Inverse gas chromatography standard solutions, device and method

Abstract

The invention relates to a standard solution for inverse gas chromatography and/or surface energy analysis; a volumetric container for preparing such a standard solution; a method of preparing such a standard solution for inverse gas chromatography and/or a surface energy analysis and a method of probing a solid sample. The standard solution comprises a series of three or more compounds of increasing carbon chain length of general formula (I): R—X wherein: for the three or more compounds R is a series of alkyl, a series of alkenyl or a series of alkynyl groups of increasing carbon chain length; and for all three or more compounds X is H, OH, CO.sub.2H, C(O)H, C(O)CH.sub.3, NH.sub.2, SH or halogen; and the relationship between carbon chain length and volume of the compounds of increasing carbon chain length of general formula (I) is determined by the following formula.

Claims

1. A standard solution for inverse gas chromatography and/or surface energy analysis comprising a series of three or more compounds of increasing carbon chain length of general formula (I):
R—X wherein: for the three or more compounds R is a series of alkyl, a series of alkenyl or a series of alkynyl groups of increasing carbon chain length; and for all three or more compounds X is H, OH, CO.sub.2H, C(O)H, C(O)CH.sub.3, NH.sub.2, SH or halogen; and the relationship between carbon chain length and volume of the compounds of increasing carbon chain length of general formula (I) is determined by the following formula: $\mathrm{Relative}{\mathrm{Volume}}_x=\frac{{\mathrm{MW}}_x\times P_y^0\times {\mathrm{Area}}_y\times {\mathrm{Density}}_y}{{\mathrm{MW}}_y\times P_x^0\times {\mathrm{Area}}_x\times {\mathrm{Density}}_x}\pm 20\%$ wherein: Relative Volume.sub.x is the volume of a specific compound x in the series relative to the volume of compound y that has the shortest carbon chain length in the series; MW.sub.x is the molecular weight of the specific compound x; P.sup.0.sub.x is the vapour pressure of the pure specific compound x at a given incubation temperature; Area.sub.x is the cross-sectional area of the compound x; Density.sub.x is the density of x; MW.sub.y is the molecular weight of the compound y; P.sup.0.sub.y is the vapour pressure of compound y at the given incubation temperature; Area.sub.y is the cross-sectional area of compound y; and Density.sub.y is the density of compound y.

2. A standard solution for inverse gas chromatography and/or surface energy analysis according to claim 1, wherein R is a series of n-alkyl groups of increasing carbon chain length, X is H, the incubation temperature is 25±1° C. and the relationship between carbon chain length and volume of the compounds of increasing carbon chain length of general formula (I) is determined by the following formula:
Relative Volume.sub.x=3.33.sup.x-yVolume.sub.y±15% wherein x is the number of carbons in the carbon chain of the specific compound x; y is the number of carbons in the carbon chain of compound y with the shortest carbon chain length; and Volume.sub.y is the volume of the compound y.

3. A standard solution for inverse gas chromatography and/or surface energy analysis according to claim 2, wherein the standard solution comprises: (i) from 0.85 to 1.15 parts by volume of compound y; (ii) from 2.83 to 3.83 parts by volume of compound y+1; (iii) from 9.43 to 12.75 parts by volume of compound y+2; wherein y is an integer selected from 5 to 38 and is the number of carbons in the carbon chain of compound y.

4. A standard solution for inverse gas chromatography and/or surface energy analysis according to claim 3, wherein the standard solution further comprises: (iv) from 31.39 to 42.46 parts by volume of compound y+3.

5. A standard solution for inverse gas chromatography and/or surface energy analysis according to claim 4, wherein the standard solution further comprises: (v) from 104.52 to 141.41 parts by volume of compound y+4.

6. A standard solution for inverse gas chromatography and/or surface energy analysis according to claim 2, wherein the standard solution comprises: from 0.85 to 1.15 parts by volume of n-pentane; from 2.83 to 3.83 parts by volume of n-hexane; from 9.43 to 12.75 parts by volume of n-heptane; from 31.39 to 42.46 parts by volume of n-octane; and from 104.52 to 141.41 parts by volume of n-nonane.

7. A volumetric container for preparing a standard solution for inverse gas chromatography and/or surface energy analysis according to claim 1, wherein the volumetric container comprises separate volumetric compartments for each of the series of three or more compounds of increasing carbon chain length, wherein the relative volume of each of the separate volumetric compartments is determined by the following equation: $\mathrm{Relative}\mathrm{Volume}\mathrm{of}{\mathrm{Compartment}}_x=\frac{{\mathrm{MW}}_x\times P_y^0\times {\mathrm{Area}}_y\times {\mathrm{Density}}_y}{{\mathrm{MW}}_y\times P_x^0\times {\mathrm{Area}}_x\times {\mathrm{Density}}_x}\pm 20\%$ wherein: Relative Volume of Compartment.sub.x is the volume of a compartment to contain specific compound x in the series relative to the volume of the compartment for compound y that has the shortest carbon chain length in the series; MW.sub.x is the molecular weight of the specific compound x; P.sup.0.sub.x is the vapour pressure of the pure specific compound x at a given incubation temperature; Area.sub.x is the cross-sectional area of the compound x; Density.sub.x is the density of x; MW.sub.y is the molecular weight of the compound y; P.sup.0.sub.y is the vapour pressure of compound y at the given incubation temperature; Area.sub.y is the cross-sectional area of compound y; and Density.sub.y is the density of compound y.

8. The volumetric container according to claim 7, wherein the volumetric container comprises a multi-compartment first container, comprising the separate volumetric compartments, with an open end separated by an axial length from an opposite end that is mounted on a base larger than the multi-compartment first container to form a closed end; and further comprises a second mixing container with an open end and a closed opposite end and with an axial length between the two ends that is greater than the axial length of the first container, wherein the second mixing container may be placed over the first container such that the base of the first container will cover the open end of the second container and when the containers are inverted the second container will be held against the base of the first container.

9. The volumetric container according to claim 8, wherein the multi-compartment first container comprises an outer cylinder and two or more inner cylinders which are located inside the outer cylinder and all the cylinders are mounted on the base, such that the inner cylinders and the outer cylinder minus the inner cylinders provide the separate volumetric compartments.

10. The volumetric container according to claim 9, wherein the multi-compartment first container comprises 3, 4 or 5 inner cylinders.

