CHAPTER 5 EFFECTIVE ATOMIC NUMBER OF SELECTED POLYMERS BY GAMMA BACKSCATTERING TECHNIQUE Page no. 5.1 Introduction 132 5.2 Methods and measurements 132 5.3 Saturation thickness of elements and polymers 136 5.4 Effective atomic number of polymers 144 5.5 Signal-to-noise ratio 147 5.6 Conclusions 152
5.1 Introduction Nondestructive nuclear radiation techniques often have a great advantage over the traditional chemical techniques used for the determination of effective atomic numbers of composite materials of various interests. For composite materials like alloys, polymers, biological materials, etc. the atomic number cannot be represented uniquely by a single number, as in the case of elements. This number, in composite materials, is called effective atomic number (Z eff )(İçelli, 2006; Prasad et al., 1998). Effective atomic number of a material is used for the interpretation of attenuation of X-ray and gamma rays by a polymer or composite materials. Effective atomic numbers of various combinations of elemental absorbers are helpful in deciding the required radiation dose to human tissues and for proper design of radiation shielding (Latha et al., 2012). The study of effective atomic number also provides conclusive information about the mixture when gamma photons interact with materials. Further, estimation of Z eff is useful in characterizing the materials useful for applications in the chemical industry, nuclear industry, space programme, scientific and engineering industries, including biological applications. 5.2 Methods and measurements In the present experimental study, the backscattered photons from targets of Carbon, Aluminium, Iron, Copper, Polypropylene, Polycarbonate, Polymethyl methacrylate (Acrylic), Polytetraflouroethylene (Teflon), and Polyvinyl chloride (PVC) were measured using a NaI(Tl) scintillation detector placed at 90 to the incident beam using gamma photons of 662 kev( 137 Cs of strength 5.8 mci). The distance of the scatterer from the detector was kept 262 mm so that the angular spread due to the detector collimator (60 mm) on the target was ± 6.5. The experimental arrangement explained in detail in Section 2.2, was 132
used to conduct these studies. The schematic diagram of the experimental setup is shown in Figure 5.1. Figure 5.1.: Schematic diagram of the experimental setup The Compton backscattering experiment was carried out as a function of sample thickness for the different materials listed above. The dead time corrected acquisition time of 1000 seconds was used to acquire the data. A minimum of 4 trials were run for each sample to reduce the statistical error (Knoll, 1988). A typical backscattered spectrum obtained for copper of 40 mm thickness as a scatterer is shown in Figure 5.2(a). The backscattered spectrum was processed, following the procedure explained in Section 2.9, to obtain multiple scattered photons. The same procedure was followed for all the scattering targets. 133
Figure 5.2.: (a) A typical experimentally observed spectrum with 40 mm thick copper target at a scattering angle of 90, (b) An observed background spectrum without target in the primary beam, (c) Background subtracted events, (d) Normalized analytically reconstructed single scattered full energy peak The typical spectra of the gamma backscattered photons for different materials such as carbon, aluminium, iron, and copper are presented in Figure 5.3. It is evident from the figure, that maximum backscattered photons are recorded for copper. This may be due to the fact that the atomic number of copper is higher, and hence, the density is higher. Further, it can be noticed that the intensity of the backscattered photons decreases with the decreasing of their atomic numbers. This observation is in accordance with the theoretical expectation that as atomic number decreases the density also decreases. 134
Figure 5.3.: Backscattered spectrum of carbon, aluminium, iron, and copper of thickness 40 mm The backscattering of gamma photons with respect to different thickness (5, 10, 20, 30, and 40 mm) of copper as a scatterer was studied and the corresponding results are demonstrated in Figure 5.4. It can be noticed that, as the thickness increases, the intensity of the backscattered photons increases and continues until it reaches its saturation thickness. It can be seen from the figure that the backscattered photon intensity for thicknesses 20, 30, and 40 mm are very close to each other. It has been observed from earlier studies that when the thickness of the scatterer approaches its saturation thickness, the difference in the backscattered intensity decreases, and finally, saturates. 135
