Partition coefficient log L16 exp. at 298.2K obtained with a C50H102 packed column at 373.2K. log L16 a : data taken from [5,14,21,31].
Gas chromatography is widely used for determining thermodynamic properties of pure substances or solvent properties of binary mixtures. From retention data, the solute activity coefficient at infinite dilution, the gas–liquid partition coefficient and others thermodynamic properties of mixing can be easily obtained. Using these parameters and appropriate models allows understanding of the intermolecular interactions responsible for solvation in the stationary phase [1-2]. The solvation parameter model is now well established as a useful tool for obtaining quantitative structure–property relationships for chemical, biomedical and environmental processes. The model correlates a free-energy related property of a system to six free-energy derived descriptors describing molecular properties. The ultimate goal is to establish a suitable quantitative structure–property relationship (QSPR) to facilitate the prediction of further system properties for compounds lacking experimental values. Two broad strategies are generally employed in QSPR studies. The first approach is based on theoretical descriptors. The advantage of using the QSPR approach based on theoretical descriptors is that all of the necessary parameters for prediction can be calculated purely from the three-dimensional representation of the molecular structure of each of the compounds of the mixtures, including mixtures of chemically diverse compounds [3-4]. The main weakness of this approach is that the selected descriptors may be difficult to understand and the models may lack obvious chemical significance. The second approach is based on descriptors determined using experimental technique such as gas chromatography.
In this review, we will present the different possibility of using chromatographic methods to facilitate the rapid and convenient measurement of the LSER model presentsed in reference . An application of the LSER model on ionic liquids will be presented. The last paragraph will be focused on the use of the LSER model coupled to a group contribution model for the estimation of the partition coefficient of organic compounds in ionic liquids.
2. Solvation models used in gas chromatography
2.1. Linear solvation energy relationship
In numerous solvation models, the partition of a solute between the gas phase and a solvent (or stationary phase) may be described by a cavity theory of solution [6-7] in which the solvation process is divided into three steps. In the step 1, a cavity of suitable size to accommodate the solute is created in the solvent. This process is endoergic because work is required to disrupt solvent–solvent interactions. In the second step, the solvent molecules around the cavity are reorganized from their original positions to the positions they will adopt when the solute is in equilibrium with the solvent. Of course, these positions are not fixed but are averages of solvent positions. The Gibbs energy change for such reorganization is assumed to be negligible, by analogy with the melting of a solid. However, enthalpy and entropy changes in reorganizations may be large, again by analogy with the melting of a solid. In the last step, the solute is introduced into the reorganized cavity, and various solute–solvent interactions are set up, all of which are exoergic.
Several thermodynamic properties are related to partitioning between water and other phases, for example octanol (Kow) or the pure compound itself (water solubility). These partitioning processes can be understood from thermodynamic concepts—like free energy, chemical potential and fugacity. The equilibrium partition constant between two phases, on a mole fraction basis, can be expressed as:
where Δ12Gi is the Gibbs energy (or free energy) of transfer between the two phases, R is the general gas constant and T is the absolute temperature. The Gibbs energy sums up both the enthalpic (Δ12H) and entropic (Δ12S) effects resulting from changes in intermolecular interactions:
The calculation of partitioning from structural or other descriptors therefore requires the modelling of these effects. The Gibbs energy change can also be separated into the contributions of van der Waals and polar interactions, assuming that these are additive:
In the early 1980’s, Taft & Kamlet [8-12] have developed the basic concept of linear solvation energy relationships (LSERs). They have demonstrated for thousands of chemical systems that some property which is linearly related to either a free energy of reaction, a free energy of transfer, or an activation energy can be correlated with various fundamental molecular properties of the solvents or solutes involved. Chromatographic retention and in particular logarithmic retention factors (log
Where SP is a solvation parameter related with the free energy change such as gas-liquid partition coefficient, specific retention volume or adjusted retention time at a given temperature. The capital letters represent the solutes properties and the lower case letters the complementary properties of the stationary phase. The solute descriptors are the excess molar refraction R2, dipolarity/ polarizability, hydrogen bond acidity basicity, and, respectively, and the gas-liquid partition coefficient on n-hexadecane at 298 K, LogL16. The solute descriptors may be determined using inverse gas chromatography or estimated using a group contribution method. A databank of descriptors for about 3000 compounds may be found in the literature [2, 20, 21]. The coefficients
2.2. Determination of LSER parameters of pure solutes
2.2.1. Determination of Log L16
To preserve the general character of equation (4), all characteristic parameters should be carefully determined and correlation between parameters should be avoided. Experimental procedures of successive determination of LSER parameters were described in the literature [20, 22-24]. Log L16 characterizes the most general interactions present in every physical system and should be determined before other parameters . The original values of log L16 were determined from retention data of organic compounds on n-hexadecane coated packed columns at 298.2 K . A number of papers proposed techniques based on the use of either capillary or packed columns in wide temperature ranges and replacing the n-hexadecane with other non-polar stationary phases. The gas liquid partition coefficient of a solute is directly related to the experimental capacity factor, k, by equation:
