Aggregation Behavior of Long-Chain Piperidinium Ionic Liquids in Ethylammonium Nitrate

Micelles formed by the long-chain piperidinium ionic liquids (ILs) N-alkyl-N-methylpiperidinium bromide of general formula CnPDB (n = 12, 14, 16) in ethylammonium nitrate (EAN) were investigated through surface tension and dissipative particle dynamics (DPD) simulations. Through surface tension measurements, the critical micelle concentration (cmc), the effectiveness of surface tension reduction (Πcmc), the maximum excess surface concentration (Гmax) and the minimum area occupied per surfactant molecule (Amin) can be obtained. A series of thermodynamic parameters (ΔGm0, ΔHm0 and ΔSm0) of micellization can be calculated and the results showed that the micellization was entropy-driven. In addition, the DPD simulation was performed to simulate the whole aggregation process behavior to better reveal the micelle formation process.

Ethylammonium nitrate (EAN) is a room-temperature ionic liquid (RTIL) discovered in 1914 [34]. EAN has been widely investigated and used in many fields. Dielectric spectroscopy studies were carried out in order to study the dielectric behavior of EAN [35]. In protein chemistry, EAN has many potential applications, for example, it can be used as an additive, a detergent, a precipitating agent or to deliver ligands to protein crystals [36,37]. Phase behaviors of surfactants and lipids in EAN were studied over 20 years ago [38][39][40][41][42][43]. EAN is a protic ionic liquid and has the ability to form a three-dimensional hydrogen-bond network, which is a characteristic supporting self-assembly of a surfactant [44]. Zheng group studied the aggregation behavior of some 1-alkyl-3-methylimidazolium bromides (CnmimBr, n = 12, 14, 16) in EAN. They concluded that CnmimBr can form micelles in EAN, then investigated the solvophobic interactions between the hydrocarbon chains of CnmimBr and EAN molecules [45]. The aggregation behavior and micelle formation mechanism of N-alkyl-N-methylpyrrolidinium bromide (CnMPB n = 12, 14, 16) in EAN were investigated through surface tension measurement and 1 H-NMR spectrometry by Shi and coworkers [46]. The Drummond group has studied the self-assembly of hexadecyltrimethylammonium bromide (CTAB), myverol 18-99 K and phytantriol in many protic ILs, including EAN [47,48]. Recently, research has focused on the aggregation behavior of surface active ILs in RTIL, including in EAN [49,50].
In the present work, we prepared a series of piperidinium ILs with different alkyl chain lengths, CnPDB (n = 12, 14, 16). The aggregation behaviors of these ILs in EAN have been investigated by surface tension measurements and dissipative particle dynamics (DPD) simulations. Our aim was to examine the influence of alkyl chain length on the aggregation behavior, so that we can offer a systematic study of the mechanism of formation of aggregations formed by surface active ILs in RTILs. Figure 1 shows the surface tension of CnPDB (n = 12,14,16) in EAN at various concentrations at 298 K. The surface tension of the CnPDB solution decreases sharply at the beginning compared with pure EAN. As CnPDB concentrations increase further, the surface tension decreases gradually. Finally, the surface tension remains constant above the critical micelle concentration (cmc). The cmc values are listed in Table 1. The cmc value of a surfactant reflects its surface properties, a smaller cmc value means better surface activity. The value of cmc declines with the increase of hydrocarbon chain length, which is similar to their aggregation behavior in aqueous solution. The result suggests that there exist solvophobic interactions between the hydrocarbon chain and EAN, similar to the hydrophobic interactions in water. The obtained cmc values of CnPDB are higher than those in aqueous solution [32]. The cmc values of CnPDBs in EAN are smaller than those of CnmimBr (0.139, 0.0350 and 0.00913 mol·L −1 ) and CnMPB (0.097, 0.026 and 0.0078 mol·L −1 ) for the same alkyl chain length [45,46]. The cations of CnmimBr and CnMPB have a great impact on that. There are two main two reasons, head groups have opposing tendencies to keep close to minimize hydrocarbon-solvent contacts and to repel as a result of electrostatic repulsion, solvation and steric hindrance [51]. The reason might be the lower hydrophilicity of the CnPDB head groups than that of CnmimBr and CnMPB.   Figure 2 shows the relationship between the number of carbon atoms in the hydrocarbon chain of CnPDB and lgcmc. Figure 2 shows that lgcmc decreases with the increase of alkyl chain length and the plot is almost liner. The rule can be expressed by the empirical formula:

