions (related to SP). These two mechanisms of Cel-solvent interactions are central to dissolution of the biopolymer [33,34]. − E T (probe) is, however, a dependent variable, i.e., its value is determined by T and χ DMSO .
Indeed, correlations of the values of E T (WB) listed in the footer of Table 1( d ) with T at fixed χ DMSO and with χ DMSO at fixed T (correlations not listed) show perfect second-order polynomials with R 2 = 1. Therefore, it is possible, in principle, to use E T (WB) instead of T or χ DMSO in Table 2, because the medium empirical polarity is strongly correlated with the independent variables studied. The relevant point, however, is that there is theoretical and experimental ground for using E T (probe) to assess the efficiency of cellulose solvents.

Conclusions
Optimization of the physical dissolution of cellulose is important for its applications. The approach of one-at-a-time variation of the experimental variables does not guarantee reaching a true dissolution maximum. Equally important, however, it gives no indication about the relative importance (to Cel dissolution) of the experimental variables. That is, chemometrics should be employed as shown here for the first time. Using a specially constructed mechanical stirrer and an established dissolution protocol that ensures reproducibility of the results, we investigated the effects of temperature and BM composition on MCC dissolution. Dimethyl sulfoxide was used as a co-solvent for aprotic AlBzMe 2 AcO and C 3 OMeImAcO and protic DBUHAcO and TMGHAcO ILs. Both IL types have potential industrial application in cellulose regeneration/recycling. Using factorial design with repetitions of the central and peripherical points, we carried out 16 experiments for each IL-DMSO mixture and used a quadratic model to fit the MCC dissolution data. The Pareto plots indicated that both experimental variables were important, and the response surface showed that maximum MCC dissolution occurred at 80 • C and a χ DMSO of approximately 0.6. The robustness of the statistical model was evidenced by the high correlation coefficients and by the small differences between predicted (by the model) and experimentally determined MCC-m%. Thus, use of chemometrics allows quantification of the relative importance of the experimental variables. Equally important, however, this use saves time, labor, and material.
Author Contributions: All authors contributed to the work reported herein. All authors have read and agreed to the published version of the manuscript.

Conflicts of Interest:
The authors declare no conflict of interest.