Open Access 
Abstract
Introduction: Recently, the free-volume hole features of poly(styrene sulfonic acid) (PSSA)-grafted poly(ethylene-co-tetrafluoroethylene) polymer electrolyte membranes (ETFE-PEMs) have been studied using positron annihilation lifetime spectroscopy (PALS) to determine the relationship between gas crossover through a PEM and a fuel cell. As one such series, this work investigates the source correction in PAL spectroscopic analysis for ETFE-PEM. Method: ETFE-PEM was prepared by radiation-induced graft polymerization and subsequent sulfonation. The free-volume hole characteristics of ETFE-PEM with a grafting degree (GD) of 106% were determined using PALS with and without source correction. Results: After source correction, the original-ETFE and ETFE-PEM strains exhibited increases in r3 (smaller radius of free-volume holes in the lamellar amorphous regions, the PSSA grafts, and the interface zones inside the lamellae) and r4 (larger radius of free-volume holes in the mobile amorphous layers and the PSSA grafts outside of the lamellae). In addition, the full width at half maximum (FWHM) of r3 is much greater than that of r4 due to the rearrangement in the mobile amorphous region and the polystyrene layers outside the lamellar structure. Conclusion: Source correction causes a significant change in the distribution curves of r3 for the original-ETFE and ETFE-PEM. Thus, source correction of positron annihilation lifetime spectroscopic analyses is an important issue for determining the o-Ps lifetime of polymers, which is near the lifetime of positrons in source materials.
INTRODUCTION
Proton exchange membrane fuel cells (PEMFCs) have received much attention for novel power generation because these devices result in no emission of environmental pollutants, high energy generation efficiency, low operating temperature, and quick operation 1 . PEMFCs can be applied in transportation, mobile communication equipment, charging stations, etc. 2 . Nafion is one of the most common commercial membranes used for PEMs 3 , 4 , 5 . However, its limitations, such as high cost and low performance at high temperature (> 100 °C) and low relative humidity (RH) (RH < 50%), have triggered the development of alternative membrane materials for PEMs. Recently, poly(styrene sulfonic acid)-grafted poly(ethylene-co-tetrafluoroethylene) (EP) electrolyte membranes (ETFE-PEMs) have been studied intensively to replace Nafion because of their competitive price, performance, and durability. Compared with Nafion, the ETFE-PEM shows greater mechanical strength, conductance, and microstructural stability under immersed conditions 6 , 7 , 8 , 9 .
Positron annihilation lifetime spectroscopy (PALS) is a potential method that provides molecular and nanoscale information on the free-volume hole features of materials through the lifetime and annihilation intensity of positron and positronium (Ps) ions. Positronium is the metastable hydrogen-like bound state of a positron and an electron. Ps freely has two intrinsic lifetimes, namely, para-positronium ( p -Ps, singlet state of Ps) and ortho-positronium ( o -Ps, triplet state of Ps). In the singlet state, p -Ps emit two energetic photons at 511 keV with a typical lifetime of 0.125 ns in vacuum. In the triplet state, o -Ps has a self-annihilation lifetime of 142 ns in vacuum and emits three continuous energies from 0 to 511 keV. In essence, the lifetime of o -Ps (142 ns) is usually shortened to a few nanoseconds (1–10 ns) by picking up a molecular electron with an opposite spin to that of the positron (the "pick-off" mechanism) 10 , 11 . Recently, free-volume hole features of ETFE-PEM have been probed by PALS 12 , 13 , 14 . The PALS of ETFE-PEM was analyzed using 4 lifetime components. The shortest lifetime, τ 1 ~ 0.125 ns, corresponds to the lifetime of the p -Ps, the moderate lifetime, τ 2 ~ 0.3–0.5 ns, is the lifetime of the free positron, and the longer lifetimes, τ 3 and τ 4 , are attributed to the lifetime of the o -Ps. The obtained results predicted that gas molecules pass more dominantly through the mobile amorphous zones and the PSSA grafts outside of the lamellae than through the inside. Moreover, the free-volume hole size of the ETFE-PEM is lower than that of Nafion, leading to less gas passing through the membrane. However, the above studies did not address in detail the effect of source correction in positron annihilation lifetime spectroscopic analysis, although this issue is quite important, as reported previously 15 , 16 , 17 , 18 . Therefore, this work studies the effect of source correction on the PAL spectroscopic analysis of ETFE-PEM.
