Inverse Gas Chromatography

Inverse Gas Chromatography Zygfryd Witkiewicz, Military University of Technology, Warsaw, Poland Piotr Słomkiewicz, Jan Kochanowski University, Kielce, Poland © 2018 Elsevier Inc. All rights reserved.

Inverse Gas Chromatography The Characteristics of Adsorbent Surface and Test Compound Interaction Acidic-Basic Properties Determining Adsorption Isotherms Isosteric Enthalpy of Adsorption Solubility Parameter Flory–Huggins Interaction Parameter References Further Reading

2 3 5 7 8 9 9 9 10

Nomenclature a aCH2 AN B11 C DN F DGda DGsp a DGads DGE DHi DHads DHE h hl j Ka Kb m M1 M n nD NA PD PDP PDS p p0 pi p01 R DSads DSE Ss Sls Sp SBET

Number of adsorbed test compound moles (mmol g1) Cross-section area of a CH2 group (m2) Acceptor number (J mol1) Second virial coefficient of the solute Constant value Donor number (J mol1) The volumetric flow-rate of carrier gas in the column (cm3 min1) Dispersive component of adsorption free energy (J mol1) Specific component of adsorption free energy (J mol1) Standard adsorption free energy (J mol1) Free energy of mixing test compound with stationary phase (J mol1) Isosteric adsorption enthalpy (J mol1) Standard adsorption enthalpy (J mol1) Standard enthalpy of mixing test compound with stationary phase (J mol1) Peak height (mV) Height of part l of peak (mV) James-Martin compressibility correction factor Acidic characteristic of solid Basic characteristic of solid Adsorbent mass in the column (g) Molar mass of the solute (g) Molar mass (g) Number of test compound moles injected into the column (mol) Refractive index Avogadro number Deformation polarization (cm3 mol1) Deformation polarization of test compound (cm3 mol1) Deformation polarization of the stationary phase (cm3 mol1) Pressure at column outlet (Pa) Pressure at column inlet (Pa) Partial pressure (Pa) Saturated vapor pressure of the solute (Pa) Universal gas constant (J mol1 K1) Standard adsorption entropy (J mol1) Standard entropy of mixing testing compound with stationary phase (J mol1) Area bounded by the height between the outflow of the non-adsorbing gas and the diffuse side of the chromatogram (mV min) Area of l part of total adsorption surface (mV min) Adsorbate peak area (mV min) Specific surface BET (m2 g1)

Encyclopedia of Analytical Science, 3rd Edition

https://doi.org/10.1016/B978-0-12-409547-2.13976-9

1

2

Inverse Gas Chromatography

t’R t0 tD T VN 0 VN 0 VN, n Vg V01 V02 Wda Wsp a XSECT

Adjusted retention time (min) Retention time of unadsorbed gas (min) Time of measurement completion (min) Column temperature (K) Net retention volume (cm3) Adjusted retention volume (cm3) Adjusted retention volume of n-alkane (cm3) Specific retention volumes of the measured substance (cm3) Molar volume of the solute (cm3 mol1) Molar volume of the test substance (cm3 mol1) Dispersive component of work of adhesion (mJ) Specific component of work of adhesion (mJ) Cross section area of adsorbate molecule (m2)

Greek letters x1 12 g ds g sp s gCH2 d g dl gi r1 r2 u

Flory–Huggins interaction parameter Dispersive component of surface energy (mJ m2) Specific component of surface energy (mJ m2) Dispersive free energy of a CH2 group (mJ m2) Dispersive energy of test molecule (mJ m2) Activity coefficient of test substance in the stationary phase Solute density (cm3 g1) Density of investigated materials (cm3 g1) Degree of coverage (dimensionless)

