M A Al-Jubbori

M Fromm

E M Awad

Strong etching formulation (time and rate) for PADC with deep depth bulk etch rate study

Keywords: PADC, Soft/strong etching, Arrhenius model, Multi-hit model, Bulk etch rate, Etching time

Aqueous NaOH with ethanol (strong) etchant is widely used. It shortens etching time effectively compared to normal etching conditions (6.25N NaOH at 70 o C). Two equations have been proposed to calculate the etching time with NaOH molarity and ethanol volume. Another two empirical equations were introduced for estimating the bulk etch rates of PADC etched in strong etchant. Up to now, there were no such equations available in the literature that can predict etching time and V b of PADC with etchant molarity and ethanol volumes. The proposed equations were compared to fundamental V b models stemming from literature. Fast etching enables the follow-up of bulk etch rate variation versus depth in the detector material up to ≈80 µm. In agreement with previous studies, an equation is given which allows such variations to be expressed under the form of a reciprocal bulk etch rate normalized to depth (i.e., removed layer).

Introduction

The standard procedure when using solid-state nuclear track detectors (SSNTD) is to reveal latent ion tracks by operating a chemical etching which makes them visible under the optical or atomic force microscope. Commonly used etching solutions in the literature are alkaline etchant such as NaOH or KOH with concentration range of 6-7 N at temperatures of 60-70 °C [START_REF] Fromm | Proton and alpha track profiles in CR39 during etching and their implications on track etching models[END_REF][START_REF] Awad | Description of the bulk etching rate of CR-39 by an extended Arrhenius-like law in increased intervals of temperature and etchant concentration[END_REF][START_REF] Kodaira | A performance test of a new high-surfacequality and high-sensitivity CR-39 plastic nuclear track detector -TechnoTrak[END_REF][START_REF] Awad | Alpha particle spectroscopy for CR-39 detector utilizing matrix of energy equations[END_REF][START_REF] Al-Jubbori | A parameterization of the chemistry-normality dependence of bulk etch rate in a CR-39 detector[END_REF][START_REF] Azooz | Alpha particles energy estimation from track diameter development in a CR-39 detector[END_REF][START_REF] Azooz | New approach of modeling charged particles track development in CR-39 detectors[END_REF][START_REF] Awad | Bulk etch rate for PADC CR-39 at extended concentration range of NaOH mixed with ethanol and etchant viscosity study[END_REF][START_REF] Hermsdorf | Measurement of bulk etch rates for poly-allyl-diglycol carbonate (PADC) and cellulose nitrate in a broad range of concentration and temperature of NaOH etching solution[END_REF][START_REF] Al-Jubbori | V-Function to Investigate Tracks of the Alpha Particle Irradiated CR-39 Detector[END_REF]. However, a new etchant solution composed of NaOH with different amounts of alcohols (ethanol and/or methanol) has been used as a strong and active etchant [START_REF] Matiullah | Discovery of new etchants for CR-39 detector[END_REF][START_REF] Rammah | Makrofol DE 1-4 as alpha dosimeter: Optimum etching conditions[END_REF][START_REF] Chavana | A new chemical etchant for the development of alpha tracks in CR-39 solid state nuclear track detector[END_REF]. Such mixtures are very effective in reducing the time needed to reveal and measure diameters of alpha tracks. Strong etching was found to provide a quadratic function of growing alpha particle tracks diameter with etching time. So, the strong etching can reduce the etching time by factor "4", and thus enhance the etching time [START_REF] Chavana | A new chemical etchant for the development of alpha tracks in CR-39 solid state nuclear track detector[END_REF].

Processing many detectors can be time-consuming using normal etching compared to strong one. Therefore, it requires fine-tuned analyses for better understanding and use in routine work.

Poly-allyl-diclycol-carbonate (PADC) is mainly made of the monomer allyldiclycol-carbonate (ADC). ADC chemical structure contains two carbonate groups and one ether function. Its alkaline dissolution results in the loss of the carbonate groups from the residual molecule (see next section). This process is activated in the presence of hydroxyl ions available in an alkali solution (alkaline hydrolysis).

The reaction is endothermic i.e., the process needs energy to be initiated and its rate increases with increasing temperature of the solution. In principle, two models were used to describe chemical etching process. The first one is Arrhenius model, accounting thermodynamic equilibrium of chemical reaction between educts and products in homogeneous phase. In this statistical consideration, the bulk etch rate can be determined as a function of etchant concentration (С), temperature (T), as follows [START_REF] Somogyi | Etching properties of the CR-39 polymeric nuclear track detector[END_REF]:

𝑉 (𝐶, 𝑇, 𝐵, 𝑛, 𝜀) = 𝐵𝐶 𝑒 (1)
Where, B is the normalization constant, the power n (not necessary integer)

indicates the chemical reaction order and the activation energy ε (eV) are the adjustable parameters. k is Boltzmann's constant. Its results are widely used as well as accepted [START_REF] Awad | Activation energy of etching for CR-39 as a function of linear energy transfer of the incident particles[END_REF][START_REF] Kodaira | Mass spectrometry analysis of etch products from CR-39 plastic irradiated by heavy ions[END_REF]. From this model, only two important parameters are deduced: the order of chemical etching (n) and the activation energy of etching (ε).

The second is Multi-hit model (MHM, also known as ν-hit) [START_REF] Ditlov | Formation model of bulk etching rate for polymer detectors[END_REF], in which the dissolution of the bulk material described by the number of hits (ν) between the molecules of etchant and detector. The model is thus combining hits frequency with thermodynamic equations for a simultaneous interpretation of chemical reactions and diffusion processes. The basic idea of this model is to claim that the processes are initiated by single or repeated interactions or hits of the target (molecules, molecular fragments, emulsion grains and/or living cells). SSNTDs are then considered as composed of sensitive nanometric volumes (SNV) and such SNV can switch from the state "No" to the etched state "Yes" after etching process with a certain probability. Poisson's distribution describes this probability as below:

𝑃 (𝜉) = 1 -∑ ! 𝑒 (2)
These centres are etched if they suffer a fluctuating number of hits, ν at the nanometre scale by etchant molecules greater than some threshold value of ν.

Parameter (ξ) represents the average number of hits per sensitive volume. Several functions for bulk etch rate proposed in terms of multi-hit approximation [START_REF] Ditlov | Formation model of bulk etching rate for polymer detectors[END_REF]. In the present study, the focus was on the effect of etchant concentration on etching rate. Therefore, two modules were considered (where the concentration effect is dominant) to calculate the detector bulk etch rate. Module 8 of multi-hit, we will call it MHM-M8, in which 𝜉 = and module 15 in which 𝜉 = 𝑒 , we will call it MHM-M15. More information about this model can be found in [START_REF] Awad | Applicability of the multi-hit model to calculate the track etch rate in µm-scale in CR-39 detectors[END_REF][START_REF] Awad | Multi-hit model on CR-39, DAM-ADC and LR-115 SSNTDs: Statistical and comparative study[END_REF][START_REF] Fromm | Many-hit model calculations for track etch rate in CR-39 SSNTD using confocal microscope data[END_REF][START_REF] Ditlov | Interpretation of the bulk etching process in LR-115 detectors by the many-hit model[END_REF][START_REF] Ditlov | The Bragg-peak studies in CR-39 SSNTD on the basis of many-hit model for track etch rates[END_REF] and references therein. MHM-M8 bulk etch rate can be written as:

𝑉 (𝐶, 𝑇, 𝐵, 𝜈, 𝜀, 𝑐 ) = 𝐵𝐶𝑒 𝑃 (3)
While bulk etch rate with MHM-M15 is as follows:

𝑉 (𝐶, 𝑇, 𝐵, 𝜈, 𝜀, 𝑐 ) = 𝐵𝐶𝑒 𝑃 𝑒

Many physical parameters can be deduced from this model, n, ε and number of hits necessary to activate the reaction between etchant molecules and detector molecules (ν). Etching process is envisioned as a macroscopic process when described by those two models; however, much information about etching processes at the microscopic scale were ignored (see etching mechanism section).

Many empirical equations have been used to calculate bulk etch rates as function of both C and T [START_REF] Fromm | A study of CR39 bulk etch properties under various temperature and concentration conditions to modelized the dissolution rate[END_REF], such as for example:

𝑉 (𝑎 |𝑎 ) = 𝑎 10 ( ) (5)
Where a 1 to a 5 are free adjusting parameters.

