Electrical impedance of composite membranes based on polyelectrolyte complexes

Journal of Membrane hence, 62 (1991) 145-154 Elsevler Science Publishers B V , Amsterdam

145

Electrical impedance of composite membranes based on polyelectrolyte complexes L E. Bromberg* “Natural Resources”Sclence

and Engcneerrng Center, Moscow (USSR)

(Received January 30,1990, accepted m revised form May 6,199l)

Abstract An mvestlgatlon was conducted on the impedance of composite membranes (CMs) conslstmg of mtrocellulose acetate ultrafilters impregnated with polyelectrolyte complexes based on weak polyelectrolytes It was d=covered that the Cole-Cole impedance diagrams of CMs could be mterpreted as arcs of two circumferences mth their centers below the abscissa The type of the CM equivalent clrcmt confirmed then heterogeneity Electrical impedance measurements evaluated the values of the effective resistance to charge transfer m the membrane phase (R,) The R, vs pH curve had a mmlmum point The effective diffusion coefficient (&) values of H+ and Na+ ions were ca 12 x lO-‘j cm2/sec at pH 6 5 At 6 5
Introduction In recent years, studies have been made on an expandmg range of properties of a new class of electrically conductive-polymeric materials-polyelectrolyte complexes (PECs) [l-4]. One of their potential applications is their use as membranes [ 5,6]. Reference [ 21 describes an effort to characterize the impedance of hydrogel membranes of PEC based on a pair of weak polyelectrolytes: poly (acryhc) acid-poly (ethylenelmine). The specific electrical resistance of free water in PEC “pores” and the specific electric resistance of bonded water near ion-exchange groups were calculated. The studied hydrogels possessed only one specific relaxation time It is important to note that hydrogel membranes of PEC are very sensitive *Present address Department of Materials Research, The Welzmann Institute of Science, P 0 Box 26, Behovot 76100 (Israel)

0376-7388/91/$03 50 0 1991 Elsevler Science Publishers B V All nghts reserved

146

to the ion composition of electrolyte solutions and they lose continuity while swellmg m solutions of high ionic strength. Storage of PEC films in the airdry state is rather difficult because of their brittleness, whereas storage of PECs in solutions causes changes in their non-equilibrium structure. Therefore strong composite membranes (CMs) based on PECs [ 5,6] were mtroduced. Such CMs are distmguished by their long-term stability while swelling m electrolyte solutions, and for their high cation/anion selectivity, which suggested their potential usefulness in ion-selective electrodes. Moreover, CMs are pH-sensitive, which helps in controlling their properties. Therefore it was considered mterestmg to study their electrical and ion-transport characteristics. The results are outlined m the present paper Experimental Methods of obtaining and studying composite membranes (CMs) have recently been described [ 61. These membranes are in fact Millipore nitrocellulose acetate ultrafilters (with pores of 0.05 pm m diameter) impregnated with PECK The components of the PECs were weak polyelectrolytes: poly (ethyleneplperazme ) (PEPP), poly (ethyleneimine ) (PEI) and poly (acrylic ) acid (PAA). The electrical conductivity and capacitance of a cell with a membrane (G and C) and without a membrane (G’ and C’ ) were measured using a bridge circuit with Pt electrodes of developed surface, as described in [ 61, m the frequency interval of applied voltage f= 60 Hz-100 kHz. The measurement error for conductivity and capacitance was ca. 5%. Membrane conductivity and capacitance (G, and C,) with correction for the impedance of the cell and electrolyte solution were derived from the equations

[71:

G,=G 41=

91-92

(91--4212+ bh93)2’ (1+&V’; q2 =G/G’;

q3 =o$/G;

0=2xf

(2)

Real (R,) and imaginary (X,) parts of the membrane impedance were determined using the equations [81:

R+=&,/[l+ W%/W21GmE, X,=c&&/[l+ bG,IGn)21G2,n

(3) (4)

where S, and 1, are operational area and membrane thickness. The impedance curves were interpreted and analyzed usmg an original software package.

147

Results and discussion Figure 1 (a)-(e) shows on the same scale impedance diagrams which were determined in the frequency range 60 Hz-50 kHz agamst pH of 0.01 M NaCl solution in which membrane samples had been swollen for 24 hr. For comparison, the inset m Fig. 1 (a) shows the same impedance diagram on a larger scale, provldmg minute analysis of Impedance curves. It can be seen that the diagrams m Fig. 1 at f> 100 Hz can be interpreted as arcs of two circumferences with then centers below the abscissa, which corresponds to two continuous relaxation time spectra of CM components. Therefore, ignoring the processes 1650

(a)

pH 31

0 X,,

k-Cl-cm

-

D 0

OOP.--c OD

0

.-__

165 0

X,,

kR_cm

Fig 1

I

1

‘--I_-_---___

pH62

---_

I

RS,

I

kR-cm

I

I

1

1650

148

165.0

(c)

pH 72

e

X,,

kR_Cm

IOOHz

-

o

8s D

oo:

./L -I

00

I.

IO kHz

, --+

‘\ ‘\

, , ------------a

‘.

