Positron spectroscopy of polyvinylidene fluoride after helium ions irradiation

Roman Laptev, Lyu Jinzhe, Natalya Dubrova (Division for Experimental Physics, School of Nuclear Science & Engineering, National Research Tomsk Polytechnic University, Lenina Ave. 43, Tomsk, 634034 Russia,) laptevrs@tpu.ru *corresponding author 2891796456@qq.com dubrova@tpu.ru ABSTRACT Free volume is an extremely important intrinsic defect in polymers. Structurally, the free volume is the randomly distributed holes in the polymer molecular chain segments. From the perspective of molecular movement, it is also the space needed for the movement of molecular segments. In proton exchange membrane fuel cells, the free volume is also the space needed for the directional conduction of protons. Irradiation grafting sulfonated polyvinylidene fluoride (PVDF) is one of the methods to produce proton exchange membrane with good proton channel rate. Using the LYS-1 program, based on the linear absorption coefficient and backscatter coefficient models, the percentage of annihilated positrons in PVDF in the two-layer model and the three-layer model was studied, and comparing the two fitting results it is determined that the model closest to the positron annihilation percentage required by the PALS experiment is the twolayer model, which allows the percentage of positrons that are annihilated in PVDF films with a thickness of 100 μm to reach 46% using the high energy positron source 44Ti without using the positron moderator. Using positron annihilation lifetime spectrum (PALS) analysis methods, based on Eldrup's classical model of free volume, the influence of absorbed doses of α particles on the free volume and crystallinity of PVDF was investigated, respectively. Based on the two test results the model of cross-linking and degradation of polyvinylidene fluoride irradiated by α particles was determined. Afterwards, X-ray diffraction (XRD) methods was used to study the change of PVDF crystal area before and after irradiation. The XRD results are consistent with the results measured by PALS.


Introduction
The research and application of irradiation effects on polymers have been paid more and more attention.The chemical changes of polymers caused by absorbed doses is not large.However, the induced changes of physical and mechanical properties of polymers are significant.
Regardless of cross-linked or degradable polymers, their inherent physical, chemical, and mechanical properties can be severely damaged when the absorbed dose is high to a certain degree, which causes materials to be unusable [1][2][3][4].Therefore, radiation stability or radiation resistance is one of the important properties of polymers, especially when polymers are used in the nuclear reactor or aerospace industry.PALS is the only sensitive method for studying the microstructure of amorphous polymers -the parameter of free volume with atomic size [5][6][7][8].Using the method of PALS, it was found that the influence of radiation on polymers is related to both the type of radiation and the type of polymers, as well as the irradiation power.For example, M. S. Abd El Keriem [9] investigated effect of Low Gamma-Irradiated dose on the structure of cellulose triacetate Films and found that I shows an increase from 0 to 10 kGy.Such an increase of I is mainly due to the presence of carbonyl groups, which are formed during irradiation [10].With a further increase in the dose to 15 kGy, I shows a gradual decrease, and then approaches a constant to 25 kGy, which is well known for γ-irradiated polymers [11].Such behavior may indicate that stability in the structure has been achieved.Xianyi ZHOU [12] and his collaborators obtained results on the change of free volumes in γ-irradiated polytetrafluoroethylene (PTFE) and polyethylene.It is found that from 0 to 300 kGy the crystallinity of PTFE continuously increases and the size of the free volume gradually decreases, while in polyethylenes both parameters show the opposite behavior depending on the dose.Khalid S. Jassim and his collaborators [13] investigated the properties of free volumes in beta-irradiated high density polyethylene (HDPE).
It is indicated that both free volumes and I increase at a dose less than 1.5 Gy, followed by a decrease to a constant volume at a dose of 1.5 to 12 Gy.These studies indicate that many factors influence the characteristics of the interaction of radiation with substances, one of which is the radiation resistance of polymers.Possessing high resistance to different types of radiation, polymers show a structural change only at a high radiation dose (several hundred kGy), otherwise the polymer structure changes and approaches a stable state even at a sufficiently low radiation dose (several Gy).
Positron annihilation technique is one of sensitive tools for investigating microscopic defects and phase transition of materials.In normal positron spectroscopy, the positron energy is in the order of MeV and the depth of injection in the sample is deep for the research of average defect density in the material.In order to achieve this goal, it is usually required that the amount of annihilation positrons in the sample be no less than 50% of the amount of positrons emitted from the positron source This places stringent requirements on the positron source and the thickness of sample.The positron emitted by 22 Na has a maximum energy of 0.545 MeV, the injection depth of which in metal is usually 0.3 to 1 mm, and is 1 to 2 mm in a polymer material with a small density [14]. 44Ti is a high-energy positron source that produces positrons with a maximum energy of 1.47 MeV, the injection depth of which will be greater in the polymer material compared to positrons emitted by 22 Na.PVDF is a material used to prepare modified proton exchange membranes [15,16,17].Due to its working environment, it is required to have a thickness in the range of 20-100 μm (a greater ohmic overpotential will be generated if it exceeds this range) [18,19,20].Since the positron energy produced by 44 Ti is in the order of MeV, and the thickness of PVDF is very small, only a few positrons are annihilated in PVDF, and most of the positrons penetrate the film without annihilation.In order to annihilate 50% of positrons in PVDF and not to use positron moderators for cost savings, this paper proposes a method to make the annihilated positron percentage in PVDF close to 50%, which is in good agreement with the requirements of the PALS method.
In this paper, PALS and XRD are combined with free volume theory to study the influence of helium ions irradiation on the microstructure of PVDF, so as to reveal the relationship between the microstructure changes and absorbed dose.