11. The volumetric container according to claim 7, wherein the series of three or more compounds of increasing carbon chain length comprises three or more n-alkane compounds of increasing carbon chain length, wherein the volumetric container comprises separate volumetric compartments for each of the three or more n-alkane compounds of increasing carbon chain length, wherein the relative volume of each of the separate volumetric compartments is determined by the following equation:
Relative Volume of Compartment.sub.x=3.33.sup.x-yVolume of Compartment.sub.y±15% wherein x is the number of carbons in the carbon chain of the specific compound x; y is the number of carbons in the carbon chain of compound y with the shortest carbon chain length; and Volume of Compartment.sub.y is the volume of the compartment for compound.sub.y.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1. The IGC chromatograms of n-hexane, n-heptane, n-octane, n-nonane, n-decane, and inverse gas chromatography standard solution containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane on silanised D-mannitol at temperature 30° C., flow rate 10 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/n.sub.m, using iGC Surface Energy Analyzer, Surface Measurement Systems, Ltd. 5 Wharfside, Rosemont Road, Alperton, Middlesex HA0 4PE, United Kingdom. To assist in allowing comparison of the chromatograms, in FIGS. 1, 2 and 3, the values of FID Signals of IGC Mixture, n-decane, n-nonane, n-octane, and n-heptane were shifted up by 1500, 1200, 900, 600 and 300 μV, respectively. The value of the FID Signal for n-hexane remains unaltered.

(2) FIG. 2. The IGC chromatograms of n-hexane, n-heptane, n-octane, n-nonane, n-decane, and inverse gas chromatography standard solution containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane on silanised D-mannitol at temperature 35° C., flow rate 10 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/n.sub.m, using iGC Surface Energy Analyzer, Surface Measurement Systems, Ltd. 5 Wharfside, Rosemont Road, Alperton, Middlesex HA0 4PE, United Kingdom.

(3) FIG. 3. The IGC chromatograms of n-hexane, n-heptane, n-octane, n-nonane, n-decane, and inverse gas chromatography standard solution containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane on silanised D-mannitol at temperature 40° C., flow rate 10 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/n.sub.m, using iGC Surface Energy Analyzer, Surface Measurement Systems, Ltd. 5 Wharfside, Rosemont Road, Alperton, Middlesex HA0 4PE, United Kingdom.

(4) FIG. 4. The IGC chromatograms of inverse gas chromatography standard solution containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane on silanised D-mannitol at temperature 30° C., flow rate 10 ml/min, and different target fractional surface coverage (the amount of injected probe) 0.05, 0.1, 0.2, 0.3, 0.4 n/n.sub.m, using iGC Surface Energy Analyzer, Surface Measurement Systems, Ltd. 5 Wharfside, Rosemont Road, Alperton, Middlesex HA0 4PE, United Kingdom. TFSC in the figure is abbreviation of “target fractional surface coverage”. To assist in allowing comparison of the chromatograms, in FIG. 4, the values of FID Signals of TFSC 0.4, TFSC 0.3, TFSC 0.2 and TFSC 0.1 were shifted by 3200, 2000, 1050 and 360 μrespectively. The value of the FID Signal for TFSC 0.05 remains unaltered.

(5) FIG. 5. The IGC chromatograms of inverse gas chromatography standard solution containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane on milled Lactohale 300 (lactose monohydrate) at temperature 30° C., different flow rate 15 and 20 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/n.sub.m, using iGC Surface Energy Analyzer, Surface Measurement Systems, Ltd. 5 Wharfside, Rosemont Road, Alperton, Middlesex HA0 4PE, United Kingdom. To assist in allowing comparison of the chromatograms, in FIG. 5, the values of FID Signals of Flow rate 20 ml/min and Flow rate 15 ml/min were shifted by 1700 and 700 μV, respectively. The value of the FID Signal for T Flow rate 10 ml/min remains unaltered.

(6) FIG. 6. The IGC chromatograms of n-hexane, n-heptane, n-octane, n-nonane, n-decane, and inverse gas chromatography standard solution containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane on milled Lactohale 300 (lactose monohydrate) at temperature 30° C., flow rate 20 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/n.sub.m, using iGC Surface Energy Analyzer, Surface Measurement Systems, Ltd. 5 Wharfside, Rosemont Road, Alperton, Middlesex HA0 4PE, United Kingdom. To assist in allowing comparison of the chromatograms, in FIG. 6, the values of FID Signals of n-hexane, n-heptane, n-octane, n-nonane, n-decane and IGC Mixture were shifted by 25000, 20000, 15000, 10000, 5000 and 1000 μV, respectively.

(7) FIG. 7. A volumetric container consists of the filling piece and the mixing piece. The filling piece is a cylinder and contains four inner cylinders. The volumes of these cylinders obey the formula (I): Relative Volume of

(8) ${\mathrm{Cylinder}}_x=\frac{{\mathrm{MW}}_x\times P_y^0\times {\mathrm{Area}}_y\times {\mathrm{Density}}_y}{{\mathrm{MW}}_y\times P_x^0\times {\mathrm{Area}}_x\times {\mathrm{Density}}_x}\pm 20\%$
wherein: Relative Volume of Cylinder.sub.x is the volume of a cylinder to contain specific compound x in the series relative to the volume of the cylinder for compound y that has the shortest carbon chain length in the series; MW.sub.x is the molecular weight of the specific compound x; P.sup.0.sub.x is the vapour pressure of the pure specific compound x at a given incubation temperature; Area.sub.x is the cross-sectional area of the compound x; Density.sub.x is the density of x; MW.sub.y is the molecular weight of the compound y; P.sup.0.sub.y is the vapour pressure of compound y at the given incubation temperature; Area.sub.y is the cross-sectional area of compound y; and Density.sub.y is the density of compound y. The mixing piece is also a cylinder, closed at one end, with diameter suitable to fit the filling piece. For example, the height of this mixing cylinder is at least twice the height of the filling piece. The mixing piece is used as a lid of the filling piece, and so its edge fits the filling piece.

DETAILED DESCRIPTION

(9) In case of gas chromatography, the injected probes are taken as liquid. However, in case of Inverse gas chromatography (IGC) or its developed version which is surface energy analyzer (SEA) apparatuses, the injected probes are taken as vapour (gas phase) from the headspaces of liquid bottles attached inside the IGC and SEA apparatus. Therefore, commercially available bottles containing similar amounts of n-alkanes are not suitable for IGC and SEA apparatuses because the headspace of a bottle containing commercially available n-alkanes' mixtures (solutions) contain significant different amounts of n-alkanes (as mentioned herein in Background Information).

(10) The invention is to prepare a standard solution for inverse gas chromatography and/or a surface energy analysis comprising a series of three or more compounds of increasing carbon chain length of general formula (I) R—X, wherein for the three or more compounds R is a series of alkyl, a series of alkenyl or a series of alkynyl groups of increasing carbon chain length; and for all three or more compounds X is H, OH, CO.sub.2H, C(O)H, C(O)CH.sub.3, NH.sub.2, SH or halogen. These standard solutions generate in the headspaces of their bottles amounts of compounds' molecules having the same target fractional surface coverage. Preferably the standard solution contains a series of three or more compounds of n-alkanes, most preferably the standard solution contains a series of three or more compounds of n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane n-undecane and/or n-dodecane.