Recently, another equation assigned in terms of the etchant concentration (C), and free adjusting (a) and (b). This equation (referred here as Al-Jubbori-2016) was proposed in [START_REF] Al-Jubbori | A parameterization of the chemistry-normality dependence of bulk etch rate in a CR-39 detector[END_REF] as follows:

𝑉 = 𝑎(𝑒 -1) (6)
Nevertheless, since the involvement of the strong etching (NaOH plus ethanol)

in 2005 [START_REF] Matiullah | Discovery of new etchants for CR-39 detector[END_REF] Besides, a reciprocal bulk etch rate equation is going to be deduced and compared with those of literature data.

Etching Mechanism

Since its discovery in 1978 [START_REF] Cartwright | A nuclear-track-recording polymer of unique sensitivity and resolution[END_REF], PADC (also known as CR-39 TM ) is considered as one of the most successful SSNTD for detection of charged particles with linear energy transfer greater than 10 keV/μm (in water) [START_REF] Szabó | Calibration of solid state nuclear track detectors at high energy ion beams for cosmic radiation measurements: HAMLET results[END_REF]. It is a highly cross-linked thermoset polymer. Soft (NaOH/H 2 O) and strong (NaOH/ethanol) etching processes follow the same etching mechanism as illustrated in Figures 123. Etching takes place due to scission of the carbonate ester bond by hydroxide ions through basic hydrolysis of ester moiety (see Fig. 1). Electron rich hydroxide ions cause the scission of ester linkage because carbonyl groups (C=O) are electrically polarized (the carbon atom site is electron deficient). Electron transfer occurs thus from electron rich region to electron deficient region, so that, OH groups will attack electron deficient ones (carbonyl group) as shown in Fig. 2. In PADC there are four possible positions which are subjected to cleavage by the hydroxide ion [START_REF] Tse | Comparative studies of etching mechanisms of CR-39 in NaOH/H2O and NaOH/ethanol[END_REF] as shown in Fig. 3. Etching of PADC in NaOH/ethanol will fierce bulk etch rate of the detector compared to NaOH/water. This may likely be due to the better reactivity during etching and presumably to a better solubilization of organic etchproducts released from PADC. Relative static permittivity (which provides a measure of polarity) of pure methanol or ethanol are respectively 33 and 24 at 25°C, with quasi-identical dipolar moments of ≈1.70 debye (D); as water has a relative static permittivity of typically 75 at 25°C (64 at 70°C) and a slightly higher dipolar moment of ≈1.85 D [START_REF] Li | Solubility of organic solutes in ethanol-water mixtures[END_REF]. A decrease of the dielectric constant (i.e., of the relative static permittivity) of a given medium has a direct consequence on both reactivity and miscibility. In media containing methanol or ethanol, the dielectric constant is small, therefore attraction forces between electrical charges are enhanced in comparison to pure water. It is therefore likely that addition of alcohols in NaOH aqueous solution may partly lower the relative static permittivity value of the etchant and thus it can enhance hydroxide ion reactivity on polar groups (carbonate ester groups).

Fig. 3 shows that etch-products are mainly: saturated, unsaturated alcohols and carbonate ions, the latter being strongly miscible in water. The basic solubility rule states that "like dissolves like" but when applied to alcohols things become a bit more complex. Alcohols are sparingly soluble in water; their solubilities decrease with carbon chain length. Higher alcohols are insoluble in water. Organic alcohols consist of a carbon chain (always non-polar) and a OH group (which is polar). It is well-known for example that after 7 th carbon atoms in a chain (i.e. for homologues longer or equal to heptanol), alcohols are considered immiscible in pure water. By mixing water and ethanol (or methanol), solubilities of both higher alcohols and aromatic hydrocarbons (non-polar in nature) increase in water/ethanol mixtures as the volume fraction of ethanol increases [START_REF] Li | Solubility of organic solutes in ethanol-water mixtures[END_REF]. PADC etched products are thus more soluble in ethanol than in water. The decrease in etching time is therefore likely to be due to both of an enhancement of reactivity of the etchant (hydroxyl ions) and an increase in solubility of organic etch products resulting in an increase in the bulk etch rate, V b .

Experiment

PADC detector sheet of thickness 650 µm, manufactured by American Acrylics (US), was used. Detector sheet aging more than 20 years old was cut to small pieces of area 1 cm 2 . Each piece was irradiated to fission fragments of 252 thicknesses using the optical microscope after the detector was mounted in its edge. After etching, track cones shaped etch-pits were found by careful polishing of the detector edge to produce ion's nuclear track profile for Si ions. The growth of the cone shaped etch-pits for Si tracks at one side of the detector were followed at different etching times. From the track cone length (L) at every etching step and the corresponding removed layer, the track etch rate V t was determined directly [START_REF] Fromm | Light MeV-ions etching studies in a plastic track detector[END_REF][START_REF] Yamauchi | Inter-comparison of geometrical track parameters and depth dependent track etch rates measured for Li-7 ions in two types of CR-39[END_REF][START_REF] Awad | Direct determination of track etch rate and response of CR-39 to normal incidence high-energy heavy ions[END_REF]. For normally incident particle, the track etch rate at given removed layer, h can be deduced if the track etching started immediately at the detector surface without delay. Thus, the time dependent track length is available by track profile technique and track etch rate is given as:

𝑉 (ℎ) = ( ) + 𝑉 (7)
Aging effect for PADC detectors was previously studied for samples stored for 8 and 12 years [START_REF] Abdelaal | Breeding behavior of radiation-induced effects in organic materials and their possible use as radiation dosimeters[END_REF]. Polymer degradation for PADC detectors was investigated microscopically using FTIR for new, medium age, and old detectors. It was proved that aging effect is not dominant and has minor effect on PADC specially for bulk and low γ-ray doses samples. Bulk etch rate of PADC (type PM-355) was found almost constant even after storage for a long time (about ten years) in air at room temperature in the absence of light in another study [START_REF] Malinowska | Change in the sensitivity of PM-355 track detectors for protons after long-term storage[END_REF]. However, for a sample of age more than 12 years, the forecasted loss of sensitivity is about 2% per year.

Data analysis

Data fitting method

The non-linear fitting procedure was carried out by minimizing the χ 2 distribution iteratively for all the considered equations. Iteration process is repeated many times using many seed numbers for the adjusted parameters till the lowest χ 2

is achieved [START_REF] Awad | Bulk etch rate for PADC CR-39 at extended concentration range of NaOH mixed with ethanol and etchant viscosity study[END_REF]. Try and error method was used to obtain the global minimization as much as possible. χ 2 values depend on degree of freedom, DF, which refers to the maximum number of the logically independent values that have the freedom to vary in the data sample (equals the number of the experimental data points minus 1). In the present work, the significant levels α was taken as 0.05. The fitting of the two models and the two equations are discussed accordingly.

New approximation for etching time

Two different equations are proposed to calculate the etching time. In the first one, the etching time t e1 necessary to reveal 18 μm diameter of fission tracks is given in terms of the etchant concentrations as follows:

𝑡 = (8)
Where q is a dimensionless adjusting parameter and G is a normalization etching time factor of dimension [min mol L ]. In the second one, the etching time t e2 is given as a function of NaOH molarity and ethanol fraction, x as follows:

𝑡 = 𝐾 (9)
Where x is the amount of ethanol volume, thus a and x are in L (litre) and C is the molar concentration with b ≠ 1, then K has the following unit [ . ].

The physical meaning of the adjusting parameters could be deduced from their physical dimensions. However, due to their phenomenological nature, the physical meaning of the current parameters is not straightforward. At least a meaning could be deduced from their physical dimensions; such an attribution remains nevertheless hypothetically. K is thus simply a scaling time constant.

New approximation for bulk etch

The present work is suggesting two bulk etch rate equations. In the first one, bulk etch rate (V b1 ) was treated as a bulk quantity without considering the added ethanol fraction, like literature ones. V b1 can be determined in terms of the etchant concentration, C as follows:

𝑉 = 𝑄𝑒 ( 10
)
Where Q is the bulk etch rate normalization factor of dimension [ ] , while i and j are two adjusting parameters have concentration dimension, [ ].

As stated before, no formula has been suggested by researchers to predict the bulk etch rate as a function of NaOH concentration, C and amount of ethanol volume, x in the etchant. Therefore, a second bulk etch rate formula, V b2 is suggested as a function of C and x simultaneously as follows:

𝑉 = 𝑈 (𝑎 + 𝑥)𝑒𝑥𝑝 (11)
Where U is a conversion adjusting factor of dimension [ ], x is amount of added ethanol in L, C is NaOH concentration. The free parameter a 1 has dimension of [L] while both of a 2 and a 3 have concentration dimension [ ].