Inverse Gas Chromatography Gas chromatography is, first and foremost, known as a chemical analysis method. It is applied to separate mixtures of compounds into particular components, also for their detection, identification and quantitative determination. For this reason, a mixture is injected into the column in which the known packed material is already present. Following physicochemical interaction of the column packing with the molecules of chromatographed substances, the substances undergo separation and are registered in the form of peaks, known as a chromatogram. Taking into account the physicochemical interactions of stationary phase in a column with chromatographed substances it is possible to investigate the interactions and the properties of stationary phase. For that an investigated material is placed into a column and known (test) substance is chromatographed. Both peak shape and retention parameters of the test substance are connected with the physicochemical properties of the substance present in the column. Physicochemical properties of the substance can be determined, as well as interaction character with test chromatographic substance, by using peak parameters. Analyzing these interactions enables specification of certain features concerning the chromatographic system and, above all, the substances placed in the columns (solids and liquids). As a result, gas chromatography utilized for physicochemical tests is named inverse gas chromatography (IGC). Fig. 1 illustrates the principle with respect to inverse gas chromatography method as compared to the analytical gas chromatography. Gas chromatograph is a relatively precise device due to the necessity to conduct the separation process in specifically defined temperature, pressure, and carrier gas flow conditions. As a consequence, it is a convenient system for accurate measurement of certain thermodynamic and physicochemical values which are connected with the chromatographic process (partition constant, solubility, adsorption, intermolecular interactions) or the phenomena associating this process (diffusion, phase transition). IGC does not differ from conventional analytical gas chromatography in terms of the chromatography process mechanism. It can use typical slightly modified chromatographs, although chromatographs suitable only for IGC are available. Due to the concentration of the test compound in the chromatographic process, one can distinguish the following: 1. Inverse chromatography in finite concentration of the test compound—it is applied in order to determine adsorption isotherms and to describe surface properties together with the porosity of the stationary phase. It is applied also to determine adsorption enthalpy and entropy together with other thermodynamic functions. 2. Inverse chromatography at infinite dilution of the test compound, that is, test compound vapors (with concentration value at the stationary phase towards zero) are injected into the column. At such concentration level, the test compound interacts merely


3

Detector signal

GC chromatogram

mixture

GC analytical column

Retention time

IGC peak

IGC column with adsorbent

Detector signal

test substance

Retention time Fig. 1 Comparison between GC and IGC columns and the relevant peaks.

with highly active areas on the solid surface. The obtained parameters of the test compound retention facilitate calculating, above other things, dispersive components of free surface energy or the component of specific adsorption energy. In the case of gasliquid inverse chromatography, the values determining the properties of liquids are determined. They are described with the Flory–Huggins interaction parameter or the solubility parameter. Test compound concentration values on the stationary phase surface are calculated as a coverage degree ywith the following equation: y¼

n XSECT NA m SBET

Specific retention volume is a thermodynamic value which characterizes the interaction of column packing with the testing substance.1 Actual retention volume, Vg is calculated with the following formula: Vg ¼

VN T j T ¼ FtR0 273:15 m 273:15 m

whereas the James-Martin compressibility factor j includes pressure difference at column inlet/outlet: 3 2 2 p 1 3 6 p0 7 j ¼ 4 3 5 2 p 1 p0

The Characteristics of Adsorbent Surface and Test Compound Interaction The interaction force of substance placed into column can be determined with the use of the proper test substance. Two main interaction types can be distinguished between the test material in the column and the injected test compounds. These are: London dispersion interactions (interactions between momentary induced dipole and induced dipole) and specific interactions (resulting from the interactions of polarized function groups). The above-mentioned interactions can be expressed with the use of free adsorption energy(DGa), free surface energy (gs), and adhesion work (Wa). Free adsorption energy is a sum of dispersive component DGda and specific DGsp a free adsorption energy:

4

Inverse Gas Chromatography DGa ¼ DGda þ DGsp a Free surface energy is a sum of dispersive component gds as well as specific gsp s surface energy: gs ¼ gds þ gsp s Adhesion work is a sum of dispersive component Wda and specific Wsp a adhesion work: Wa ¼ Wad þ Wasp

