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Ph. D. ThesisPh. D. Thesis 3. Theory – Quantification of the Refrigerants R22 and R134a: Part I3. Theory – Quantification of the Refrigerants R22 and R134a: Part I 3.2. Single Analytes3.2. Single Analytes
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Ph. D. Thesis
  Table of Contents
  1. Introduction
  2. Theory – Fundamentals of the Multivariate Data Analysis
  3. Theory – Quantification of the Refrigerants R22 and R134a: Part I
    3.1. Experimental
    3.2. Single Analytes
    3.3. Sensitivities
    3.4. Calibrations of the Mixtures
    3.5. Variable Selection by Brute Force
    3.6. Conclusions
  4. Experiments, Setups and Data Sets
  5. Results – Kinetic Measurements
  6. Results – Multivariate Calibrations
  7. Results – Genetic Algorithm Framework
  8. Results – Growing Neural Network Framework
  9. Results – All Data Sets
  10. Results – Various Aspects of the Frameworks and Measurements
  11. Summary and Outlook
  12. References
  13. Acknowledgements
Research Tutorials
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3.2.   Single Analytes

The first step was the characterization of the polymers in respect to the sensor responses for the analytes. The responses of the 6 sensors coated with the different polymers were simultaneously measured by the array setup. The sensor responses of the polymers PUT, PDMS and HBP are shown on the left side of figure 6. These 3 polymers contain polar groups and should therefore show different response characteristics for analytes with different polarities or polarizabilities [157]. The sensor responses of the polymers UE 2010 and M 2400 are shown on the left side of figure 7. Both polymers are amorphous glassy polymers with a microporous structure whereby the mean size of the pores of M 2400 is 0.1 nm3 [158] and the mean size of the pores of UE 2010 is 0.08 nm3 [159]. These polymers can discriminate analytes due to different sizes of the analytes as only analytes with a smaller volume of the molecules than the volume of the pores sorb into the pores of the polymers. Further discussions regarding the pores can be found in chapter 5.

According to both figures, all polymers show a fast and reversible swelling when exposed to R22 whereby the polar polymers PUT and PDMS are reaching an equilibrium state instantly. These two polymers were measured above their static glass transition temperature. The glass transition temperature is the temperature, above which the molecules in the polymer backbone can move relatively to one another resulting in a quasi-liquid state [160],[161]. Thus, the interactions between vapor and coating can be described as dissolution of a solute vapor in a solvent coating resulting in a very fast sorption and desorption of the analytes, which can be modeled by linear solvation energy relationships (LSERs) [162]-[164]. Consequently, these two polymers show also an immediate sorption and desorption of R134a. On the other hand, exposed to R134a the microporous polymers UE 2010 and M 2400 do not reach an equilib­rium state within 30 minutes and the signals need 2 hours to return to the baseline. Due to the bigger volume of the molecules of R134a, the sorption process is kinetically inhibited and the molecules are less (and more slowly) sorbed into the polymers.

figure 6:    Sensor responses, calibration curves and standard deviations of 3 measure­ments of the polar polymers recorded with the array setup.

figure 7:    Sensor responses, calibration curves and standard deviations of 3 measure­ments of the microporous polymers recorded with the array setup.

The right sides of figure 6 and figure 7 show the signals of the 6 sensors versus the concen­trations of the 2 analytes. This type of plots is often referred to as calibration curve. The correlation of the polymer swellings (the sensor signals) with the analyte concentrations is often described as a Henry sorption [165], a Langmuir sorption [166] or a combination of both types [167]-[169]. For all polymers under investigation, the sorption of R134a is best described as a linear Henry type sorption. This type of sorption process is an indication of an unspecific sorption process [170]. The molecules of R134a are too big for the micropores and therefore only an unspecific sorption process into the polymer matrix of the microporous polymer can be observed. The sorption causes a swelling of the polymer matrix, which can be observed as an increase of the thickness of the sensitive layer. The sorption of R134a and of R22 into the two polar polymers is also of the Henry type, since both analytes do not have distinctive polar groups and thus do not specifically interact with the polymers.

On the other hand, the sorption of R22 into the microporous polymers UE 2010 and M 2400 shows a calibration curve, which can be best described by the combination of the Henry and Langmuir sorption. The Langmuir type sorption can be found, if there is a specific interaction and if the amount of sorption and interaction sites is limited [170]. The combination of both sorption types can be best detected when examining the curve for high analyte concentrations, as the Henry sorption and the Langmuir sorption are identical for small concentrations. If the sorption is a pure Langmuir sorption, the calibration curve should pass into saturation for high concentrations whereas the combination of both types of sorption results in a curve with a positive slope for high concentrations. In figure 7, both polymers show for R22 this latter case of a Langmuir sorption with a small portion of a Henry sorption. Furthermore, the figures demonstrate that the microporous polymers show a much higher slope for R22 than for R134a. Both findings can be explained by a sorption of the small molecules of R22 into the micropores. This results in higher signals of the R22 sorption, as the unspecific Henry sorption into the polymer matrix (which is also present for R134a) is overlaid by a specific Langmuir sorption into the pores (which is not present for the bigger R134a molecules). The number of pores is limited and consequently the sorption of the molecules into the pores and with it the Langmuir part of the sorption reaches saturation for higher concentrations.

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