(11) A bottle containing mixture of compounds consist of liquid phase and gas phase (the headspace of the bottle). At equilibrium between its liquid phase and gas phase (its headspace), the partial pressure of each compound, for example compound i, in the headspace of the bottle can be calculated according to Raoult's law as following:
P.sub.i=X.sub.iP.sub.i.sup.ºγ.sub.i  (Equation 1)
where P.sub.i is the partial pressure of the compound i in the gas phase (headspace), X.sub.i is the mole fraction of the compound i in the liquid phase, P.sub.i.sup.º is the vapour pressure of the pure compound i at the given temperature, and γ.sub.i is the activity coefficient of the compound i.

(12) The gas phase (the headspace of the bottle) can be described according to general gas law and Dalton's law of partial pressures as follows:
P.sub.i=n.sub.i(RT/V)  (Equation 2)
where V is the volume occupied by the gas phase (the volume of the headspace of the bottle), R is the universal gas constant, and T is the temperature in Kelvin (K), P.sub.i is the vapour pressure of a compound i and n.sub.i is the number of moles of this compound in the gas phase (the headspace of the bottle).

(13) Inverse gas chromatography standard solutions, for example, containing a series of n-alkanes, for example n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane n-undecane and/or n-dodecane (which are the most used probes to measure the surface free energy using IGC and SEA), were prepared according to the following principles.

(14) The bottle of the mixture of the n-alkanes (n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane, n-undecane and n-dodecane) contain the same number of n-alkanes' molecules in its headspaces (gas phase) when
n.sub.c5=n.sub.c6=n.sub.c7=n.sub.c8=n.sub.c9=n.sub.c10=n.sub.c11=n.sub.c12  (Equation 3)
where n.sub.c5, n.sub.c6, n.sub.c7, n.sub.c8, n.sub.c9, n.sub.c10, n.sub.c11 and n.sub.c12 is the mole number of n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane, n-undecane and n-dodecane, respectively, in the headspace of the bottle (gas phase).

(15) Combining Equation 3 which describes the above bottle of n-alkanes' mixture (in which all n-alkanes have the same number of moles in its headspace) with Equation 2 gives:
P.sub.c5/(RT/V)=P.sub.c6/(RT/V)=P.sub.c7/(RT/V)=P.sub.c8/(RT/V)=P.sub.c9/(RT/V)=P.sub.c10/(RT/V)=P.sub.c11/(RT/V)=P.sub.c12/(RT/v)  (Equation 4)
where P.sub.c5, P.sub.c6, P.sub.c7, P.sub.c8, P.sub.c9, P.sub.c10, P.sub.c11 and P.sub.c12 are the partial pressure of n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane, n-undecane and n-dodecane respectively, in the gas phase of the bottle (the headspace).

(16) The compounds (n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane, n-undecane and/or n-dodecane) occupy the same volume (V) (which is the volume of the headspace of the bottle). Therefore, the factor (RT/V) of Equation 4 can be cancelled out from the all sides of Equation 4, and by combining Equation 4 and Equation 1, we obtain Equation 5:
X.sub.c5P.sub.c5.sup.ºγ.sub.i=X.sub.c6P.sub.c6.sup.ºγ.sub.i=X.sub.c7P.sub.c7.sup.ºγ.sub.i=X.sub.c8P.sub.c8.sup.ºγ.sub.i=X.sub.c9P.sub.c9.sup.ºγ.sub.i=X.sub.c10P.sub.c10.sup.ºγ.sub.i=X.sub.c11P.sub.c11.sup.ºγ.sub.i=X.sub.c12P.sub.c12.sup.ºγ.sub.i  (Equation 5)
where X.sub.C5, X.sub.C6, X.sub.C7, X.sub.C8, X.sub.C9, X.sub.C10, X.sub.C11 and X.sub.C12 is the mole fraction of n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane, n-undecane and n-dodecane in the liquid phase of the bottle, respectively. P.sub.C5.sup.º, P.sub.C6.sup.º, P.sub.C7.sup.º, P.sub.C8.sup.º, P.sub.C9.sup.º, P.sub.C10.sup.º, P.sub.C11.sup.º and P.sub.C12.sup.º is the vapour pressure of the pure n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane, n-undecane and n-dodecane at the given temperature, and γ.sub.i is the activity coefficient of n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane, n-undecane and n-dodecane.

(17) For a system obeying Raoult's law (ideal solutions), the activity coefficient for each component would be unity. The mixtures of the alkanes are nearly ideal, and so γ.sub.i for n-alkanes is considered as one [Phase equilibrium mixtures by M. B. King: International series of monographs in chemical engineering. General Editor P. V. Danckwerts. Volume 9. Pergamon Press Ltd., Headington Hill Hall, Oxford, First edition 1969.]. Therefore, Equation 5 can be written as follows.
X.sub.C5P.sub.C5.sup.º=X.sub.C6P.sub.C6.sup.º=X.sub.C7P.sub.C7.sup.º=X.sub.C8P.sub.C8.sup.º=X.sub.C9P.sub.C9.sup.º=X.sub.C10P.sub.C10.sup.º=X.sub.C11P.sub.C11.sup.º=X.sub.C12P.sub.C12.sup.º  (Equation 6)

(18) The mole fracture of each compound in the liquid phase of the bottle (X.sub.i) equals its number of moles in the liquid phase (n.sub.i.sup.l) divided by the total number of moles in the liquid phase of the bottle (n.sub.T.sup.l), and so Equation 6 becomes:
(n.sub.C5.sup.l/n.sub.T.sup.l)P.sub.C5.sup.º=(n.sub.C6.sup.l/n.sub.T.sup.l)P.sub.C6.sup.º=(n.sub.C7.sup.l/n.sub.T.sup.l)P.sub.C7.sup.º=(n.sub.C8.sup.l/n.sub.T.sup.l)P.sub.C8.sup.º=(n.sub.C9.sup.l/n.sub.T.sup.l)P.sub.C9.sup.º=(n.sub.C10.sup.l/n.sub.T.sup.l)P.sub.C10.sup.º=(n.sub.C11.sup.l/n.sub.T.sup.l)P.sub.C11.sup.º=(n.sub.C12.sup.l/n.sub.T.sup.l)P.sub.C12.sup.º  (Equation 7)
where n.sub.C5.sup.l, n.sub.C6.sup.l, n.sub.C7.sup.l, n.sub.C8.sup.l, n.sub.C9.sup.l, n.sub.C10.sup.l, n.sub.C11.sup.l and n.sub.C12.sup.l is the number of moles of n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane, n-undecane and n-dodecane in the liquid phase of the bottle, respectively.