Free adsorption energy values in the conditions of infinite dilution of test substance can be calculated with the Dorris–Gray, Schultz, and polarization methods. They consist in injecting n-alkanes into the column with the investigated substance together with the measurement of their retention parameters. In the Dorris–Gray method,2,3 there are only dispersive interactions between n-alkanes and the adsorbent in the column. In this case, dispersive free adsorption energy of the methylene group DGCH2 can be calculated from the direction coefficient concerning the dependence of free adsorption energy DGa of the n-alkane from the number of carbon atoms in the molecule (Fig. 2). Dispersive free adsorption energy of a single CH2 group can be calculated with the equation below ! 0 VN, nþ1 CH2 DG ¼ RT ln 0 VN , n According to ref. [4] adhesion work (Wa) of mutual interaction of the stationary phase with CH2 groups depends on dispersive free surface energy of the stationary phase as well as CH2 groups: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi WaCH2 ¼ 2 gs d gCH2 d According to the Dorris–Gray method, dispersive free adsorption energy of the methylene groupDGCH2 and adhesion work WaCH2 are given by the following equation: DGCH2 ¼ NA aCH2 Wa

CH2

and after transition: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DGCH2 ¼ 2 NaCH2 gs d gCH2 d þ C The value of gCH2 d depends on temperature according to the following equation:

Fig. 2 The diagram for determining dispersive free energy by the Dorris–Gray method.


5

gCH2 d ¼ 35:6 0:058ð293 T Þ 0

Fig. 2 shows RT ln VN ¼ f(the carbon number of n - alkane). The value of inclination coefficient of the graph towards the axis of abscissae enables determination gs d for the tested stationary phase from the equation below 0 12 0 V RT ln VN0, nþ1 C 1 B slope2 N, n C ¼ B gs d ¼ A 2 4gCH2 @ NaCH2 4 N ðaCH2 Þ2 gCH2 In the Schultz method,5,6 free adsorption energy comprises only the dispersive part: 0 DGa ¼ DGda ¼ RT ln VN, n þ C The Schultz method also uses the adhesion work equation (Wa) together with free adsorption energy of the methylene group, which is analogical to the Dorris–Gray method in describing the mutual interaction of the examined substance (adsorbent) with the test one DGCH2 qffiffiffiffiffiffiffiffiffiffi Wa ¼ 2 gds gdl DGCH2 ¼ NaCH2 Wa Cross-section area aCH2 of the alkane molecule is provided with the following equation: 2 M 3 aCH2 ¼ 1:09 1014 rNA The transition of the three equations enable obtaining an expression in the linear form, from which gs d can be determined. qffiffiffiffiffiffi qffiffiffiffiffiffi 0 RT ln VN, n ¼ 2NA aCH2 gs d gl d þ C qffiffiffiffiffi 0 The dependence diagram RT ln VN, n ¼ f aCH2 gdl is a straight line. The inclination coefficient facilitates the determination of the value of dispersive free surface energy at the stationary phase. Polar substances which are to be injected into the column with the test substance in identical conditions of the conducted measurements will not be in the n-alkane line. The vertical distance on 0 the axis RT ln (VN, n) from the n-alkane line to the point of polar substance is a component of specific adsorption energy DGsp a. Therefore, the Schultz method enables the determination of gs d and DGsp a. The Polarization method6 of calculating adsorption energy consists in injecting a series of n-alkanes to the column to determine the following dependence: 0 0 RT ln VN, n þ C ¼ C PDP PDS 0

whereas constants C and C depend on the selected reference system. Deformation polarization PD is a characteristic feature of the test substance (alkane) and can be calculated with the equation given below: PD ¼ 0

n2D 1 M n2D þ 1 r1 0

The dependence diagram RT ln (VN, n) ¼ f(PDP) is a straight line. Inclination coefficient of this straight line is C PDP and it is proportional to the dispersive interactions. Vertical distance between the point of the polar substance and the n-alkane line is specific adsorption energy DGsp a (Fig. 3).

