In situ observation of ion concentration profiles in lithium ion-conducting gels

In situ observation of ion concentration profiles in lithium ion-conducting gels

Solid State Ionics 127 (2000) 199–205 www.elsevier.com / locate / ssi In situ observation of ion concentration profiles in lithium ion-conducting gel...

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Solid State Ionics 127 (2000) 199–205 www.elsevier.com / locate / ssi

In situ observation of ion concentration profiles in lithium ion-conducting gels R.A.M. Hikmet* Philips Research, Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands Received 19 August 1999; accepted 5 October 1999

Abstract A gel electrolyte was produced by photo-polymerisation of poly(ethyleneglycol diacrylate) in an electrolyte mixture containing LiPF 6 in propylene carbonate in a cell containing lithium metal electrodes. The cell was placed in a Schlieren optical set-up and a potential difference was applied across the electrodes. Using the optical set-up, the change in refractive index across the cell could be measured and then translated into concentration values. In this way, concentration change across the electrolyte could for the first time be measured in situ while monitoring the current passing through the cell during the application of an external potential difference. After the applied potential difference had been removed, the decay of the concentration gradient across the cell and the open circuit potential were monitored. Good agreement between the experimental results and the theory was observed. The transport number estimated for lithium using the concentration difference values was in good agreement with the value estimated on the basis of the diffusion coefficients of the anion and the cation.  2000 Elsevier Science B.V. All rights reserved. Keywords: Gel electrolyte; Photo-polymerization; Lithium; Schlieren optical method; Ion concentration profiles

1. Introduction Convective flow is retarded in practical electrochemical devices such as batteries, in which the electrolyte is confined in the pores of the separator and between the particles of the anode and cathode material. In the case of gel and polymeric electrolytes the convective flow may be totally neglected and the ion transport is only by (i) migration in an electric field, and (ii) diffusion in response to a concentration gradient. In a comprehensive theoretical study, Bruce and Vincent [1,2] considered the *Corresponding author. E-mail address: [email protected] (R.A.M. Hikmet)

flow of ions in an ideal electrolyte to present an equation to show the effect of the increased concentration gradient on the voltage–current relationship. The theory is then generalised to take into account of finite electrode kinetics as well as ion–ion interactions [2]. On the basis of this theory expressions leading to the definitions of transference numbers for cations and anions were devised and used in electrical measurements in the estimation of transference numbers. Here we describe the use of the Schlieren optical method in the observation of salt concentration across an electrochemical cell during and after the application of a potential difference. Using the in situ current and voltage measurements a comparison with

0167-2738 / 00 / $ – see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S0167-2738( 99 )00285-4

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the theory could be made and the transport number for lithium could be estimated.

2. Experimental

2.1. Materials The polyethylene glycol diacrylate PEGDA-400 used in the experiments was purchased from Kayarad. The battery-grade liquid electrolyte consisting of 11% hexafluorophosphate (LiPF 6 ) in propylene carbonate (PC) was purchased from Merck. A mixture containing 10 wt% acrylate in the electrolyte was produced. In order to initiate polymerisation, 0.5 wt% Irgacure 651 photoinitiator (Ciba Geigy) was added to the mixture. The mixture containing the initiator was brought into the cell used in the experiments. The polymerisation of the mixtures was initiated using 1 mW cm 22 UV radiation from a PL lamp ( lmax 5 360 nm). Samples were prepared in dry air atmosphere in order to avoid problems with moisture.

2.2. Schlieren optical set-up The Schlieren optical set-up has been devised by Prast [3] and has been used by Wimberger Friedl [4] to determine density distributions in poly(carbonate)s. A schematic drawing of the optical set-up is shown in Fig. 1. A rectangular stabilised light source with a height h and a lens L 1 with a focal distance f 5 120 mm was used to illuminate the object. Using lens L 2 ( f 5 120 mm) and L 3 ( f 5 400 mm) the image of the object was projected onto a Machine

Vision (CNM 300) CCD camera. The image was captured using a screen grabber and processed using Image Pro-plus software. A knife placed at the focal point of L 2 could be moved in and out of the field. The position of the knife was chosen so that when it was inserted into the optical path (without an object in the set-up) the intensity measured at a given point at the detector was reduced by about a factor of two.