(19) The number of moles of each compound in the liquid phase of the bottle (n.sub.i.sup.l) equals its weight in the liquid phase of the bottle divided by its molecular weight (M.sub.W), and so Equation 7 becomes:
(Weight.sub.C5/Mw.sub.c5)P.sub.C5.sup.º=(Weight.sub.C6/Mw.sub.C6)P.sub.C6.sup.º=(Weight.sub.C7/Mw.sub.C7)P.sub.C7.sup.º=(Weight.sub.C8/Mw.sub.C8)P.sub.C8.sup.º=(Weight.sub.C9/Mw.sub.C9)P.sub.C9.sup.º=(Weight.sub.C10/Mw.sub.C10)P.sub.C10.sup.º=(Weight.sub.C11/Mw.sub.C11)P.sub.C11.sup.º=(Weight.sub.C12/Mw.sub.C12)P.sub.C12.sup.º  (Equation 8)
where Weight.sub.C5, Weight.sub.C6, Weight.sub.C7, Weight.sub.C8, Weight.sub.C9, Weight.sub.C10, Weight.sub.C11, and Weight.sub.C12 is the weight of n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane, n-undecane and n-dodecane in the liquid phase of the bottle, respectively, Mw.sub.C5, Mw.sub.C6, Mw.sub.C7, Mw.sub.C8, Mw.sub.C9, Mw.sub.C10, Mw.sub.C11 and Mw.sub.C12 is the molecular weight of n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane, n-undecane and n-dodecane, respectively.

(20) Equation (8) can be abbreviated as:

(21) $\begin{array}{cc}\mathrm{Relative}{\mathrm{Weight}}_x=\frac{{\mathrm{MW}}_x\times P_y^0}{{\mathrm{MW}}_y\times P_x^0}& \left(\mathrm{Equation}9\right)\end{array}$
wherein: Relative Weight.sub.x is the relative weight of a specific compound x of formula (I) (in our example a series of n-alkane) with a carbon chain length of x; relative to the weight of compound y that has the shortest carbon chain length in the series (in our example n-pentane); MW.sub.x is the molecular weight of the compound x; P.sup.0.sub.x is the vapour pressure of the pure specific compound x at the given temperature; MW.sub.y is the molecular weight of the compound y; P.sup.0.sub.y is the vapour pressure of the pure compound y at the given temperature.

(22) If a bottle containing a mixture of a series of compounds (in our example a series of n-alkane), in which the relative weight of each compound obeys Equation 9, is enclosed, the mixture generates in the headspace of the bottle the same number of moles of each compound because Equation 9 is derived herein from Equation 3.

(23) Dividing the relative weight of each specific compound of the series (in our example a series of n-alkanes) by the relative cross-sectional area of each compound to obtain the relative weight of each compound which generate the same surface coverage, wherein the relative cross-sectional area of a specific compound is the cross-sectional area of that specific compound x divided by the cross-sectional area of compound y; and so Equation 9 becomes:

(24) $\begin{array}{cc}\mathrm{Relative}{\mathrm{Weight}}_x=\frac{{\mathrm{MW}}_x\times P_y^0\times {\mathrm{Area}}_y}{{\mathrm{MW}}_y\times P_x^0\times {\mathrm{Area}}_x}& \left(\mathrm{Equation}10\right)\end{array}$
wherein: Area.sub.x is the cross-sectional area of the compound x and Area.sub.y is the cross-sectional area of compound y.

(25) If a bottle containing a mixture of a series of compounds (in our example a series of n-alkane), in which the relative weight of each compound obeys Equation 10, is enclosed, the mixture generates in the headspace of the bottle the number of moles of each compound generating the same surface coverage.

(26) Dividing the relative weight of each specific compound which generates the same surface coverage by the relative density of each specific compound to obtain the relative volume of each specific compound which generates the same surface coverage, wherein the relative density of a specific compound is the density of that specific compound divided by the density of compound y; and so Equation 10 becomes:

(27) $\begin{array}{cc}\mathrm{Relative}\mathrm{Volume}\mathrm{of}{\mathrm{compound}}_x=\frac{{\mathrm{MW}}_x\times P_y^0\times {\mathrm{Area}}_y\times {\mathrm{Density}}_y}{{\mathrm{MW}}_y\times P_x^0\times {\mathrm{Area}}_x\times {\mathrm{Density}}_x}& \left(\mathrm{Equation}11\right)\end{array}$
wherein: Density.sub.x is the density of x and Density.sub.y is the density of compound y.

(28) If a bottle containing a mixture of a series of compounds (in our example a series of n-alkane), in which the relative volume of each compound obeys Equation 11, is enclosed, the mixture generates in the headspace of the bottle the number of moles of each compound generating the same surface coverage.

(29) The molecular weight, the molecular cross sectional area, the density and the vapour pressure of pure n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane, n-undecane and n-dodecane were summarized in the following table:

(30) TABLE-US-00001 Vapor cross- pressures P.sub.0 sectional Density (kN .Math. m.sup.−2) Molecular area (g/ml at n-Alkane at 25° C.* Weight** (Å.sup.2)*** 25° C.)**** n-Pentane 68.351 72.15 46 0.626 n-Hexane 20.179 86.18 51.5 0.659 n-Heptane 6.095 100.2 57.3 0.684 n-Octane 1.867 114.23 63 0.703 n-Nonane 0.573 128.26 69 0.718 n-Decane 0.173 142.28 75 0.73 n-Undecane 0.052 156.31 81 0.74 n-Dodecane 0.016 170.33 87 0.75 *Data are taken from [M. Nardin, E. Papirer, Journal of Colloid and Interface Science. 137 (1990) 534.]. **Data are taken from [Sigma-Aldrich Copyright © 2015 Sigma-Aldrich Co. LLC.]. ***Data are taken from [J. Schultz, L. et al, Journal of Adhesion, 23 (1987) 45; IGC Analysis Macros, Version 1.3.3 Standard, Surface Measurement Systems Ltd UK, London © Surface Measurement System Ltd UK 1999-2007; iGC Surface Energy Analyzer (SEA), Operation Manual, Cirrus Control Software, Version 1.3, Surface Measurement Systems Ltd UK, London © Surface Measurement System Ltd UK October 2011]. ****Data are taken from [Sigma-Aldrich Copyright © 2015 Sigma-Aldrich Co. LLC.].