where VM and VS are the volumes of the mobile and stationary phases, respectively, and Φ is the phase ratio (VS/ VM). Experimental determination of log L16 is often very difficult. Adsorption phenomena introduce an important error in determination of the capacity factor. Zhang et al.  determined log L16 with capillary columns coated with n-hexadecane and concluded that results were not influenced by adsorption in this case. However, recent results presented in reference  showed that this improvement is not general and that an interfacial adsorption still exists with capillary columns. Moreover, it is very difficult to obtain absolute retention data using this technique. Li et al.  and Abraham et al.  studied influence of the solute support and of the stationary phase loading on adsorption phenomena. They concluded that the high loading ratio (up to 20 %) of the stationary phase and the high temperature of the column allow to reduce adsorption. In this case, the knowledge of R2, and parameters is necessary. The number and the nature of parameters needed for calculation depend on the stationary phase used.
Serious difficulties arise when log L16 of non-volatile compounds is to be measured. This is due to the definition of log L16 itself. Indeed, direct experimental determination of log L16 of compounds less volatile than n-hexadecane is impossible. In the case of heavy compounds slightly more volatile than n-hexadecane the experiment is possible but difficult, especially at 298.2 K. Often it is recommended to measure retention times at higher temperatures and then extrapolate partition coefficients to the ambient temperature. In this case, the quality of results depends strongly on the extrapolation method used. The problem of the temperature dependence of retention times was often discussed in literature. A suitable extrapolation procedure was described in reference . In the case of compounds less volatile than n-hexadecane several authors proposed to work with columns coated with long chain branched paraffins and to establish relationships between corresponding partition coefficients and log L16 [16, 26]. Defayes et al.  worked with apolane coated stationary phase (apolane is a C87H176 branched alkane). This column can be used at temperatures up to 550 K without a weight loss of the stationary phase. Moreover, it was shown that the effect of adsorption at the liquid-gas interface is negligible in this case . However, this opinion is not generally accepted and Werckwerth et al.  found the influence of adsorption in the case of strongly polar compounds. The same authors observed that a linear relationship exists between gas-apolane partition coefficients, log L87 and log L16 and that the data obtained with apolane can be used to estimate the value of log L16. Moreover, they demonstrated that strong correlation between both partition coefficients exists also for log L87 determined at significantly higher temperature . Recently, several authors investigated the use of predictive methods to estimate log L16 [27, 28]. This approach is particularly interesting to determine the log L16 of nonvolatile compounds.
2.2.2. Determination of LogL16 using capillary columns
A direct determination of the stationary phase mass is difficult in the case of capillary or Megabore columns and the use of relative methods to determine partition coefficient from retention data is often preferred. In this case, different approaches were proposed to calculate partition coefficient based on the well-established value of log Ln-hexane . Corresponding equation is as follows:
where tR and tm are the solute retention time and the dead time of the column respectively. Retention data of the solute X and of n-hexane should be determined at the same temperature. Available data of log Ln-hexane on apolane were determined at 312.4 K . On the other hand, it was shown that partition coefficients determined at two temperatures are linearly correlated .
New relationship can be established between the partition coefficient of the solute X at temperature T and the partition coefficient of the n-hexane at temperature T’. This relationship is based on the observation verified with several n-paraffin stationary phases that equation (7) for one stationary phase is reduced to the following form:
Equations (6) and (8) lead to relationship between the partition coefficient at temperature T of the solute X and the partition coefficient of n-hexane determined at temperature T’:
Apolane coated capillary columns are considered as an appropriate tool to determine log L16 of heavy compounds. Studies of Defayes et al.  and Werckwerth et al.  provided arguments supporting this opinion. As it can be seen in Table 1, results obtained with a similar but deactivated column are in good agreement with literature. Chromatographic peaks obtained with non-polar and polar compounds were symmetric. While this method gave good results at high temperatures, the column was deactivated irreversibly within few hours. A probable explanation of this phenomenon is that the adhesion between apolane and the deactivated silica does not assure the film stability at higher temperature [24, 27]. Our experience indicates that the use of commercially available apolane coated capillary columns should be limited to low temperature ranges. In the case of heavy compounds this implies very long retention times and imposes injection of samples of important volume, which induces adsorption effects. Consequently, to determine log L16 of heavy compounds we decided to use packed columns with long chain n-alkane stationary phase. Moreover, results obtained with a non-deactivated column indicate that retention times are influenced by adsorption phenomena. Indeed, polar solutes exhibited severely asymmetric peaks and their retention times strongly depended on the sample size. Retention times of alcohols are longer than the literature values that may indicate the presence of active sites.