Development of a model for increasing the number of annihilation positrons in the sample layer PVDF
The transfer profile or the path of positrons through the material is calculated using the LYS-1 program, which is based on a multi-scattered model [21,22].For the calculation, only the linear absorption coefficient, backscatter factor and material thickness are required.
Linear absorption coefficient is [23] where z -the atomic amount of the substance; E -maximum positron energy, Mev; ρ -the density of the substance, g.
Backscatter coefficient is [24]: In positron annihilation measurements, in order to ensure that all positrons are annihilated in the measured material, the sample and the radioactive source must adopt a "sandwich" structure, that is, the same sample is placed on both sides of the source.In addition, in order to make a great amount of incident positrons stay in the material, an ordinary method is making the thickness of the sample be greater than the incident depth of positrons.For PVDF polymers with small thickness to increase the amount of annihilated positrons in films, the following two models are developed, while the positron source is 44 Ti, which emits positrons with a maximum energy of 1.47 MeV: 1) two-layer model: source e + PVDF (first layer) + metal (second layer) (fig.1).According to the formulas (1), (2), in order to obtain the linear absorption coefficient and backscatter coefficient of each layer, it is necessary to know the energy of positrons that reach to the surface of each layer.This requires that the energy loss of positrons in each layer must be known, which is determined by braking ability of each layer for positrons.
The energy loss of positrons in substance is divided into two types: the collision loss and bremsstrahlung energy losses.The collision loss of positron energy is determined by the following formula: Where -the atomic amount of the substance; -the classical radius of an electron, cm; -mass of an electron, g; -constant avogadro; а -atomic mass of substance, a.e.m; с -speed of light, cm/s; * -the average excitation energy of the substance's atom, erg; -positron velocity, cm/s; = ; = ; -kinetic energy of a positron, эрг; ( ) -function for positrons; The bremsstrahlung energy losses of positrons related to the bremsstrahlung energy losses of electronics.In the Born approximation without taking shielding into account, the calculation of the braking ability caused by the radiation of electrons with non-relativistic energies gives the following result: Where -kinetic energy of electrons, MeV; А -atomic mass of substance, a.e.m; For the relativistic case: The loss of positron energy to radiation can be calculated by loss of electrons, multiplying them by the function: Where = ln(7.52• 10 ), в GeV.
The total energy losses of positrons on per unit path (total braking ability) are equal to the sum of energy losses due to collisions and radiation [25] Table 1 shows the amount of annihilated positrons in PVDF using different metals as the material of the second layer.It can be seen from Table 1 that in the two-layer model the maximum amount of annihilated positrons in PVDF was obtained using Pb as the material of the second layer, which has the largest backscattering coefficient of all the metals listed.
Since the location of the Pb metal behind the PVDF film allows the most significant increase in the amount of annihilated positrons in a PVDF film, it is necessary to settle calculation for the model "source e + PVDF (first layer) + Pb (second layer)" with different thicknesses of the PVDF film (Table 2).From the data shown in Tables 3, 4, it follows that the larger the proportion of hydrogen atoms in the polymer (first layer), the smaller the thickness of the polymer (first layer), the larger the thickness of PVDF (second layer), the larger the amount of annihilated positrons in PVDF (second layer).
In order to increase the amount of annihilated positrons in a PVDF film, two models were developed, differing from one another in the amount of layers.
The first model is the two-layer model.In this model, the maximum amount of positrons annihilated in the PVDF film was obtained using lead (Pb) as the material of the second layer, which has the greatest backscatter coefficient from all the metals considered in the work.With a thickness of PVDF film 100 μm, the amount of annihilated positrons is 46.94% The second model is the three-layer model.The essence of this model is that any material should be placed on the first layer in order to reduce positron energy.
In 2) As already mentioned above, the smaller the thickness of the polymer (first layer), the greater the amount of annihilated positrons in the PVDF film (the second layer), i.e. with a polymer thickness of zero, the maximum amount of annihilated positrons in a PVDF film (the second layer) is observed, and this is a two-layer model.

