On the use of polyethyleneterephthalate as solid state nuclear track detector: Kinetics and mechanism of particle track etching

On the use of polyethyleneterephthalate as solid state nuclear track detector: Kinetics and mechanism of particle track etching

Nuclear Instruments and Methods 213 (1983) 507-511 North-Holland Publishing Company 507 ON THE USE OF POLYETHYLENETEREPHTHALATE AS SOLID STATE NUCLE...

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Nuclear Instruments and Methods 213 (1983) 507-511 North-Holland Publishing Company

507

ON THE USE OF POLYETHYLENETEREPHTHALATE AS SOLID STATE NUCLEAR DETECTOR: KINETICS AND MECHANISM OF PARTICLE TRACK ETCHING

TRACK

H.B. LOCK A kademie der Wissenschaften der DDR, Zentralinstitut fiir Kernforschung, Rossendorf/Dresden, DDR Received 8 January 1982 and in revised form 19 October 1982

Kinetics of particle track etching in polyethyleneterephthalate is controlled by different rate-determining mechanisms. While at a low etchant activity the track etch rate vt depends on the product of water activity and the second power of the hydroxide activity a saturation of v t is reached at higher etchant activity. For NaOH the whole vt curve can be calculated in a normality range of 0.25-10 moles/1 when the saturation value is known. The discrepancy between the hydroxide activity dependence of the surface etch rate vs and vt found at low etchant activity can be explained in terms of the Donnan law and the condition of over-all electroneutrality in the track solution. The saturation of vt may be the result of a transport equilibrium between the produced terephthalic anions and the hydroxide ions required for etching at the track tip. The response functions for both the kinetic regions have been established.

1. Introduction

2. Experimental

Because of its low radiation sensitivity polyethyleneterephthalate (PETP) film can be used as a solid state nuclear track detector ( S S N T D ) for the registration of rare fission fragments [1], while its high tensile strength a n d low price make it suitable for the p r o d u c t i o n of nuclear track microfilters [2-4]. In spite of the scientific a n d technical applications of P E T P for particle track etching only a few a t t e m p t s have b e e n m a d e to elucidate the kinetics of particle track etching in this material [5-7]. It is the aim of this study to forward the knowledge of the f u n d a m e n t a l chemistry involved in particle track etching in PETP, particularly its kinetics and m e c h a n i s m to find correlations which allow the influence of e t c h a n t p a r a m e t e r s o n the track etch rate v t to be predicted. T h e m e c h a n i s m a n d kinetics of surface etching were discussed in a preceding p a p e r [8].

P E T P film with a n o m i n a l thickness of 10 /~m (Lavsan, m a d e in U S S R ) was used for this study. The samples were irradiated by means of the cyclotron U-300 at the Joint Institute of Nuclear Research at D u b n a . T h e particle density o n the film was in the order of 107-10 8 p a r t i c l e s / c m 2. T h e parameters of the particles employed are summarized in table 1. The b r e a k t h r o u g h time was measured to determine v t by following the electrical resistance between the two c h a m b e r s of a temperature-controlled cell separated by the irradiated P E T P sample.

Table 1 Total energy loss L~ and radius-restricted energy loss L 3 (r = 3 nm) [15] of the particles used for vt measurements Particle

16O

Energy entrance

[MeV] exit

24.0 12.0

4°Ar

220 195

132Xe

140 39

L~ [MeV/ /~m]

L3

[MeV/ /~m]

1.07 1.30

0.77 0.99

2.27 2.40

1.69 1.79

10.6 9.0

8.2 7.7

0 1 6 7 - 5 0 8 7 / 8 3 / 0 0 0 0 - 0 0 0 0 / $ 0 3 . 0 0 © 1983 N o r t h - H o l l a n d

3. Results 3.1. Effect o f etchant activity on v t

T h e activity d e p e n d e n c e of v t was studied in a normality interval from 0.25 to 10 m o l e s / 1 using N a O H a n d K O H solutions. The results are given in fig. 1 as a function of the p r o d u c t of the hydroxide a n d water activities ( a o H aH2o). It has been f o u n d that the surface etch rate vs correlates well with aoH all2 o [8]. However, in the case of particle track etching no linear correlation between v t a n d the activity product is displayed in fig. 1. This discrepancy will be discussed later in detail. In agreement with surface etching n o difference of v t was f o u n d between the use of N a O H a n d K O H solution in the region of low e t c h a n t activity. A t almost the same activity product of 4 - 5 , however, the v t curve of each particle turns to a higher value with KOH.

