Memoire Online - Infinite dilution activity coefficient measurements of organic solutes in fluorinated ionic liquids by gas-liquid chromatography and the inert gas stripping method

The activity coefficient of species in a solution is defined by the following ratio:

where, is the fugacity of component in solution, its pure component fugacity and, its

molar fraction. Activity coefficient is also defined as the proportionality constant between the activity of a substance and its mole fraction in a given solution.

In the study of phase equilibria and therefore the design and optimization of separation processes, the concept of activity coefficient is used rather than activity.

The infinite dilution activity coefficient , also referred to as limiting activity coefficient is the

limiting value of the activity coefficient of a solute when its concentration tends towards zero. Alessi et al. (1991) defined the infinite dilution region as one where each molecule of the solute is surrounded by molecules of the solvent only. Only solute-solvent interactions take place. This can be assumed for mole fractions ranging between 10^-7 and 10^-4, depending on components under investigation. The infinite dilution region of solutions attracted much interest for couple of reasons underlining its great importance (Raal and Mühlbauer 1998):

Sandler (1996) discusses theoretical and practical applications of infinite dilution activity coefficient (IDAC) values in chemical and environmental engineering. The most important ones that are related to chemical engineering are listed below:

Separation is a critical stage in most of chemical processes by virtue of its sensitive impact on the global cost, as well as the quality of the product. One of the most important applications of IDACs is found in separation processes. IDAC values are used in the preliminary selection of solvent in view of extractive distillation, as well as, liquid-liquid extraction (Tiegs et al. 1986). The potentially best separating agent, called entrainer, is the one allowing the highest selectivity and capacity values. In other words, when solvents are investigated to find out the most suitable separating agent for a mixture containing two components and , their respective IDAC

values in each solvent are determined. Equation (2-3) is then used to calculate the selectivity at infinite dilution of each solvent with respect to the system.

and represent the limiting activity coefficients of and respectively in the solvent,

. is the limiting selectivity of solvent for the system consisting of components and

. Thus, selectivity values at infinite dilution are important for a preliminary selection of an
entrainer. A second quantity to look at is the solvent capacity at infinite dilution, which is

Additionally, capacity reveals how much solvent is used during the separation process. The greater the solvent capacity, the smaller the amount of solvent used. In principle, the solvent to use as separating agent is supposed to have the greatest value of both selectivity and capacity. But in practice, a compromise is to be found, since these two quantities are in inverse variation with respect to one another. A criterion that incorporates both selectivity and capacity together

is called performance index, given by the product of these properties (Kumar and Banerjee

The determination of permits one to evaluate the potential use of solvents. Therefore, it

serves as a preselection criterion. Other criteria (Lydersen 1983) leading to the definitive choice of a solvent include: recoverability, distribution coefficient, solvent solubility, density, interfacial tension, viscosity, cost, corrosiveness, non-flammability, low toxicity, etc.

There is a relationship between the Henry`s law constant of a solute in a solvent and its limiting activity coefficient:

represents the Henry`s law constant for solute i in the solvent and is the vapour pressure

of solute i at the temperature for which the IDAC is determined. Equation (2-6) shows that
Henry`s law constants can be found through IDAC values. In cases where the temperature of the
system is above the critical temperature of the solute, the Henry`s law constant, rather than the

IDAC is useful (Eike et al. 2004). Design calculations for gas separation applications commonly ln e j

Conditions for the occurrence of an azeotrope in binary systems can be established using infinite dilution activity coefficient data (Gmehling and Möllmann 1998). For a system showing positive deviation from Raoult`s law, an azeotrope with a temperature-minimum (pressure-maximum) takes place when

(2-7) For a system exhibiting negative deviation from Raoult`s law, an azeotrope with a temperature- maximum (pressure-minimum) takes place when:

From equations 2-7 and 2-8, it obviously appears that the knowledge of the IDAC values can help in predicting conditions leading to an azeotropic mixture.

Values of infinite dilution activity coefficient are important for the development of new thermodynamic models, the adjustment of parameters, as well as the expansion of the applicability for the existing group contribution models (Gmehling 2003 and Nebig et al. 2009). With the aid of an appropriate correlation, one can use infinite dilution activity coefficient values to come up with VLE data in the intermediate concentration range. Additionally, it is recommended to fit group interaction parameters simultaneously to all available VLE, LLE and infinite dilution activity coefficient experimental data (Weidlich and Gmehling 1987).

