Pedro Silva ^1*, Carmen Albano ^2,3, Rosestela Perera ⁴

¹Instituto Venezolano de Investigaciones Científicas (IVIC), Centro de Física, Carretera Panamericana Km. 11. Caracas 1020-A, Venezuela.

²Universidad Central de Venezuela (UCV), Facultad de Ingeniería. Caracas, Venezuela.

³Instituto Venezolano de Investigaciones Científicas (IVIC), Centro de Química, Carretera Panamericana Km. 11. Caracas, Venezuela.

⁴Universidad Simón Bolívar (USB), Departamento de Mecánica. Caracas, Venezuela. ^* E-mail: silva@ivic.ve

Publicado On-Line: 27-Ene-2009

Disponible en: www.polimeros.labb.usb.ve/RLMM/home.html

Abstract

The Electron Paramagnetic Resonance (EPR) had its most important development at the end of World War II. It is a non destructive technique of characterization and is the technique used for excellence to detect and characterize free radicals. It is well known that the presence of free radicals in polymeric materials is responsible for the appearance of a variety of effects in the polymer chains. There are, fundamentally, two ways for the generation of free radicals in a polymeric chain: chemical methods and irradiation with electromagnetic waves of medium and high energy. Gamma and x-rays produce ionization in all solids. In insulators and polymers chemical reactions may be promoted, some of which cannot be induced by other means. These last methods have the advantage that they do not leave polluting agents into the polymer. EPR has been used to interpret quantitatively and qualitatively the free radicals generated by the irradiation of polymeric materials. EPR results from different polymers and polymeric blends irradiated with gamma irradiation at low dose rates will be presented in this article. The behavior of allyl, alkyl, peroxide and polyenyl radicals, among others, is studied using a decay model.

Resumen

La Resonancia Paramagnética Electrónica (RPE) tuvo su desarrollo más significativo a finales de la segunda guerra mundial. Es una técnica no destructiva de caracterización y es la técnica por excelencia usada en la detección y caracterización de radicales libres. Es bien sabido que la presencia de radicales libres en materiales poliméricos es responsable de la aparición de una gran variedad de efectos en las cadenas poliméricas. Existen fundamentalmente dos formas de generación de radicales libres en una cadena polimérica: métodos químicos e irradiación con ondas electromagnéticas de mediana y alta energía. Los rayos gamma y los rayos X producen ionización en todos los sólidos. En aislantes y en polímeros pueden iniciar reacciones químicas, algunas de las cuales, no pueden ser iniciadas por otros métodos. La irradiación tiene la ventaja de que no dejan agentes contaminantes en el polímero. La RPE ha sido usada para interpretar de manera cuantitativa y cualitativa los radicales generados por irradiación de materiales poliméricos. En este trabajo se presentan resultados de RPE para diferentes polímeros y mezclas poliméricas irradiados con radiación gamma a bajas dosis. El comportamiento de los radicales alquilo, alilo peroxido y polienilo entre otros es estudiado usando un modelo de decaimiento.

Palabras Claves: Resonancia paramagnética electrónica (RPE), Radiación gamma, Antioxidantes, Polipropileno, Polietileno

Recibido: 16-May-2008; Revisado: 31-Oct-2008; Aceptado: 14-Nov-2008

1. INTRODUCTION

Radiations can produce several types of defects in solids. These defects are mainly: (a) vacancies, (b) interstitial atoms, (c) impurity atoms and (d) ionization effects, among others.

The studies of the ionization effects, using Electron Paramagnetic Resonance (EPR), are the most important feature in this work. They are related to the passage of charged particles or gamma-rays through a solid causing extensive ionization and electronic excitation, which in turn lead to bond rupture, free radicals coloration, luminescence, etc., in many types of solids. These effects are very important in insulators and dielectrics, ionic crystals, glasses, organic polymers, etc.

