Short Commentary - (2021) Volume 10, Issue 6
Received: 03-Jun-2021 Published: 24-Jun-2021
Inverse gas chromatography (IGC) at infinite dilution is one of the most used techniques to characterize the physicochemical and surface properties of solid substrates. The surface specific free energy of model organic molecules adsorbed on solid surfaces, as well as their dispersive component of the surface energy was determined by IGC technique since 1982. The specific surface enthalpy and entropy of adsorption of polar molecules derived from the determination of the variations of the specific free energy of interaction of such molecules with the solid particles as a function of the temperature. Using the concept of the donor and acceptor numbers of electrons of polar molecules, the acid base constants KA, KD of solid surfaces can be determined by an empirical relationship. Many methods and models were used in the literature to quantify the surface properties of solid materials. However, many irregularities were found when applying the different methods to various solid substrates. The conclusions concerning the dispersive surface energy and the acid base properties in Lewis terms of many solids revealed some errors committed by using the different models and methods of IGC.
• Specific free energy of adsorption • Dispersive surface energy • Enthalpy and entropy of adsorption • Acid base constants • Lewis concept • Hamieh model
Inverse gas chromatography (IGC) at infinite dilution is the most important technique to characterize the surface properties of solid substrates such as oxides, polymers or copolymers in bulk or adsorbed phases IGC. This powerful technique first used by Conder and Young in 1970’s [1-5] took an important development after 1980 where much research was devoted to the physicochemical determination of oxides, glass fibers and polymers [6-13]. Many specific thermodynamic variables were evaluated, especially, the free energy, the enthalpy and entropy of adsorption of organic model molecules on the solid substrates. Many studies treated the second order transition temperatures of polymers and copolymers in both the bulk and adsorbed phases.
Polar molecules and n-alkanes of known properties are injected in the column containing the solid. The retention times of these probes, measured at infinite dilution, allow us to determine the interactions between the organic molecules and the studied solid, if we suppose that there are no interactions between the probe molecules themselves. Measurements were carried out with a chromatograph equipped with a flame ionisation detector of high sensitivity. The retention data are obtained with a stainless steel column of length 15 to 60 cm and 2 to 5 mm internal diameter packed with 1 to 2 g of solid powders of fibres. The net retention volume Vn was calculated from:
Vn=jD(tR-t0) (1)
where tR is the retention time of the probe, t0 the zero retention reference time measured with a non-adsorbing probe such as methane, D the flow rate and j a correction factor taking into account the compression of the gas [14].
The free energy of adsorption -ΔGa0 of n-alkanes is given by:
-ΔGa0=RT ln Vn+C (2)
Where R is the ideal gas constant, T the absolute temperature and C a constant depending on the reference state of adsorption. In the case of n-alkanes, ΔGa0 is equal to the free energy of adsorption corresponding to dispersive interactions ΔGad only.
If polar probes are injected into the column, specific interactions are established between these probes and the solid surface and ΔGa0 is now given by:
ΔGa0=ΔGad+ΔGasp (3)
Where ΔGasp refers to specific interactions. By plotting ΔG_a^spof the polar molecules as a function of the temperature, we can deduce the specific enthalpy ΔHasp from:
ΔGa sp=ΔHasp-TΔSasp
Polar molecules used to determine the specific interactions with the solid substrates are characterized by their donor (DN) and acceptor (AN) numbers [15]. The concept of donor acceptor interactions is an extension of the Lewis acid base reactions, dealing with coordinate bonds which are formed by sharing a pair of electrons between donor and acceptor species. Knowing ΔHasp of the various polar molecules, we will be able to determine the acidic constant KA and basic constant KD, the two constants characterizing the solid substrate, using the following relatio nship [16]:
-ΔHasp=(KA DN+KD AN) (5)
And plotting (-ΔHasp/AN) as a function of (ND/NA), according to equation (5). Model organic solvents are used in IGC at infinite dilution, such as n-alkanes (from n-pentane to n-dodecane) and polar organic molecules (toluene, methanol, ethanol, ethyl acetate, acetone, diethyl ether, benzene, dichloromethane, chloroform, tetrachloromethane, acetonitrile, etc…) as probes to examine the surface properties of solid materials. The methods proposed in literature used some thermodynamic parameters of organic molecules as the vapor pressure, P0 [8,9], the dispersive component of the surface tension, γld [17], the boiling point, B.P. [18], the deformation polarizability, α0 [19] or the standard enthalpy of vaporization, ΔH(vap.)0, [20] and the topological index χT concept [21,22].