New approximation for reciprocal bulk etch rate

The reciprocal bulk etch rate using strong etching normalized to depth (by taking the whole removed layer as z=1) was obtained as follows:

( ) = 𝑓 + 𝑔𝑒 (12)
Where f and g are the reciprocal bulk etch rate factors of dimension of .

Results and Discussion

Etching time

Fig. 4 shows the variation of etching time with the different NaOH molarity for soft and strong etching, respectively. Tables 1 and2 compile the adjusting parameters G and q of Eq. 8 and K, a and b of Eq. 9, respectively. From Fig. 4 and Table 1&2, one can observe that the suggested two equations produce the etching time with exactly same accuracy. However, Eq. 9 has the advantage of incorporating the ethanol volume, x. of energies which is dependent on the etching temperature. Etching reaction would take place if energies of colliding species are greater than activation energy of etching (ɛ). The evaluated activation energies (ɛ) are given in Table 3. The mean value 0.676 eV (with deviation ±0.023 eV, i.e., <3.5%) remains in agreement with previous resulted, reported in [START_REF] Awad | Activation energy of etching for CR-39 as a function of linear energy transfer of the incident particles[END_REF]. The activation energy of etching is weakly dependent (or almost independent) on the amount of ethanol added to the solution.

Bulk etch rate

This proves that etching process and chemical reaction rate within such extended concentration range is still at equilibrium. prediction to bulk etch rates of the extended concentration range incorporated with the experimental data. Fitting parameters of multi-hit models are given in Table 4.

Inspecting Fig. 6 and Table 4 one can conclude that multi-hit model can reproduce bulk etch rate with good accuracy. Activation energy, ε deduced by multi-hit model is less than previously reported value (≈0.70 eV) [START_REF] Awad | Description of the bulk etching rate of CR-39 by an extended Arrhenius-like law in increased intervals of temperature and etchant concentration[END_REF][START_REF] Awad | Activation energy of etching for CR-39 as a function of linear energy transfer of the incident particles[END_REF][START_REF] Awad | Multi-hit model on CR-39, DAM-ADC and LR-115 SSNTDs: Statistical and comparative study[END_REF] however, still have the same order of magnitude. Values of number of hits, ν required for activating the sensitive volume of the polymer were 2 for 0 ethanol and 1 in the presence of ethanol as expected. This is one advantage for the multi-hit model where this number of hits, ν is another indicator about the etchant activity. As ν decreases (=1) for ethanol solution, as the etchant activity probably increases compared to ν=2 for soft etching.

Bulk etch rates can also be predicted using an equation with only two adjusting parameters [START_REF] Al-Jubbori | A parameterization of the chemistry-normality dependence of bulk etch rate in a CR-39 detector[END_REF]. This simple equation can reproduce the bulk etch rate with accuracy where the best fitting parameters are: α=0.05, DF=10, and χ 2 < 18.307 as given in Table 5 and illustrated in Fig. 7.

Experimental bulk etch rate and the non-linear fit using Eq. 10&11 for the limited In the previous paragraphs, the different equations for bulk etch rate were studied individually. All the equations were succeeded to reproduce the bulk etch rate as depicted in Fig. 10 but with different accuracy Tables 34567. However, Eq. 11

is more advantageous since it adds both NaOH molarity and ethanol fraction as etching parameter. Eventually, this equation can be applied to other SSNTDs and chemical etchants, such as KOH.

Rigorous bulk etch rate V b of PADC in NaOH/ethanol compared to NaOH/water and lowering etching time, t e can be attributed to the fact that media containing methanol or ethanol has smaller dielectric constant. Attraction forces between electrical charges are enhanced in comparison to pure water. Therefore, it is likely that addition of alcohols in NaOH aqueous solution may partly lower the relative static permittivity of the etchant and thus enhances hydroxide ion reactivity on polar groups (carbonate ester groups).

Reciprocal bulk etch rate

PADC bulk and track etch rate variation with depth up to ≈ 80 µm was intensively investigated where strong etching allows successive etching effectively with reasonable etching time. The variation in V b and V t with depth for swift Si ion are illustrated in Fig. 11. It was found that bulk etch rate is slightly increasing with depth in agreement with Fujii and Nishimura, 1986 [START_REF] Fujii | Generalized etch-pit equations and their application to analyses of tracks in CR-39 with depth dependent etching properties[END_REF]. Simultaneously, the track shaped etch-pits were measured for limited number of cones, and the corresponding track etch rate V t was determined. The track etch rate V t is found to be almost constant as expected for swift heavy ions passes through the bulk of SSNTD.

Detector sensitivity, V for Si ion was determined and normalized to value achieved at the first etched-off layer of a detector where V = . Variation in normalized sensitivity as a function of the removed layer h is presented in Fig. 12.

One can observe that the detector sensitivity decreases with depth and reaches between 60-80% and becomes more stable at depth 25 µm inwards. This reduced In progress, etching time (t e ) for a given etching conditions will be estimated in terms of the Multi-hit model. Using geometric considerations, it is possible to estimate the frequency of collisions of ethanol molecules with the sensitive link of the detector molecules and obtain the release time of a given thickness in connection with the etching time.

Figures Caption

Fig. 1 Ester group hydrolysis in PADC CR-39 and the cleavage of ester linkage caused by hydroxide ion.

Tables Caption

Table 1 Fitting parameters for etch time formula (Eq. 8).

Table 2 Fitting parameters for etch time formula (Eq. 9).

  Experimental bulk etch rates for PADC SSNTD in the extended concentrations range of NaOH (2-22N) and added ethanol volumes of (0, 1, 2 and 3 mL) in 8 mL of NaOH aqueous solutions are illustrated in Fig.5. Experimental uncertainty or error bars (≈15%) is relatively high. It represents the standard deviation of the measured fission fragment diameters, D ff . This higher uncertainty may be accepted in terms of the manual track diameter measurements, extended concentration range, highly active and strong etching process implemented.Arrhenius-like model successfully reproduce the experimental data in the extended molarity range, as shown in Fig.5. The best fitting parameters are: α=0.05, DF=10, and χ 2 < 18.307. Table3compiles the fitting parameters of the Arrhenius-like model. The degree of fitting is slightly degraded with increasing amount of ethanol and NaOH concentration. Considering physical data of bulk etch rates and Arrhenius fitting, the bulk etch kinetics can be explained chemically based on collision theory. During etching process, etching species in the etching solution collide with the molecules and atoms of the PADC detector with a range

Fig. 6

 6 Fig. 6 illustrated the two multi-hit models (MHM-M8 & MHM-M15)

( 2 -

 2 10N) and extended molarity are shown in Fig.8 and 9, respectively. The new equations are predicting the bulk etch rate with the same high accuracy as illustrated in Tables 6&7. The different adjusting parameters Q, i, j, U, a 1 , a 2 and a 3 of equations 10&11 are compiled. The adjusting parameters are showing slight dependence on C and x. Of course, the 27 % ethanol content (3 mL) data shows higher χ 2 value compared to the other ethanol volumes. However, it is statistically accepted. This is expected in terms of bulk etch rate has been duplicated compared to the closest ethanol volume of 20%. The best fitting parameters are: α=0.05, DF=4, χ 2 < 9.488 and α=0.05, DF=10, χ 2 < 18.307 for the limited and extended concentration ranges. By the goodness of the fitting curves in comparison with the well-known models (Arrhenius and Multi hit) the validity of suggested empirical formula has been determined.

Fig. 2

 2 Fig. 2Stages of the hydroxyl attack on the carbonyl during the etching

Fig. 3

 3 Fig. 3The possible positions of the cleavage and the yielded etching outputs.

Fig. 4

 4 Fig.4Eqs. 8 and 9 prediction to the etching time necessary to obtain D ff ≈18

Fig. 5

 5 Fig. 5Arrhenius equation fit of bulk etch rate in extended NaOH/ethanol

Fig. 6

 6 Fig. 6Multi hit model of MHM-M8 and MHM-M15 fit of bulk etch rate in

Fig. 7

 7 Fig. 7Al-Jubbori-2016 equation fit of bulk etch rate in extended

Fig. 8

 8 Fig. 8Prediction of the newly suggested equations (Eq. 10 and Eq. 11) to

Fig. 9

 9 Fig. 9Prediction of the newly suggested equations (Eq. 10 and Eq. 11) to

Fig. 10

 10 Fig. 10Experimental bulk etch rate and the corresponding calculated ones

Fig. 12 PADC

 12 Fig.12PADC sensitivity (V) normalized to value, achieved at the first

Fig. 13

 13 Fig. 13Experimental and calculated reciprocal bulk etch rate with normalized

Table 3

 3 Arrhenius equation fitting parameters for the extended NaOH concentration and different ethanol volume at B=1.25×10 9 .