The infinite dilution activity coefficient value is an indication of the nature of interactions between solute and solvent molecules (McMillan and Mayer 1945). A high IDAC value is synonymous of weak solute-solvent interactions i.e. low solubility (Cheong 2003). The IDAC value is also a limiting measurement of the nonideality (Bao and Han 1995) of a solution. For an

ideal system, whereas a departure from ideality corresponds to IDAC values greater or

The Gibbs-Helmholtz equation (2-9) depicts the effect of temperature change on activity coefficient.

				(2-9)

Using experimental ã⁸ data, the partial excess enthalpy at infinite dilution for a given solute i,

can be directly obtained from the slope of a straight line derived from equation (2-11), where is the gas constant. It only takes an approximation of experimental values by the linear regression,

Predictive thermodynamic models are very important in separation processes (Lei et al. 2008) as they allow:

It is beyond the scope of this study to review all the thermodynamic models used to predict infinite dilution activity coefficients. Only the most promising models used for systems involving ionic liquids are dealt with in this section. The most successful models used by various researchers to predict activity coefficients of various solutes in ionic liquids can be classified into two categories:

These methods are based on the group contribution concept which assumes that the interaction energy of a system is the sum of functional groups interaction energies, provided that groups are properly defined (Gmehling 2009). Molecules are therefore split into smaller structures called groups to which parameters are assigned. These activity coefficient models are mostly based on the relationship between the latter and the excess free energy.

The ASOG (Analytical Solution of Group) model was developed by Derr and Deal (1969) who exploited previous works by Wilson and Deal (1962). It was redefined by Kojima and Tochigi (1979) who modified several parameters in order to account for the effect of temperature changes. In this method, the expression of the activity coefficient is composed of two parts: the size contribution term and the group interaction one. Go et al. (2007) used the ASOG model to correlate experimental infinite dilution activity coefficient data of n-octane, n-nonane and ndecane in the ionic liquid 4-methyl-n-butylpyridinium tetrafluoroborate in the temperature range from 297 to 344 K. Their results were in good agreement with the experimental measurements. Twelve interaction parameters related to three structural groups, _CH2, pyridinium and BF4 were determined.

After its publication by Fredenslund et al. (1975), the UNIFAC (Uniquac Quasi-Chemical Functional Activity Coefficient) underwent a plethora of revisions and extensions which are outlined in reviews by Lei et al. (2008) and Castells et al. (1999).

The original UNIFAC, as stated by Lohmann and Gmehling (2001), presented the following advantages:

In an attempt to remedy these limitations, more advanced versions of the UNIFAC model were developed, the most important ones being UNIFAC (Dortmund) by Weidlich and Gmehling (1987) and UNIFAC (Lynby) by Larsen et al. (1987). The modified UNIFAC (Dortmund) differs from the original UNIFAC model in that it uses a different combinatorial part and it reliably takes into account the temperature dependence of group interaction parameters. Its developers introduced new van der Waals quantities as well. No thermodynamic model can claim as much popularity as UNIFAC (Do). This is attributed to the amount of research work and publications related to it in the last twenty years. Moreover, around fifty companies and

institutions work actively in the UNIFAC Consortium to support directly or indirectly its perfections. The Thermodynamics Research Unit, at the University of KwaZulu-Natal is part of this organization. Successes recorded in improving the predictability of properties using UNIFAC (Dortmund) are presented in publications by Gmehling and Schiller (1993), Hansen et al. (1991), Gmehling (1995), Gmehling et al.(1998), Gmehling et al.(2002), Gmehling et al.(2009), Lohmann and Gmehling (2001), Wittig et al.(2001) and Jakob et al. (2006). Recently, Prof. Gmehling`s group started to assess the predictive ability of UNIFAC (Do) for systems involving ionic liquids. The parameter matrix of this model has been expanded, allowing for the prediction of infinite dilution activity coefficients of:

It is clear that the parameter matrix remains very limited when one looks at the number of ions involved in the structure of ionic liquids. The major weakness of GCMs is their inability to deal with isomers, proximity effects and systems involving groups for which experimental data have never been compiled (Putnam et al. 2004).