Sample preparation and irradiation
The sample under investigation is F-2M (PVDF) films with a thickness of 20 μm produced by "Fluoropolymer" (St.Petersburg).The R-7M accelerator of physicotechnical institute of Tomsk Polytechnic University was used as a source of ionizing radiation producing a beam of helium ions with energy 27 MeV discharged into the air.Absorbed dose rate is 0.26 MGy/min, total absorbed doses are 0.13, 0.26, 0.395, 0.525, 0.655 MGy respectively.The corresponding sample code is PVDF0, PVDF0.5, PVDF1, PVDF1.5, PVDF2, PVDF2.5.

PALS Analysis
A conventional fast-fast coincidence spectrometer with a time resolution 240 ps was used for PALS measurements [26,27].In PALS spectrum about 3-5 million counts were accumulated.
The PALS spectra were analyzed into three components (τ , τ and τ ) with their intensities (I 1 , I and I ) using MELT.At present, several computer programs with various mathematical models have been developed to obtain the spectrum of PALS.PATFIT-88 [28], considering the spectrum of the PALS as a convolution of superposition of multiexponential components with the instrument's resolution function, estimates the parameter values based on the method of semilinear least squares; LifeTime10 [29] obtains the PALS spectrum the same as PATFIT-88, but estimates the parameter values using non-linear least squares; CONTIN [30,31] considers the spectrum of the PALS as a convolution of the resolution function and Laplace transform function, while the continuous spectrum of the PALS is obtained through the inverse Laplace transform; the MELT program [31,32] also allows one to obtain a continuous distribution of positron time, analyzing the spectrum of the PALS based on the maximum entropy principle.Unlike other spectrum analysis programs, the program MELT has the following advantages: 1) application of the program for filtering Poisson noise and application of the filtered solution as the initial solution of MELT allows obtaining a more stable result; 2) there is no requirement to measure the reference spectrum, and a low number of counts (generally 1 million counts) makes it possible to get a stable solution.

XRD analysis
X-ray diffraction studies were performed with CuKα radiation (1.5410Å wavelength) using XRD-7000S diffractometer (Shimadzu, Kyoto, Japan) in Bragg-Brentano geometry from 30° to 80° with the scan speed of 10.0°/min, the sampling pitch of 0.0143°, the preset time of 42.972 s at 40 kV and 30 mA.The diffraction patterns were collected using OneSight (Shimadzu, Kyoto, Japan) wide-range array high speed detector with 1280 channels.