Table 4 MHM

 4 -M8 and MHM-M15 fitting parameters for the extended NaOH concentration and different ethanol volume at B=1.25×10 9 .

	Table 5	Al-Jubbori-2016 equation fitting parameters for the extended NaOH
		concentration and different ethanol volume.

Table 6

 6 New equation (Eq. 10) fitting parameters for limited and extended NaOH concentration range at different ethanol volume.

Table 7

 7 New equation (Eq. 11) fitting parameters for limited and extended NaOH concentration range at different ethanol volume.

Acknowledgment

The authors are grateful to the unknown reviewers for their constructive suggestions. The authors are very thankful to Ms Eman Bebers for providing the data from her M.Sc thesis, Prof. A. Khafagy, Prof. of Physics, Faculty of Science, Menoufia University and Mr. Atta H. Lakho, of GBDC, Karachi for English revising and editing the manuscript. Mushtaq Abed Al-Jubbori is grateful to the University of Mosul/ College of Education for Pure Sciences.

sensitivity with depth is due to the slight increase in V b while V t is almost constant.

The variation of V b is an effect, probably specific for long etching time periods as already mentioned in literature [START_REF] Fujii | Generalized etch-pit equations and their application to analyses of tracks in CR-39 with depth dependent etching properties[END_REF] (and references therein) in the case of a 2

GeV/nucleon iron nucleus track etched for more than 20 hours. The reasons for V b (and hence V) variation with depth may be due to a property of used plastic, structural inhomogeneity in the detector material linked with its curing process during fabrication and finally the successive etching process that follows heating and drying of the detector sample many times. It was mentioned by Fujii and Nishimura [START_REF] Fujii | Generalized etch-pit equations and their application to analyses of tracks in CR-39 with depth dependent etching properties[END_REF] that "most of the thick CR-39 sheets commercially available show the depth dependence". However, this phenomenon deserves further investigation.

Experimental and calculated reciprocal bulk etch rate with normalized depth (total depth, z=1) are illustrated in Fig. 13 where the best fitting of Eq. 12 was obtained at f=0.04 and g=0.07. Prolonged etching with the amount of bulk-etch exceeding 80 μm is necessary for producing swift heavy ions thick track membrane [START_REF] Awad | Strong etching investigation on PADC CR-39 as a thick track membrane with deep depth profile study[END_REF] and study the track wall curvature development with removed layer through the entire detector depth. Eq. 12 is fundamental for simulating the etched track profiles and the shape of the track curvature developed with depth inside the polymer and it can describe the reciprocal V b as a function of (z) for soft etching conditions as well.


Tamon Kusumoto
email: kusumoto.tamon@qst.go.jp

Shogo Okada

Hisaya Kurashige

Kazuo Kobayashi

Michel Fromm

Quentin Raffy

Nicolas Ludwig

Masato Kanasaki

Keiji Oda

Yoshihide Honda

Sachiko Tojo

Jean-Emmanuel Groetz

Ryo Ogawara

Satoshi Kodaira

Rémi Barillon

Tomoya Yamauchi

Evidence for a critical dose above which damage to carbonate ester bonds in PADC appear after

Keywords: PADC, gamma ray, Ultra Soft X-ray, carbonate ester, ESR, FT-IR

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Introduction

Poly(allyl diglycol carbonate) (PADC), commonly known under the trade name CR-39, has been recognized as the most sensitive polymeric nuclear track detector [START_REF] Cartwright | A nuclear-track-recording polymer of unique sensitivity and resolution[END_REF]. PADC can record tracks of protons (or neutrons from recoil protons) and heavy ions as etch pits without background noise from electrons, X-rays and gamma rays even in complex radiation mixed fields [START_REF] Fukuda | Energy increase in multi-MeV ion acceleration in the interaction of a short pulse laser with a Cluster-Gas target[END_REF][START_REF] Kanasaki | The precise energy spectra measurement of laser-accelerated MeV/n-class high-Z ions and protons using CR-39 detectors[END_REF]. The fragmentation of ions, such as 12 C ions, can be followed using PADC thanks to its high charge resolution (Hirano et al., 2018). We have engaged in Fourier

Transform Infrared (FT-IR) spectrometric studies on latent track structure of protons and heavy ions (from He to Xe ions) to elucidate an open question "why does PADC have such excellent features as a nuclear track detector?" from a point of view of molecular arrangements [START_REF] Yamauchi | Studies on the nuclear tracks in CR-39 plastics[END_REF]Mori et al., 2011&2013;Kusumoto et al., 2015&2016a). Other approaches for clarifying the structure and mechanism of latent tracks have been conducted [START_REF] Kodaira | Mass spectrometry analysis of etch products from CR-39 plastic irradiated by heavy ions[END_REF][START_REF] Fromm | Role of intermediate species in the formation of ion tracks in PADC: A review[END_REF]. The importance of the low-energy secondary electrons has been shown [START_REF] Fromm | Low energy electrons and swift ion track structure in PADC[END_REF][START_REF] Kusumoto | Elucidation of the Two-Step Damage Formation Process of Latent Tracks in Poly(allyl diglycol carbonate), PADC: Role of Secondary Low-Energy Electrons[END_REF][START_REF] Kai | A significant role of non-thermal equilibrated electrons in the formation of deleterious complex DNA damage[END_REF]. Figure 1 illustrates a repeat unit of PADC, whose molecular formula is (C 12 H 18 O 7 ) n and density is 1.31 g/cm 3 . PADC is constituted by the combination of a radiation-sensitive section and a less radiation-sensitive one. The former contains an ether moiety in the center and two carbonate esters in the symmetric positions, and the latter is "polyethylene-like" network formed during the polymerization. The structure of PADC is a three-dimensional network consisting of polyallyl chains [START_REF] Stejny | The polymer physics of CR-39 -The state of understanding[END_REF]. Four methylene (two ethylene) groups belong to the radio-sensitive part of the structure lying between ether and carbonate ester moieties in each unit. Through FT-IR studies, we have estimated the effective track core radius for each functional group, in which the considered groups were damaged [START_REF] Mori | Radiation chemical yields for loss of ether and carbonate ester bonds in PADC films exposed to proton and heavy ion beams[END_REF]. Figure 2 shows the three different regions, where typical functional groups with specific vibration bands in PADC are damaged by 4.8 MeV/u C ion irradiations, observed by FT-IR analysis. It appears that the radial extent of specific damages depends upon the type of chemical group analysis. In a first region, close to the ion's path, CH groups, carbonate ester and ether functions are affected. In a second, wider one, only carbonate ester and ether functions are affected. In the third, outer part, only ether function appears to be damaged. In these three regions of the latent track in PADC, mechanisms of damage formation by incoming ions are expected to be different from each other. Ether is clearly the most sensitive and carbonate ester is the second one. Similar spatial distribution of defects within the latent track were observed in some polymers such as poly(vinylidene fluoride) [START_REF] Balanzat | Swift heavy ion modification of polymers[END_REF][START_REF] Bouëdec | Swift heavy ion irradiation effects in α poly(vinylidene fluoride): spatial distribution of defects within the latent track[END_REF] and polybisphenol A carbonate [START_REF] Yamauchi | On the tracks of proton and heavy ions in PC and PADC plastics detectors[END_REF].

In our recent study on the irradiation effect of PADC films with 28 MeV electron beam, which was performed in ambient air, the relative density of ether decreased monotonically with absorbed doses (i.e., fluence) in the range from 0 to 200 kGy (Kusumoto et al., 2016b). In comparison to this, the carbonate ester was lost only above a critical dose of 50 kGy. The existence of a critical dose indicates a kind of threshold for the degradation of carbonate ester. Such a decreasing behavior was explained by a "two-electron model", in which the carbonate ester should be broken after the breaking of the ether in the same unit. Similar trends were observed with low-energy electrons up to 30 eV and UV photon of a wavelength of 222 nm (Kusumoto et al., 2018&2019a).