508

H.B. Lack / Polyethyleneterephthalate as track detector Table 2 Apparent activation energy E~ of 4°Ar track etching for different etching conditions

iO

Etchant

/ / /

1.0

'3ZXe,lA0I~Va/*

/

// .,jl/

/ / oi ./,~'~

E E =L

¢ / 0.1

iY

//

o.-~ ' r ' " + =~__._o_o

/, ./

,~+--+

t~t(343K )

[kJ/mole]

[/~m/min]

84 83 85 74 75

1.00 +_0.04

5 N NaOH

3.80

7N NaOH 4N KOH 5 N KOH 7N KOH

7.02 3.84 5.66 10.6

1.00 _+0.05 0.99 _+0.06 1.36 _+0.05 1.55 -t-0.06

I" z 4. Kinetic equations

0.06

0.0~

0.02 0.01

02

Ea

[mole/l]

,;/ /y,,'/ g"

,o ,,:oMevi

0.1

aOH •an20

0.A 0.0

10

I0

The curves shown in fig. 1 suggest the existence of two v t regions governed by different rate-determining processes. These regions are connected by an extended transition region characterized by a mixed kinetics. In a very dilute etchant ( k I region) the track etch rate yr, 1 in 160, 4°Ar and l n X e tracks obey the following relation V,,, = k l a ~ H a H 2 0 ,

(1)

a0H-x OH~ Fig. 1. Track etch rate vt as a function of etchant activity aoHar% o. The vt increase for pure kl kinetics is marked by dashed lines.

Whereas the v t curve of 1 6 0 tracks exhibits only a tendency to saturate, a real saturation of v t is reached with 4°Ar tracks at 6 N N a O H and with 132Xe tracks at 4 N N a O H . The saturation value of v t increases with the radius-restricted energy loss L 3 (radius = 3nm) [9] given in table 1. In the case of K O H the v t curves reach a new saturation value at a higher level, which is characterized by a fixed ratio to the N a O H value of 1.46 + 0.02. In order to test wether the saturation value of v t is influenced by the track length to be etched, the 4°mr tracks were etched from only one side in a second run. In this case the breakthrough time was exactly twice as high as for etching from both sides giving evidence that the etched track length has no influence on v t. 3.2. Apparent activation energy The temperature dependence of v t of the 4°mr tracks at varous normalities was measured to establish the a p p a r e n t activation energy E a. The results obtained with N a O H and K O H are listed in table 2. (For comparison: E a of vs is 66 k J / m o l e [8].) While in the activity region of consistent v t values with b o t h the etchants also E a has an identical value of 83-86 k J / m o l e , in the region of different v t curves a lower E a of 74-75 k J / m o l e was found for the higher v t curve obtained with KOH.

where the rate constant k I includes vs which, however, is negligible c o m p a r e d to k v The rate constant is influenced by L3, the storage conditions and the etching temperature. Since the activity of the hydroxide ions in the track being etched is determined by eq. (9) as outlined in 5.1. an exponent x = 2 can be expected at maximum. While x = 2 provides curves calculated by means of eq. (4) which correlate well with the experimental data as shown in fig. 1 the corresponding v t data of UV-irradiated 132Xe tracks and soaked 4°Ar tracks were found to fit to an exponent of x = 1.5 [10]. The v t increase for pure k~ kinetics was marked in fig. 1 by hatched lines for comparison. While the v t curves obtained for I60 and 4°Ar tracks approach the respective lines in the low activity region, the v t curve for 132Xe tracks shows that pure k 1 kinetics was not reached in the activity region studied. With increasing etchant activity the v t curves for 4°Ar and 132Xe tracks approach to constant v t values ( k 2 region). Vt, 2 = k 2 .