Acidic-Basic Properties IGC allows testing acidic-basic properties of solids. For this reason, polar substances with known donor-acceptor properties are applied. They can be acidic (electron acceptors), basic (electron donors) or amphoteric in character. A modified Gutmann equation7,8 is used for calculations:

6


Fig. 3 Diagram for determining the specific free energy (DGSP) by the Schultz and the Polarization method.

DGsp a ¼ DNKa þ ANKb Donor number DN, given in kJ mol1 is described as the negative enthalpy of forming an addition compound of a given base (donor) with Lewis acid SbCl5 (acceptor) in a 103 M solution of 1,2-dichloroethane. Acceptor number AN is, in turn, defined as a non-dimensional number corresponding to spectrum diffraction NMR3I for triethylphosphine oxide (standard donor) diluted in the tested acceptor. It is the number given in non-dimensional conventional units (hexane ¼ 0; 1,2-dichloroethane ¼ 100). sp

DGa DN Ka þ Kb ¼ AN AN sp DN a While creating the dependence diagramDG from the directional coefficient of the AN ¼ f AN , a constant Ka can be calculated sp a axis (Fig. 4). diagram; in turn, the value Kb can be calculated using the intersection with theDG AN The ratio KKba facilitates specifying the character of the test surface. If the ratio is KKba > 1, then the surface is basic (donor properties prevail over the acceptor ones). If, however, the ratio is KKba < 1, then the surface is acidic. On the other hand, if KKba 1, then the surface is amphotheric.9

Fig. 4 Diagram for determining the acidic-basic properties.


7

Determining Adsorption Isotherms Adsorption isotherms are determined with the peak profile, which is also named as division peak one, and the peak maximum method. In the peak maximum method, various volumes of test substance are dosed into the column, and sorptive surface, which corresponds to the peak, is utilized. Each peak corresponds to the isotherm point, whereas the dependence ai ¼ f (pi), which corresponds to the series of dosed samples, is a function of adsorption isotherm. The peak maximum method10 consists of the determination of adsorption ai of the test substance i when the equilibrium concentration of the compound at the gas phase is ci and can be expressed by the following equation: 0

dai VN ¼ dci m According to ref. [10], complete surface between the non-adsorbing peak and the diluted adsorption peak (the surface between ABCD point in Fig. 5A), which is given the name of total adsorption surface Ss can be expressed with: ðh Ss ¼ ðtD t0 Þdh 0

On the basis of total adsorption surface, defined in such manner, the equation below can be applied in order to determine the number of moles as regards the adsorbed test compound ai: ai ¼

nSs mSp

Calculating equilibrium pressure corresponding to the number of moles concerning the adsorbed test compound can be performed on the basis of the following: pi ¼

nh RT FSp

Injection of adsorbate

(B)

C

Voltage [mV]

B

SS h

D

A t0

C

B

Time [min]

tD

Voltage [mV]


(A)

Unadsorbed gas

Unadsorbed gas

Peak surface Sp of the test compound is illustrated in Fig. 5B. The method of peak division enables determining adsorption isotherm on the basis of one chromatographic peak. The manner of conducting calculations is described in ref. [11]. The application of the peak division method requires splitting the whole adsorption surface Ss into parallel parts to the basic chromatogram line (Fig. 6A) as well as measuring the surface area of each segment. The surfaces of particular segments meet the dependence:

Sp h

D

A t0

Time [min]

tD

Fig. 5 Depiction of the application of the maximum peak method to calculate the values of ai and pi to determine the isotherm. (A) total adsorption surface area, Ss, that is, the area between the points A, B, C, and D; (B) total surface area of the chromatographic peak, Sp.


