Transport of calcium species in PVC + NPOE membranes

137

J. Electroanal. Chem., 319 (19911 137-144 Elsevier Sequoia S.A., Lausanne

JEC 01747

Transport

of calcium species in PVC + NPOE membranes

R.D. Armstrong and Hong Wang Liepttrtment of Chemistry, The University, Newcastle upon Tyne NEI 7RU (UK)

C.A. Vincent department of Chemistry, University of St. Attdrews, Fife KY16 9ST (UKI

(Received 13 May 1991; in revised form 22 July 1991)

Abstract The mobilities of the ions present in a plasticized poly(vinyl chloride) (PVC) membrane containing Ca2+ BPh; (at < 4 mM) and an excess of the ionophore ETH129 have been measured. The contributions of the cation (Ca2+(ETH1291,1 and anion have been separated by measuring steady state currents in a thin-layer cell. The ratio of the cation mobility to the anion mobility lies between 2.4 and 1.4 over a range of temperatures (2%50°C) and PVC contents.

INTRODUCTION

Plasticized poly(viny1 chloride) (PVC) membranes are used extensively in potentiometric ion sensors. A typical membrane will consist of 33 wt.% PVC and 66 wt.% plasticizer. The membrane will have dissolved in it an ionophore (e.g.

Fig. 1. Structure of ETHf29. ~22-0728/92/$05.~

0 I992 - Elsevier Sequoia S.A. All rights reserved

138

ETH-129 (Fig. 1)) when Ca2+ is the ion being sensed and a salt (e.g. Ca(BPh,),). Generally the salt is present at a low concentration, perhaps 1 mM and the ionophore is present at a much higher concentration. The membrane is contacted on both sides by aqueous solutions, one of which contains the ion being measured (e.g. Ca’+) at a well-defined concentration, whilst the other contains the ion at an unknown con~ntration. The emf across the membrane is used to determine the difference in ion concentrations between the aqueous phases. In order to investigate the ion motion in these polymer membranes we have made measurements of the bulk conductivity of plasticized PVC containing Ca2”, BPh, and an excess of ETH129 in relation to the Ca*+ using impedance measurements. In addition we have measured the cation mobility within the polymer by rapidly applying a small dc voltage across a polymer membrane where the cations in the membrane are in equilibrium with those in two contacting aqueous phases (0.1 M CaCl,) and measuring the resultant current transients, using the method devised by Bruce and Vincent Elf. This method gives the mobility ratio from the ratio of the final (I,) to the initial (I,) currents which fIow in response to a potentiostatic perturbation provided that the cell written as CaCl, (water) I Ca(ETH129),(BPh,) (polymer) ICaCI, (water) fulfils the following conditions: (a) the electrolyte is fully dissociated [2], (b) the charge transfer of Ca”’ across the interface is fast [3], (c) no convection occurs and (d) the diffuse double layer can be neglected. After the application of a small d.c. potential step AE, the concentration gradient of the anion develops since the anions cannot leave the membrane and this concentration gradient will reduce the potential difference across the polymer electrolyte which leads to the decrease in the current with time and finally a steady-state current. Thus if the cation (Ca2i(ETH129)2) mobili~ is U, and the anion (BPh,) mobility is ua, then u,/(u, + u,) =f,/l,. In these membranes the Debye length (- 2.4 nm) is far less than the thickness of the membranes (- 0.01-0.02 cm) so that condition (d) is met. From a combination of these measurements we have been able to determine the mobility of the Ca2+ species in the polymer much more accurately than previously [21. We have made measurements from a very low plasticizer level to 66wt.%. Plasticized PVC behaves in most respects like a single-phase material. The effect of increasing the level of plasticizer is to change the dielectric constant C41(in the present case to increase it from a value of 4 at 25wt.% plasticizer to 14 at 66wt.% plasticizer) and to reduce the microscopic viscosity. The plasticizer which we have worked with is o-nitrophenyi octyl ether (NPOE). Some of the measurements have been cross-checked by measuring the conductivity of membranes containing the salt AsPh,BPh,. Because of the equal size of the ions in this salt it can safely be assumed that they have identical mobilities. Thus the mobility of the BPh; ion can be obtained. However, the fact that the membranes may have low dielectric constants means that it is generally necessary to determine the conductivity of membranes with a number of different salt concentrations and then use the Ostwald dilution law to determine the numbers of ion pairs and free ions.