In the present study, we have investigated effects of irradiation on PADC due to exposures to gamma rays and X-rays, paying a special attention to a critical dose of about 50 kGy, above which carbonate ester begins to decrease. We examine the irradiation effects of PADC films with Co-60 gamma rays at absorbed doses up to 150 kGy, using FT-IR method, as well as Electron Spin Resonance (ESR) spectrometry.

Some ESR studies were carried out for PADC after gamma irradiations (Khazal&Habubi, 1990;[START_REF] Ranjbar | Investigations of the use of electron sping resonace for nuclear track counting and gamma-ray dosimetry in CR-39[END_REF], but only with much lower doses.

Darraud-Taupiac et al., also made an ESR study of PADC with gamma rays, as well as ion beams, investigating a dose region ranging from 2 to 150 kGy [START_REF] Darraud-Taupiac | Study of free radicals in poly(diethylene glycol bis(allyl carbonate)) irradiated by γ rays[END_REF]. However, it was difficult to avoid the radical recombination during exposures due to the off-line measurements. Other ESR studies were also performed by Böhlke et al. using proton and He ion beams under vacuum [START_REF] Böhlke | Investigation of free radicals induced by light ions in CR-39 using ESR spectroscopy[END_REF]Böhlke&Hermsdorf, 2008). Unfortunately, the radicals generated could not be identified in any of these studies. In the present one, ESR was applied to detect the free radicals induced in PADC films by gamma rays, avoiding most chemical reactions (e.g., radio-oxidation) by performing the experiments performed at 77 K using liquid nitrogen. Gamma ray exposures were also followed by ESR measurements at room temperature (RT). FT-IR studies for Ultra Soft X-ray (USX: photon energy < 2 keV)

were also conducted to understand roles played by low-energy electrons compared to that produced by gamma ray.

Experiments

Thin PADC films were prepared by chemical etching in KOH solution (6 M, 70 ) from BARYOTRAK sheets (Fukuvi Chemical Industry Co., Ltd., Japan) with a nominal thickness of 100 µm, which were made from monomer of purity higher than 99% [START_REF] Yamauchi | Study on response of CR-39 detector to light ions[END_REF]. Detailed thinning process is described elsewhere [START_REF] Yamauchi | Loss of carbonate ester bonds along Fe ion tracks in thin CR-39 films[END_REF]. We used thin PADC films with thicknesses of less than 3 µm to obtain unsaturated IR spectra (absorbance < 2), including carbonate ester, which has the strongest IR absorption, as indicated in panels from (c) to (f) of Fig. 3. Additionally, films of a thickness of about 20 µm were used to efficiently detect free radicals formed during gamma ray exposures.

Gamma ray exposures were carried out in ambient air at 77 K (using liquid nitrogen) and RT using the intense Co-60 source "Rabbit 11", an equipment of The in the present study. The beam profile was guaranteed to be uniform on at least a diameter of 3 mm [START_REF] Ounoughi | Beam characterization of a lab bench cold cathode ultra-soft X-ray generator[END_REF]. The mean absorbed dose rate in PADC films was 1.0 Gy/s. The examined dose range was up to 180 kGy. The derivation process of the mean absorbed dose rate in a medium is presented elsewhere (Fullford et al., 1999;[START_REF] Groetz | Conception and realization of a parallel-plate free-air ionization chamber for the absolute dosimetry of an ultra soft X-ray beam[END_REF]. In the energy region of USX, the photoelectric effect is the main interaction. The molecular chains of PADC mainly consist of C atoms. The peak of binding energy of C K-shell to the atom is 0.28 keV. Thus, as an approximation, we calculated the stopping power of photoelectrons (1.21 keV) to be 13.3 eV/nm using the stopping power and range tables for electron, ESTAR [START_REF] Berger | and ASTAR: Computer programs for calculating stopping-power and range tables for electrons, protons, and helium ions[END_REF].

To detect free radicals after gamma exposures, Electron Spin Resonance, ESR, spectroscopy was carried out at both 77 K and RT using JES-RE2X (JEOL, Japan) (Resolution: 2 µT, Range of magnetic field: 275~375 mT). Since the chemical reactions at 77 K after the gamma ray exposures proceed much slower than at RT, we could detect other radicals, which are likely to be less stable than that at RT, although they were not necessary the initial ones. For examining created chemical damages in PADC after gamma ray exposures, FT-IR measurements were also carried out before and after the exposures with spot of 1 cm in diameter using FT/IR-6100S (JASCO, Japan) equipped with a DTGS detector (Resolution: 2 cm -1 , Range of wavenumber: 500~2000 cm -1 , Repetitions: 50). In addition, microscopic FT-IR measurements using IRT-5000 (JASCO, Japan), equipped with a MCT detector, with a spot area of 50×50 µm 2 were conducted (Resolution: 2 cm -1 , Range of wavenumber: 500~2000 cm -1 , Repetitions: 50).

The uniform intensity of USX was guaranteed with spot of 6 mm in diameter, which is smaller than that of FT/IR-6100S. Therefore, we adapted the IRT-5000 for investigating created damages in PADC after exposures to USX. In the present study, we focused on the peaks of ether, carbonate ester at 1250 and 1770 cm -1 for carbonyl (C=O) and C-O-C, respectively, and CH groups at 789 cm -1 as shown in Fig. 3 (Lounis-Mokrani et al., 2003). Concerning ether, we can find three peaks from 1000 to 1200 cm -1 . In the present study, the peak at 1026 cm -1 , which is isolated compared to the others, was chosen for the analysis.

Results and Discussions

The track registration sensitivity of PADC has been considered to be related to the oxygen concentration in ambient air rather than in water and under nitrogen [START_REF] Ishigure | An investigation to assess which component in the air is concerned with the vacuum effect on plastic track detector sensitivity[END_REF]. In practice, the track registration sensitivity of PADC significantly drops under vacuum [START_REF] Yamauchi | An evaluation of the radial life-time in CR-39 track detectors outgassed under vacuum[END_REF][START_REF] Dörschel | Influence of oxygen on the track etch rate along light ion trajectories in CR-39[END_REF].

However, focusing on the latent track structure, which is strongly related to the track registration sensitivity, radiation chemical yields (G value) for losses of carbonate ester in PADC irradiated with He and C ions under vacuum are well agreement with those in ambient air [START_REF] Mori | Vacuum effects on the radiation chemical yields in PADC films exposed to gamma rays and heavy ions[END_REF]. Aside from this, the creation of OH groups as new end-chain points after the irradiation under vacuum is dramatically smaller than that in ambient air (Kusumoto et al., 2019b). Namely, the track registration sensitivity could be governed by the amount of OH groups after the irradiations, which are created by radio-oxidation effects [START_REF] Fujii | The effect of vacuum and UV-exposure on the sensitivity of polymeric track detectors[END_REF]Böhlke&Hermsdorf, 2008). Therefore, ESR spectrometry is carried at 77 K and RT to elucidate the chemical reaction of created radicals with oxygen. We observe clearly different ESR signals measured after exposures to Co-60 gamma rays at 77 K compared to that at RT. Additionally, the ESR signals depend on absorbed dose (details are discussed in section 3.1.), so that we carefully examine the reduction behavior of the relative density of the radiation-sensitive moieties in PADC (described in section 3.2). when exposures and ESR measurements were done at RT (Figure 5). Indeed, typical ESR spectra of hyperfine structure of hydrogen radicals were observed around 300 and 350 mT by other researchers (e.g., [START_REF] Kiselev | ESR investigation of hydrogen and deuterium atoms in impurity-helium solids[END_REF]Nakashima&Yamauchi, 2005;Stöβer&Herrmann, 2013). Note that experimental conditions of previous studies were different from the present study (e.g., measurement temperature and polymer used).

ESR measurements

However, signals assigned to hydrogen radicals were observed at 77 and 100 K (Sevilla et al., 1997). Thus, we may guess that the signals at 300 and 350 mT are assigned to hydrogen radicals. Generated hydrogen radicals react with themselves or other radicals and then hydrogen gas can be released. Hydrogen radicals are known to have high reaction rates in aqueous organic materials (typically 10 4 -10 9 mol/s) [START_REF] Neta | Rate Constants for Reaction of Hydrogen Atoms with Compounds of Biochemical Interest[END_REF] and are in consequence characterized by very short lifetimes. In solid state polymers, lifetimes are thus even shorter. In comparison to this, it is well known that hydrogen gas is easily released from the polymer after bombardment [START_REF] Rowntree | Anion yields produced by low-energy electron impact on condensed hydrocarbon films[END_REF][START_REF] Ferry | Effect of cumulated dose on hydrogen emission from polyethylene irradiated under oxidative atmosphere using gamma rays and ion beams[END_REF]Kusumoto et al., 2019b), so signals at 300 and 350 mT are not observable at RT.