All the above methods are based on the linearity of the variations the free energy change of adsorption as a function the intrinsic thermodynamic parameters of n-alkanes and polar probes. Hamieh in a recent paper [23] showed a linear dependency of any thermodynamic parameters yi as a function of another physicochemical variable xj of n-alkanes. This linearity can be represented by:
yi (xj )=ai xj+bi,i≠j (6)
Where ai and bi are constants relative to n-alkanes, yi and xj can be one of the above parameters (P0, γld, B.P., α0, ΔH(vap.)0, χT, …).
Any used couple (xj, yi) will lead to the specific interactions ΔGasp between the polar solvents and the solid surfaces. The deduction of ΔHasp from the variation of ΔHasp allowed to obtain the acid base constants of the solids. However, by applying the different IGC methods, the obtained results presented large deviation. There is no universal method that can be used to better quantify the true values of the surface physicochemical properties of any solid substrates.
By using the well-known relationship of Fowkes [24], Dorris and Gray [25] correlated the adhesion work Wa to the free enthalpy of adsorption by the help of the surface area a of adsorbed molecule and the geometric mean of the dispersive components of the liquid solvent γ ld and the solid γsd.
ΔGa0=Na Wa=2Na √(γld γsd ) (7)
Where N is the Avogadro’s number. Dorris and Gray determined the dispersive component of the surface energy of a solid by supposing the surface area of methylene group a-CH2- equal to 6 Å2 independently of the temperature.
Later, Schultz et al. [17] used the same concept of Fowkes and proposed the determination of the dispersive component of the surface energy of a solid substrate by plotting the variation of RTlnVn versus 2Na (γld )1/2 o f n-alkanes and by supposing the surface areas a of molecules constant at any temperature and obtained a straight line:
RT ln Vn=(γsd )1/2 [2Na (γl d )1/2 ]+C (8)
Where C is constant. The slope of the alkane straight line given by relation (48) will give the value of (γsd )1/2 and therefore γsd of the solid. These two methods were criticized by Hamieh’s works [26-31] who demonstrated that the surface area of organic molecules varies as a function of the temperature and showed an important dependence of the surface area of molecules and also the methylene group a-CH2- versus the temperature. Hamieh et al. proposed other molecular models of the surface areas of organic molecules and obtained other values of the dispersive surface energy of solid materials.
Consequently, the results published by several scientists in literature by using the methods based on the Fowkes relation should be corrected.
The acid base constants KA and KD of solid surface were calculated by using the relation (5) in the following form:
(-ΔHasp)/AN=KA (DN/AN)+KD (9)
The representation of (-ΔHa sp)/AN versus DN/AN will give in general a straight line of slope KA and intercept KD. However, in several cases, Hamieh et al. [26,29,31] proved the non-validity of equation (5) and introduced a third parameter K reflecting the amphoteric character of solid substrates according to:
(-ΔHasp)=KA DN+KD AN – K DN AN (10)
The constants KD, KA and K can be obtained by resolution of the linear system (10) by using N organic solvents and give more accurate description of the acid base character of the solids.
We proposed in this section a new general method for the determination of surface physicochemical properties of solid substrates. For n-alkanes (alk.), for example, we gave the following free energy of adsorption:
ΔGa0 (alk.)=A (B.P.)(alk.)+B α0,l (alk.)+C ΔHvap.0 (T)(alk.)+D χT (alk.)+E logP0 (alk.)+F
For polar molecules (pol.), one obtained the specific values of free energy of adsorption:
ΔGasp (pol.)=ΔGa0 (pol.)-A (B.P.)(pol.)-B α0,l (pol.)-C ΔHvap0 (T)(pol.)-D χT (pol.)-E logP0 (pol.)-F
Where ΔGa0 (alk.) and ΔGa0 (pol.)are determined experimentally from the values of RTlnVn of the various molecules, whereas, the constants A, B, C, D, E and F are determined by the physicochemical characteristics of the organic molecules.
Now the obtained values of ΔGasp (pol.) of the polar solvents adsorbed on the solid surfaces will describe more accurately the solid surface properties.
In this editorial note, we presented the different methods of the inverse gas chromatography technique at infinite dilution by showing some irregularities resulting from the use of Fowkes relation, Dorris Gray and Schultz methods. The values of the dispersive component of the surface energy, the specific free energy of adsorption, the specific enthalpy and entropy of adsorption; and the acid base constants of silica particles should be reviewed and corrected on the light of the new findings proposed by hamieh et al. Finally, a new general essay was proposed to better quantify the acid base properties of solid surfaces.
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