(31) The values for the density, molecular weight and vapour pressure for other compounds of formula (I) may be obtained from standard reference sources, such as the “CRC Handbook of Chemistry and Physics”, 96th Edition, (2015) Ed. Haynes, W. M.; CRC Press. Typically, values of density and molecular weight may also be obtained from the supplied or the compound of formula (I) such as Sigma-Aldrich. With regard to vapour pressure, the Dortmund Data Bank (DDB) contains over 180,000 data points for both solid and liquid vapour pressure and access to this data bank may be obtained from DDBST Dortmund Data Bank Software & Separation Technology GmbH, Center for Applied Thermodynamics, Marie-Curie-Str. 10, D-26129 Oldenburg, Germany.

(32) The cross-sectional area for other compounds of formula (I) may be obtained from a number of reference sources for example, the cross-sectional area of a range of compounds (including alkanes, alkenes, aromatics, noble gases, alkyl halides, amines, and alcohols) have been tabulated in [Gray, M. J., Mebane, R. C., Womack, H. N., & Rybolt, T. R. (1995). Molecular mechanics and molecular cross-sectional areas: a comparison with molecules adsorbed on solid surfaces. Journal of colloid and interface science, 170(1), 98-101] and in [McClellan, A. L., & Harnsberger, H. F. (1967). Cross-sectional areas of molecules adsorbed on solid surfaces. Journal of Colloid and Interface Science, 23(4), 577-599.]. Methods of determining cross-sectional areas of compounds are also provided in these two references. Further information regarding determining the cross-sectional area can be found in [T. Hamieh, J. Schultz, New approach to characterise physicochemical properties of solid substrates by inverse gas chromatography at infinite dilution: I. some new methods to determine the surface areas of some molecules adsorbed on solid surfaces, J. Chromatogr. A 969 (2002) 17-25.]. In addition, the cross sectional area of many different solvents are reported in [IGC Analysis Macros, Version 1.3.3 Standard, Surface Measurement Systems Ltd UK, London© Surface Measurement System Ltd UK 1999-2007; iGC Surface Energy Analyzer (SEA), Operation Manual, Cirrus Control Software, Version 1.3, Surface Measurement Systems Ltd UK, London© Surface Measurement System Ltd UK October 2011].

(33) The density, molecular weight, cross sectional area and vapor pressure of pure compound of the series of n-alkanes (n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane, n-undecane and n-dodecane) stated in the above table, Equation 10 and Equation 11 were used to calculate the relative weight and the relative volume of the n-alkanes, the calculated values are tabulated in the following table.

(34) TABLE-US-00002 n-Alkane Probes Relative weight Relative volume n-Pentane 1.0 1.0 (compound y) n-Hexane 3.6 3.4 n-Heptane 12.5 11.4 n-Octane 42.3 37.7 n-Nonane 141.4 123.3 n-Decane 477.9 409.8 n-Undecane 1617.2 1368.1 n-Dodecane 5332.3 4450.7

(35) Measuring each of the three or more compounds of the n-alkanes of increasing chain length in the ratios of the relative volume or the relative weight of each compound which generates the same surface coverage ±20% and mixing the three or more compounds to produce the inverse gas chromatography standard solutions.

(36) The calculated relative volumes of the n-alkanes (n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane, n-undecane and n-dodecane) (stated in above table) can be herein correlated as follows:
Relative Volume.sub.x=3.33.sup.x-yVolume.sub.y±15%  (Equation 12)
wherein x is the number of carbons in the carbon chain of the specific compound x; y is the number of carbons in the carbon chain of compound y with the shortest carbon chain length.

(37) For example, suitably, the standard solution for inverse gas chromatography and/or surface energy analysis according to above equation, wherein the standard solution comprises: from 0.85 to 1.15 parts by volume of n-pentane; from 2.83 to 3.83 parts by volume of n-hexane; from 9.43 to 12.75 parts by volume of n-heptane; from 31.39 to 42.46 parts by volume of n-octane; and from 104.52 to 141.41 parts by volume of n-nonane.

(38) For example, suitably, the standard solution for inverse gas chromatography and/or surface energy analysis according to above equation, wherein the standard solution comprises: from 0.85 to 1.15 parts by volume of n-hexane; from 2.83 to 3.83 parts by volume of n-heptane; from 9.43 to 12.75 parts by volume of n-octane; from 31.39 to 42.46 parts by volume of n-nonane; and from 104.52 to 141.41 parts by volume of n-decane.

(39) In another aspect, the present invention provides a volumetric container for preparing a standard solution for inverse gas chromatography and/or surface energy analysis as described herein.

(40) Equation 12 correlates the relative volumes of the n-alkanes (n-pentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane, n-undecane and n-dodecane) which are eligible to prepare a mixtures of series of n-alkanes which can generate in the headspace of its bottle the same surface coverage ±20% for each n-alkane. These mixtures are the inverse gas chromatography standard solutions.

(41) Suitably, the volumetric container comprises separate volumetric compartments for each of three or more n-alkane compounds of increasing carbon chain length, wherein the relative volume of each of the separate volumetric compartments is determined by the following equation:
Relative Volume of Compartment.sub.x=3.33.sup.x-yVolume of Compartment.sub.y±15%  (Equation 13)
wherein x is the number of carbons in the carbon chain of the specific compound x; y is the number of carbons in the carbon chain of compound y with the shortest carbon chain length; and Volume of Compartment.sub.y is the volume of the compartment for compound.sub.y.

(42) This volumetric container described herein is used to prepare inverse gas chromatography standard solutions containing three or more compounds (in our example n-alkanes) of increasing chain length in the ratios of the relative volume of each compound which generates the same surface coverage ±20% and the prepared relative volumes are described in the following equation:

(43) $\begin{array}{cc}\mathrm{Relative}{\mathrm{Volume}}_x=\frac{{\mathrm{MW}}_x\times P_y^0\times {\mathrm{Area}}_y\times {\mathrm{Density}}_y}{{\mathrm{MW}}_y\times P_x^0\times {\mathrm{Area}}_x\times {\mathrm{Density}}_x}\pm 20\%& \left(\mathrm{Equation}14\right)\end{array}$

(44) This volumetric container can be used to prepare IGC standard solutions. These solutions can prepared within bottles containing, for example, 15 ml or 10 ml (because this amount is enough to fill a bottle of IGC or SEA) of the mixtures which consisting from at least three n-alkanes, preferably, any four n-alkanes, preferably from n-pentane to n-octane, from n-hexane to n-nonane, from n-heptane to n-decane, from n-octane to n-undecane, and from n-nonane to n-dodecane, most preferably, any five n-alkanes, preferably, from n-pentane to n-nonane, from n-hexane to n-decane, from n-heptane to n-undecane, and from n-octane to n-dodecane. The suitable n-alkane series is chosen according to the surface free energy and surface area of the analysed materials, the lighter n-alkanes are suitable for materials with high surface area and/or surface free energy, and vice versa.