The clear signals (labeled "a" and "b") are observed already after an exposure at 33 kGy. At 67 kGy, new signals (labeled "d" and "e") are seen near to 326.5 mT.

Additionally, the signal labeled "b" is shifted to a lower magnetic field. This implies that at higher accumulated dose, one can observe the formation of a new radical. Based on the previously proposed two-electron model, we can postulate that the new signals can be assigned to the radicals induced by damage to the carbonate ester. A similar spectrum is seen for 100 kGy. However, the peak height at 100 kGy is lower than at 67 kGy. This might indicate the saturation of damage to ether. Generally, oxygen radicals exhibit anisotropy signals [START_REF] Swarts | An Electron Spin Resonance Investigation of the Structure and Formation of Sulfinyl Radicals: Reaction of Peroxyl Radicals with Thiols[END_REF], in that way the observed signals might be assigned to radicals centered on carbon atoms in PADC. Unfortunately, we have no further evidence for the identification of the observed radicals presently.

The ESR spectra measured at RT are more complex than those at 77 K (Figure 5). It is well known that free radicals induced on ether and/or carbonate ester groups immediately re-arrange at RT [START_REF] Faucitano | The mechanism of gamma-radiolysis of polymethylene, polypropylene and poly-n-butylene oxides: An ESR investigation[END_REF][START_REF] Shiryaeva | Ion-radical intermediates of the radiation-chemical transformations of organic carbonates[END_REF]. The carbon radicals are easily oxidized into peroxyl radicals [START_REF] Jahan | Investigation of the oxygen-induced radicals in ultra-high molecular weight polyethylene[END_REF][START_REF] Csige | Post-irradiation sensitization of CR-39 track detector in carbon dioxide atmosphere[END_REF], which recombine faster than the carbon radicals. Such recombination processes must be considered to clarify the kinetics of further chemical etching. As it will be observed just after, below a critical dose, we have observed the reduction of the density of ether in PADC, while those of carbonate ester and CH groups are almost constant.

This trend indicates that ether is the weakest moiety in PADC network. In our previous work [START_REF] Kusumoto | Yields on the formation of OH groups and the loss of CH groups along nuclear tracks in PADC films[END_REF], we have demonstrated that ratio of OH groups formed/ether lost was between 1 and 2. This finding implied that one damage to ether produced formation of one or two OH group. The formation process of OH groups is in competition with recombination processes in the original structure or in the altered structure. These reactions spread along ion trajectory (i.e., secondary electron trajectories). Consequently, it is now considered that OH groups are created at new chain-end points. To clarify the difference between etchable tracks and un-etchable ones, the role of OH groups, which is hydrophilic and governs etching velocity along ion tracks, is crucial.

In the present study, the radical species at both 77 K and RT could not be identified. However, notable differences in ESR spectra above and below the critical dose are observed at both temperatures, so that FT-IR studies are carried out to examine the chemical damage structure at both sides of the critical dose (section 3.2). In addition, the difference in ESR spectra between 77 K and RT seems to indicate the influence of oxygen in ambient air. The radical annihilation process should be traced by annealing to clarify the role of oxygen in ambient air in a further step.

FT-IR measurements

After the exposure to Co-60 gamma rays, the changes in absorbance at each peak are observed (Figure 3). After the exposure with absorbed dose of 60 kGy, the peak height of net absorbance of ether slightly decreases as shown in Fig. 3 (a).

Conversely, the other peaks of carbonate ester (C-O-C and C=O) and CH groups as represented in Fig. 3 (c), (e) and (g) do not decrease. In comparison to these spectra at 60 kGy, clear decreases are seen in the all peaks after the exposure with 300 kGy [START_REF] Mori | Radiation chemical yield for loss of carbonate ester bonds in PADC films exposed to gamma ray[END_REF]. Similar trends were observed in the cases of 28 MeV electron and UV photons (Kusumoto et al., 2016(a)&2019(a)). We call such trends "two-step damage formation process" as discussed later.

The Beer-Lambert law has been usually applied to analysis of degradation process on polymer irradiated with ionizing radiations as,

A 0 =εc 0 l, ( 1
)
where A 0 is absorbance before irradiation, ε the molar extinction coefficient (in M -1 cm -1 , c 0 molar density (in M=mol/L) before irradiation and l sample thickness (in cm).

Generally, the changes in absorbance are correspond to those in the density of functional groups because the molar extinction coefficient and the sample thickness can be considered as constant before and after exposures. Figure 6 (a) and (b) show the decrease of relative absorbance; A/A 0 the ratio of the net absorbance of considered functional groups after the exposure, A, to that of original one, A 0 , of typical functional groups in PADC exposed to gamma ray and USX, respectively. Here, exposures were performed at RT in ambient air. As discussed above, the reductions of relative absorbance are proportional to those of relative density; N/N 0 the ratio of the density of considered functional groups after the exposure, N (in mol/kg), to that of original one, N 0 . Concerning obtained results of Co-60 gamma ray, the relative absorbance of ether drops linearly with absorbed dose. This trend implies that the overlapping effect by electron tracks is negligible (Kusumoto et al., 2019b). Conversely, the relative absorbance of carbonyl, which composes carbonate ester, does not decrease below a critical dose of 60 kGy. Seeing the present results together with previous one (open symbols of inset of Fig. 6 (a)) [START_REF] Mori | Radiation chemical yield for loss of carbonate ester bonds in PADC films exposed to gamma ray[END_REF], a monotonic decrease of the relative absorbance of C=O is observable above that critical dose. The reduction behavior of C-O-C, which also composes carbonate ester, is almost identical to that of carbonyl.

The critical dose for damage to CH groups is clearly higher than that of carbonate ester under gamma ray exposure. Furthermore, the relative absorbance of ether decreases slowly above 110 kGy due to the induced modification in PADC. A similar trend is seen on USX exposures (Figure 6 (b)). In the case of USX, the critical dose of carbonate ester loss is 50 kGy and the reduction behavior of ether becomes slower above 75 kGy.

The two-step damage formation process implies that the carbonate ester is often broken after damage to ether in the same molecule [START_REF] Kusumoto | Elucidation of the Two-Step Damage Formation Process of Latent Tracks in Poly(allyl diglycol carbonate), PADC: Role of Secondary Low-Energy Electrons[END_REF]. Ethylene like molecules are released when carbonate ester is damaged (Yamauchi et al., 2005). Hence, we can suggest that detected free radicals at 33 kGy (see Fig. 4) could be due to damages to ether. Those observed at 67 and 100 kGy would then be created by the breaking of carbonate ester.

A similar dependence on the absorbed dose was observed with 28 MeV electrons irradiation of PADC (Kusumoto et al., 2016a). This phenomenon was interpreted as the overlapping of electron tracks, with a critical dose of 50 kGy, which is well in agreement with the present gamma ray and USX experiments, within experimental error. Due to the random motions of low energy electrons, we cannot apply the conventional track overlapping model using random numbers in the present cases of gamma ray and USX [START_REF] Yamauchi | Studies on the nuclear tracks in CR-39 plastics[END_REF]. However, it is certain that the two-step damage formation process is related to changes in the damage creation mechanism to PADC above the critical dose discussed in the section 3.1.

The decrease of relative absorbance of ether can be described as,

A/A 0 = 1 -kD. ( 2
)
where D is the absorbed dose in units of Gy and |k| ((8.9±0.3)×10 -7 for Co-60 gamma rays and (12.8±0.5)×10 -7 for USX) an experimental constant in units of Gy -1 , which is concordant with the slope of the fitted lines in Figs. 6 (a) and (b). Using k, we can easily calculate the G value (in scissions/100 eV) as,

G value = 9.64×10 6 N 0 k, (3)
where N 0 is 3.65 mol/kg for ether and 7.3 mol/kg for carbonate ester [START_REF] Mori | Radiation chemical yield for loss of carbonate ester bonds in PADC films exposed to gamma ray[END_REF].