139 EXPERIMENTAL.

PVC (high molecular weight), sodium tetraphenylborate, tetraphenylarsonium chloride and ETH129 (Fluka) were used as received. NPOE (Fluka) and tetrahydrofuran (THF; BDH) were distilled before use. Tetraphenylarsonium tetraphenylborate was prepared by precipitation by mixing aqueous tetraphenylarsonium chloride and sodium tetraphenyl~rate solutions. All other chemicals were reagent grade. Deionized water was used for preparing solutions. The membranes were made by dissolving appropriate amounts of NPOE, PVC (with a total weight of PVC + NPOE of 450 mg), ETH129 and NaBPh, in the redistilled THF using a shaker. The resulting solution was cast in level polytetrafluoroethylene (PTFE) moulds and the solvent allowed to evaporate over 2 days at room temperature. Sections were taken from the membranes and these were then placed in bottles containing 0.1 M CaCl, solution for 1 week to exchange Nai for Ca2+. For membranes containing 80% PVC, the temperature was controlled at 50°C for the exchange reaction. A Solartron 1170 frequency response analyser (controlled by an Apple II + microcomputer) and a Solartron 1186 electrochemical interface were used for the ac impedance measurements, and the measurements were made in a four-electrode PTFE cell with two Ag/AgCl reference electrodes and two Ag/AgCl current-carrying electrodes. 0.1 M CaCl, was used as the contacting solution on both sides of the membrane with 0.78 cm2 contact area. The thickness of the membranes was measured by a specially modified micrometer with two stainless steel jaws, which could also be used for conductivi~ measurements in the blocking electrode mode. A home-made four-electrode potentiostat was used for the potential step experiment and current-time transients were recorded using a BBC SE120 chart recorder and monitored by the current meter which was built into the potentiostat. The membranes were soaked in 0.1 M CaCl, for at least one night prior to the measurements. To correct for the possible error caused by bias in the reference electrodes (generally they were less than 0.2 mV apart), the measurements were made in both directions, i.e. + 10 mV and - 10 mV (applied between the reference electrodes). The measurement temperature was controlled to f 1°C. RESULTS

For a membrane containing 33wt.% PVC, it usually took 100-200 min at 20°C for the current to reach a steady value after a 10 mV voltage was applied across the cell, depending on the thickness of the membrane. The current-time transient for a membrane containing 1 mmol kg-’ Ca2+ salt with an ETH129/Ca2+ ratio equal to 35 is shown in Fig. 2 where the current ratio 1,/Z, was found to be 0.71. The bulk resistances of a membrane before and after the current transient measurement were virtually the same if the temperature was well controlled. In

2.0

1 0

I 50

I 100

t 150

t 200

i 250

I 300

tlmin Fig. 2. Current-time transient for a 33wt.% PVC membrane containing 1 mmol kg-’ Ca2+ salt with ETH129/Ca2+ equal to 35: (A) + 10 mV, (B) - 10 mV, immediately after curve A (- I).

order to reduce the errors caused by reference electrodes and temperature fiuctuations to the lowest possible level, initial currents were calculated from the bulk resistances and the average value of the current ratio 1,/r, in the two directions was used. There are two main differences between the “ideal” system described by Bruce and Vincent [II and the rea1 system investigated here. One is that cations in the polymer phase are different from those in the aqueous phase. In the membrane one Ca*+ is complexed by two ETH129 molecules [2] which always remain in the membrane. This means that, whilst current flows, ETH129 is transported to one side of the membrane and released on the other side of the membrane which may have some influence on the current ratio I,/&. One possible way to reduce this influence is to increase the ~ncentration of ETH129 whilst the salt concentration remains constant. Figure 3 shows the variation of J./Z, with the ETI-1129/Ca2+ ratio, from which it can be seen that the effect of ETH129 can be neglected when ETH129/Ca*+> 28 and the mobility ratio uc/(uc -I-u,) = 0.71. Another difference is that the membrane is not contacted directly with electrodes but through aqueous 0.1 M CaCI, solutions, which means that a fraction of the applied 10 mV will be used for driving the current in the aqueous phases. The error caused by this effect can be shown to be negligible. Finally, there is the fact that 1, could in part be determined by the impedances of the interfaces. There is strong evidence in this case that this is not a problem since Ca*’ is in Nernstian equilibrium across each interface.

141

0.8 I 0.7 -

““I__.t----__ 20

25

30

35

40

ETH I 29/Ca2+ Fig. 3. Effect of ETH129 (with 1 mmol kg-’ Ca*+ salt) on the current ratio I, /I, membranes.

in 33wt.% PVC

For membranes with different salt concentration but the same ETH129/Ca*+ ratio, the conductivity was, within experimental error, proportional to the salt concentration, indicating the full dissociation of the salt which agrees with previous work in our laboratories [2], whilst the current ratio 1,/I, remained virtually unchanged (Table 1). , Measurements were made over a wide range of membranes with different PVC contents and at different temperatures. Figure 4 illustrates the conductivity change with temperature for membranes with different PVC content. The effect of temperature on the conductivity increased significantly with the PVC content increase, as indicated by the activation energy which increased from 32.5 kJ mol- ’ for 33wt.% PVC membranes to 129 kJ mol-’ for 8Owt.% PVC membranes. The conductivity decreased sharply with the PVC increase, and in fact the conductivity of 8Owt.% PVC membranes became too low to enable us to determine the mobility

TABLE 1 Mobility ratio u, /(u, + u,) and conductivity for 33wt.% PVC membranes with ETH129/Ca*+ to 35 but different salt concentrations Salt cont. /mmol kg-’

Conductivity/ (10’ K/~-I cm-‘)

U, /(u, + u,)

0.5 1 2

3.2 6.1 13

0.71 0.71 0.72

equal

142

-11

I

2.9

3.0

t

I

I

t

3.1

3.2

3.3

3.4

Pig. 4. Arrhenius plots of the conductivity for membranes with different PVC contents: (A) 33wt.% PVC; (B) 45wt.% PVC, (C) 6Owt.% PVC; (D) 8Owt.% PVC.

ratio using the steady-state current method. However, at lower PVC levels such as 45wt.% and 6Owt.% PVC, the mobility ratio could still be determined reasonably accurately. For these membranes the conductivi~ of membranes with 0.5 and 1 mmol kg-l Ca2+ salt but the same ETH129/Ca2’ ratio (35) indicated the full dissociation of the salt at various temperatures, and membranes with ETH129/ Ca*+ ratios equal to 30 and 35 also gave similar IS/Z0 ratios.