(2)

The rate c o n s t a n t k 2 is obviously a function of L 3 and is probably influenced by the storage conditions prior to etching. In the extended transition region v t is governed by a mixed kinetics which can be expressed by the following relation vt

1)t,lVt,2

Vt, I + Vt, 2

.

(3)

By inserting eq. (1) and (2) into eq. (3) an equation is

509

H.B. Lfick / Polyethyleneterephthalate as track detector

Table 3 Rate constants for track etching of various particles in NaOH and KOH k2(KOH)

Particle

k~

k2(NaOH )

160 4°Ar

0.0555 0.535

0.54 1.148

132 Xe

5.31

2.47

k2(KOH )

obtained which can be used for calculating v t curves in the whole activity range studied (fig. 1). v,

=

klk2a2HaH2o k 2+kla2HaH20

.

(4)

Using the rate constants summarized in table 3 the calculated curves correlate well with the experimental data. When the N a O H etchant was used a constant ratio k32/kl = 2.83 was observed with the three particle types investigated. In spite of the small variety of particles studied it may be allowed to substitute k~ in eq. (4) by 0.353 k23 with respect to the constant ratio mentioned above. 0.353k3 a2HaH20

k2(NaOH)

kl NaOH

1.65

1.44

2.84 2.83

3.60

1.46

2.84

tion) behaves as in a channel in a cation exchange membrane. The activity d o n of hydroxide ions in the track solution can be calculated using the formalism employed for the co-ion uptake of a cation exchange membrane [11,12]. The co-ions have the same sign of charge as the fixed charge. In the k I region d o n is the result of two equilibria provided any interference by the hydrolysis reaction and its products can be neglected. Firstly, the equilibrium between the hydroxide activity in the track solution a o r t a c and the respective activity in the external solution a o r t a c is determined by the Donnan law (6)

a o r t a c = aorta c or -

(5)

k23

-

-

2

2

(7)

C o n C c f ± - CoHCcf ±,

The practical importance of eq. (5) results from the fact that k 2 can be determined by only two measurements of the breakthrough time at different activities in the region of a high hydroxide activity while it is very timeconsuming to experimentally establish the whole curve given in fig. 1.

where 6c, a c represent the cation activities in the internal and external solution, respectively, and f ± , f ± the associated mean activity coefficients. Secondly, in order to maintain the over-all electroneutrality in the track the total charge of the dissolved anions and the terephthalic anions fixed at the track wall 6v must be compensated for by the charge of the cations in the track solution. Assuming that all the ions are singly charged, the condition for the over-all electroneutrality takes the form

5. R a t e - d e t e r m i n i n g m e c h a n i s m s

~c = ~on + ~F.

5.1. k t region

Substituting eq. (8) into eq. (6) and rearranging yield relations which provide the activities d c and d o n

vt = 1 + 0 . 3 5 3 k 2 a ~ n a H 2 0

In the k 1 region vt, 1 is assumed to be determined by the rate of the same hydrolysis reaction as it proceeds at the surface [8]. In both cases it is implied that the reaction rate is not restricted by diffusion processes. Therefore a similar dependence of l)t,1 and vs on the activity of the hydroxide ions could be expected. However, an apparent discrepancy can be noticed between a~) H in eq. (1) for particle track etching and the linear aoH dependence of v s [8]. The discrepancy is the result of a negative charge fixed at the etched track wall. The fixed charge is established by dissociated C O 0 - groups which are produced by the hydrolysis of the ester linkages. Hence, the solution in the etched track (referred to as track solu-

ac = ~

_

+

~'Ff± +

aon

2

(8)

+ a2oH

_e _ ±

+agH.