The molecular weight of PADC, M, is equal to 274 g /mol, namely the reciprocal is 3.65 mol/kg. As in one PADC unit, there is one ether, so that N 0 is for this function is equal to 3.65 mol/kg. Similarly, as one PADC unit contains two carbonate ester moieties, accordingly, N 0 value for this function is twice that of PADC (i.e., 7.3 mol/kg). Figure 7 represents the G values for loss of ether (G (ether losses)) as a function of the stopping power. Overall, surprisingly high G values (> 10 scissions/100 eV) have been observed

in the case of PADC. In the past, Yamauchi et al., verified derivation processes (e.g., analysis procedures, irradiations and so on) of effective track core radius, which can be derived from same analysis with the G value, using bisphenol a polycarbonate [START_REF] Yamauchi | On the tracks of proton and heavy ions in PC and PADC plastics detectors[END_REF]. The results were well agreement with the others using FT-IR [START_REF] Dehaye | Chemical modifications induced in bisphenol A polycarbonate by swift heavy ions[END_REF]Sun et al., 2003a&2003b) and other approaches (Petersen&Enge, 1995;[START_REF] Apel | Track structure in polyethylene terephthalate irradiated by heavy ions: LET dependence of track diameter[END_REF]. Also, regarding the effective track core radii derived using FT-IR method by Mori et al., [START_REF] Mori | Radiation chemical yields for loss of ether and carbonate ester bonds in PADC films exposed to proton and heavy ion beams[END_REF], they corresponded to the ones evaluated by conductimetric method [START_REF] Oganesyan | Investigation of the response of thin CR-39 polymer foils irradiated with light ions[END_REF], AFM and UV-visible methods (Yamauchi et al., 2005b). In other words, the high G values obtained in the present study express the great radiation-sensitivity of PADC already observed. The solid squares on Fig. 7 indicate the present result related to Co-60 gamma ray. In the present case, abscissa coordinates for gamma rays and 28 MeV electrons are respectively represented as average LET in water of gamma rays (0.2 eV/nm) and the deposited energy per unit distance of 28 MeV electrons in water (0.03 eV/nm). The latter was approximated under non-electron equilibrium condition using well calibrated cellulose triacetate (CTA) dosimeter and electric current [START_REF] Oda | Effects of low-LET radiations on CR-39 track detector[END_REF]. The definitions of the stopping power and LET are different. LET is local energy deposition only, so that it does not include Bremsstrahlung or delta-rays. In comparison to this, the stopping power is the total energy deposition by incoming particles. However, we compare G values to elucidate both of the discrete damages along electron tracks and dense damages along proton and heavy ion tracks. The previously obtained G value with gamma rays is smaller than the present one. In the previous study, the G value for ether loss was underestimated because data sets above 100 kGy, where chemical structure of PADC was completely modified, were used [START_REF] Mori | Radiation chemical yield for loss of carbonate ester bonds in PADC films exposed to gamma ray[END_REF]. On one hand, the G value obtained with USX is greater than that of gamma rays. This may imply that the lower energy of secondary electrons produces more efficiently irreversible damages in PADC. On the other hand, the G values related to gamma ray and USX exposure are greater than those of protons, He and C ions with energies in the Bragg peak regime (open circles in Fig. 7). By contrast, higher G values are observed for high energy protons and semi-relativistic heavy ions (C and Fe), as shown in open diamonds in Fig. 7 [START_REF] Mori | Greater radiation chemical yields for losses of ether and carbonate ester bonds at lower stopping powers along heavy ion tracks in poly(allyl diglycol carbonate) films[END_REF]Kusumoto et al., 2016a). The higher G values indicate that the PADC molecular network is efficiently damaged by dense-secondary electrons along heavy ion tracks, and is mainly modified not only in the close vicinity of the ion trajectory, but also at distant locations [START_REF] Mori | Greater radiation chemical yields for losses of ether and carbonate ester bonds at lower stopping powers along heavy ion tracks in poly(allyl diglycol carbonate) films[END_REF]. For example, in the case of 10 MeV protons, low-energy secondary electrons (e.g. < 40 eV) represent the major components in the energy spectrum [START_REF] Fromm | Low energy electrons and swift ion track structure in PADC[END_REF]. The inelastic mean free path of electrons has a minimum value at an energy of about 40 eV (Seah&Dench, 1979). Then, it increases with energy. Secondary electrons with higher energies (> 40 eV), which are rare components, mainly could interact with PADC at distant location from the ion's path. Therefore, we should consider the energy distribution of secondary electrons at each location to more accurately discuss the damage formation mechanism in PADC.

Eq. ( 1) is inapplicable to the carbonate ester and CH groups in PADC exposed to gamma ray in the normal manner, because monotonic decrease of the relative absorbance can be observed only above the critical dose (Fig. 6). Since the relative absorbance of carbonate ester is constant below the critical dose, the G values of gamma ray and USX should be extremely small below the critical dose. Above the critical dose, the G values with gamma ray and USX were evaluated from the slope of fitted lines in (Figure 8). Noteworthy, the trend of C-O-C is identical to that of carbonyl (Figure 8). In the case of carbonate ester, it is difficult to compare the G values of Co-60 gamma rays and USX to those of proton and heavy ions because the overlapping of electron tracks is not negligible above the critical dose. But it is sure that radiation-sensitivity of carbonate ester becomes high when the ether in the same molecule is broken. In other words, more than two electrons are mandatory to break carbonate ester in PADC.

The present results obtained using ESR and FT-IR spectrometric methods strongly show that the concept of the number of electrons (and their energies), which interact with a molecule, may represent an appropriate parameter to the damage formation process of PADC. We will tackle the calculation of number of electrons, which hit molecules, at critical doses of Co-60 gamma rays and USX using MPEXS-DNA, a GPU-based Monte Carlo simulation [START_REF] Okada | MPEX-DNA, a new GPU-based Monte Carlo simulator for track structures and radiation chemistry at subcellular scale[END_REF] and an improved computer code of Geant4-DNA (Agostinelli et al., 2003;Allison et al., 2013&2016), and PHITS code [START_REF] Sato | Features of Particle and Heavy Ion Transport Code System PHITS version 3.02[END_REF]. The number of electrons from Co-60 gamma rays and USX will be compared to that experimentally obtained with an energy of 28 MeV.

Conclusions

In the present study, the creation mechanism of latent tracks in PADC, which was exposed to gamma rays and USX, was investigated by means of ESR and FT-IR spectrometry. For gamma rays at RT and 77 K, different ESR spectra were observed below and above the critical dose. The present study did not achieve the identification of free radicals formed during gamma ray exposures. Nevertheless, the results suggest that damage formation mechanism is dose-dependent. While the relative absorbance (IR signal) for loss of ether decreased linearly with increasing absorbed dose, those of carbonate ester and CH groups decreased only above critical doses of 60 kGy and 50 kGy for gamma rays and USX, respectively, which are in agreement with that found when using 28 MeV electrons. The dose-dependent damage formation process was verified from both approaches. Based on our previously proposed two-electron model, we summarize that more than two electrons are necessary to induce damage to carbonate ester in PADC and number of electrons interacting with molecules is a suitable parameter to describe the damage formation process in PADC. Fig. 3 IR spectra before (dotted red line) and after (solid blue line) exposure to Co-60 gamma rays. In the panels (a), (c), (e) and (g), the evolutions of spectra after the exposure with absorbed dose of 60 kGy is shown. Additionally, the evolutions after the exposure with 300 kGy are shown in the panels (b), (d), (f) and (h) [START_REF] Mori | Radiation chemical yield for loss of carbonate ester bonds in PADC films exposed to gamma ray[END_REF]. The relative absorbance of typical functional groups in PADC after the

Figure captions

Figure 4

 4 Figure 4 shows ESR spectra of PADC exposed to Co-60 gamma rays with absorbed doses of 33 (full red line), 67 (dotted black line) and 100 kGy (chain green line). Both gamma ray exposures and ESR measurements were performed at 77 K. In this case, we can observe signals at 300 and 350 mT. These signals are not observed

Fig. 6

 6 Fig. 6 for carbonate ester. The G values for loss of carbonyl (G (carbonate ester losses) are summarized in Fig. 8. As with Fig. 7, the present result of gamma ray is plotted as solid square and previous ones are described as open triangles, as well as 28 MeV electrons. The G values of gamma ray and USX drastically rises above the critical doses

Fig. 1 A

 1 Fig.1A repeat unit of PADC.

Fig. 2

 2 Fig. 2Layered structure in PADC after irradiation with 4.8 MeV/u C ions.

Fig. 4

 4 Fig.4ESR spectra measured at 77 K. The full red, dotted black and chain green lines describe the spectra after exposure to Co-60 gamma rays at 77 K with absorbed doses of 33 (below the critical dose), 67 (around the critical dose) and 100 kGy (above the critical dose), respectively.