The interaction of energetic radiation with matter is a complex phenomenon, and it is useful to resolve it into primary and secondary stages. The primary or direct effects consist in the displacement of electrons (ionization), the displacement of atoms from lattice sites, excitation of both atoms and electrons without displacement, and the transmutation of nuclei. Irradiation with gamma-rays produces ionization as the important primary effect, and atomic displacements sometimes result secondarily. On the other hand, the secondary effects of the interaction of radiation with matter are further excitation and disruption of the structure by electrons and atoms. The basic laws governing the secondary stages are in all cases the same as those governing the primary stage of the bombardment of charged particles.

Gamma-rays and x-rays produce ionization in all solids, and this is the most important effect. In insulators and polymers, chemical reactions may be promoted by the action of these rays, some of which cannot be induced by other means.

In all three processes electrons are ejected with energies comparable to the original g-ray energy, and thus g-ray irradiation inevitably causes a substance to be internally bombarded by fairly energetic electrons. Most of the energy of these electrons is dissipated producing further ionization, but occasionally, they displace atoms by elastic collisions.

Ionizing radiation brings about the formation of ions, and free radicals result upon neutralization of this ions. Both the ions and the free radicals may be chemically highly reactive. Displaced atoms, since they represent quite drastic disturbances in the solid, may have an important effect on any chemical reaction involving the solid itself, particularly in its surface properties and surface reactions.

An interesting manifestation of free-radicals formation is the gamma-ray induced polymerization in the solid state, a process which does not occur thermally in some crystals that have been studied. The first experiments were carried out with acrylamide, a monomer which shows little or no tendency to polymerize thermally below its melting point [1,2]. It has been reported that the polymerization rate, however, changed linearly with the intensity and did not depend on the energy of radiation [3]. Recent studies demonstrate that gamma radiation can be used to initiate processes of rupture and crosslinking of chains in samples already polymerized which is of supreme interest in the study of very complex processes of transformation of polymers [4-14].

Most reactions initiated by thermal energy, light, g-radiation and mechanical forces involve the formation of free radicals. In such reactions a two-electron chemical bond is cleaved either symmetrically or asymmetrically

A: B ® A^· B^·             (1)

 A: B  ®  A⁺  + B^-    (2)

In reaction (1) free radicals are formed, whereas in reaction (2) ions are formed. A free radical is defined as an atom, a group of atoms, or a molecule in a certain state containing one unpaired electron which occupies an outer orbital. Free radicals are usually very reactive and their unpaired electrons have a strong tendency to interact with other electrons and form electron pairs (chemical bonds). A radical ion is a free radical with positive or negative charge.

2. EPR and Free Radicals

An unpaired electron, as in a free radical, has magnetic properties due to the intrinsic angular momentum which is known as the electron spin. The unpaired electron has a magnetic dipole which is assigned to a spinning motion of the electric charge. In a magnetic field, the electron spin has a tendency to align itself parallel or antiparallel  to the applied external magnetic field by making a precession motion around an axis in the direction of the field. This is the basis of the paramagnetic properties of the matter.

Typical free radical reactions are chain reactions that occur in three steps:

1. “The initiation step”:  radical formation process.

2. “The propagation step”: transfer reaction of free radicals in which the site of free radicals is changed. There are four types of propagation reactions:

a) “Atom Transfer reactions”: abstraction of hydrogen by a free radical:

 A^· + RH ® AH + R^·    (3)

b) “Addition Reactions”:  free radicals are added to a double bond:

A^·  + C = C ® A - C - C^·    (4)

c) “Fragmentation reactions”: “b-scission” is a known example of this reaction, in which an unpaired electron in a molecule splits a bond in b position and produces a free radical and a molecule containing a double bond:

 R: C - C^· ® R^· + C = C    (5)

d) “Rearrangements reactions”: a free radical changes position in a molecule, giving rise to two types of termination reactions:

                     (6)

3. “Termination reactions”: occur in all systems where free radicals are present. There are two types of termination reactions:

a) “Combination” of two radicals:

b) “Disproportionation” involving the transfer of hydrogen:

(8)

Both (7) and (8) are common termination reactions in free radical polymerization.