2.2.3. Determination of LogL16 using packed columns
Problems of the capillary column stability encouraged us to review the possibility of application of packed columns for determining log L16 of non-volatile compounds. Stationary phases used were long chain n-alkanes, n-hexatriacontane and n-pentacontane. They were used at temperatures up to 320 K without significant loss of weight. The essential problem encountered with packed columns concerned adsorption effects [30, 23]. Mutelet & Rogalski  used teflon columns, inert and stable up to 330 K. Selecting an appropriate support material can reduce the adsorption on the surface of the support. Preliminary tests showed that the best results were obtained with the Chromosorb PAW DMCS and the Chromosorb WHP. Both supports were loaded with 25% of n-pentacontane. The fact that with Chromosorb PAW DMCS retention times depend on the sample size and chromatographic peaks are asymmetric indicates the presence of adsorption. Moreover, retention times of alcohols are longer than expected, indicating the presence of active adsorption sites on the support surface. The Chromosorb WHP support has a lower specific area and a smaller concentration of hydroxyl groups which reduces the adsorption. Results obtained are in good agreements with literature data for most of the compounds studied and retention times depend only slightly on the sample size. However, retention times observed with polyaromatic hydrocarbons are still longer than expected. Good results were obtained by deactivating the column (Table 1) with Silyl 8, as recommended by . The use of packed columns with Chromosorb WHP coated with n-alkane and deactivated with Silyl 8 made it possible to obtain a homogenous set of log L16 in good agreement with literature data.
2.2.4. Determination of LogL16 using temperature gradient method
The packed column technique can be used to measure log L16 data of volatile organic compounds. The reasonable limit of application of this method is the retention time of n-eicosane. Experimental difficulties make hazardous quantitative determination log L16 of heavier compounds. To enlarge the applicability of chromatographic methods to organic compounds less volatile than n-eicosane, a method based on the temperature gradient chromatography can be used. Recently, Donovan  showed that retention times of heavy organic compounds obtained in a gradient mode are linearly related to the logarithm of the vapor pressure at 298.2 K. The authors used a DB-1 megabore column at high flow rates of the gas phase. This method making it possible to reduce considerably retention time was applied to determine vapor pressures of pesticides and polyaromatic hydrocarbons. Nevertheless, the stationary phase DB-1 is slightly polar . Corresponding system parameters of the poly(dimethylsiloxane) immobilized in DB-1 column were published in the reference . Values determined at t= 60°C are as follows: r =0, s = 0.211, a = 0.308 and b = 0. Therefore, experimental results obtained with a DB-1 column can be used to determine log L16 only if LSER parameters expressing solute polarity are known. No general relationship between the reduced retention time and log L16 valid with all organic compounds can be obtained without the knowledge of above parameters.
However, this approach can be used to establish relationship between the reduced retention time and log L16 within a series of compounds. Indeed, polar parameters vary only slightly and in a regular way within a series. Moreover, certain parameters decrease strongly with rising temperature . Therefore, it can be supposed that the effect of the stationary phase polarity is nearly constant within a homologous series of moderately polar compounds. Measurements performed in a gradient mode with several homologous series confirmed this hypothesis. However, linear relationship does not afford the precision required for the log L16 determination. It was noticed that not only the reduced retention time tR but also the corresponding temperature T is needed to establish the appropriate function. Function log L16 = f(tR,T) is linear with R=0.996 that is not enough to represent the log L16 with the precision required. We found that the suitable function is as follows:
In the case of n-alkanes, function f(tR) was obtained with log L16 literature data of n-alkanes from n-dodecane up to n-docosane. The plot of f(tR) and values of parameters determining this function are given in Figure 1. The log L16 of n-alkanes up to n=38 calculated with equation (10) using gradient mode results are presented in Table 2. It is reasonable to suppose that partition coefficients of heavy n-alkanes up to approximately C45H92 can be obtained with gradient method. It should be pointed out that the present approach based on the gradient mode chromatography can be used only to determine log L16 within a homologous series of moderately polar compounds. The use of the present method with less polar stationary phase (recently, Li et al.  shown that in the case of SPB columns r = 0, a = 0, b = 0) can facilitate the study of polar compounds and perhaps obtain more general results.