Figure 5.4.: Variation of backscattered photons for different thicknesses of copper target 5.3 Saturation thickness of elements and polymers The number of multiple scattered counts due to the backscattering of gamma photons for various thicknesses of elements and polymers at an angle of 90 are presented in Table 5.1. As expected, the multiple scattering increases with increase in sample thickness and saturates at its saturation thickness. This process is explained in detail in Section 4.1.2.2. The sudden increase in the intensity of multiple scattered photons at lower thicknesses can be seen from the table for both elements and polymers. Conversely, the incremental increase of multiple scattered photons decreases with increasing target thickness for all the targets, including polymers. 136
Table 5.1.: The number of multiple scattered counts for various thicknesses for different elements Thickness (mm) Multiple scattered counts Carbon 20 6,551 (Z = 6) 40 20,271 60 36,787 90 49,182 120 50,524 150 50,431 180 51,992 Aluminium 20 46,414 (Z = 13) 40 72,834 60 85,559 80 91,055 100 93,059 120 92,452 150 94,579 Iron 5 46,395 (Z = 26) 10 69,202 20 94,663 30 102,073 40 104,719 50 109,664 Copper 5 42,452 (Z = 29) 10 63,916 15 101,522 20 111,635 30 118,823 40 119,010 137
Table 5.2.: The number of multiple scattered counts for various thicknesses for different polymers Polymers Thickness (mm) Multiple scattered counts Polycarbonate 20 13,807 (Z eff = 6.09) 40 38,230 60 52,361 80 61,602 100 65,764 120 66,003 140 67,057 160 65,006 Polypropylene 20 9,651 (Z eff = 5.44) 40 23,050 60 42,302 80 50,440 100 53,654 120 53,672 140 55,140 160 56,641 Polymethyl 20 11,229 methacrylate 40 32,319 (Z eff = 6.47) 60 48,061 80 58,729 100 63,064 120 63,741 140 63,550 160 63,810 138
continuation of Table 5.2 Polytetrafluoroethylene (Z eff = 8.43) Polyvinyl chloride (Z eff = 13.86) Thickness (mm) Multiple scattered counts 20 30,104 40 58,070 60 68,367 80 74,034 100 76,832 120 79,313 140 88,981 160 84,557 20 19,415 40 40,849 60 55,317 80 63,452 100 66,051 120 67,391 140 67,552 160 67,483 The verification and validation of the experimentally obtained results is an important process and is necessary to strengthen the accuracy in the experimental measurements. To validate the results obtained, an experimental setup has been simulated using the Monte Carlo code as explained in Section 4.1.2. The MCNP plot of target geometry is shown in Figure 5.5. The 137 Cs source of 662 kev with an active dimension of 10 mm in diameter and 6 mm in length used in the experimental study was used in the simulation study as well. The relative error noticed in the MCNP calculation was about 4%. The dotted curves are the best-fitted curves of the simulated data. 139
Figure 5.5.: MCNP plot of target geometry The experimental results and the results obtained through MCNP simulation studies were plotted and demonstrated in Figures 5.6 to 5.8. The plots of all the elements and polymers show that the intensity of the multiple scattered photons increases with increase in target thickness and attains saturation as explained earlier. It can be noticed that the MCNP simulation results plotted along with the experimental results agrees well and this observation validates the present experimental results. The experimental and MCNP simulation results for carbon, aluminium, iron, and copper are compared in Figure 5.6. It can be seen from the figure that the experimentally measured values agree well with the simulated data. However, a small deviation can be noticed at the lower thicknesses for elements of lower atomic numbers (aluminium and carbon). This deviation may be due to the higher signal-to-noise ratio levels at lower thickness and materials with lower atomic numbers. The single scattered photons contribute more to the backscattered spectrum compared to multiple scattered photons at lower thickness and lower density of scattering material. This may be the main factor 140
for the discrepancy in the experimental and MCNP results at lower thickness and lower atomic number of the scattering materials. y = a*exp (x/b) + y 0 Figure 5.6.: Multiple scattered photons as a function of target thickness for elements The variations in multiple scattered photon intensity of polymers as a function of target thickness were compared with the results of the MCNP simulated results in Figures 5.7 and 5.8. There was an overall good agreement between the experimental results and the simulated data for all the polymers used in the present investigation. 141