The EPR is the technique for excellence used to observe free radicals. This technique evaluates the absorption of energy of microwaves for unpaired electrons. A fundamental theorem of quantum mechanics states that the electronic state of an atom or molecule containing an odd, and therefore, unpaired electron must be at least twofold degenerate in the absence of a magnetic field. Upon application of a magnetic field, the degeneracy is removed and the energies of the erstwhile-degenerated states are shifted by an amount.

 E_M = g b H M   (9)

where H is the intensity of the applied magnetic field, b represents the Bohr magneton (0.927 x 10^-20 erg/G), g is a pure number customarily referred to as the g-value, 2.0023 for a free electron, and M is the magnetic quantum number of the electron which has the value ± ½ for a free electron. The g-values for most paramagnetic molecules are of similar magnitude. According to (9), in first approximation, the splitting of the energy levels is proportional to the field strength (Figure 1).

Transitions of electrons in which the magnetic quantum number changes by unity (DM = 1) can be induced by a radiofrequency field having a magnetic component at right angle to the steady field H, provided the quantum of energy carried by the photons equals the energy difference between the doublet levels:

When this condition is satisfied, a resonant absorption of energy occurs.

These transitions result in a net absorption of energy only because of the larger populations of electrons in the lower energy state. At equilibrium, the distribution of populations between energy levels is given by the Boltzman distribution.

The absorption of energy in the EPR experiment is proportional to the difference in populations in the states unfolded. An EPR spectrum is obtained by recording the derivative of the absorption of microwave energy as the applied field is swept through the resonance condition.

If the unpaired electron interacts with magnetic nuclei in its vicinity, the EPR spectrum takes on an added character called hyperfine structure e.g., if there is an interaction with a single proton. The energy levels of this two-spin system are given by:

                E_Mm = g b H M  -  g_N b_N h_N m    (11)

where b_N is the nuclear magneton (5.05 x 10^-23 erg/G) and g_N is the nuclear g factor (for a proton, g is 5.58). The quantity h_M is the magnitude of the effective magnetic field seen by the proton, a quantity which depends upon the magnetic quantum number of the electrons as well as on the strength of the applied field. The proton, like the electron, is a spin one-half particle and its magnetic quantum number m takes the values ± ½ [14].

The EPR technique can be used to study, among others, the following effects of the ionizing radiations on polymers:

1. Polymerization processes

]]> 2. Degradation processes in polymers

3. Oxidation of polymers (Antioxidants)

4. Graft copolymerization

5. Crosslinking

2.1 Polymerization Processes

Chain growth polymerization occurs by free radical or ionic mechanisms. The growth of a single polymer chain is due to the propagation of one kinetic chain reaction. Every free-radical chain reaction requires a separate initiation step in which a radical species is generated in the reaction mixture.

Radical polymerization can be divided into two general types according to the manner in which the initial species is formed:

a) Homolytic cleavage of a covalent bond in the monomer by energy absorption (radiation, photo, thermal or ultrasonic initiation)

  (12)

R - R ® 2R^·    (13)

    (14)

In initiation by radiation, the energy absorbed by the monomer is often higher than that required for the excitation of the molecule and dissociation of the covalent bond, and sufficient for the ionization of the molecule. An electron is ejected and the ionization of the monomer molecule produces a radical-cation containing one unpaired electron and a positive charge:

  (15)

Such ion-radicals are often unstable and may dissociate into a free radical and a cation:

  (16)

But this dissociative process can also occur in the same step in which the electron (e^-) is ejected from the irradiated monomer:

   (17)

When the electron does not have an excessive energy it may be attracted back to the cation, and a second free radical is produced:

Otherwise, the ejected electron is eventually trapped by another monomer molecule and either forms a radical-anion:

 AB  +  e^-  ®  AB^·-   (19)

or causes molecular dissociation to one radical and one anion species:

 AB  +  e^-  ®  A^· +  B^- (20)

In conclusion, the ejection of an electron from a molecule by ionizing radiation can produce two free radicals (A^· and B^·), and one cation (A₊) and one anion(B^-).

