Calibrations were performed for the temperature probes, pressure transducer, and the gas chromatograph-thermal detector as has already been discussed in Chapter 5. The mathematical formulae used in the correlation of the calibration data and the resulting charts for the temperature and pressure measuring devices are published in Appendix A. However, detail on the calibration of the GC thermal detector is published in this chapter, as the procedure used deviated slightly from the norm. The determination of the uncertainties for all the measured variables was achieved through the use of the method outlined by the National Institute of Standards and Technology (NIST) in conjunction with the instructions formulated by Soo (2011) and Nelson (2012), which were specific to VLE measurements.
Composition
The initial calibration polynomials for the thermal detector which were generated for each chemical species and achieved via direct injection were not capable of covering the mole fraction range of the sampled data. Thus mixtures of each component with a compatible solvent/gas were made, in a bid to inject smaller amounts of the required component into the GC, resulting in calibration polynomials which cover a wide mole fraction range. The generation of multiple calibration polynomials from injecting pure components as well as mixtures could be useful in one of two ways:
Results and discussion
69 | P a g e
Allow for the accurate calculation of the errors obtained when only one polynomial is extrapolated below or above its calibration range.
Allow for the use of different polynomials in the calculation of mole fractions from the samples, depending on the range each polynomial covers.
In this study, the first option was utilised as it was noted to be the most efficient. Thus data from the calibration polynomial obtained through the direct injection of pure components were compared to those generated by injecting mixtures, and the deviation of the pure component calibration from the mixture calibration was noted. This error was then used appropriately in the calculation of compositional uncertainty for the data points which had GC peak areas that were below the pure component calibration range. The linear plots of the calibration polynomials, as well as the plots depicting the errors induced by the aforementioned polynomials, are displayed in the following section.
Carbon dioxide
GC calibrations for carbon dioxide were undertaken via the direct injection of the pure component as well as the injection of a carbon dioxide + helium mixture. The errors induced by the calibration polynomials on the number of moles did not exceed 1% for both scenarios.
Figure 7-1: Deviation plots for true and calculated carbon dioxide number of moles, (Left) injection of pure carbon dioxide, (Right) injection of a carbon dioxide helium mixture.
-0,015 -0,010 -0,005 0,000 0,005 0,010 0,015
0,00E+00 6,00E-06 1,20E-05
(nTrue-ncalc)/nTrue[mol]
nTrue[mol]
-0,015 -0,010 -0,005 0,000 0,005 0,010 0,015
0,00E+00 1,70E-06 3,40E-06
(nTrue-nCalc)/nTrue[mol]
nTrue[mol]
Results and discussion
70 | P a g e Figure 7-2: GC calibration plots for carbon dioxide via direct injection from a 250µL syringe, (●) pure carbon dioxide, (▲) carbon dioxide + helium mixture. (Left) The superimposed plot for the two calibrations, (Right) The expanded plot. (—) mixture calibration polynomial, (—) pure component calibration polynomial.
Figure 7-2 indicates the deviation obtained when the pure carbon dioxide calibration equation is used to extrapolate for moles in the low peak area range. Comparison of the two calibration equations indicated that the pure carbon dioxide calibration polynomial could be effectively extrapolated to the lower peak area regions at an error of approximately 4%. The value for this discrepancy was obtained by first multiplying the G.C peak areas of the pure component calibration with the gradients of both the pure component and mixture calibration equations, resulting in two sets of mole values. Thereafter the percentage error between the two sets of values was computed. The same procedure was used for all the other components were extrapolation of the calibration polynomial was necessary. A sample calculation for this procedure is published in Appendix B.
1,1,2,2-tetrafluoroethyl 2,2,3,3-tetrafluoropropyl ether.
Calibration for the hydrofluoroether was undertaken for only the pure compound without the employment of any mixtures because for this particular system; the pure component calibration was deemed sufficient, as the linear plot passed through the origin.