y = a*exp (x/b) + y 0 Figure 5.7.: Multiple scattered photons as a function of target thickness for Polypropylene, Polycarbonate, and Polytetraflouroethylene y = a*exp (x/b) + y 0 Figure 5.8.: Multiple scattered photons as a function of target thickness for Polymethyl methacrylate and Polyvinyl chloride 142
The saturation thicknesses of the elements and polymers used in this study were estimated using the processed experimental data. The comparison between the experimentally obtained and MCNP simulated saturation thicknesses for elements and polymers are tabulated in Table 5.3. It can be noticed that as expected, the saturation thickness decreases with increasing atomic or effective atomic number of the target material (column 2). The saturation thickness estimated using MCNP code is tabulated in column 4. It can be seen from the table, that the saturation thickness obtained from the MCNP simulation studies are in accordance with the experimentally measured values. The deviations between these two are tabulated in column 4 and are found to vary from 0 to 7.2 %. This observation validates and supports the experimental studies. Table 5.3.: The experimental and MCNP simulated saturation thickness Elements Z (or Saturation thickness (mm) Difference Z eff ) Experimental MCNP in % Carbon 6 101 101 0 Aluminium 13 75.3 76.4 1.4 Iron 26 30.4 32.6 7.2 Copper 29 23.1 23 0.4 Polypropylene 5.44 102 103.4 1.4 Polycarbonate 6.09 98 96 2.0 Polymethyl methacrylate 6.47 97 99 2.0 Polytetrafluoroethylene 8.43 91.4 90 1.5 Polyvinyl chloride 13.86 71.7 72.5 1.1 143
5.4 Effective atomic number of polymers Effective atomic number (Z eff ) is a convenient parameter in designing radiation shielding, computing absorbed dose and energy absorption, and build-up factors studies. Compounds or mixtures can be characterized by Z eff, by providing insight about the photon interaction processes involving absorption as well as scattering. The effective atomic number of composite materials can be found by the simple power law of the form (Taylor et al., 2012) Whereby, the relative electron fraction of the i th element Z i is given by f i, such that 1. Mayneord (Khan, 2003) used the value of exponent m in the above relation as 2.94.Hence, the above equation can be written as Using the elemental composition, the effective atomic numbers of the polymers were estimated and tabulated in column 5 of Table 5.4. A graph of experimentally measured saturation thickness versus atomic number of elements is plotted and shown in Figure 5.9. It is clear from the figure that the saturation thickness for particular incident energy of gamma photons (in this case 662 kev) decreases with increasing atomic number. 144
Figure 5.9.: Plot of saturation thickness for elements and polymers. Experimental errors are represented by the size of the data points From the above graph, the measured saturation thicknesses of polymers were used to assign the corresponding effective atomic numbers, and so the obtained effective atomic numbers are tabulated in column 6 of Table 5.4. It can be noticed that the effective atomic numbers obtained experimentally (column 6) compares well with the values estimated using the empirical equation (column 5). Table 5.4.:The saturation thickness and effective atomic number of selected polymers Polymer Monomer Saturation Effective atomic number Elemental thickness weightage Empirical (mm) Experimental equation Polypropylene C 3 H 6 75% C, 25% H 102 5.44 5.64 (±0.3) Polycarbonate C 15 H 16 O 2 74% C, 13% H, 13% O 98 6.09 6.63 (±0.4) Polymethyl C 5 O 2 H 8 55% C, 30% O, methacrylate 15% H 97 6.47 6.91 (±0.3) Polytetrafluoroethylene C 2 F 4 25% C, 75% F 91.4 8.43 8.34 (±0.4) Polyvinyl chloride C 2 H 3 Cl 38% C, 9% H, 53% Cl 71.7 13.86 13.77 (±0.2) 145