The application of EPR spectroscopy to study polymerization mechanisms was done for the first time by Bresler et al. [15]. These authors measured the concentration of free radicals formed during the polymerization of vinyl monomers such as methyl methacrylate, methyl acrylate and vinyl acetate.

2.2 Degradation processes in polymers

The formation of free radicals in polymers exposed to the simultaneous action of g-radiation and light has been studied by Russian scientists [16]. Free radical formation in polyethylene by high energy radiation (g-rays) has been the subject of a large number of EPR studies [4-8,11-14,16].

Ionizing radiation of polyolefins induces excitation and ionization of the molecules. Irradiation of polyethylene gives the formation of an alkyl radical,

which is observed as a six-line EPR spectrum. Figure 2 shows the EPR spectrum of a high-density polyethylene (HDPE) irradiated at 900 (a) and 150 kGy (b) of integral doses in a ⁶⁰Cobalt source in air, at a dose rate of 4.8 kGy/h. A multiple peak spectrum is observed due to different free radicals generated in the irradiation process. This spectrum can be interpreted as an overlapping of several spectra belonging to different paramagnetic centers and is a typical spectrum for a mixture of alkyl (21), allyl (22) and polyenyl (23) free radicals

    (22)

     (23)

The peaks corresponding to the alkyl radical are marked with the number (1) in the spectrum; those corresponding to the allyl radical with the number (2) and the central and very intense one are attributed to the polyenyl radical. The hyperfine splitting constant, which in this case is the separation in field of the corresponding EPR peaks is, for the alkyl radical, a₁ = 17.5 G and that for the allyl radical, a₂ = 11.3 G [5]. The inset shows the spectra of the sample irradiated at 900 kGy, 30 days after irradiation; as we can observe all the peaks belonging to alkyl and allyl radicals disappears, remaining only that for the polyenyl radical.

The EPR spectra of different blends of polyethylenes with polyamide 6 (PA6) irradiated at 930 kGy can be observed in Figure 3. As in the previous case, the results can be interpreted in terms of a superposition of alkyl, allyl and polyenyl free radicals in the EPR signals. The hyperfine constants, obtained from the spectra, are a₁ = 16.6 G for alkyl and a₂ = 11.7 G for allyl radicals [6]. The inset in the figure shows the spectrum for pure PA6. In this polymer, the predominant free radical is formed on the carbon atom a to the amide nitrogen. The multiplet of the allyl and alkyl radicals is not observed due to their low concentrations. Once the radicals are formed, in this case, they quickly react and are readily consumed owing to the lower degree of crystallinity of the PA6. However, a strong signal is present around g = 2.003, corresponding to polyenyl radicals, which are very stable in time.

2.3 Oxidation of Polymers (Antioxidants)

Most polymers show asymmetric single-line spectra attributed to alkyl peroxy (ROO^·) and alkoxy (RO^·) radicals, which are formed after the introduction of air to samples containing free radicals (R^·) or irradiating the sample in presence of air. There is some difficulty in distinguishing between (ROO^·)  and (RO^·) radicals, since both have the unpaired electron mainly concentrated on oxygen atoms and neither shows a hyperfine interaction with alkyl protons.

Initiation occurs through the formation of some free radicals R^·. If oxygen is present, the free radicals react rapidly with it to form peroxy radicals, which are also highly reactive and propagate the chain reaction. Their elimination through radical scavengers step (2), therefore, is an important stabilizing approach. Otherwise, peroxy radicals will react with other chains by hydrogen abstraction, thus transforming into hydroperoxides (ROOH) and, at the same time, creating a mid-chain radical in the attacked chain. Hydroperoxides are known to be relatively unstable, and their scission into two active radicals, RO^· and ^·OH, leads to branching of the chain, multiplication of free radicals and formation of main-chain alkoxy and peroxy radicals [17].