2.2.5. Determination of polar LSER parameters
The excess molar refraction E is defined by the difference between the value for the solute molar refraction and the molar refraction for an alkane of the same characteristic volume:
The solute molar refraction is calculated from the following equation:
Where VX is the specific volume in cm3.mol-1/100 and n the refractive index of the solute.
Abraham et al.  set out to construct scales of solute hydrogen bond acidity and hydrogen bond basicity using logK values for reaction 1 in tetrachloromethane. The authors set out logK values for a series of acids against 45 given bases. If log K values for acids in a given reference base is plotted against log K values for acids in another reference base, a series of straight lines is observed with an intersection at a magic point of -1.1 log units. It is found that:
Where LB and DB characterize the base and values characterize the series of acids. The and parameters are then defined by:
At first, the LSER parameters c, s, a, b and l of each stationary phase are determined by multiple linear regression using solutes for which R2, , , and logL16 are known. Then, , , can be determined by multiple linear regression.
2.2.6. Group contribution Method for calculation of LSER parameters of organic compounds
Predictive methods allow to calculate these physico-chemical parameters which are inacessible via direct experiment. This alternative is particularly interesting in the case of log L16 of nonvolatile compounds. We consider that experimental methods described in the preceeding paragraph are useful for determination of LSER parameters of volatile and moderatly non-volatile compounds. Therefore, the large data bank of log L16 values already available in the literature can be used to establish group additivity rules and to predict log L16 of less volatile compounds. Havelec & Sevcik [27,28] presented a general group contribution method making it possible to calculate accurate estimates of log L16 of about 2000 organic compounds. The number of groups necessary to obtain good estimates of log L16 depends on the complexity of the molecular structure and rises in the case of polyfunctional molecules. This explains a high number of adjustable parameters used in the model [27,28]. For instance, log L16 of non-aromatic hydrocarbons is established with 33 parameters and 9 structural contributions. The total number of all group parameters, interactional parameters and structural contributions is of 131. The contribution of a given group is represented in the reference [27,28] with three parameters related to the structure of the molecule and to its interactions with the stationary phase. As log L16 is dependent on the solute vapor pressure and on the infinite dilution activity coefficient this approach is basically correct. However, molecular interactions are always related to n-hexadecane and certain parameters can be correlated. Platts et al.  recently proposed a new predictive method based on a careful analysis of contributions of various functional groups to establish log L16 and other LSER parameters. Therefore, molecular segments were defined in view to obtain good estimates of each. The log L16 of hydrocarbons is calculated with 9 parameters only. This method was established with 81 parameters, using a databank of 1908 compounds. A new model was proposed to calculating log L16 for nonvolatile organic compounds with special attention paid to heavy hydrocarbons. Data for 550 organic compounds containing mainly hydrocarbons and members of homologous series were used in regression. Basic heteroatom segments were taken into account but the polyfunctional organic compounds were not dealt with. Values of log L16 were taken from literature [5, 21]. To elaborate the group contribution method a simple and efficient approach was used. Accordingly, log L16 of the compounds X was calculated with the following expression:
where ci is the contribution of the group “i” and ni is the number of groups “i” in the compound X.
Platts et al.  have developed and tested additive models for six important molecular LFER descriptors, namely, R2, , , and logL16. Five of these six, all bar are calculated from a single set of 81 atom and group fragments, while is calculated from a separate set of 51 fragments. In general, the linear fit obtained with these additive models is good, with R2 and log L16 in particular giving excellent correlation. Splitting the data into training and test sets has also tested the predictive ability of such models, and is found to be almost as accurate as the full regressions. The performance of the method in calculating descriptors for “difficult” structures, ones containing intramolecular interactions such as hydrogen bonds, has been analyzed. Variations in descriptors due to such interactions are generally found to be reproduced, though inevitably some small discrepancies are found. In conclusion, this model is particurlarly powerful and useful for the prediction of LSER parameters of heavy and complicated molecules.