TABLE 2 Summary of mobility ratio u,/(u, steady-state current measurements

+ u,) and ionic a mobility for PVC+ NPOE membranes

PVC/(wt.%)

T/“C

U, /(u, + u,>

106u, /cm+’

33

20+1 35*1 50+1

0.71 F 0.03 0.66 rt:0.01 0.61 kO.01

2.0 3.5 6.0

0.8 1.8 3.8

45

20+1 35*1 50*1

0.7orto.04 0.66 Ir 0.02 0.61+ 0.02

0.51 1.3 2.4

0.22 0.67 1.5

60

20+1 35+1 5Oil

0.65 f: 0.05 0.59 & 0.04

0.13 0.42

0.68 0.29

a Cation, Ca(ETH129f~f;

anion, BPh;

V-l

106u, /cm’s_’

V-t

from

143

TABLE 3 Results from the equal-mobility assumption: u(AsPh; ) = u(BPh; ) PVC/(wt.%o)

T/“C

10’~/0-‘cm-’

33

20*1 35*1 50*1

45

60

a

106u,(BPh; )/ cm2s-l V-l

u, /(u, + u,) b

2.1 4.5 8.5

0.95 2.0 3.9

0.66 0.62 0.60

20*1 35*1 50*1

0.59 1.6 3.1

0.27 0.73 1.4

0.63 0.63 0.64

20+1 35*1 50*1

0.054 0.19 0.54

0.025 0.086 0.25

0.51 0.57 0.65

a Conductivity of membranes containing 1 mmol kg-’ AsPh,BPh,. b Cation: [Ca(ETH129):+ I

From the mobility ratio uJ(uc + u,) and the conductivities, the mobilities of the cation [Ca(ETH129),]*+ and anion BPh; were calculated using K =

2CF( U, + Ua)

where K is the conductivity and c/mol cmm3 is the concentration of Ca2+ salt. (The volume of a 0.45 g membrane was approximately 0.4 cm-3.) Cation and anion mobilities from steady-state current measurements for different PVC compositions and at various temperatures are listed in Table 2. Listed in Table 3 are mobilities calculated on the assumption that AsPhi and BPh, have the same mobility. This assumption has previously been used to estimate ionic mobility ratios in PVC di-octyl sebacate (DOS) membranes [5]. For PVC + NPOE membranes comparison of Tables 2 and 3 suggests that results from the equal-mobility assumption agree well with those from the steady-state current method at low PVC levels and high temperatures. These are exactly the conditions which favour low concentrations of ion pairs upon which both methods, as used here, depend. DISCUSSION

It is interesting to note that the mobility ratio only changed slightly with temperature and PVC level. The simplest model for the ion motion in the polymer is that of a hard sphere moving through a continuous fluid, so that Stokes law applies. In this case we would expect that

where r is the radius of the ion. The radius of Ca(ETH129);+ would at first sight seem to be about twice of that of BPh; since each ETH129 molecule contains four

144

cyclohexyl groups. If this were the case, the mobility ratio u,/(u, + u,> would be ca. 0.5. The experimental value of ca. 0.6-0.7 suggests, however, that Ca(ETH129);+ has a similar radius to that of BPh; (if r, = r,, u,/(u, + u,) = 0.67). This means that Ca(ETH129);+ probably has a very compact structure, with all the cyciohexyl groups packed as close as possible to the Ca*+, thus giving a radius which is perhaps just a little larger than the distance between the two diagonal carbon atoms in a cyclohe& group. ACKNOWLEDGEMENTS

We would like to thank the European Community for their support of this work under Contract BREU-0167(SMA). Hong Wang would also like to thank the Committee of Vice-Chancellors and Principals of the Universities of the United Kingdom for the Overseas Research Students award, and Dr. M. Todd and Dr. M.L. Marcos for helpful discussions. REFERENCES 1 2 3 4 5

P.G. R.D. R.D. R.D. R.D.

Bruce and Armstrong Armstrong Armstrong, Armstrong

C.A. Vincent, J. Electroanal. Chem., 225 (1987) 1. and M. Todd, J. Electroanal. Chem., 257 (1988) 161. and M. Todd, J. Electroanal. Chem., 266 (1989) 175. Hong Wang and M. Todd, J. Electroanal. Chem., 266 (1989) 173. and M. Todd, Electrochim. Acta, 32 (1987) 155.