(B)

C

B Voltage [mV]

I10 I9 I8 I7 I6 I5 I4 I3 I2 I1

A t0

C

B

I10 I9 I8 I7 I6 I5 I4 I3 I2 I1

Voltage [mV]


(A)

Unadsorbed gas


Unadsorbed gas

8

SS h

SIS A

D Time [min]

t0

tD

Time [min]

h

D tD

Fig. 6 The illustration of applying the peak division method to calculate the value for drawing the isotherm. (A) The division of the adsorption surface area, Ss, into segments parallel to the base line, where SIs is segment area corresponding to part I of total adsorption surface area; (B) the division of the total height, h, of the adsorption peak into segments, where l is the height of the corresponding segment of the total chromatographic peak.

Ss ¼

X PI

S 1 Is

The number of moles of the adsorbed test compound aiI can be calculated with the use of the equation given below: P n I1 SIs aiI ¼ mSp Partial pressure piI is calculated through dividing the height of chromatographic peak into I parts (Fig. 6B), according to the following equation: X h¼ PI h 1 I

and thus the equilibrium pressure equation is given by: piI ¼

n

PI

1 hI RT FSp

The calculations of partial pressure piI as well as the number of moles as regards the adsorbed test compound aiI enables obtaining dependence ai ¼ f (pi), which is the function of the adsorption isotherm. The number of points determining the isotherm depends on the selected number of adsorption area division into I-segments.

Isosteric Enthalpy of Adsorption Isosteric enthalpy of adsorption, DHi, can be determined by IGC, based on the changes in retention times or retention volumes with column temperature, employing the Clausius–Clapeyron equation for the following calculations12: 0 V d ln TN 2 DHi ¼ RT dT It is reasonable to use the Clausius–Clapeyron equation for calculating the isosteric enthalpy of adsorption as long as the equilibrium pressures are low (within Henry’s law region) and the measurement temperatures are fairly close. Isothermal chromatographic measurements must be undertaken with changes of column temperature of 10 K at most.


9

Partition coefficient, K, of the solution between test substance and a stationary phase is the only retention mechanism between the liquid deposited on the solid carrier and the gaseous phase. In such a case, the K value can be calculated using the specific retention value: K ¼ Vg

T r1 273:15

Thermodynamic partition constant, Ki, has to be employed for calculating adsorption free energy of any adsorbate, which differs in nature from the chromatographic partition constant, K. Actually, the thermodynamic partition coefficient, Ki, is the ratio of partial pressure of the chromatographed solute pi and activity coefficient gi. For designing chemical processes, thermodynamic Ki values are usually expressed as: Ki ¼ gi p01 Ki and activity coefficient values are used for calculating other magnitudes and thermodynamic quantities. Partition coefficient Ki can be correlated to thermodynamic parameters of the stationary phase with the following equations: DGads ¼ RT ln VN þ C d ln Ki DHads ¼ R 1 dT DSads ¼

1 ðDHads DGads Þ T

Solubility Parameter Partition and activity coefficients are used for determining excess thermodynamic functions of chromatographed substances on the stationary phase: free energy, DGE, enthalpy, DHE, and entropy, DSE. The values of these thermodynamic functions characterize intermolecular interactions in the dissolution process. They can be calculated using the following dependencies: DGE ¼ RT ln Ki d ln g DHE ¼ R 1i dT DSE ¼

1 ðDHE DGE Þ T

Flory–Huggins Interaction Parameter IGC can be utilized in determining solubility parameter of high-molecular non-volatile substances, used as a stationary phase.13,14 Flory–Huggins interaction parameter w1 12 between the tested polymer (polymer mixture) and a series of purposefully selected test compounds is described with the following equation: ! 273:15R p0 r V0 1 w12 ¼ ln 0 0 0 1 B11 V10 þ ln 1 1 10 RT r2 V2 p1 V g M1 These interactions can be either weak or strong, which is specified by the parameter value w1 12, which can take the values below or above zero. Negative value (w1 12 < 0) means that the polymer-test compound system parts strongly interact with each other. 1 A positive value w1 12, close to zero (w12 > 0) indicates weak interactions. The parameters determined by the described dependencies of IGC have great importance in practical studies of the properties of solids and non-volatile liquids. Among these are adsorbents, catalysts, abrasive materials, liquid crystals and lubricants.15,16. There are also attempts described which concern inverse liquid chromatography. The interactions between investigated material and test substance are however much more complicated than in gas chromatography due to presence of active liquid mobile phase.