(45) This volumetric container can be designed for example as a container consisting of two pieces (FIG. 7); the first piece, which is called filling piece, is a cylinder containing four inner cylinders. The volumes of the five cylinders obey the formula 13. If all these cylinders have same height, and so their inner areas obey (Equation 13). These five cylinders, which are called the first cylinder, the second cylinder, the third cylinder, the fourth cylinder and the fifth cylinder starting from the narrowest to the widest. They are fixed on a circle base whose radius larger than the radius of the main cylinder by, for example, 5 mm, i.e., the base has edge of 5 mm. The filling piece is used to fill the required volumes of the n-alkane series (up to five subsequent n-alkanes or less). For example, if you fill n-alkane (C.sub.n) in the first cylinder, the second, the third, the fourth and the fifth cylinders are filled by the n-alkanes C.sub.n+1, C.sub.n+2, C.sub.n+3, and C.sub.n+4, respectively. The second piece of the volumetric container is called the mixing piece. The mixing piece, for example, is a cylinder, close from one side, with diameter suitable to fit the fifth cylinder of the filling piece, and the height of this mixing cylinder is at least twice the height of the filling piece. This is to facilitate pouring the n-alkanes form the filling piece to the mixing piece. The mixing piece is used as a lid of the filling piece, and the edge of the filling piece completely match the mixing piece.

(46) The n-alkanes are filled in the first piece (filling piece) are mixed in the second piece (mixing piece) to form inverse gas chromatography standard solutions. For example, after filling the cylinders of the filling piece to the same height with a series of n-alkanes, the mixing piece is fixed over the filling piece and both pieces are turned over to allow the content of the filling piece to pour completely within the mixing piece, and then the n-alkanes are mixed to make an inverse gas chromatography standard solution.

(47) When IGC standard solutions are consumed by continuous injections, the lighter n-alkanes will be consumed faster than the counterpart heavier n-alkanes. This is because during injecting, similar amounts of all n-alkanes are consumed and so the mole fractions of the lighter n-alkanes decrease and the mole fractions of the heavier n-alkanes increase in the liquid phase. Therefore, the inverse gas chromatography standard solutions become unsuitable to generate the same target fractional surface coverage after long use. In our case, 13 ml of inverse gas chromatography standard solution containing five n-alkanes from n-hexane to n-decane was placed within SEA (iGC Surface Energy Analyzer, Surface Measurement Systems, Ltd. 5 Wharfside, Rosemont Road, Alperton, Middlesex HA0 4PE, United Kingdom.) and it maintained the peak areas of all probes without significant changes after about 50 infinite injections. Therefore, inverse gas chromatography standard solutions can be used for a lot of experiments but they should be changed with a fresh inverse gas chromatography standard solution when a significant decrease in the peak area (or height) of the lighter n-alkanes is noticed. The standard deviations of ±20% and ±15% in Equation 13 and Equation 14 is to rectify this issue.

(48) The principle of the invention is the same for other series of general formula I.

(49) The vapour pressures and densities of n-alkanes which were used in this invention are at room temperature 25° C. These properties will change in similar manner when temperature changes, and so the ratio would not change, and so the relative weight and relative volumes would not change. Also the standard deviations of ±20% and ±15% in Equation 13 and Equation 14 is to rectify this issue. Usually Bottles attached to IGC and SEA apparatuses are incubated at temperature either 25 or 30° C.

(50) Calculation Methods:

(51) Mohammad methods [M. A. Mohammad, Journal of Chromatography A, 1318 (2013) 270; M. A. Mohammad, Journal of Chromatography A, 1399 (2015) 88; M. A. Mohammad, Journal of Chromatography A, 1408 (2015) 267.] were used to calculate the dispersive surface energy and to verify the accuracy of retention time measurements. These methods firstly calculate the dispersive retention factor (In K.sub.CH.sub.2.sup.a) using the measured retention times of the injected n-alkanes as follows:
ln(t.sub.r−t.sub.0)=(ln K.sub.CH.sub.2.sup.a)n+C  (Equation 15)
wherein: n is the carbon number of the homologous n-alkanes, t.sub.r and t.sub.0 are the retention times of the n-alkanes and a non-adsorbing marker, respectively, K.sub.CH.sub.2.sup.a is the dispersive retention factor of the analysed powder and C is a constant. The linear regression statistics of Equation 15 generates the value of t.sub.0 which gives its best linear fit. The slope of Equation 15 gives the value of ln K.sub.CH.sub.2.sup.a. The dispersive surface energy of the analysed powder (γ.sub.s.sup.d) is then calculated as follows:

(52) 0$\begin{array}{cc}{\gamma }_s^d=\frac{0.477{\left(T\ln K_{{\mathrm{CH}}_2}^a\right)}^2}{{\left({\alpha }_{{\mathrm{CH}}_2}\right)}^2{\gamma }_{{\mathrm{CH}}_2}}\mathrm{mJ}.Math.m^{-2}& \left(\mathrm{Equation}16\right)\end{array}$
wherein: T is the column temperature, α.sub.CH.sub.2 and γ.sub.CH.sub.2, are the cross-sectional area and the dispersive free energy of a methylene group (CH.sub.2), respectively. The units of α are Å.sup.2 and of γ are mJ.Math.m.sup.−2 in Equation 16. The parameters of CH.sub.2 ((α.sub.CH.sub.2).sup.2γ.sub.CH.sub.2) is calculated as follows:
(α.sub.CH.sub.2).sup.2γ.sub.CH.sub.2=−1.869T+1867.194 Å.sup.4.Math.mJ.Math.m.sup.−2  (Equation 17)
The percentage coefficient of variation of ln K.sub.CH.sub.2.sup.a (% CV.sub.ln K.sub.CH2.sup.a) is the indicator of the accuracy of the surface energy measurements. The error of the slope of Equation 15 (SD.sub.ln K.sub.CH2.sup.a) is used to calculate % CV.sub.ln K.sub.CH2.sup.a as follows:
%CV.sub.ln K.sub.CH2.sup.a=(SD.sub.ln K.sub.CH2.sup.a/ln K.sub.CH.sub.2.sup.a)×100  (Equation 18)
% CV.sub.ln K.sub.CH2.sup.a should be less than 0.7% to accept the accuracy of the measurement, the lower the value of % CV.sub.ln K.sub.CH2.sup.a, the better the accuracy of the measurement.

EXAMPLES

(53) Equipments: iGC Surface Energy Analyzer, Surface Measurement Systems, Ltd. 5 Wharfside, Rosemont Road, Alperton, Middlesex HA0 4PE, United Kingdom.