The effective atomic numbers experimentally obtained, theoretically estimated and reported in literature are compared in Table 5.5. It can be seen from the table that experimentally measured values of the present study are very close and compares well with the empirically derived values. The percentage deviation between these values ranges from 0.6 to 8.8. This shows the very good agreement between the two. Further, it can be noticed that the values for Polyvinyl chloride reported by Naydenov et al. (2004) and Polytetrafluoroethylene reported by Prasanna Kumar et al. (2010) are comparable with the corresponding values of the present study. The values reported for Polypropylene and Polymethyl methacrylate by Kucuk et al. (2013) and for Polymethyl methacrylate by Prasanna Kumar et al. (2010) disagree and deviate by about 50 % compared to the results of the present study. Table: 5.5. :The comparison of atomic number of selected polymers with literature Polymer name Empirical equation Experimental Effective atomic number (Kucuk et al., 2013) Naydenov et al., 2004) (Prasanna Kumar et al., 2010) Polypropylene 5.44 5.64 (3.6) 2.6 (52.2) - - Polycarbonate 6.09 6.63 (8.8) - - - Polymethyl methacrylate 6.47 6.91 (6.8) 3.4 (47.4) - 3.7 (42.8) Polytetrafluoroethylene 8.43 8.34 (1.0) - - 8.8 (4.4) Polyvinyl chloride 13.86 13.77 (0.6) - 14.04 (1.3) - Numbers in parenthesis shows the percentage deviation from the empirically derived values 146
5.5 Signal-to-noise ratio The ratio of the number of single scattered events to the number of multiple scattered events is considered as the signal-to-noise ratio. In Compton profiles and cross-section measurements, only single scattered photons are desired and multiple scattered photons act as background noise to the original signal. Therefore, estimation of the signal-to-noise ratio becomes one of the important parameters and plays an important role in these studies. The signal-to-noise ratio is estimated using measured multiple scattered photons and single scattered photons from reconstructed spectrum using measured FWHM values. The results obtained for the elements are tabulated in Table 5.6 and for polymers in Table 5.7. It can be noticed from Table 5.6 that the incremental increase of both single and multiple scattered photons decreases with increasing target thickness for all the targets. This observation is more predominant in the case of single scattered photons. It can also be noticed that the signal-to-noise ratio (Table 5.6, column 5) is relatively higher at lower thickness for elements. However, among the elements, it is higher by orders of magnitude in carbon compared to the other three elements aluminium, iron, and copper. Among these three elements, it is slightly higher in aluminium. This can be attributed to their lower atomic numbers. From these observations, it is evident that as the atomic number of the elements increases, the signal-to-noise ratio decreases. This signal-to-noise ratio is stable above 90 mm of thickness in case of carbon, above 60 mm in case of aluminium, above 20 mm in case of iron and it is above 15 mm of thickness in the case of copper. These results show that the signal-to-noise ratio varies with respect to both thickness and atomic number of the scatterer. Based on this observation, one can conclude that, the thicker the 147
scattering material, the lower the signal-to-noise ratio. In addition, higher the atomic number of the scattering material, lower the signal-to-noise ratio. Table 5.6.: The number of multiple and single scattered counts for various thicknesses for different metals Thickness (mm) Single scattered Multiple scattered Signal -tonoise ratio Carbon (Z = 6) Aluminium (Z = 13) Iron (Z = 26) Copper (Z = 29) counts counts 20 113,135 6,551 17.26 40 131,078 20,271 6.46 60 133,489 36,787 3.62 90 129,026 49,182 2.62 120 130,433 50,524 2.58 150 128,806 50,431 2.55 180 147,953 51,992 2.84 20 233,266 46,414 5.02 40 250,627 72,834 3.44 60 250,121 85,559 2.92 80 250,647 91,055 2.75 100 245,450 93,059 2.63 120 245,698 92,452 2.65 150 246,044 94,579 2.60 5 181,786 46,395 3.91 10 222,229 69,202 3.21 20 241,077 94,663 2.54 30 244,366 102,073 2.39 40 248,027 104,719 2.36 50 247,356 109,664 2.25 5 155,536 42,452 3.66 10 193,617 63,916 3.02 15 257,072 101,522 2.53 20 266,104 111,635 2.38 30 269,671 118,823 2.27 40 268,082 119,010 2.25 148
It can be seen from Table 5.7, that the variations of multiple backscattered photons for different polymers commensurate with their thicknesses. This observation is similar to that occured in the case of elements. A similar trend to that of elements in variation in the signal-to-noise ratio, multiple and single scattered events with respect to thickness, and their effective atomic numbers have been noticed. It is very clear from the table, that signal-to-noise ratio is orders of magnitude higher for lower thicknesses of polymers, and is still more predominant in the case of materials with lowest effective atomic numbers presented in the table (ranging from 5.64 to 6.91). Table 5.7.: The number of multiple and single scattered counts for various thicknesses for different polymers Polymers Polycarbonate (Z eff = 6.09) Polypropylene (Z eff = 