(9a)

(9b)

When g F f ± >> aOH, the second term in the square root of eq. (9) will be small compared to the first, and eq. (9) may be written with good accuracy as a c = CFf ±

(10a)

a2oH aoH = CFf± "

(10b)

510

H.B. Liick / Polyethyleneterephthalate as track detector

From a preliminary study of the pH dependence of the electrolytic conductivity of the track solution a magnitude of the fixed charge density of about 2 moles/1 can be estimated for the situation considered here [13]. Therefore it may be allowed to employ eq. (10b) for diluted etchants. In any case, however, it can be assumed that in the k 1 region the hydrolysis rate has the same functional dependence on the activity of hydroxide ions in the track as at the surface. The apparent aZH dependence of vt, 1 is only the result of the fixed wall charge. Finally, it should be noted that a lower exponent in eq. (1) can be expected when gv is comparable tO aOH. 5.2. Transition region

The deviation of the experimental v t values from the line of pure k I kinetics in fig. 1 with increasing vt is supposed to be caused by an increasing discrepancy between the real d o n at the tip of the track being etched and the equilibrium value of doll which can be calculated by eq. (9b). The enhanced v t is associated with an increased production rate of terephthalic anions which gives rise to a concentration of these anions in the track solution ~T which cannot be neglected any longer

CC = COH + CT + t~F"

(l l)

The steady state concentration gT at the tip of the track is the result of a balance between the production rate and the diffusion rate of terephthalic anions through the thinnest part of the etched track at the tip. The total length of the tapered track has neither an effect on the diffusion rate nor on vt as it was confirmed by the results obtained with a one-side etching of 4°Ar tracks. From this reason the compensation of the hydroxide ions consumed by hydrolysis of ester linkages or neutralization of C O O H groups is controlled by the diffusion rate of the slow terephthalic anions. Consequently, the actual doll is expected to decrease with increasing v t leading to a growing deviation from pure k~ kinetics.

ward the track tip is equal to the opposite flux of terephthalic anions, in which the diffusion rate is controlled by the lower mobility of the terephthalic ions. C o n s e q u e n t l y , k 2 is expected to depend on the flux of terephthalic ions and the amount of hydroxide ions required for etching out a unit track length, i.e. the amount of hydroxide ions required for hydrolysis and neutralization. Therefore k 2 is supposed to be affected by the degree of decarboxylation and decarbonylation in the latent track which, in turn, is a function of L 3. The diffusion rate of terephthalic anions in the track solution may be strongly affected by electrical repulsion resulting in a reduced effective track diameter for diffusion [14]. Thus, the diffusion rate and also k 2 should be sensitive to a varying wall charge density. As it is known for anion exchange polymer [11] the counter-ion (Na + and K +) may have an influence on the diffusion rate of the co-ion (terephthalic anion) by mutual shielding of the fixed ionic charges. That may be the reason for the increase of v t with K O H at higher activity. The fact that the increase starts at almost the same value of a o H a m o but different v, values suggests that the increase cannot be caused by diffusion processes. The assumption of a shielding effect to be responsible for elevating vt. 2 in K O H solution is in agreement with the lower apparent activation energy obtained with K O H in this k 2 region.

6. Response function As mentioned above k I includes v~, whereas k 2 is independent of ~s as a consequence of the different etching mechanism. Taking into account k I = 0.353k~

10

/

1

5. 3. k 2 region



Firstly, it should be mentioned that the appearance of a constant vt, 2 which is independent of a o n and only affected by L 3 and the storage conditions, cannot be caused by a diffusion layer formed by precipitated etching products, otherwise v t should decrease with increasing etchant concentration as a consequence of a reduced dissolution rate of the diffusion layer. It is rather supposed that a steady state condition is established in the k 2 region, which is characterized by a constant concentration of hydroxide ions at the tip of the track, which is independent of external hydroxide activity. Because of the condition of electroneutrality formulated by eq. (11) the flux of hydroxide ions to-

©

.2 .~ 01 O

010, . 0. 1

J

I

/ ~604OAr L

1

Ji

L

132)~, L ~ I 10

Fig. z. Relation between the rate constants k~ and k2 and the radius-restricted energy loss L 3 (r = 3 nm).