(54) Analysed Materials:

(55) 1-Silanised D-mannitol filled into a standard glass column (P15f00068) was obtained from Surface Measurement Systems, Ltd. 5 Wharfside, Rosemont Road, Alperton, Middlesex HA0 4PE, United Kingdom.

(56) 2-Lactohale 300 (Lactose monohydrate) was obtained from DFE pharma, Germany.

(57) The used solvents were n-hexane, n-heptane, n-octane, n-nonane, n-decane were obtained from Sigma-Aldrich. An inverse gas chromatography standard solution containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane was prepared according Equation 14 mentioned above in this invention. This standard solution comprised 0.5 ml n-hexane, 1.7 ml n-heptane, 5.7 ml n-octane, 18.8 ml n-nonane and 54 ml n-decane.

(58) The powders were packed into pre-silanised glass columns (300 mm×3 mm i.d.). The column was analysed at zero relative humidity, using anhydrous helium gas as the carrier. The retention times of injected vapour solvents followed from detection using the flame ionization detector (FID) installed within the iGC Surface Energy Analyzer.

(59) Example one: An experiment using n-hexane, n-heptane, n-octane, n-nonane, and n-decane on silanised D-mannitol at temperature 30° C., flow rate 10 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/n.sub.m:

(60) TABLE-US-00003 t.sub.rC6 t.sub.rC7 t.sub.rC8 t.sub.rC9 t.sub.rC10 t.sub.0 γ.sub.s.sup.d Run min min min min min min (mJ .Math. m.sup.−2) K.sub.CH.sub.2.sup.a 1 0.7522 1.1737 2.2967 5.2607 12.9464 0.4746 30.63 2.5944 0.468 2 0.7489 1.1713 2.2917 5.2374 13.1422 0.5063 32.82 2.6825 0.363 3 0.7464 1.1638 2.2792 5.2457 12.9555 0.4708 30.78 2.6004 0.539

(61) Example two: An experiment using inverse gas chromatography standard solution containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane (inverse gas chromatography standard solution was in the Undecane position) on silanised D-mannitol at temperature 30° C., flow rate 10 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/nm:

(62) TABLE-US-00004 t.sub.rC6 t.sub.rC7 t.sub.rC8 t.sub.rC9 t.sub.rC10 t.sub.0 γ.sub.s.sup.d Run min min min min min min (mJ .Math. m.sup.−2) K.sub.CH.sub.2.sup.a 1 0.7597 1.1838 2.3109 5.2948 13.1205 0.4918 31.35 2.6232 0.240 2 0.7573 1.1813 2.3059 5.2840 13.1022 0.4910 31.41 2.6257 0.203 3 0.7564 1.1779 2.2992 5.2582 13.0572 0.4955 31.66 2.6356 0.109

(63) FIG. 1. shows the IGC chromatograms of n-hexane, n-heptane, n-octane, n-nonane, n-decane, and inverse gas chromatography standard solution containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane (inverse gas chromatography standard solution was in the Undecane position) on silanised D-mannitol at temperature 30° C., flow rate 10 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/nm.

(64) Example three: An experiment using n-hexane, n-heptane, n-octane, n-nonane, and n-decane on silanised D-mannitol at temperature 35° C., flow rate 10 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/nm:

(65) TABLE-US-00005 t.sub.rC6 t.sub.rC7 t.sub.rC8 t.sub.rC9 t.sub.rC10 t.sub.0 γ.sub.s.sup.d Run min min min min min min (mJ .Math. m.sup.−2) K.sub.CH.sub.2.sup.a 1 0.6923 1.0147 1.8452 3.9886 9.4301 0.4764 30.51 2.5411 0.322 2 0.6915 1.0097 1.8327 3.9670 9.4384 0.4839 31.12 2.5650 0.216 3 0.6898 1.0122 1.8352 3.9654 9.4135 0.4813 30.97 2.5589 0.133

(66) Example four: An experiment using inverse gas chromatography standard solution containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane (inverse gas chromatography standard solution was in the Undecane position) on silanised D-mannitol at temperature 35° C., flow rate 10 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/nm:

(67) TABLE-US-00006 t.sub.rC6 t.sub.rC7 t.sub.rC8 t.sub.rC9 t.sub.rC10 t.sub.0 γ.sub.s.sup.d Run min min min min min min (mJ .Math. m.sup.−2) K.sub.CH.sub.2.sup.a 1 0.7014 1.0255 1.8594 3.9995 9.4776 0.4919 31.00 2.5602 0.078 2 0.6998 1.0222 1.8560 3.9936 9.4326 0.4858 30.63 2.5457 0.239 3 0.6990 1.0230 1.8569 3.9887 9.4593 0.4920 31.14 2.5657 0.032

(68) FIG. 2. shows the IGC chromatograms of n-hexane, n-heptane, n-octane, n-nonane, n-decane, and inverse gas chromatography standard solution containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane (inverse gas chromatography standard solution was in the Undecane position) on silanised D-mannitol at temperature 35° C., flow rate 10 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/nm.

(69) Example five: An experiment using n-hexane, n-heptane, n-octane, n-nonane, and n-decane on silanised D-mannitol at temperature 40° C., flow rate 10 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/nm:

(70) TABLE-US-00007 t.sub.rC6 t.sub.rC7 t.sub.rC8 t.sub.rC9 t.sub.rC10 t.sub.0 γ.sub.s.sup.d Run min min min min min min (mJ .Math. m.sup.−2) K.sub.CH.sub.2.sup.a 1 0.6490 0.8964 1.5212 3.0823 6.9826 0.4819 30.61 2.4989 0.108 2 0.6489 0.9014 1.5279 3.1006 6.9784 0.4733 29.81 2.4691 0.255 3 0.6515 0.9014 1.5253 3.0956 6.9627 0.4754 29.75 2.4670 0.361

(71) Example six: An experiment using inverse gas chromatography standard solution containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane (inverse gas chromatography standard solution was in the Undecane position) on silanised D-mannitol at temperature 40° C., flow rate 10 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/nm:

(72) TABLE-US-00008 t.sub.rC6 t.sub.rC7 t.sub.rC8 t.sub.rC9 t.sub.rC10 t.sub.0 γ.sub.s.sup.d Run min min min min min min (mJ .Math. m.sup.−2) K.sub.CH.sub.2.sup.a 1 0.6581 0.9089 1.5387 3.1123 6.9843 0.4807 29.68 2.4643 0.348 2 0.6599 0.9114 1.5437 3.1123 7.0243 0.4906 30.46 2.4933 0.057 3 0.6573 0.9114 1.5395 3.1123 6.9859 0.4809 29.73 2.4660 0.218

(73) FIG. 3. shows the IGC chromatograms of n-hexane, n-heptane, n-octane, n-nonane, n-decane, and inverse gas chromatography standard solution containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane (inverse gas chromatography standard solution was in the Undecane position) on silanised D-mannitol at temperature 40° C., flow rate 10 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/nm.