2.2.1. Theory When an object is inserted in the set-up with a refractive index profile along the z-axis, the position of the light beam will at that point be deflected by an angle of f. As a result, a displacement of the beam by Dh will be caused at the position of the knife as shown in Fig. 1. For small values of f this displacement is given by: Dh 5 f2 tan f ¯ f2 f

(1)

The angle f can be rewritten in terms of the difference in the optical path d x between two adjacent rays in the object with a thickness of l as d x 5 d nl, if the difference is caused only by the refractive index variation along the z-axis. The horizontal shift can then be written as:

dx ld n Dh ¯ f2 f 5 f2 ] 5 f2 ] dz dz

(2)

Without a refractive index variation in the sample the knife will block half of the light when it is inserted. In the case of a sample with a refractive index variation, due to the horizontal shift an extra change in the light intensity DI(z) at a position z at the detector will be observed. This change in the intensity can be represented by the equation below as:

Fig. 1. Schematic drawing of the Schlieren optical set-up.

R. A.M. Hikmet / Solid State Ionics 127 (2000) 199 – 205

DI(z) Dh ld n ]] 5 ] 5 f2 ] 5M(z) h hd z I(z)

(3)

The following equation is used to correct for the background and faults in the alignment: Io (z) DI(z) I(z) M(z) 5 ]] 5 ]] 2 ]] I(z) I9(z) I 9o (z)

(4)

where Io (z) and I o9 (z) are the intensities with and without the knife before the start of the experiment, and I(z) and I9(z) are the intensities with and without knife after the start of the experiment measured at a position z at the detector. The refractive index n(z) was calculated using the equation below: d

E

h n(z) 5 n o 1 Dn(z) 5 n o 1 ] M(z)d z f2l

(5)

0

where d is the width of the cell and n o is the refractive index before the start of the experiment.

2.3. Electrochemical cell The schematic drawing of the cell used in the experiments is shown in Fig. 2. The cell consisted of lithium metal electrodes placed between two glass plates. The gap between the electrodes was filled with the reactive electrolyte mixture which was then polymerised. The cell was sealed using an epoxy

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adhesive. Contact with the electrodes was established using 10-mm thick nickel connectors. A constant voltage of 20 mV was applied across the electrodes using a Keithley-230 voltage source. Keithley-2000 multi-meters coupled to a computer were used to monitor the current and the voltage as a function of time during the experiments.

3. Results and discussion A gel containing 10 wt% PEGDA was used. The cell was placed in the optical set-up so that the applied electric field would be in the direction of the z axis indicated in Fig. 2. A potential difference of 20 mV was applied across the cell and the light intensity profile across the cell was monitored at regular intervals. Intensity measurements recorded at the CCD detector were used in Eqs. (3) and (4) to calculated d n(z) /d z. Fig. 3 shows an example of the a curve obtained by plotting d n(z) /d z measured 5 min after the application of the voltage as a function of the position across the cell gap. On the assumption that the refractive index at the centre of the cell (z 5 d / 2) remains unaltered after the application of the potential, Dn(z) was calculated using Eq. (5). The result is also shown in Fig. 3. The dependence of the refractive index (n) on the salt concentration (c) is given as Dn 5 KDc, where K is a constant which was

Fig. 2. Schematic drawing of the electrochemical cell used in the experiments.

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Fig. 3. Refractive index gradient and refractive index change (with respect to d50.5 mm) across the cell 5 min after the application of 20 mV.

found to be K57.3310 24 in refractive index measurements. Fig. 4 shows Dn and Dc across the cell gap at various times during the application of the potential difference. It can be seen that, shortly after the application of the potential difference, the salt concentration increases close to the positive electrode and decreased at the negative electrode. At

longer times the magnitude of the gradient increases and its form across cell gap changes. This is in accordance with the theoretically predicted behaviour and shows that the concentration changes which start close to the electrodes move towards the centre of the cell, eventually becoming a slightly curved line. A linear concentration gradient was not observed

Fig. 4. Concentration (refractive index) change across the cell observed at various times after the application of 20 mV.