Results of PALS analysis
In high-molecular polymers positrons not only directly annihilate with electrons, but also form a metastable state "positronium" with electrons, followed by annihilation.There are two basic states of positronium: 1) parapozitronium (p-Ps), the spins of the electron and the positron are antiparallel, the intrinsic lifetime of p-Ps in vacuum is 125 ps; 2) orthopositronium (o-Ps), the spins electron and positron are parallel, the intrinsic lifetime of in vacuum is 140 ns.Due to the fact that the positronium size is only 1.06 Å and most o-Ps are formed in free volumes with subsequent annihilation, measurement of o-Ps annihilation parameters allows obtaining information about the microstructure of high-molecular polymers, while the lifetime and intensity show the size and quantities of the free volume, respectively [33].
A high-molecular polymer is a complex system.Generally, it is considered that in a highmolecular polymer there are 2 regions: crystalline and non-crystalline.The free volumes are distributed in the non-crystalline region.Thus, there are several mechanisms of positron annihilation in solid polymers: Pick-off annihilation of o-Ps, self-annihilation of p-Ps, annihilation of free positrons in the crystalline region, and annihilation of positrons in various capture states.
Attention should be paid to the fact that in practical polymers there are many different capture states, for example, in a non-crystalline region there is a capture state with a a long lifetime component, value of which is close to lifetime of o-Ps and in the crystalline region there is possibly the capture state with a short lifetime component, value of which is close to lifetime of p-Ps.In spite of many possible types of capture states, in the practical work of analyzing the spectrum of the PALS, the model of the 3 lifetime components allows obtaining a good processed result, in this case, τ -the lifetime of p-Ps and positrons annihilating in the capture states with a short lifetime, τ -the lifetime of free positrons annihilating in the crystalline region, τ -the lifetime of the Pick-off annihilation of o-Ps and positrons annihilating in the capture states with a long lifetime.τ only depends on the crystalline part, whereas only the non-crystalline region affects τ .As a result, the model of the 3 lifetime components satisfies the requirement to study the change of free volumes that exist only in the non-crystalline region.Table 5 shows the lifetimes of the 3 components and their corresponding intensities [34].
According to the principle of quantum mechanics, the Tao and Eldrup scientists obtained a relation between the radius of a spherical free volume and the lifetime of o-Ps [35]: Where -lifetime of o-Ps in free volume; -The lifetime of o-Ps in the electron layer surrounding the free volume, = ns; R -The radius of the spherical free volume; ∆ -Thickness of the electron layer formed on external electrons of free volume, on which annihilation of o-Ps occurs, ∆ = 1.656Å.
Free volume is   whereas with further increase in the absorbed dose, the intensity increases, this is explained by the fact that at a low absorbed dose the main process that occurs when α particles interact with high-molecular chains of PVDF is the cross-linking of chains, with a further increase in the absorbed dose, degradation of chains predominates over cross-linking of chains, which leads to an increase in the non-crystalline region.It is known that the energy of the C-C bond is 332 kJ /mol , the energy of C-H bond is 414 kJ /mol , the energy of C-F bond is 489 kJ /mol .As a result, it is believed that the cross-linking and degradation of the molecular chains of PVDF is mainly carried out by the formation and decomposition of the C-C bonds.It can be seen from Figures 5 and 6 that at an absorbed dose below 0.25 MGy, the free volume decreases rapidly, it is noted that in this range of absorbed dose the crystallinity does not change.This behavior is explained by the characteristics of the cross-linking and degradation processes of the molecular chains of PVDF, which are presented in Fig. 7.At a low dose, segments of molecular chains in the non-crystalline region begin to move and are prepared for cross-linking with each other (processes (a), (b)).In this process, a redistribution of space occupied by free volumes and segments of molecular chains occurs in such a way that several segments enter the free volume and leave in their place a new free volume.As a result, the proportion of noncrystalline region is not changed, but the size of the free volume decreases.In the range 0.25 ~ 0.4 MGy, the discrete previous segments of the molecular chains, having entered in the free volumes, begin to cross-link and transform into ordered long molecular chains, which leads to the growth of the crystal region with an unchanged size of free volumes in PVDF (process (c)).In the range 0.4 ~ 0.65 MGy occurs the reverse process of process (c) (process (d)).It should be noted that not only new cross-linked molecular chains are degraded, but also inherent ("old") long molecular chains in the crystalline region, it is for this reason that an increase in the non-crystalline region and in the size of free volumes is observed at a high absorbed dose.