(74) Example seven: An experiment using IGC mixture containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane (inverse gas chromatography standard solution was in the Hexane position) on silanised D-mannitol at temperature 30° C., flow rate 10 ml/min, and different target fractional surface coverage (the amount of injected probe) 0.05, 0.1, 0.2, 0.3, 0.4 n/n.sub.m:

(75) TABLE-US-00009 t.sub.rC6 t.sub.rC7 t.sub.rC8 t.sub.rC9 t.sub.rC10 t.sub.0 γ.sub.s.sup.d Coverage min min min min min min (mJ .Math. m.sup.−2) K.sub.CH.sub.2.sup.a 0.05 0.7639 1.1921 2.3142 5.3423 13.2488 0.4886 31.09 2.6127 0.453 0.1 0.7664 1.1929 2.3242 5.3248 13.2313 0.5018 31.65 2.6353 0.143 0.2 0.7664 1.1946 2.3325 5.3273 13.1430 0.4925 31.03 2.6103 0.275 0.3 0.7672 1.1979 2.3342 5.3573 13.2021 0.4856 30.69 2.5968 0.456 0.4 0.7681 1.1971 2.3442 5.3582 13.2988 0.5015 31.62 2.6341 0.132

(76) FIG. 4. shows the IGC chromatogram of inverse gas chromatography standard solution containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane (inverse gas chromatography standard solution was in the Hexane position) on silanised D-mannitol at temperature 30° C., flow rate 10 ml/min, and different target fractional surface coverage (the amount of injected probe) 0.05, 0.1, 0.2, 0.3, 0.4 n/n.sub.m.

(77) Example eight: An experiment using inverse gas chromatography standard solution containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane (inverse gas chromatography standard solution was in the Undecane position) on milled Lactohale 300 (lactose monohydrate) at temperature 30° C., different flow rate 15 and 20 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/n.sub.m.

(78) TABLE-US-00010 Flow rate t.sub.rC6 t.sub.rC7 t.sub.rC8 t.sub.rC9 t.sub.rC10 t.sub.0 γ.sub.s.sup.d ml/min min min min min min min (mJ .Math. m.sup.−2) K.sub.CH.sub.2.sup.a 15 0.6081 0.9589 2.0560 5.5239 16.2070 0.4279 42.32 3.0666 0.584 20 0.4782 0.7548 1.6145 4.3594 13.0039 0.3490 44.27 3.1457 0.135

(79) FIG. 5. shows the IGC chromatogram of inverse gas chromatography standard solution containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane (inverse gas chromatography standard solution was in the Undecane position) on milled Lactohale 300 (lactose monohydrate) at temperature 30° C., different flow rate 15 and 20 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/nm.

(80) Example nine: An experiment using n-hexane, n-heptane, n-octane, n-nonane, and n-decane on milled Lactohale 300 (lactose monohydrate) at temperature 30° C., flow rate 20 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/nm:

(81) TABLE-US-00011 t.sub.rC6 t.sub.rC7 t.sub.rC8 t.sub.rC9 t.sub.rC10 t.sub.0 γ.sub.s.sup.d Run min min min min min min (mJ .Math. m.sup.−2) K.sub.CH.sub.2.sup.a 1 0.4690 0.7198 1.4662 3.8987 11.0729 0.3166 38.57 2.9147 1.697 2 0.4649 0.7264 1.4879 3.8454 11.1704 0.3534 43.70 3.1226 0.827

(82) Example ten: An experiment using inverse gas chromatography standard solution containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane (inverse gas chromatography standard solution was in the Undecane position) on milled Lactohale 300 (lactose monohydrate) at temperature 30° C., flow rate 20 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/nm:

(83) TABLE-US-00012 t.sub.rC6 t.sub.rC7 t.sub.rC8 t.sub.rC9 t.sub.rC10 t.sub.0 γ.sub.s.sup.d Run min min min min min min (mJ .Math. m.sup.−2) K.sub.CH.sub.2.sup.a 1 0.4665 0.7131 1.4770 3.8370 11.1395 0.3489 43.01 3.0947 0.017 2 0.4590 0.7131 1.4862 3.8437 11.0987 0.3406 42.73 3.0833 0.273

(84) FIG. 6. shows the IGC chromatogram of inverse gas chromatography standard solution containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane (inverse gas chromatography standard solution was in the Undecane position) on milled Lactohale 300 (lactose monohydrate) at temperature 30° C., flow rate 20 ml/min, and target fractional surface coverage (the amount of injected probe) 0.005 n/nm.

(85) The inverse gas chromatography standard solution (n-hexane, n-heptane, n-octane, n-nonane and n-decane) enabled to measure dispersive surface free energy and the retention times of the n-alkanes accurately, as values were less than 0.7% (as illustrated by Tables of the above examples 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10). Also, the experiment running time was shortened to around the fifth when one injection of the inverse gas chromatography standard solution (containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane) was used instead of five injections of n-hexane, n-heptane, n-octane, n-nonane, and n-decane. The measurement accuracy was enhanced when the inverse gas chromatography standard solution (containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane) was used instead of five injections of n-hexane, n-heptane, n-octane, n-nonane, and n-decane, as the value of were smaller when inverse gas chromatography standard solution (containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane) was used instead of five injections of n-hexane, n-heptane, n-octane, n-nonane, and n-decane (as clarified in Example 9 and Example 10).

(86) The peak areas reflect the target fractional surface coverage. The peak areas were consistence with the amount of injected (target fractional surface coverage) of the inverse gas chromatography standard solution (containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane) (as clarified in FIG. 4). Also FIG. 6 shows the peak areas of the inverse gas chromatography standard solution (containing n-hexane, n-heptane, n-octane, n-nonane, and n-decane) were equal to the peak areas of their counterparts of n-hexane, n-heptane, n-octane, n-nonane, and n-decane within the limit stated herein in Equation 14 (±20%).

(87) FIG. 7 is an example of a volumetric container which can be designed according to Equation 13 (mentioned herein) and used to prepare inverse gas chromatography standard solutions.

(88) All publications mentioned in the above specification are herein incorporated by reference. As a person of ordinary skill in the art will appreciate, many modifications and variations of the embodiments described herein may be made without departing from the scope of the invention, which is defined by the following claims. The specific embodiments described herein are offered by way of example only.