Surface Tension of CnPDB in EAN
In this formula, A and B are constants. A stands for the ability of forming micelles of a surfactant and B stands for the average contribution to the micelle formation by the methylene in the hydrophobic chain. The value of A is obtained by extrapolation of the straight line and A and B were calculated to be 0.1807 and 0.1736, respectively. The value of B for CnPDB is similar with CnMPB (0.28) and CnmimBr (0.30). The value of A for CnMPB and CnmimBr in EAN are 2.25, and 2.10, respectively. The lower value of A for CnPDB indicates that CnPDB is easier to form micelle in EAN, which is in accordance with the result from the comparison of surface tension. This phenomenon is resulted from the special interactions between the different head groups and EAN.
The effectiveness of surface tension reduction (Πcmc) can be obtained using the following formula: where γ0 is the surface tension of pure solvent and γcmc is the surface tension of the solvent. The values are listed in Table 1. The results indicate that Πcmc decreases with the increase of the length of hydrocarbon chain, and when n = 16, the IL behaves best in reducing the surface tension, which indicates the ILs with longer hydrocarbon chains can reduce surface tension easier. The maximum excess surface concentration (Гmax) and the minimum area occupied per surfactant molecule (Amin) at the air/liquid surface can be obtained from the Gibbs adsorption isotherm: where R is the gas constant (8.314 J·mol −1 ·K −1 ), T is the absolute temperature and the value of n is taken as 2 [52], dγ/d(lnC) is the slope of γ versus lnC dependence while the concentration is near cmc, NA is Avogadro's number (6.022 × 10 23 mol −1 ). The value of Гmax and Amin obtained from the Gibbs adsorption isotherm reflects the molecule arrangement of ILs at the air/liquid interface [53] and they are listed in Table 1. With the increase of alkyl chain length, Гmax increases but Amin decreases, which means the longer alkyl chain can make the CnPDB molecules packing more closely. Compared with the values of CnPDB with the same alkyl chain length in water, Гmax is larger but Amin is smaller in EAN than that of in water. [31] This indicate that less CnPDB molecules would aggregate in air/EAN interface. The estimated Гmax values for CnMPB in EAN are 0.96, 1.36 and 1.85 μmol/m 2 , the Amin of that are 173, 122 and 89 Å. This means CnMPB molecules have a higher packing density at the air/EAN interface.

Temperature Dependence of cmc
Plots of surface tensions against CnPDB concentrations at various temperatures are shown in Figure 3. The values of cmc for CnPDB at various temperatures are listed in Table 2. Figure 4 gives the correlations between cmc and temperature. It indicates that the value of cmc decreases with the temperature increase in a trend of U-shape and fits with a second-order polynomial. This trend is similar to the other ILs in EAN [46,47].

Thermodynamic Analysis on the Micelle Formation of CnPDB in EAN
As is shown in Figure 4, the temperature has a significant relationship with the micelle formation of CnPDB in EAN. The standard Gibbs free energy of micelle formation is given as follows: where is the standard Gibbs free energy; R is the gas constant; T is the absolute temperature; XS is the mole fraction of surfactant monomer coexisting with the micelle.
Then, the enthalpy of aggregation formation can be calculated by the Gibbs-Helmholtz Equation: On the basis of and ∆ , ∆ can be derived as the following equation: The value of at different temperatures can be calculated based on Equation (5). As is shown in Figure 5, the value of / increases along with the increase of 1/T. The plot fits with a second-order polynomial and the quadratic equations can be obtained. The values of ∆ and − ∆ of C12PDB, C14PDB and C16PDB at different temperatures can be calculated according to Equations (6) and (7). Figure 6 shows the plots of , ∆ and − ∆ versus temperature of CnPDB (n = 12, 14, 16). is negative and decreases with the increase of temperature which is similar to the other ILs in EAN. From 298 K to 318 K, − ∆ increases with the temperature while the value of ∆ decreases. The figure indicates that the negative is mainly contributed by the large negative − ∆ . Thus, the micelle formation of CnPDB (n = 12, 14, 16) in EAN is an entropy-driven process.

Dissipative Particle Dynamics (DPD) Simulation on the Micelle Formation of CnPDB in EAN
The DPD simulation was performed using the Material Studio software. The theory of this simulation method has been discussed previously [31,54]. In the simulation model, the CnPDB molecule is shown in Figure 7 and the amphiphilic molecule is divided into two parts, the hydrophilic part C and the hydrophobic part H, which are connected by a harmonic spring and the monomer particle E represents for EAN. The model is simulated in a 10 × 10 × 10 cubic box. The temperature is kept at 298 K and the step size of the Newton equation for the integration is set to Δt = 0.05. In order to represent dynamic process for the micelle formation, 20% CnPDB is used to perform the DPD simulation and the results are shown in Figure 8. At first, the system is unstable and the beads are unordered, which can be seen from Figure 8a structure is finally formed and the structure is more ordered (Figure 8d). The process often happens in tens of μs and is difficult to observe in a lab experiment, so the simulated result is regarded as an effective method supplying valuable information about microphase separation.

Apparatus and Procedures
Surface tension measurements were carried out by a model JYW-200B surface tensiometer (Chengde Dahua Testing Instrument Co., Ltd., Chengde, Hebei, China). The temperature was controlled with the help of a thermostatic bath. The surface tension was measured through a single-measurement method and all tests were repeated at least twice until the results were repeatable.

Conclusions
In summary, the aggregation behavior of long-chain piperidinium ILs CnPDB (n = 12, 14, 16) in EAN were investigated in this work. Through surface tension measurements, the cmc, γcmc and Πcmc can be obtained and thermodynamic parameters related to the micellization can be calculated. Through an investigation of the effect of the alkyl chain length of the ILs, it can be concluded that the longer the alkyl chain the better characteristics the ILs possess. By analyzing the thermodynamic parameters at different temperatures, it can be established that the CnPDB micelle formation is an entropy-driven process. The DPD simulation clearly showed the micellization process of CnPDB in EAN. We expect our work will help better understand the aggregation behavior ILs in EAN.