3. Application of linear solvation energy relationship on ionic liquids
The LSER model may be used to characterize the stationary phases in chromatography. In this case, a large number of solutes (between 20 and 50) for which LSER parameters R2, , , and logL16 are known have to be injected. The LSER parameters characterizing the stationary phases (c, s, r, a, b and l) are determined by multiple linear regression. In the literature, there is a large amount of data of partition coefficients or activity coefficients measured by gas–liquid chromatography or by dilutor technique. Some system constants for various ionic liquids and classical solvents at 25 °C are summarized in Table 3. The data for the 1-ethanol-3-methylimidazolium tetrafluoroborate, 1-ethanol-3-methylimidazolium hexafluorophosphate, 1,3-dimethylimidazolium dimethylphosphate and 1-ethyl-3-methylimidazolium diethylphosphate , 1-Butyl-3-methylimidazolium tetrafluoroborate , n-Acryloyloxypropyl-N-methylimidazolium bromide and n-Methacryloyloxyhexyl-N-methylimidazolium bromide , 1-Propenyl-3-alkyl-imidazolium bromide , 1-butyl-3-methylimidazolium octyl sulfate and 1-ethyl-3-methylimidazolium tosylate , Triethylsulphonium bis(trifluoromethylsulfonyl)imide , 1-Methyl-3-ethylimidazolium bis(trifluorosulfonyl)-amide and 1.2-Dimethyl-3-ethylimidazolium bis(trifluorosulfonyl)-amide  were taken from the sources indicated. Poole & Poole  found that the system constants of LSER model for the room temperature ionic liquids fall into the range
The (c + lL) term gives information on the effect of cohesion of the ionic liquids on solute transfer from the gas phase. In general, the ionic liquids are cohesive solvents; they interact weakly via nonbonding and π-electrons (
4. Predictive models based on LSER model coupled to a group contribution method
Solvation model may be also used to set up correlation between thermodynamic properties and LSER parameters. Abraham et al. [41,42] reported mathematical correlations based on the general Abraham solvation parameter model for the gas-to-solvent,
by rewriting each of the six solvent equation coefficients as a summation of their respective cation and anion contribution. The dependent variables in equations (18) and (19) are solutes descriptors as follows: E and S refer to the excess molar refraction in units of (cm3.mol-1)/10 and dipolarity/polarizability descriptors of the solute, respectively, A and B are measures of the solute hydrogen-bond acidity and basicity, V is the McGowan volume in units of (cm3.mol-1)/100 and L is the logarithm of the gas-to-hexadecane partition coefficient at 298 K. Sprunger et al. calculated equation coefficients for 8 cations and 4 anions using a database that contained 584 experimental log
In the development of Mutelet et al. , the cation with its alkyl chains is splitted in different contributions: (CH3, CH2, N, CHcyclic…). The approach allows to have a predictive model. The aim of this work was to develop a group contribution method allowing to estimate the log
Where ni is the number of group i present in the ionic liquid.
Mutelet et al.  proposed to extend the temperature dependent GC-LSER in view of determining the partition coefficient of organic compounds in ionic liquids. The GC-LSER can be rewriting as followed:
The experimental data used to calculate Abraham’s model ion-specific equation coefficients were taken from the collection of [43-46] and were updated with recent data. A total of 1450 gas-liquid partition coefficients and 1410 water-to-liquid partition coefficients were used for the calculation. Solutes were mainly n-alkanes, cycloalkanes, alkenes, alkynes, aromatics, alcohols, ethers, aldehydes, ketones, chloroalkanes. The
More precisely, Ncyclic represents two structures: and. Nine groups are used for anions: bis(trifluoromethylsulfonyl)imide :, hexafluorophosphate:, tetrafluoroborate:, ethylsulfate:, octylsulfate:, thiocyanate:, trifluoromethylsulfonate :, trifluoroacetate : and dicyanamide:. As an example, let’s have a look at the decomposition of 1-butyl-3-methylimidazolium hexafluorophosphate. In this case, the decomposition of the molecule into elementary groups is: 2 group 1 (-CH3) + 3 group 2 (-CH2) + 3 group 7 ( Ccyclic) + 2 group 9 (Ncyclic) + 1 group 14 (PF6-).
Group contribution model coupled to LSER (GC-LSER) for estimating the gas-to-ionic liquids partition coefficients and water-to-ionic liquids partition coefficients allows to predict with good accuracy Log
The solvation parameter model is suitable for describing the retention properties of molecules in chromatographic systems. To establish the system properties requires identification of a group of compounds with well known descriptor values. We have shown that all LSER parameters of solutes may be determined using gas chromatography or experimental techniques. The solvation model may be used either for the physico-chemical characterization of the stationary phases or for the establishment of a suitable quantitative structure–property relationship to facilitate the prediction of further system properties for compounds lacking experimental values.