The effects of irradiation over samples of polypropylene (PP) with two different stabilizers added (a) a hindered phenol (butyl-hydroxy-toluene, BHT) and (b) a hindered amine stabilizer (HAS,poly[[6-[(1,1,3,3-tetramethylbutyl)amino]-s-triazine-2,4-diyl]-[(2,2,6,6-tetramethyl- 4-piperidyl)imino]-hexamethylene-[(2,2,6,6-tetramethyl-4-piperidyl)imino]], Chimassorb 944) were studied [18]. The main difference between the two systems resides in the fact that the phenolic stabilizers are active from the beginning whereas the stabilizing HAS-species, the nitroxyl radical (NO^·), has first to be formed by oxidation.

The concentration of the total free radicals S, associated with the above-mentioned types of antioxidants, was calculated. The ratio S/S₀ of the total number of spin per gram, S, to the total number of spin per gram in the sample just after being irradiated, S₀, was obtained from the area under the curve in the recorded spectrum. No EPR signal could be obtained at zero doses, because of the detection limits of the spectrometer.

Figure 5 shows the unnormalized EPR spectra of samples of PP with Chimassorb 944 and BHT just irradiated. Both spectra are very similar. The inset of the figure shows the spectra ten months later. The sample containing Chimassorb 944 even shows an EPR signal after that time period. With ageing, a characteristic spectrum of nitroxyl radicals, with a slight contribution of peroxy radicals, is observed. On the other hand, the sample containing BHT shows no detectable EPR signal after ageing. Hence, it could be said that alkyl radicals have decayed totally in the PP-BHT sample, whereas persisting peroxy radicals and when time elapsed, nitroxyl radicals were present in the PP-Chimassorb 944 sample. Figure 6 displays the spectra of the PP-Chimassorb 944 sample just after irradiation and ten months later. The change of the lineshape from that of a pure PP irradiated in air to that corresponding to the nitroxyl radical with a slight contribution of remaining peroxy radicals is clearly seen at the central line of the spectrum, ten months later.

Figure 7 displays the time decay of the S/S₀ ratio of the PP and all its stabilized samples. In all cases, a decrease of the S/S₀ ratio is observed in the first hours. Samples containing Chimassorb 944 reach a minimum and then the S/S₀ ratio slightly increases. This can be explained taking into account the cycle of formation of nitroxyl radicals in the HAS, which once produced, grows until reaching a maximum. Then, their amount falls until a critical value where they are no longer effective as scavengers. The sample with BHT shows a continuous decay until the EPR signal was undetectable 4000 hours later. In the samples containing Chimassorb 944, a higher S/S₀ ratio was obtained. The decrease of the S/S₀  ratio was observed when other stabilizers, in addition to Chimassorb 944, were incorporated. In conclusion, it can be said that the stabilizing phenol was consumed during ageing and its concentration decayed quickly below a critical value, which is no longer sufficient to prevent the accumulation of highly unstable hydroperoxides. On the contrary, the concentration of the stabilizing HAS-species (NO^·) increased with time.

2.4 Graft Copolymerization

Under ionizing irradiation of solid polymers free radicals are formed which are trapped into the polymer matrix. Under certain conditions, these radicals can initiate graft polymerization. The grafting reaction is dependent on the physical state of the polymer and the properties of the free radicals formed in the polymer. Results displayed in Figure 8 are an example of the use of the EPR technique in the characterization of free radicals generated in the grafting processes of polyethylene with diethyl maleate (DEM). That figure shows the spectrum of HDPE with 15% of DEM in decalin irradiated at 15 kGy. A very noisy spectrum of six absorption lines is observed. The inset in the figure shows the effect of ageing in the sample one year later. As it can be seen, the spectrum becomes well resolved as time elapses, making it possibly to separate the absorption lines. After a longer time period, the spectrum is a typical spectrum of a nitroxyl radical that corresponds to a HAS stabilizer. This is in agreement with an activation of the antioxidant under the effects of gamma irradiation.