The conductor-like screening model (COSMO) is a predictive method for thermophysical properties using a quantum chemical approach. Its two most widely used variants for infinite dilution activity coefficients in ionic liquids are COSMO-RS (The conductor-like screening model for real solvents), developed by Klamt (1995) and COSMO-SAC (The conductor-like screening model, solvation activity coefficients) (Lin and Sandler 2002). These two models involve statistical thermodynamics, along with quantum chemical calculation (Eckert and Klamt 2003). They require -profiles of molecules in the same manner as group contribution methods rely on group interaction parameters. A -profile is defined by Klamt and Eckert (2000) as a distribution function of the amount of surface having a screening charge density between and

?. COSMO-based models are parameterized for 9 elements so far: hydrogen, carbon, nitrogen, oxygen, fluorine, chlorine, bromine, iodine and sulfur. They rely on a very small

number of parameters (Eckert and Klamt 2003) which are not specific regarding molecules types or functional groups. This represents a great advantage as compared to GCMs which involve a large number of functional groups. Even components that have never been synthesized before can be studied since no experimental data are needed to carry out predictions as shown by Klamt et al. (1998). Long computation time and high computation costs are the major disadvantages of these COSMO-based models. In a paper discussing comparisons between COSMO-RS and GCMs, Grensemann and Gmehling (2005), taking into account another article to which Klamt himself contributed (Putnam et al. 2004) reveal the following:

This paper prompted a strong reaction from the developer of COSMO-RS (Klamt 2005) who found its conclusions biased in order to clearly favour the Modified UNIFAC (Do). From a neutral point of view, more time is required to confirm whether COSMO-RS is inferior or superior to GCMs (Klamt and Eckert 2008). More importantly, extensions are under way to improve both models. Infinite dilution activity coefficients of a large spectrum of solutes in some ionic liquids have been predicted using COSMO-RS. In a study on the removal of thiophene from diesel oil (Kumar and Banerjee 2009), COSMO-RS predictions of infinite dilution activity coefficient of alkanes, alk-1-enes and cycloalkanes in [HMIM] [PF6], [HMIM] [BF4], [MOIM] [Cl] and [EMIM] [Tf2N] are reported. The average absolute deviation of their predictions was found to be 12% with respect to experimental data. Larger errors are observed in a quantum chemical approach work by Sumon (2005) when predicting of toluene and

heptane in a large number of ionic liquids. Other similar predictive works (Banerjee and Khanna 2006, and Lei et al. 2007b) were in fair agreement with experimental measurements, exhibiting the same range of errors.

Various experimental methods exist for determining infinite dilution activity coefficients:

The two methods used in this work, are the most popular ones for ionic liquids. They are discussed here, with an emphasis on their suitability for this class of solvents. A useful review paper by Kojima et al. (1997) gives more details on other experimental techniques used for direct IDAC measurements.

In this technique, the solvent, used as stationary phase, is loaded onto the column. The solute, which is the mobile phase, is injected in a carrier gas through the column. The eluted solute is detected and its retention time, along with other experimental parameters, is used in an equation to compute the IDAC. Gas-liquid chromatography can be used for IDACs of volatile solutes in non-volatile or low volatility solvents. It is not applicable to systems involving a mixture of solvents. Table 2-4 summarizes the advantages and disadvantages of Gas-Liquid Chromatography.

Table 2-4: Advantages and disadvantages of the Gas Liquid Chromatographic method

In this method, a highly dilute solute is stripped from a solution by a constant inert gas flow under isothermal conditions. The vapour leaving the cell is periodically analyzed by gas chromatography. It is observed that the peak area depicting the solute concentration in the vapour phase decreases exponentially with time. Under this particular condition of exponential dilution, the infinite dilution activity coefficient of the solute in the solvent is related to the

decreasing rate of its corresponding peak area with time. The IGS method is used to measure

of volatile solutes in non-volatile or volatile solvents. Systems with solvent mixtures can be
investigated. The method is alternatively called the dilutor technique, as well as continuous gas

extraction technique (Vitenberg 2003; Dobryakov and Vitenberg 2006). Table 2-5 presents the advantages and disadvantages of this technique.