0,E+00 2,E-06 4,E-06 6,E-06 8,E-06 1,E-05 1,E-05
0 15 000 000 30 000 000
nTrue[mol]
Peak areas
0,E+00 5,E-07 1,E-06 2,E-06 2,E-06 3,E-06
0 5 000 000
nTrue[mol]
Peak areas
Results and discussion
71 | P a g e Figure 7-3: Calibration plots for 1,1,2,2-tetrafluoroethyl-2,2,3,3-tetrafluoropropyl ether. (Left), Linear calibration plot (Right) Deviation plot of true and calculated 1,1,2,2-Tetrafluoroethyl 2,2,3,3- tetrafluoropropyl ether number of moles.
The deviations in the calibration of the fluorinated ether did not exceed 2% and were thus deemed acceptable.
Perfluorocarbons
In order to effectively extrapolate data using the generated calibration polynomials for the perfluoroheptane and perfluorononane, mixtures of each PFC with pentane and hexane (respectively) were formulated, and these were utilised in the same manner as highlighted for carbon dioxide above. The rationale behind the selection of the two hydrocarbons was discussed in Chapter 5.
0,E+00 1,E-06 2,E-06 3,E-06 4,E-06 5,E-06 6,E-06 7,E-06
0 30 000 000 60 000 000
nTrue[mol]
Peak area
-0,02 -0,01 0,00 0,01 0,02
0,00E+00 4,00E-06 8,00E-06 (nTrue-nCalc)/nTrue[mol]
nTrue[mol]
Results and discussion
72 | P a g e Figure 7-4: Deviation plots for true and calculated perfluoroheptane number of moles, (Left) injection of pure perfluroheptane, (Right) injection of a perfluoroheptane + pentane mixture.
Figure 7-5: Deviation plots for true and calculated perfluorononane number of moles, (Left) injection of pure perflurononane, (Right) injection of a perfluorononane + hexane mixture.
The errors induced by the calibration polynomials for both PFCs were well below 2%. For both PFCs the pure component calibration polynomial was used for sample analyses, and the errors which were incurred during extrapolation for the perfluoroheptane and perfluorononane were 3%
and 2% respectively.
-0,01 0,00 0,01
0,00E+00 2,50E-06 5,00E-06
(nTrue-nCalc)/nTrue[mol]
nTrue [mol]
-0,02 0,00 0,02
0 1,5E-08 3E-08
(ntrue-ncalc)/nTrue[mol]
nTrue [mol]
-0,02 -0,01 0,00 0,01 0,02
0,00E+00 2,00E-06 4,00E-06
(nTrue-nCalc)/nTrue[mol]
nTrue[mol]
-0,02 -0,01 0,00 0,01 0,02
0,00E+00 3,00E-07 6,00E-07
(ntrue-nCalc)/nTrue[mol]
nTrue[mol]
Results and discussion
73 | P a g e Figure 7-6: GC calibration plots for perfluoroheptane via direct injection from a 250µL syringe, (●) pure perfluoroheptane, (▲) perfluroheptane + pentane mixture. (Left) The superimposed plot for the two calibrations. (right) The expanded plot, (—) mixture calibration polynomial, (—) pure component calibration polynomial.
Figure 7-7: GC calibration plots for perfluorononane via direct injection from a 250µL syringe, (●) pure perfluorononane, (▲) perflurononane + hexane mixture. (Left) The superimposed plot for the two calibrations. (Right) The expanded plot, (—) mixture calibration polynomial, (—) pure component calibration polynomial.
The expanded plots displayed on Figures 7-6 and 7-7 highlight that the pure component and mixture calibration polynomials had near identical slopes, which further indicates that
0,00E+00 1,00E-06 2,00E-06 3,00E-06 4,00E-06 5,00E-06
0 20000000 40000000
nTrue[mol]
Peak area
0,00E+00 1,00E-08 2,00E-08 3,00E-08 4,00E-08 5,00E-08
0 100000 200000
nTrue [mol]
Peak area
0,00E+00 5,00E-07 1,00E-06 1,50E-06 2,00E-06 2,50E-06 3,00E-06 3,50E-06 4,00E-06
0 20000000 40000000
nTrue[mol]
Peak area
0,00E+00 2,00E-08 4,00E-08 6,00E-08 8,00E-08 1,00E-07
0 500000 1000000
nTrue[mol]
Peak area
Results and discussion
74 | P a g e extrapolation of the pure component calibration to the lower peak area ranges could be effectively performed.