EXPERLMENTAL
Materials and preparation
Figure 1 shows that the preparation process of ETFE-PEM consists of two main steps: graft polymerization and sulfonation. Commercial ETFE films were obtained from Asahi Glass Co. Ltd., Tokyo, Japan, and had the same thickness of 50 μm. The ETFE films were irradiated by gamma rays from a 60 Co source with an absorbed dose of 15 kGy under an argon atmosphere. The irradiated samples were immersed immediately in a styrene solution of toluene at 60 °C for 24 h for graft polymerization. These obtained films were subsequently immersed in a toluene solution at 50 °C for 24 h to eliminate the homopolymers and the residual monomers. Then, a polystyrene-grafted ETFE film (grafted-ETFE) was obtained. The grafting degree (GD) was determined by the formula GD (%) = 100(Wg – Wo)/Wo, where Wo and Wg are the weights of the film before and after graft polymerization, respectively. The grafted-ETFE was then sulfonated with chlorosulfonic acid in 1,2-dichloroethane at 50 °C for 6 hours. The membrane was washed again with pure water at 50 °C for 24 h to obtain ETFE-PEM 19 , 20 . In this study, grafted-ETFEs and ETFE-PEMs with a GD of 106% were utilized for positron annihilation lifetime spectroscopic analysis. This GD was selected because the graft layers are high enough to clearly investigate the effects of source correction.
Figure 1 . Synthetic scheme and molecular structures of ETFE-PEM obtained via radiation-induced graft polymerization of styrene onto an ETFE substrate to obtain the grafted-ETFE film and subsequent sulfonation .
PALS measurement
PALS measurements were performed using a 22 NaCl (20 μCi) positron source at room temperature under vacuum. Several pieces of identical samples were cut into 1x1.5 cm 2 pieces and stacked with a total thickness of 1 mm to ensure that all annihilation events occurred within the samples. Before conducting the PALS measurements, the ETFE-PEM was dried in a vacuum oven at 40 °C for 24 h to remove water molecules. Figure 2 shows the function and operation of a photon‒photon delay random coincidence spectrometer for lifetime detection 21 , 22 . When a positron (E max = 0.54 MeV) is emitted from a 22 NaCl source, a high-energy gamma-ray of 1.274 MeV is produced simultaneously and marked as the start signal of the positron. The positron penetrates, heats, and diffuses in the sample and then annihilates with an electron to provide annihilation photons (stop signal). The time difference between the start and stop signals is specified as the positron or positronium lifetime. In this study, source correction was carried out at 372 ps with a 10% annihilation intensity 23 . The PAL spectrum was combined into (1–3)x10 6 counts or more to ensure statistical support for subsequent analyses. The analysis was performed by using LT v9 software 24 .
Figure 2 . Experimental diagram for the PALS measurements. The setup included a photomultiplier tube (PMT), a constant–fraction differential discriminator (CFDD), a fast coincidence unit (FCC), a time–to–amplitude converter (TAC), a multichannel analyzer (MCA), and a computer (PC) .
PALS analysis
In this study, the subnanometer holes in all the samples are assumed to be spherical. This assumption is used for many PAL spectroscopic analyses of polymers 13 . The relationship between the hole radius and the lifetime of ortho-positronium trapped in the holes is shown by the Tao–Eldrup (TE) model, which is represented by the following formula 25 , 10 :
where τ i (ns) (i = 3, 4) is the lifetime component, r i is the pore radius (nm), and ∆R (≈ 0.166 nm) is the thickness of the electron layer.
The nanohole volume, , is determined by the equation 10,25 :
In addition, the radius distribution provides important information about the distribution features calculated based on the following equation 24 , 26 :
where α i (λ) is the probability density function of the o-Ps annihilation rate (λ io ) defined through the following formula:
where λ io is the maximum position of α i (λ)λ and is the standard deviation quantity of the i-th distribution.