GC calibration is not required since only peak area ratios are involved in calculations

2.3. Advances in the design of IGS equipment 2.3.1. Major developments in the use of the IGSM

Since its establishment by Leroi et al. (1977), the IGSM underwent some improvements in terms of modernization of the analytical tool (GC), temperature and pressure sensors, achievement of isothermal conditions during experiments, etc. But the most important advance in this technique lies in a better understanding of factors affecting the accuracy of measurements provided by many research works. This resulted in various cell designs in order to suit different types of systems. Bao and Han (1995) sum up the major advances in the inert gas stripping technique as follows:

2.3.2. The number of cells required for IDAC measurements

Either one or two cells can be used to measure infinite dilution activity coefficients by the inert gas stripping method. The single cell technique is suitable for systems with low volatility solvents and relatively high volatility solutes. The double cell technique is required when the solvent is a high volatile compound or mixture. In this variant, a presaturation cell is used to saturate the stripping gas with the solvent before the solute stripping process. This prevents any transfer of the solvent from the liquid to the vapour phase which would lead to changes of the amount of solvent in the dilutor cell. The single cell technique is appropriate to systems involving ionic liquids since they are generally very high boiling compounds and non volatile. Krummen et al. (2002) reported infinite dilution activity coefficient data for n-alkanes and alk1-enes, cyclic hydrocarbons, aromatic hydrocarbons, ketones, alcohols, and water in the ionic liquids 1-methyl-3-methylimidazolium bis (trifluoromethylsulfonyl) imide, 1-ethyl-3- methylimidazolium bis (trifluoromethyl sulfonyl) imide, 1-butyl-3-methylimidazolium bis (trifluoromethylsulfonyl) imide, and 1-ethyl-3-methylimidazolium ethylsulfate in the temperature range between 293.15 K and 333.15 K. Activity coefficients at infinite dilution of alkanols in the ionic liquids 1-butyl-3-methylimidazolium hexafluorophosphate, 1-butyl-3- methylimidazolium methylsulfate, [BMIM][MeSO4], and 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide, [HMIM][Tf2N], were measured by Dobryakov et al (2008). Using the same method, Nebig et al. (2009) determined for n-alkanes and alk-1-enes in the

ionic liquids 1-butyl-1-methylpyrrolidinium bis (trifluoromethylsulfonyl) imide, 1-hexyl-1- methyl pyrrolidinium bis (trifluoromethylsulfonyl) imide and 1-methyl-1-octylpyrrolidinium bis (trifluoromethylsulfonyl) imide. Kato and Gmehling (2005a, b) presented infinite dilution activity coefficient data for seven solutes in the ionic liquids 1-butyl-3-methylimidazolium bis (trifluoromethylsulfonyl) imide and 1-ethyl-3-methylimidazolium bis (trifluoromethylsulfonyl) imide using the methods of gas liquid chromatography and the inert gas stripping technique. Their results show a good agreement between the two methods.

Thermodynamic equilibrium between the gas leaving the dilutor cell and the remaining liquid is instrumental in obtaining accurate infinite dilution activity coefficient data.To achieve this, three conditions must be met (Leroi et al. 1977):

Studies mentioned in the two previous sections threw light on these factors which affect the

For accurate measurements of IDAC, it is essential to take into account these factors when designing dilutor cells. The impact of each of these parameters is briefly explained in the light of expressions derived by Richon et al. (1980) which are reviewed in Chapter 3 of this thesis.

In the original version of the method by Leroi et al (1977) (See Figure 2-2), a fine porosity fritted glass was used as dispersion device. Recently constructed dilutor cells are generally provided with stainless steel capillaries with very small inner diameters. Stainless steel is known as a non corrosive material. To ensure that the total mass transfer area is large, the inert gas, generally helium or nitrogen, is dispersed into very small bubbles. Capillaries must be in reasonable number and well spaced to avoid any bubble coalescence. Dobryakov et al. (2008) designed a very small cell, of volume 5 cm³, with just a single capillary tube used as the dispersion device.

The liquid level in the cell must be high enough for sufficient contact time between the bubbles and the investigated solution. This is a very important condition in view of attaining the required thermodynamic equilibrium.

Efficient solute mass transfer from the liquid phase to the gaseous phase requires low inert gas flow rates as this results in longer contact times. The optimum flow rate depends on the system under investigation. It has been shown that when thermodynamic equilibrium has been attained between the two phases inside the dilutor cell, measured infinite dilution activity coefficients do not depend on the flow rate value. Additionally, the size of bubbles is affected by the flow rate, increasing up when the flow rate is increased. In previous works, experiments were performed with inert gas flow rates ranging between some tenths to tens of cm³ (Kutsuna and Hori 2008, and Krummen et al. 2002)

The smaller the bubble size, the more efficient is the mass transfer. In effect, when the inert gas is dispersed into the solution as small bubbles, the total mass transfer area is increased. If bigger bubbles are used, the height of the cell must be high enough to ensure a long residence time of the gaseous phase in the solution.