Results of XRD analysis
XRD analysis is a technology for analyzing the structure of substances based on the diffraction effects of x-rays in crystalline materials.Each condensed material has a certain crystalline structure, including the type of lattice, the distance between the crystalline planes, and etc.When the crystalline plane of a substance is irradiated by X ray with sufficient energy, backscattering takes place, which obeys the Bragg's law.
Where d -Distance between crystal planes; θ -Diffraction angle; λ -The wavelength of the X ray.
It is known that d in the non-crystalline region is greater than d in the crystalline region.This is because the crystal region is a group of ordered folded high-molecular chains, whereas in the non-crystalline region the segments of long chains are randomly distributed and the directions of the chains are different.From Bragg's law it follows that the more value of θ is, the smaller value of d and the larger crystallinity.The XRD spectrum of PVDF samples irradiated with different doses is shown, the result is shown in Fig. 8.It is found that the largest strong peak is about 20°, which is a characteristic peak of the crystalline phase.This means that in the PVDF the main part is occupied by the crystalline phase, and also explains the low intensity of obtained by the PALS method.Based on the XRD spectrum, the dependence of the diffraction angles on the absorbed dose was obtained (Fig. 9).

Summary
Analyzing the test results measured by different methods it can be drawn that PVDF has a high resistance to radiation, and after PVDF is irradiated by Helium ions, cross-linking and degradation take place at the same time.Under different doses, the reaction mechanism is different.
At an absorbed dose less than 0.25 MGy, a decrease in the free volume is observed, the crystallinity is practically unchanged.In the absorbed dose range 0.25 ~ 0.4 MGy, an increase in the crystallinity and no significant change in the free volume are observed.With a further increase in absorbed dose, a continuous decrease in the crystallinity is observed, when the dose is raised to 0.5 MGy there is no significant change in the free volume, and a further increase in the dose to 0.6 MGy leads to its insignificant growth.This is due to the movement and cross-linking of segments of molecular chains in the non-crystalline region at a low absorbed dose and the degradation of long molecular chains at a high absorbed dose.Therefore, it is determined that the absorbed dose

Funding
The research is carried out within the framework of the grant of the Program for Enhancing Competitiveness of Tomsk Polytechnic University
comparison with the three-layer model, the two-layer model allows obtaining a larger amount of annihilated positrons in a PVDF film.The disadvantages of the three-layer model include the following: 1) The braking ability of polymers (the first layer) is in the range (1~4) • 10 MeV/μm, then the energy losses of the positrons in the first layer are: ∆Е = • ℎ ≤ (4 • 10 MeV/μm) • (100 μm) = 0.04 MeV The energy of the positrons emitted from the source 44 Ti: = 1.47 MeV The energy of positrons incident on the second layer (PVDF film): = − ∆Е ≥ 1.47 MeV − 0.04 MeV = 1.43 MeV It is observed that polymer materials almost can't reduce the energy of positrons.When the thickness of the second layer (PVDF) is increased to 100 μm, the maximum amount of annihilation positrons in the PVDF film is only 40.80%.

Fig. 7 .
Fig.7.Process of cross-linking and degradation of molecular chains of PVDF under irradiation of helium ions.

0. 6
MGy has exceeded the maximum damage dose of the PVDF material, at which degradation of the intrinsic crystal region of the polymer begins to occur.The results of XRD analysis confirmed the results obtained by PALS method.Interpretation and analysis of data are based on the theory of cross-linking or degradation of molecular chains (formation or decomposition of C-C bonds) PVDF.

Table 2 .
-Results of calculation for the model "source e + PVDF (first layer) + Pb (second In this model, a polymer is placed on layer 1 in order to hold back the positrons.Three different polymers are taken for calculation: polyethylene C H (PE), PVDF C H F and Teflon (PTFE)(C F ). Table3and Table4show the amount of annihilated positrons in PVDF using C H , C H F and C F as the material of the first layer with various thicknesses.

Table 3
. -Results of calculation for the tree-layer model "source e + polymer (first layer) + PVDF (second layer) + Pb (third layer)" with a thickness of the second layer of 50 μm:

Table 4 .
-Results of calculation for the tree-layer model "source e + polymer (first layer) + PVDF (second layer) + Pb (third layer)" with the thickness of the second layer of 100 μm:

Table 5 .
The lifetimes of the 3 component and their corresponding intensities.