The pore volume distribution is also estimated using the following equation:
RESULTS
Figure 3 shows typical decay curves of positron annihilation in the original ETFE, grafted-ETFE, and ETFE-PEM with a GD of 106%. The PALS of the original ETFE plot shows at least two slopes with a decrease at approximately 2 ns. The decay curves of grafted-ETFE and ETFE-PEM differ from each other and from that of pristine ETFE. Based on the decay curve features, the spectra of all the samples were analyzed using a four-component model, as shown in Table 1 .
Figure 3 . PAL spectra of the pristine ETFE, grafted-ETFE, and ETFE-PEM samples with a GD of 106% .
Table 1 shows the positron lifetime (τ i ) and intensity (I i ) (i = 1–4) for the original ETFE, grafted-ETFE, and ETFE-PEM at a GD of 106% with and without source correction. For the pristine ETFE, the first component (τ 1 = 0.170 ns) is attributed to the mean lifetimes of para-positronium and free positrons in the crystalline lamellar region 27 , 28 . The value of τ 1 is not significantly changed by the source correction (0.174 ns). The second lifetime component (τ 2 = 0.441 ns) is assumed to be the mean lifetime of the free positron in the amorphous phases 27 . The value of τ 2 (0.463 ns after source correction) is near the correction value of the source material (0.372 ns), so it significantly changes. The longer lifetimes (τ 3 = 1.620 ns and τ 4 = 3.556 ns) are attributed to the annihilation of o -Ps in the free-volume voids in the amorphous lamellar and interfacial regions (τ 3 ) and the mobile amorphous region (τ 4 ), respectively 12 . Like for τ 2 , for τ 3 (1.790 ns after source correction), the value is close to the correction value of the source material, so the change is more significant than that for τ 4 (3.610 ns). For the grafted-ETFE film, the values of τ 1 and τ 2 are similar to those of the original ETFE film. However, τ 3 is assigned to the mean lifetime of o -Ps in different amorphous phases within the lamella, and τ 4 is assigned to the mean lifetime of o -Ps in mobile amorphous phases and polystyrene layers outside of the lamella 27 , 28 .
Figure 4 shows the distribution curves of hole radii a) r 3 and b) r 4 for the original ETFE, grafted-ETFE, and ETFE-PEM with source correction (solid line) and without source correction (break line). As shown in Figure 4 a, the hole radius r 3 of the original ETFE is quite symmetrical, and the radius distribution peak is shifted to a higher position by source correction. Moreover, the distribution curve of the grafted-ETFEs shows symmetry and no change in peak position. For the ETFE-PEM, the curve features are similar to those of the original ETFE, the two peaks are more separated, and the peak is shifted to a higher position after source correction. In Figure 4 b, the hole radius distribution r 4 for the original ETFE is similar to that of r 3 . In the grafted-ETFE and ETFE-PEM samples, two peaks show symmetry and no change in peak position.
Figure 4 . Hole radius distributions (r 3 and r 4 ) of the original ETFE, grafted-ETFE, and ETFE-PEM with a GD of 106% with and without source correction .
Figure 5 shows the free hole volume distribution curves of a) V 3 and b) V 4 for the original ETFE, grafted-ETFE, and ETFE-PEM without (solid line) and with source correction (break line). As shown in Figure 5 a, the distribution curves of both the original ETFE and ETFE-PEM products show partially separated peaks, no symmetry with the presence of tails, and peak positions that shift to higher values after source correction. In contrast, the distribution curve of grafted-ETFEs is quite symmetrical with a small tail and shows little change in peak position. Figure 5 b shows more symmetry in the distribution curves of V 4 for all the samples, but the peak position shifted to a higher value after source correction was applied for the pristine ETFE sample.
Figure 5 . Hole volume distributions (V 3 and V 4 ) in the original ETFE, grafted-ETFE, and ETFE-PEM with a GD of 106% with and without source correction .