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even after 2.5 h after the application of the voltage. It is well known that a thin passivation layer is formed at the lithium / electrolyte interface. However, such a thin layer is not expected to be observed in the set-up. The current flowing through the cell during the experiment was also measured as a function of time. The result is shown in Fig. 5. It can be seen that the application of the voltage across the cell causes the current to decrease as a function of time and reach an almost steady state. The decrease in the current is due to the concentration gradient build-up, resulting in the reduction in the potential drop across the electrolyte. The magnitude of the gradient is determined by the diffusion constants of the anion (D 2) and the cation (D 1 ). The transport number of lithium t 5 (D 1 /D 1 1 D 2) is often used to characterise electrolytes. In electrochemical experiments is calculated using the following equation:

dance spectroscopy (Eq. (6)), the transport number for lithium was calculated to be t 1 50.33. This is much higher than the value determined using the diffusion coefficients obtained in pulse field gradient experiments [5]. This difference is often associated with the problems of the electrochemical technique especially the high interfacial resistance of the samples. A good review of various methods used in determination of the transport numbers can be found in Ref. [6]. An alternative method for calculating the transport number is also described below. The open circuit voltage measured across the cell after the removal of the potential difference at the end of the experiments will be related to this gradient. The open circuit potential DE across the cell is represented as:

Is (DV 2 Ii R i ) 1 t 5 ]]]] Ii (DV 2 Is R s )

where R is the molar gas constant, F is the Faraday constant and Ca and Cc are the ion concentrations at the positive and negative electrodes, respectively. The first term in Eq. (7) is related to the Nernst potential as a result of the concentration difference, while the second term describes the junction potential.

(6)

where Ii , R i and Is , R s are the initial and steady-state values of the current and the interfacial resistance. Using the current measurements (Fig. 5) and the values of R i 5R s 52900 V measured using impe-

DE 5 RT /F ln(Ca /Cc ) 2 RT /F(t 2 2 t 1 ) ln(Ca /Cc ) 5 2(1 2 t 1 ) ln(Ca /Cc )RT /F

Fig. 5. Current flowing through the cell as a function of time.

(7)

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Fig. 6. Open circuit voltage across the cell as a function of time. The line and the points correspond to the measured the calculated values, respectively.

The open circuit potential across the cell was measured as a function of time after the cell had been disconnected from the voltage source as shown in Fig. 6. Using the Schlieren optical set-up the concentration gradient across the cell was also measured (Fig. 7). In Fig. 6 it can be seen that, as

expected, an open field voltage was present across the cell at end of the experiment, which decreased almost exponentially as a function of time. In Fig. 7 it can be seen that the magnitude of the concentration gradient also decreases at longer times, while the profile of the curves remains almost the same. Using

Fig. 7. Concentration (refractive index) change across the cell observed at various times after the removal of the applied voltage.

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the values obtained from Fig. 7 for Ca and Cc in Eq. 6 together with the value of t 1 50.06 (obtained in Ref. [5] on the basis of the diffusion coefficients of the anion and the cation as determined in pulse field gradient experiments), DE was calculated. The results are also plotted in Fig. 6. It can be seen that the measured and the calculated values of DE are in good agreement especially immediately after the removal of the voltage. This indicates that the concentration gradient measurements described here can also be used to estimate transport numbers in electrolytes

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which is in good agreement with the theory. After the removal of the voltage an open circuit voltage was detected across the cell, which decreased as a function of time accompanied with a decrease in the concentration gradient across the cell. The open circuit voltage was calculated using the concentration values at the negative and the positive electrodes. The values obtained were in a good agreement with the experimentally determined values. The transport number obtained for lithium in diffusion measurements was used in the calculations. The results show that the method can be used to estimate transport numbers in electrolytes.

4. Conclusions References It has been shown that the Schlieren optical set-up can be used to study changes in ion concentration in a gel placed between two lithium metal electrodes during the application of a voltage. It was found that soon after the application of the voltage the ion concentration at the positive electrode increases while at the negative electrode the salt concentration decreases. The change in the ion concentration gradient increased in magnitude and the curve depicting the gradient across the cell became a smooth line. The increase in the gradient coincided with a decrease in the current flowing through the cell,

[1] P.G. Bruce, C.A. Vincent, J. Electroanal. Chem. 225 (1987) 1. [2] P.G. Bruce, C.A. Vincent, J. Electroanal. Chem. 271 (1989) 27. [3] G. Prast, Philips Tech. Rev. 43 (1987) 184. [4] R. Wimberger-Friedl, G. Prast, A.V. Kurstjens, J.G. de Bruin, J. Polym. Sci., Polym. Phys. 30 (1992) 83. [5] R.A.M. Hikmet, M. Peeters, Solid State Ionics 126 (1–2) (1999) 25. [6] B. Scrosati (Ed.), Applications of Electroactive Polymers, Chapman and Hall, London, 1993, p. 18.