Fig. 5

 5 Fig.5ESR spectra measured at RT. The full red and chain green lines describe the spectra after exposure to gamma ray at RT with absorbed doses of 33 (below the critical dose) and 100 kGy (above the critical dose), respectively.

Fig. 6

 6 Fig. 6The relative absorbance of typical functional groups in PADC after the

Fig. 1

 1 Fig. 1

  Fig. 2

  Fig .4

  Fig.8

Acknowledgments

This work was performed by the Cooperative Research Program of "Network Joint Research Center for Material and Devices", and was supported by JSPS KAKENHI Grant Number 16K05002. This work was conducted thanks to the funds of Kobe University for the Cotutelle program with Universite de Strasbourg. The authors gratefully thank to Mr. Takuya Otani for his large supports during the experiments and express our appreciation to all the staff of The Institute of Scientific and Industrial Research of Osaka University for their cooperation in this experiment.

Author statement TK, MF, JG, SK, RB, QR and NL carried our experiments (USX exposures) at Bourgogne-Franche-Comte. Also TK, KK, MK, TY, KO, YH and ST performed experiments (gamma exposures and ESR measurements) at Osaka University. TK spoke about data analysis with SO, HK, KK and TY. exposures to Co-60 gamma rays (a) and USX (b) at RT. The open symbols in Fig. 2 (a) indicates the previous results [START_REF] Mori | Radiation chemical yield for loss of carbonate ester bonds in PADC films exposed to gamma ray[END_REF]. The reduction trend of relative absorbance after in a wide dose range is represented in the inset of Fig. 6(a). (Kusumoto et al., 2016a;[START_REF] Mori | Greater radiation chemical yields for losses of ether and carbonate ester bonds at lower stopping powers along heavy ion tracks in poly(allyl diglycol carbonate) films[END_REF]. The previously obtained G values of gamma ray and 28 MeV electrons are also described as open triangles [START_REF] Mori | Radiation chemical yield for loss of carbonate ester bonds in PADC films exposed to gamma ray[END_REF]Kusumoto et al., 2016b). (Kusumoto et al., 2016a;[START_REF] Mori | Greater radiation chemical yields for losses of ether and carbonate ester bonds at lower stopping powers along heavy ion tracks in poly(allyl diglycol carbonate) films[END_REF]. The previously obtained G values of gamma ray and 28 MeV electrons are also described as open triangles [START_REF] Mori | Radiation chemical yield for loss of carbonate ester bonds in PADC films exposed to gamma ray[END_REF]Kusumoto et al., 2016b).

Conflict of Interest

We have no interesting to confliction.


A Hubau

D Pino-Herrera

A G Guezennec

BIOLEACHING TO REPROCESS SULFIDIC POLYMETALLIC MINING RESIDUES: TWO CASE STUDIES FROM THE H2020 NEMO PROJECT

Keywords

Bioleaching, mining residues, sulfides, reprocessing, metals 2. Highlights  Mining residues can be considered as a metal resource that could be reprocessed.  Bioleaching processes recover metals by microorganism-catalysed dissolution.  In H2020 NEMO project bioleaching was applied to Aïtik and Sotkamo mining residues.  The residues composition highly influences the efficiency of bioleaching.

Purpose

In Europe, most of metallic high-or moderate-grade primary sources that are reasonably accessible and easy to process are exhausted. In today's context of resource scarcity, complex low-grade ores and extractive wastes are receiving increasing attention. In particular, mining waste may be evaluated as a metal resource while their reprocessing might mitigate environmental impacts related to mining waste disposal [START_REF] Lottermoser | Recycling, reuse and rehabilitation of mine wastes[END_REF]. Many efforts are being made to develop recycling or reuse options at reduced costs, with low environmental impacts and economic benefits. Conventional processes and technologies are often not profitable, sometimes due to the complexity of composition [START_REF] Bodénan | Final Report n°BRGM/RP-67562-FR[END_REF]. In this context, bio-hydrometallurgy, i.e. the use of microorganisms in hydrometallurgical operations, is increasingly being recognised as an ecologically acceptable and yet economic alternative for the recovery of metals in low-grade sulfide materials. The European research project NEMO (Near-zerowaste recycling of low-grade sulfidic mining waste for critical-metal, mineral and construction rawmaterial production in a circular economy) aims to valorise sulfidic mine waste by combining innovative hydrometallurgical processes for the recovery of valuable metals and critical raw materials with the transformation of the residue in clean mineral to be used for mass production of cement, concrete and construction products [3]. In the framework of this project, this study focuses on the development of enhanced bioleaching methods (i.e. the dissolution of metals catalysed by microorganisms) on two mining residues from Sotkamo mine (Terrafame, Finland) and Aïtik mine (Boliden, Sweden).

Materials and methods

In the Sotkamo mine, bio-heap leaching is applied to process a pyrrhotite-rich pentlandite-containing black schist ore to extract Ni (and Zn and Cu to a lesser extent). The residues still contain 3.2%(w/w) sulfides, 1310 ppm Ni, 1370 ppm Cu and 3460 ppm Zn [START_REF] Hubau | Bioleaching to reprocess sulfidic polymetallic primary mining residues: Determination of metal leaching mechanisms[END_REF]. In the Aïtik mine, Cu concentrates containing Au and Ag are produced by flotation. The process also produces low and high sulphur tailings, the latter being targeted in our study. They contain 41.6%(w/w) pyrite, 900 ppm Co and 2240 ppm Cu. For both materials, bioleaching kinetics were first evaluated in 2 L stirred tank reactors (STR) to define basic operational parameters (pH, temperature, nutrients media…) before scaling up the process to 114 L-continuous stirred tank reactor (CSTR). The solid load was maintained at 20%(w/w) for both materials, while the nutritive medium was identical (0Km medium). The microbial consortia, mainly composed by the genera Leptospirillum, Acidithiobacillus, Sulfobacillus and Acidithiomicrobium, which are either iron or sulfur-oxidizers or both, were slightly different for the two case studies. Two different temperatures were used (55°C for Sotkamo material and 40°C for Aïtik material).

Results and discussion

Both materials have highly different sulfidic contents (2.6% and 22.2% of sulfur as sulfides respectively) and thus highly different bioleaching amenability. The bioleaching of Sotkamo material demonstrated that reprocessing mining residues should be carefully studied, due to the complexity of composition of this material. Part of the metals are still contained in sulfidic minerals, while some of them were precipitated in SO4-phases during primary metallurgy activities. The presence of remaining minerals as pyrrhotite and other soluble sulfides consumes acid and oxygen, thus playing a role in the dissolution of metals. The microbial activity promoted the dissolution of Co. Due to the simultaneity of all these mechanisms, the fine monitoring of the hydraulic residence time in the bioreactors is of primary importance to ensure a good efficiency of the bioleaching of Sotkamo residues. Pilot operation allowed gathering fundamental information regarding the material balance of the process, including metal and sulphide dissolution yields, reagent and gas consumption and process kinetics, which will serve as input data for the economic, environmental and social assessment of the process. The bioleaching of Aïtik material, which is more favourable due to the high content of pyrite, revealed the importance of heat balance during the process, as the dissolution of pyrite is exothermic. The use of different temperatures during bioleaching process influences the microbial communities composition, which then highly affects the metal dissolution yield and rates. In particular, the predominance of Leptospirillum species (an iron-oxidizer micro-organism) increased the Co recovery from the material, up to more than 90% in STR. Controlling the temperature during pilot operation is required to ensure high efficiency of the process. The high efficiency of mass transfers in bioreactors is also necessary, as the oxygen demand is high. The development of new process designs should include all these requirements, in addition to the economic, environmental and social constraints.

Conclusions and perspectives

Bioleaching efficiency was evaluated on two mining residues in the framework of H2020 NEMO project. The materials composition was highly different, with sulfidic content varying from 2.6 to 22.2%(w/w). Consequently, the operating conditions that should be optimised were physico-chemical parameters (pH and nutrients medium composition, to prevent excessive precipitation as an example) in the case of Sotkamo material and operating parameters (heat and mass transfers) in the case of Aïtik material. High metal dissolution efficiency was demonstrated in both cases. The results of the pilot demonstration were used to perform a Life Cycle Analysis and to identify the main environmental impacts of the process. The reprocessing of such materials should be carefully studied to ensure that all parameters are taken into account when developing new bioreactor designs and assessing the economic, environmental and social feasibility of these activities.