DISCUSSION
The lifetime and annihilation intensity parameters before and after source correction are shown in Table 1 . It is clear that Ï„ 3 and Ï„ 4 of grafted-ETFE do not show the effect of the source correction. In contrast to those of the grafted-ETFE, the lifetime of the ETFE-PEM significantly changes in response to source correction, in which Ï„ 3 and Ï„ 4 increase from 1.074 and 2.436 to 1.270 and 2.444 ns, respectively. The annihilation intensities IÂ 1 , I 3 , and I 4 increase in all three samples, while I 2 decreases after source correction. The results of the distribution curve ( Figure 4 a) show that the source correction has an effect on the size of the free hole radius in the amorphous lamellar region, most clearly in the original ETFE and ETFE-PEM. Like in Figure 4 b, according to the obtained results, the hole radius in amorphous lamellae but not in mobile amorphous phases or polystyrene layers outside the lamellar regions is strongly affected by source correction.
Table 2 shows the r 3 , r 4 , FWHM(r 3 ), and FWHM(r 4 ) values for the original ETFE, grafted-ETFE, and ETFE-PEM without and with source correction. The pore sizes r 3 and r 4 obtained from the distribution curves are consistent with those calculated using the Tao–Eldrup equation. The FWHM(r 3 ) and FWHM(r 4 ) values of the original ETFE and ETFE-PEM increase after source correction, which is similar to the changes in the corresponding r 3 and r 4 values . Moreover, the FWHM(r 4 ) is much lower than the FWHM(r 3 ). The result can be elucidated from the fact that the amorphous lamellar region is stiffer and less mobile than mobile amorphous phases and polystyrene layers outside of the lamellar structure, which can be rearranged, resulting in a smaller FWHM(r 4 ) 12 , 13 . Table 3 presents the V 3 , V 4 , FWHM(V 3 ), and FWHM(V 4 ) values. The hole volume distributions of V 3 and V 4 obtained from the distribution curves are also in agreement with those calculated using the Tao–Eldrup equation. The FWHM(V 3 ) and FWHM(V 4 ) values of the original ETFE and ETFE-PEM increase after the source correction, which is similar to the changes in the corresponding V 3 and V 4 . Moreover, the FWHM(V 4 ) is much lower than the FWHM(V 3 ), which is similar to the FWHM(r 3 ) and FWHM(r 4 ) values, as shown in Table 2 . Thus, the same mechanism can be proposed for this result.
CONCLUSION
Positron annihilation lifetime spectroscopic analyses were performed to observe the effect of source correction for the original ETFE, grafted-ETFE, and ETFE-PEM with a GD of 106%. r 3 , r 4 , FWHM (r 3 ), and FWHM (r 4 ) of the original ETFE and ETFE-PEM but not the grafted ETFE increase after source correction. Similar results are also obtained for V 3 , V 4 , the FWHM (V 3 ), and the FWHM (V 4 ). Interestingly, the FWHM (for r 4 and V 4 ) was much lower than the FWHM (for r 3 and V 3 ). This result indicates that the amorphous lamellar region is less mobile than the amorphous phases and polystyrene layers located outside of the lamellar structure; additionally, the amorphous lamellar region can be rearranged, leading to smaller FWHM values (r 4 and V 4 ). Note that source correction significantly influences the distribution curves of r 3 and V 3 of the original-ETFE and ETFE-PEM. This result suggested that source correction during positron annihilation lifetime spectroscopic analyses is an important issue for determining the o -Ps lifetime of polymers, which is near the lifetime of the positron in the source materials.
LIST OF ABBREVIATIONS
ETFE: Poly(ethylene-co-tetrafluoroethylene)
ETFE-PEM: Polystyrene Sulfonic Acid (PSSA)-Grafted Poly(ethylene-co-Tetrafluoroethylene) Polymer Electrolyte Membranes
FWHM: Full width at half maximum
GD: Grafting degree
grafted-ETFE: Polystyrene (PS)-Grafted Poly(ethylene-co-Tetrefluoroethylene) Polymer Electrolyte Membranes
o -Ps: Ortho-Positronium
PALS: Positron Annihilation LifeTime Spectroscope
PEM: Polymer electrolyte membrane
p-Ps : Para-Positronium
Ps: Positronium
PSSA: Polystyrene Sulfonic Acid
RH: Relative humidity
TE: Tao-Eldrup
AUTHOR CONTRIBUTION
Tran Duy Tap: Conceptualization, Project Administration, Fundingacquisition, Supervision, Resources, Investigation, Methodology, Data curation, Formalanlysis, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing. Nguyen Huynh My Tue: Investigation, Methodology, Data curation, Formalanysis, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing. Tran Hoang Long, Dinh Tran Trong Hieu, Lam Hoang Hao, Vo Thi Kim Yen, Nguyen Manh Tuan: Visualization, Validation, Investigation, Writing – review & editing. Huynh Truc Phuong, Le Quang Luan, Pham Thi Thu Hong, and Tran Van Man: Visualization, Validation, Datacuration. All authors read and approved the final manuscript.