A detailed study of these kinds of radicals is shown in Figure 9, where the total free radical concentrations in samples of HDPE/DEM irradiated at different doses and from different concentrations of DEM are reported. In the time period 0 £ t £ 100 h, the total free radical concentration falls for all the samples studied. This is the expected behavior in this kind of samples. After this period, the total free radical concentrations increase with time; this behavior is in agreement with that for the HAS stabilizer as it can be seen in the inset of the figure [17].

2.5 Crosslinking

Enhanced crosslinking occurs via a chain reaction involving both a polymer and a monomer. The initiation of a chain reaction via a single radical allows the formation of a sequence of crosslinks. An EPR study of the changes produced in crosslinking polymers included the determination of the total free radical concentration (TFRC) as a function of the integral dose supplied to the samples as well as the TFRC decay is made here. A model that explains the generation and recombination of damages produced by irradiation was used to evaluate the behavior of the TFRC [9,10].

Figure 10 shows the total spin concentration per grams as a function of the integral dose of irradiation in blends of polypropylene with Styrene-Butadiene-Styrene radial copolymer (SBS) at different concentrations (0%, 10%, 20%, 30% and 40% of SBS) in the integral dose range of 5 ≤ D_I ≤ 100 kGy. An increase in the number of free radicals with the integral dose of irradiation is observed in all the samples. For the lowest absorbed dose, the number of generated radicals is similar, within the experimental error, in all the samples including that of pure polypropylene. At the higher dose, a slight decrease in the number of radicals when SBS is present in the sample was obtained. That is, the sample of pure PP shows a higher free radical concentration for ID ³ 50 kGy.

       (24)

where N is the number of total free radicals generated during the irradiation process and the K´s are the zero and first order generation and recombination rate constants. Defining K₀ º (K_0G - K_0R) and K₁ º (K_1R - K_1G), and assuming that these new constants depend on the energy deposited into the sample by the incident radiation in the time unit, the total free radical concentration as a function of the total incident dose was obtained using the following expression:

     (25)

where k'₀ and k'₁ are proportionality constants, and N₀ gives an idea of the radical concentration at zero dose. The concavity of the curve depends on the sign of these constants. For positive values of both k'₀ and k'₁, the curve will be concave down and the rate of recombination would be higher than that of the generation of free radicals. For a positive and a negative value of k'₀ and k'₁, respectively, the curve is concave up (convex). This means that the rate of generation of free radicals is higher than that of their recombination.

A study of radical decay for the sample with 40% of SBS for all the integral doses studied was done. The results are displayed in Figure 11. The decay of the total radical concentration was fitted assuming a mixed first and zero order processes, as those described by equation (26):

   (26) 

where p₁, p₂, p₃, p₄ and p₅ are fitting parameters. The inverse of p₂ and p₅ are somehow exponential time decays, t₁ and t₂, of the total free radicals concentration. The best fitting parameters of the data in Figure 11 are shown in Table 1. From that table it is immediately inferred that there are effectively two mechanisms involved in the recombination of the free radicals. The first one, associated with the exponential decay time constant t₂, shorter in time 16 < t₂ < 65 h, which can be associated to the reaction of the radicals with their nearest neighbors, and the other one, related to the mobility of the radicals, associated with t₁, which is larger in time 258 < t₁ < 685 h. These results can be interpreted assuming that a group of radicals reacts rapidly with their neighbors, may it be the alkyl and allyl radicals that disappear at very short times, and another group of radicals that takes much more time, because they are impeded by their mobility (may them be the peroxy radicals).

Table 1. Fitting Parameters obtained using equation (26) for the PP/SBS (40%) blend irradiated at different integral doses.

Except for the 25 kGy dose, an increase in the exponential decay time is observed with the integral dose. Certainly, this behavior can not be associated with the mobility. Instead, this behavior must be associated with the concentration of free radicals generated at each dose. There is not an explanation for the behavior obtained at the dose of 25 kGy.