A high viscosity hinders mass transfer. Its other effect consists of reducing the bubble rise and consequently allowing larger contact times. The two effects with regards to mass transfer and equilibrium conditions in the cell compensate each other. However, more sophisticated features need to be incorporated in the design of the dilutor cell, more especially its stirrer, for very viscous mixtures (Richon et al. 1985).

When very high infinite dilution activity coefficient values have to be measured, large amounts of solute are stripped out of the solution in a very short period of time, since there are very weak interactions between the components involved in the mixture. If care is not taken, this will compromise the attainment of equilibrium and reduce the mass transfer extent as the contact time may be insufficient. It is not therefore surprising that the worst agreement between infinite dilution activity coefficient data obtained with the GLC method and the dilutor technique were observed for very high activity coefficients (Leroi et al. 1977). The designer should take into account the range of IDACs values the cell is supposed to deal with in order to tune other parameters such as the height and the dispersion device.

Various cell designs have been reported over the last forty years as part of the inert gas stripping set up for the determination of infinite dilution activity coefficient, Henry`s law constant and partition coefficient. The most efficient ones, taken from the open literature are reviewed. The various researchers who designed the cells discussed in this section reported a good agreement with infinite dilution activity coefficient data obtained by the GC method. And, reproducibilities better than 2% were obtained. However, the reliability seemed to be compromised when very

high values had to be measured. The other issue of concern is the determination of in

Leroi et al. (1977) used the pyrex glass cell represented in figure 2-2 to measure infinite dilution activity coefficient for n-hexane and benzene in ten different nonvolatile solvents, including Nmethyl-2-pyrrolidone (NMP), dimethylsulfoxide (DMSO), dimethylformamide (DMF), nitrobenzene, ethylene glycol and hexadecane. A solution of volume 25 cm³ could be accommodated by the still and an experiment lasted one to two hours. Solutes were introduced into the cell by means of a 10 syringe via the septum. Inert gas flow rates ranged from 50 to

150 cm³ .min^-1. To ensure accurate measurements, liquid drop entrainment was limited by a dead space above the solution. This gas phase volume was kept small enough to ensure accurate measurements. The dispersion device consisted of a fine porosity fritted glass disk as mentioned previously.

Richon et al. (1980) designed the dilutor cell shown in figure 2-3, similarly to the one constructed by Leroi et al. (1977). Their major improvements to the first cell include the following features:

They investigated infinite dilution activity coefficients of alkanes from C1 to C9 in hexadecane. Experiments undertaken concluded that the inert gas stripping method could be easily extended to Henry`s law constant measurements. For Henry`s law constants greater than 30 atm., their work showed the necessity to keep a very small and homogeneous vapour phase in the cell.

Figure 2-3: Equilibrium cell constructed by Richon et al. (1980)
A - glass still body, B - conical collector of gas outlet, C - gasket, D - plug, E - capillaries, F -
Teflon seal, G - magnetic stirrer, H - metallic ring used to adjust the depth of the conical
collector B in the still, I - tube for carrier gas inlet, J - gas outlet.

In this design, Richon and Renon (1980) abandoned the previous conical shape in favour of a simpler shape as shown in figure 2-4. A considerably reduced 1 cm high gas phase is kept above the solution inside the dilutor cell. Their cell was used to determine infinite dilution activity coefficients of light hydrocarbons in n-hexadecane, n-octadecane and 2, 2, 4, 4, 6, 8, 8- heptamethylnonane.

Figure 2-4: Dilutor cell used by Richon and Renon (1980).
A - vapour phase outlet, B - inert gas inlet, C - Teflon seal, D - plug, E - O-ring, F -
capillaries, G - glass still body, H - baffles, I -magnetic stirrer.

Legret et al. (1983) used the cell below (figure 2-5) to determine partition coefficients which are related to activity coefficients at infinite dilution. Their study involved some alkanes as solutes in the methane/n-decane system. The pre-saturator and the dilutor cell were fitted with 20 and 50 capillaries respectively. The capillary inner diameter was 0.3 mm for the pre-saturation cell and 0.1 mm for the dilutor cell. Both cells contained 40 cm³ of solvent.

B - body, C - cap, Ca - capillaries, H - capillary holder, M - magnet, V - O?-ring

Infinite dilution activity coefficient measurements of organic solutes in fluorinated ionic liquids by gas-liquid chromatography and the inert gas stripping method

2.2. Infinite dilution activity coefficients

2.3.2. The number of cells required for IDAC measurements