5.44) Polymethyl methacrylate (Z eff = 6.47) Thickness (mm) Single scattered counts Multiple scattered counts Signal -tonoise ratio 20 158,587 13,807 11.48 40 197,502 38,230 5.16 60 195,818 52,361 3.74 80 185,531 61,602 3.01 100 187,100 65,764 2.84 120 190,076 66,003 2.88 140 180,565 67,057 2.69 160 186,508 65,006 2.86 20 139,663 9,651 14.47 40 168,829 23,050 7.32 60 167,980 42,302 3.97 80 159,542 50,440 3.16 100 159,243 53,654 2.96 120 161,325 53,672 3.01 140 158,439 55,140 2.87 160 161,060 56,641 2.84 20 155,029 11,229 13.80 40 186,183 32,319 5.76 60 187,862 48,061 3.90 80 187,215 58,729 3.18 100 183,898 63,064 2.91 120 181,963 63,741 2.85 140 182,217 63,550 2.86 160 186,311 63,810 2.92 149
continuation of Table 5.7 Polytetrafluoroethylene (Z eff = 8.43) Polyvinyl chloride (Z eff = 13.86) Thickness Single scattered counts Multiple scattered counts Signal -tonoise ratio 20 219,017 30,104 7.27 40 237,725 58,070 4.09 60 231,801 68,367 3.39 80 233,378 74,034 3.15 100 232,806 76,832 3.03 120 229,875 79,313 2.89 140 233,941 88,981 2.62 160 233,098 84,557 2.75 20 144,314 19,415 7.43 40 186,059 40,849 4.55 60 186,050 55,317 3.36 80 183,932 63,452 2.89 100 178,629 66,051 2.70 120 176,580 67,391 2.62 140 172,310 67,552 2.55 160 182,060 67,483 2.69 The signal-to-noise ratio for all the materials as a function their thickness are plotted in Figure 5.10. It can be noticed that as the thickness increases the signal-to-noise ratio decreases. This indicates the presence of more multiple scattered photons in comparison to the single scattered events as the thickness of the scatterer increases. If, multiple scattering events are to be avoided for any particular purpose, maintaining of high signal-to-noise ratio is a must, and which can be obtained by using very thin targets. Further, it can be noticed that the higher the atomic number, the lower the signal-to-noise ratio. It is further evident from Figure 5.10, that the ratio is lowest for copper (Z=29) followed by iron (Z=26), which are elements of higher atomic numbers amongst the materials used in this investigation. The signal-to-noise ratio for aluminium (Z=13) is more than that of copper and iron as its atomic number is almost half 150
of iron and copper, but is closer to Polyvinyl chloride (Z eff =13.86) and Polytetrafluoroethylene (Z eff =8.43), as their atomic numbers are relatively closer to that of aluminium. The maximum signal-to-noise ratio is recorded for carbon (Z=6) followed by Polypropylene (Z eff =5.44), Polymethyl methacrylate (Z eff =6.47), and Polycarbonate (Z eff =6.09). The effective atomic numbers of all these materials are between 5 and 7. As the value of the atomic number decreases, the signal-to-noise ratio increases. Increase in atomic number of the scatterer increase its density, and thereby, it increases the intensity of the multiple scatter photons, and that may be one of the main reasons for the higher signal-to-noise ratio for elements of lower atomic numbers. y = a*exp (-x/b) + y 0 Figure 5.10.: Signal-to-noise ratio for elements and polymers 151
5.6 Conclusions The following conclusions are drawn from the detailed results and discussions presented above: The major contribution in the backscattering of thick targets is from multiple scattered photons, having energy equal to that of single scattered photons. The intensity of the multiple scattered events increases with increase in the target thickness and becomes almost constant beyond a particular value called saturation thickness. The saturation thickness decreases with increasing atomic number of the scattering material. There is a good agreement between the experimentally obtained results of the saturation thickness and the results obtained from the MCNP simulation studies for all the targets used in the present investigation. The effective atomic numbers of the selected polymers were estimated using their experimentally measured saturation thicknesses and they closely agree with the theoretically estimated values. The values of the effective atomic numbers of the present investigation agree well with Naydenov et al. (2004) for Polyvinyl chloride and Prasanna Kumar et al. (2010) for Polytetrafluoroethylene with a deviation of about 4%. However, the result of the present work disagrees with the reported values for Polypropylene and Polymethyl methacrylate by Kucuk et al. (2013) and for Polymethyl methacrylate by Prasanna Kumar et al. (2010). The signal-to-noise ratio decreases with the increase in atomic (or effective) atomic numbers of the scattering materials. 152