3. FINAL REMARKS

The usefulness of the EPR technique in the study of the different processes occurring in polyolefins as a consequence of their gamma irradiation was established. The use of EPR for the characterization of these polyolefins is advantageous, because free radicals are generated fundamentally in the process of irradiation. Radicals are present in the whole subsequent dynamics in the material and EPR is, as it was pointed out at the beginning, the technique par excellence in the characterization of free radicals. Independently of the doses or the type of radiation used, the dynamics of formation and recombination of free radicals in these polyolefins, which will be associated with the life of the polymer, can be studied in the temperature range of 1.6 £ T £ 750 K.

4. CONCLUSIONS

The Electron Paramagnetic Resonance technique can be used to evaluate quantitatively and qualitatively the presence of free radicals in irradiated polymers. The line-shape, line-width and line position give very important information about the system. These radicals, responsible for scission and crosslinking of chains, are evaluated using an expression that takes into account the generation of defects considering a mixture of first and second order effects. The sign of the constant of the generation and recombination reactions obtained from the fitting of the data of the behavior of the free radicals concentration as a function of the integral dose gives an idea of the generation and recombination rates of the free radicals after being irradiated. The behavior of these constants can be related to the processes of crosslinking and chain scission.

On the other hand, the parameters obtained from the fitting of the decay curves give an idea of the dynamics of the generation and recombination of these radicals. Then, the relaxation times of these processes can be estimated.

In a single process, where only free radicals generated by irradiation are evaluated, an exponential decay is observed; in the presence of antioxidants this behavior is modified and depends on the type of antioxidant used. The concentration of free radicals associated to antioxidants of the HAS type increase when ageing up to a maximum from where it decays below a critical value. On the contrary, the total free radical concentration associated to the BHT antioxidant decays quickly until reaching the critical concentration, below which the radicals are no longer observed. When studying the variation of the total free radicals generated in irradiated polymers, it was found that the radical nitroxyl is activated by the action of the ionizing radiations.

An EPR study of the changes produced in crosslinking polymers included the determination of the TFRC as a function of the integral dose supplied to the samples, as well as the TFRC decay. There are two mechanisms involved in the recombination of the free radicals. The first one, associated to the reaction of the radicals with their nearest neighbors, the other one, related to the mobility of the radicals.

The authors acknowledge the UTN team at Instituto Venezolano de Investigaciones Científicas for the technical support in the irradiation of the samples.

Nota:

1 A Gy is a derived unit of the International System of Units and it measures the dose of ionizing radiations absorbed by a certain material. A Gy is equivalent to the absorption of a joule of ionizing energy for a kilogram of irradiated material (1 Gy = 100 Rad).

Pedro José Silva Mujica.

Físico egresado de la Universidad de Los Andes (ULA) de Venezuela en 1985, con un M.Sc. en Física obtenido en 1992 en el Instituto Venezolano de Investigaciones Científicas (IVIC) y un Doctorado en Ciencia Mención Física de la Universidad Central de Venezuela (UCV) alcanzado en el año 2001. Actualmente es Investigador Asociado Titular del IVIC, institución en la que labora desde el año 1986, en donde también es profesor de postgrado en el área de Física. Fue coordinador académico del Centro de Física del IVIC desde 2004 al 2007 y actualmente es jefe de dicho Centro. También es Profesor Titular a tiempo convencional de la Universidad Simón Bolívar (USB) desde 1992, Profesor Asociado a tiempo convencional de la UCV desde 2002 y Profesor Ad Honorem de la Maestría en Enseñanza de la Física en la Universidad Pedagógica Experimental Libertador-Instituto Pedagógico de Caracas (UPEL-IPC). Ha sido tutor de seis tesis de Licenciatura en Física y actualmente dirige dos tesis de Licenciatura en Física, tres de Maestría en Física y tres de Doctorado. Cuenta con 73 contribuciones en congresos nacionales e internacionales, 61 artículos publicados en revistas nacionales e internacionales arbitradas y 1 capítulo de libro (en prensa). Distinguido como Investigador Nivel III por el Programa de Promoción del Investigador (PPI) del Observatorio Nacional de Ciencia, Tecnología e Innovación (ONCTI) de Venezuela.

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