References 1. Conder, J. R.; Young, C. L. Physicochemical Measurement by Gas Chromatography; John Wiley & Sons: Chichester, 1979. 2. Dorris, G. M.; Gray, D. G. Adsorption of N-alkanes at Zero Surface Coverage on Cellulose Paper and Wood Fibers. J. Colloid Interface Sci. 1980, 77, 353–362.

10

3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.


Vukov, A. J.; Gray, D. G. Properties of Carbon Fiber Surfaces. Inverse Gas Chromatography. ACS Symp. Ser. 1988, 391, 168–184. Fowkes, F. M. Attractive Forces at Interfaces. Ind. Eng. Chem. 1964, 56, 40–52. Schultz, J.; Lavielle, L.; Martin, C. The Role of the Interface in Carbon Fibre-Epoxy Composites. J. Adhes. 1987, 23, 45–60. Schultz, J.; Lavielle, L. Interfacial Properties of Carbon Fiber-Epoxy Matrix Composites. Inverse Gas Chromatography Characterisation of Polymers and Other Materials. ACS Symp. Ser. 1989, 391, 185–202. Voelkel, A. Inverse Gas Chromatography in the Examination of Acid–Base and Some Other Properties of Solid Materials. Stud. Surf. Sci. Catal. 1996, 99, 465–477. Lara, J.; Schreiber, H. P. Specific Interactions and Adsorption of Film-Forming Polymers. J. Coating Technol. 1991, 63, 81–88. Voelkel, A.; Adamska, K. Properties of Materials as Determined by Inverse Gas Chromatography. Ann. UMCS Chem. 2009, 64, 169–183. Paryjczak, T. Gas chromatography in adsorption and catalysis; Warszawa, PWN, Ellis Horwood Limited Publisher: Chichester, 1986. Słomkiewicz, P. M. Determination of Adsorption Equilibrium of Alcohols and Alkenes on a Sulfonated Styrene Divinylbenzene Copolymer. Adsorption Science & Technology 2006, 24 (3), 239–256. Witkiewicz, Z.; Hetper, J. Chromatografia gazowa; Wydawnictwa Naukowo Techniczne (WNT): Warszawa (Warsaw), 2009. Milczewska, K.; Voelkel, A. Characterization of the Interactions in Polymer–Polymer Systems by Inverse Gas Chromatography. J. Chromatogr. A 2002, 969, 255–259. Voelkel, A. Inverse Gas Chromatography: Characterization of Polymers, Fibers, Modified Silicas, and Surfactants. CRC Rev. Anal. Chem. 1991, 22, 411–439. Strzemiecka, B.; Voelkel, A.; Zie˛ ba-Palus, J.; Lachowicz, T. Assessment of the Chemical Changes During Storage of Phenol-Formaldehyde Resins Pyrolysis Gas Chromatography Mass Spectrometry, Inverse Gas Chromatography and Fourier Transform Infrared Methods. J. Chromatogr. A 2014, 1359, 255–261. Fall, J.; Voelkel, A. Inverse Gas Chromatography and Other Chromatographic Techniques in the Examination of Engine Oils. J. Chromatogr. A 2002, 969, 181–191.

Further Reading Paryjczak, T. Gas Chromatography in Adsorption and Catalysis, PWN, Warszawa; Ellis Horwood Limited Publisher: Chichester, 1986. Dong, S.; Brendle, M.; Donnet, J. Study of Solid Surface Polarity by Inverse Gas Chromatography at Infinite Dilution. Chromatographia 1989, 28, 469–472.