H.B. Liick / Polyethyleneterephthalate as track detector

eq. (1) and (2) can be rewritten v,j = v s +O.353(k*L3)

~,,2 = ( K ' L 3 )

b OOHaH20 2

(12)

(13)

b/3

F r o m the lines in fig. 2 a n e x p o n e n t b = 3 can be derived for the k 1 region. The deviation of the data o b t a i n e d with 132Xe tracks indicates a lower yield of species relevant for e n h a n c e d track etching [9]. The deviation m a y be caused by different material parameters a n d / o r by varying irradiation a n d storage conditions. The ratio k 3 2 / k ] , however, remains c o n s t a n t (table 3). F o r the conditions subjected to 160 a n d 4°Ar tracks the following eqs. were established. vt, , = v s + 0.353(0.650L3)

3

2

ao,aH2 o

vt, 2 = 0.650L 3 .

(14) (15)

In the very initial stage of track etching, i.e. in the vicinity of the c h a n n e l tip, v s is supposed to exhibit the same d e p e n d e n c e on the hydroxide activity as v t. Therefore the response function in the k 1 region becomes i n d e p e n d e n t of e t c h a n t activity. v t j / v s = 1 + 0.353(0.650L3) 3.

(16)

In contrast to eq. (16) the response function in the k 2 region shows that the etch rate ratio decreases with increasing etchant activity. 0.650L 3

/)t, 2/l)s

kra~)HaH20.

(17)

NORMALITY/ 'c

t0

5N 3N

0.01 1N 0.001.I

, ~iI

J

,

IO

L~ [M~V-~Jm-'] Fig. 3. Calculated response curves for different normalities of the NaOH etchant.

511

T h e term k r is the rate c o n s t a n t for radial etching in the track. It should be mentioned, however, that, i n a s m u c h as the etched track is enlarged the e x p o n e n t for the hydroxide activity for radial track etching approaches 1 as a result of a decreased cv.

7. Conclusions For particle track etching in P E T P the use of N a O H solutions is r e c o m m e n d e d because of the advantage that v t can be calculated in a normality range of 0 . 2 5 - 1 0 m o l e s / 1 by eq. (5) once k 2 is determined. In addition in the k 2 region a N a O H solution of poor accuracy in n o r m a l i t y can be used. As a consequence of the L 3 d e p e n d e n c e of the transition from the k~ to the k 2 region a response curve with a decreasing slope can be expected at a given normality. As shown in fig. 3 this effect is more p r o n o u n c e d with tracks initiated by particles of a high L 3 value, a n d by use of a c o n c e n t r a t e d etchant. I wish to t h a n k Prof. G.N. Flerov at the J I N R D u b n a for supplying the irradiated PETP samples. I a m also grateful to Dr. G. Pretzsch at the T U Dresden for calculating Loo and L 3.

References [1] R.L. Fleischer, P.B. Price and R.M. Walker, Nuclear tracks in solids, principles and applications (University of California Press, Berkeley, 1975). [2] G.N. Flerov, JINR Preprint R7-7551, Dubna (1973). [3] S.R. Tretyakova, T.I. Koslova and G.N. Akapyev, JINR Preprint R 14-10235, Dubna (1976). [4] A. Gerhard, A. Schempp and H. Klein, GSI 81-2 (1981) p.180. [5] G. Somogyi, K. Grabisch, R. Scherzer and W. Enge, Nucl. Instr. and Meth. 134 (1976) 129. [6] A. Bernas, A. Chambaudet and Ph. Romary, Rad. Effects 32 (1977) 1. [7] S.R. Tretyakova, P. Apel, L. Jolos, T. Mamonova and V. Shirkova, Nucl. Tracks, Suppl. 2 (1980) 283. [8] H.B. Liack, Nucl. Instr. and Meth. 200 (1982) 517. [9] H.B. LOck, Nucl. Instr. and Meth. 202 (1982) 497. [10] H.B. Liick, to be published. [11] P. Meares, Transport in ion-exchange polymers, in Diffusion in polymers, eds., J. Crank and G.S. Park (Academic Press, London and New York, 1968). [12] L. Dresner, J. Phys. Chem. 69 (1965) 2230. [13] H.B. Liick, to be published. [14] L. Dresner and K.A. Kraus, J. Phys. Chem. 67 (1963) 990. [15] G. Pretzsch, Exper. Technik Physik 27 (1979) 31.