CONFLICT OF INTEREST
The authors declare that they have no conflicts of interest.
ACKNOWLEDGMENTS
This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 103.99-2020.59. The authors thank Dr. Luu Anh Tuyen (Center for Nuclear Techniques, Vietnam Atomic Energy Institute) for the PALS experiments.
DATA AVAILABILITY STATEMENT
The datasets are not publicly available but are available from the corresponding author upon reasonable request.
References
- Tanç B, Arat HT, Baltacıoğlu E, Aydın K. Overview of the next quarter century vision of hydrogen fuel cell electric vehicles. Int J Hydrogen Energy. 2019;44(20):10120-8. . ;:. Google Scholar
- Wang Y, Ruiz Diaz DF, Chen KS, Wang Z, Adroher XC. Materials, technological status, and fundamentals of PEM fuel cells - A review. Mater Today. 2020;32(xx):178-203. . ;:. Google Scholar
- Karimi MB, Mohammadi F, Hooshyari K. Recent approaches to improve Nafion performance for fuel cell applications: A review. Int J Hydrogen Energy. 2019;44(54):28919-38. . ;:. Google Scholar
- Ke Y, Yuan W, Zhou F, Guo W, Li J, Zhuang Z, et al. A critical review on surface-pattern engineering of nafion membrane for fuel cell applications. Renew Sustain Energy Rev. 2021;145(July 2020):110860. . ;:. Google Scholar
- Liu F, Yi B, Xing D, Yu J, Zhang H. Nafion/PTFE composite membranes for fuel cell applications. J Memb Sci. 2003;212(1-2):213-23. . ;:. Google Scholar
- Tap TD, Nguyen LL, Hasegawa S, Sawada S ichi, Luan LQ, Maekawa Y. Internal and interfacial structure analysis of graft-type fluorinated polymer electrolyte membranes by small-angle X-ray scattering in the high-q range. J Appl Polym Sci. 2020;137(35). . ;:. Google Scholar
- Hao LH, Hieu DTT, Long TH, Hoa D Van, Danh TT, Man T Van, et al. Investigation of the Lamellar Grains of Graft-type Polymer Electrolyte Membranes for Hydrogen Fuel Cell Application using Ultrasmall-angle X-ray Scattering. VNU J Sci Nat Sci Technol. 2021;1-9. . ;:. Google Scholar
- Dinh TTH, Lam HH, Tran TD, Le QL, Tran VM, Huynh TP, et al. Investigation of the water states of poly(styrene sulfonic acid) grafted poly(ethylene-co-tetrafluoroethylene) copolymer using FT-IR analysis. Minist Sci Technol Vietnam. 2022;64(2):3-9. . ;:. Google Scholar
- Hieu DTT, Hao LH, Long TH, Van Tien V, Cuong NT, Van Man T, et al. Investigation of chemical degradation and water states in the graft-type polymer electrolyte membranes. Polym Eng Sci. 2022;62(9):2757-68. . ;:. Google Scholar
- Tao SJ. Positronium annihilation in molecular substances. J Chem Phys. 1972;56(11):5499-510. . ;:. Google Scholar
- Eldrup M, Lightbody D, Sherwood JN. The temperature dependence of positron lifetimes in solid pivalic acid. Chem Phys. 1981;63(1-2):51-8. . ;:. Google Scholar
- Tap TD, Long TH, Hieu DTT, Hao LH, Phuong HT, Luan LQ, et al. Positron annihilation lifetime study of subnano level free volume features of grafted polymer electrolyte membranes for hydrogen fuel cell applications. Polym Adv Technol. 2022;33(9):2952-65. . ;:. Google Scholar
- Long TH, Hieu DTT, Hao LH, Cuong NT, Loan TTH, Van Man T, et al. Positron annihilation lifetime spectroscopic analysis of Nafion and graft-type polymer electrolyte membranes for fuel cell application. Polym Eng Sci. 2022;62(12):4005-17. . ;:. Google Scholar
- Sawada S ichi, Yabuuchi A, Maekawa M, Kawasuso A, Maekawa Y. Location and size of nanoscale free-volume holes in crosslinked- polytetrafluoroethylene-based graft-type polymer electrolyte membranes determined by positron annihilation lifetime spectroscopy. Radiat Phys Chem. 2013;87:46-52. . ;:. Google Scholar
- Mcguire S, Keeble DJ. Positron lifetimes of polycrystalline metals: A positron source correction study. J Appl Phys. 2013;103504(2006). . ;:. Google Scholar
- Kanda GS, Keeble DJ. Nuclear Instruments and Methods in Physics Research A Positron annihilation lifetime spectroscopy source correction determination : A simulation study. Nucl Inst Methods Phys Res A. 2015;1-6. . ;:. Google Scholar
- Staab TEM, Somieski B. The data treatment influence on the spectra decomposition positron lifetime spectroscopy Part 2 : The effect of source corrections. Nucl Instruments Methods Phys Res Sect A Accel Spectrometers, Detect Assoc Equip. 1996. . ;:. Google Scholar
- Search H, Journals C, Contact A, Iopscience M, Address IP. Source correction in positron annihilation lifetime spectroscopy. J Phys Condens Matter. 1996;2081. . ;:. Google Scholar
- Trai N, Chi Minh H, Nam Correspondence Tran Duy Tap V, Nam V, Hoang Hao L, Tran Trong Hieu D, et al. Surface features of polymer electrolyte membranes for fuel cell applications: An approach using S2p XPS analysis. Sci Technol Dev J. 2021;24(3):2100-9. . ;:. Google Scholar
- Tran TD, Pham HM, Nguyen AH, Luong AT, Luu TA. Study of lamellar structures of graft-type fluorinated proton exchange membranes by small-angle X-ray scattering: preparation procedures and grafting degree dependence for fuel application. Sci Technol Dev J. 2015;18(3):153-61. . ;:. Google Scholar
- Jean YC. Positron annihilation spectroscopy for chemical analysis: A novel probe for microstructural analysis of polymers. Microchem J. 1990;42(1):72-102. . ;:. Google Scholar
- Minor H, Murthy NS. General procedure for evaluating amorphous scattering and crystallinity from X-ray diffraction scans of semicrystalline polymers. Polymer. 1989;31:996-1002. . ;:. Google Scholar
- Shpotyuk O, Ingram A, Shpotyuk O. Photopolymerization shrinkage in dimethacrylate-based dental restorative composites probed by means of positron annihilation lifetime spectroscopy. Polymer. 2020;196(April):122485. . ;:. Google Scholar
- Kansy J. Microcomputer program for analysis of positron annihilation lifetime spectra. Analysis. 1996;9002(96):235-44. . ;:. Google Scholar
- Tap TD. Study on the structure of polymer electrolyte membrane using small angle X-ray scattering and positron annihilation spectroscopy. VNUHCM J Nat Sci. 2017;1(6):197-205. . ;:. Google Scholar
- Liu J, Deng Q, Jean YC. Free-Volume Distributions of Polystyrene Probed by Positron Annihilation: Comparison with Free-Volume Theories. Macromolecules. 1993;26(26):7149-55. . ;:. Google Scholar
- Del RÃo J, Etxeberria A, López-RodrÃguez N, Lizundia E, Sarasua JR. A PALS contribution to the supramolecular structure of poly(l -lactide). Macromolecules. 2010;43(10):4698-707. . ;:. Google Scholar
- Jean YC, Van Horn JD, Hung WS, Lee KR. Correction to Perspective of Positron Annihilation Spectroscopy in Polymers. Macromolecules. 2013;46(20):8392-8392. . ;:. Google Scholar