R,,

‘\

165 0

kR_cm

‘\ ‘1 ‘\ ‘. ‘\ ‘1 ‘0

Cd)

I

001 00

kHZ

Z-l0 -

_

---_

----

----

----___

--16’

----____

0

--o RS, kR_cm

of ion transfer at the CM-electrolyte solution interface [9,10], the electrical diagram of a membrane can be visuahzed as a sequence of two parallel capacitances and resistances [ 111:

149

1650-

(e)

pH 95

Xs,

kR_cm

$7

_

P0

100

HZ

0

Jo

7 HZ

r 8/ _____v1OkHz Q --c--L-%,=r,,_L===

oo,-_ 00

7 __A___--4 :- ;~-----_--__-_-_-_-___~

16 5 RS,

k-Q-cm

Fig 1 Typical impedance dmgrams of composite membranes vs pH of 0 01 M NaCl solution m which membranes were swollen Circles designate experimental data, pomts deslgnate calculated mterpretatlon of the dmgrams, circles with pomta designate the circumference centers All the calculations were carried out according to formulae ( 1) - (4) m the frequency range f= 60 Hz-50 kHz

where Rk, Rg are resistance components of the membrane R,, CL, Cl are capacitance components of the membrane C,; R, 1s the resistance of the electrolyte layers flowing around the CM. The type of eqmvalent circuit confirms the CM heterogeneity. Unlike CM, the individual PEC of PAA and PEPP is characterized by an impedance diagram with only one arc center, whrch IS situated on the abscrssa (Frg. 2). Therefore the PEC hydrogel possesses only one relaxation time and is homogeneous [ 111. It is essential that the indivrdual PEC hydrogel 1s characterized by a value of R, lower by an order of magnitude than the R, of a porous membrane impregnated with this PEC at the same pH of 7.2 (cf. Figs. lc and 2). The method for evaluation of the R, value is discussed later. This difference 1s due to a much greater percentage of the conductive water solution in an mdividual PEC than m a polycomplex, where it 1s situated in the CM pores

[51.

At pH values of 7.2 and 8.3 (Figs. lc and ld) there appears in the diagrams a branch at f< 100 Hz, correspondmg to a Warburg impedance (2,) in the equivalent circuit:

150

47

R;

Z,

As shown by monographs [8,12], an X-intercept between arcs helps to evaluate the value of R,, i.e. the effective resistance to charge transfer in the membrane phase. Figure 3 shows the results of R, calculated for a series of CMs vs. the pH of solutions flowing around the membrane. The conditions for R, evaluation tests were the same as for Fig. 1. As Fig. 3 shows, the R, vs. pH curve does have a minimum point and its type does not coincide with CM titration curves [ 61. R, variation appears to be influenced by two processes. As was previously shown [ 61, at pH < 6.5 in the pores of an electrically neutral membrane there form mtra- and mtermolecular hydrogen bonds between excess polyacryhc acid COOH groups not linked with polybase amino-groups in PEC. With pH decrease the hydrogen bond network becomes more intersected and, subsequently, the density of the PEC hydrogel in the pores increases and hydration decreases. At pH > 6.5 the hydrogen bonds start to break and the excess carboxyl groups are ionized. This causes an uncompensated negative charge in the CM. The nature of the curve in Fig. 3 confirms these hypotheses. The results obtained enable the evaluation of transport properties of the CM. Indeed, the relation between the effective values of R, and the diffusion 50pH 72

c 0

X,,

o

P

es

@

kR_cm

RS, kR_cm

Fig 2 Impedance diagram of PEC hydrogel of PAA and PEPP contammg covalent PAA-PEI bonds, 60~ thick, and swollen at pH 7 2 m 0 01 M NaCl solution, the diagram has been calculated m the frequency range f= 60 Hz-50 kHz

151

400 R M,

-

kR_cm 350-

250

-

200 4

5

6

7

8

9

PH

Fig 3 pH curves of effective reswtance to charge transfer through the membrane phase (R,) The test condltlons are the same as for Fig 1

coefficients of transported ions m a membrane D, can be described by the Nernst-Einstein equation, as is formulated m [lo] :

D, = RT/Z’F 2R,C?f

(5)

where Gf is the effective equilibrium concentratron of transferred (free) ions m a membrane, R is the universal gas constant, T is temperature, 2 is the ionic charge and F 1s the Faraday constant. Let us assume that the electrical conductivity of a CM 1s due only to the presence of the free counter-ions H+ and Na+ m it with a total concentration. Cf = CL, + Gf,

(6)

Hereafter the overbar above the symbols designates the membrane phase, and the absence of an overbar means the phase of the solution. The ion exchange reaction of H + and Na+ ions at a membrane CM-COOH+Na+%M-COONa+H+ CH

CNa

CNNe

CH

is described with the effective equilibrium constant: K = G-&/C,*~n

= CH( Ga + G, ) /

(G + G ) C,,

(7)

Here PNa,n and CL,,, are respectively the concentrations of the counter-Ions linked wrth ion-exchange groups and the free counter-ions m the CM phase. The dlssoclation of carboxyl groups on a membrane: Kd

CM-$OOH Ii

= CM-COO+%+ (?200 Ii

152

can be described with the constant:

(8) Let us formulate the prerequisite for electrical neutrality of a membrane:

(9) and the material equilibrium equation:

PO0 + eb,, + c”, = c,

(10)

where Cx is the effective concentration of ion-exchange groups at the CM As a first approximation let us assume that a highly swollen CM satisfies the condition [ 131:

(11) Solvmg eqns. (6)- (11) for total concentration of free cations at the membrane Cf yields.

(12) Let us consider the ion exchange at a CM at pH 6.5 when the apparent degree of ion-exchange group dissociation a=0.5 [6]. In this case, the experiments were carried out by titrating the CM in NaCl solutions of different concentrations and membrane swellability measurements were carried out as described m [ 131;the experiments yielded the values of K,, Kd and Cx: 1,3.2 X 10m7M and 3.7 M, respectively. In 0.01 M NaCl solution at pH=6.5, the value (C&/C,,) is 3 2 x 10F5. Substitution of all these values into eqn. (12) yields: cf x 1.1 x 10m3M, and this, together with eqn. (5) at R,= 200 kQ-cm, yields D,= 12 x 10m6cm’/sec. This value is lower by an order of magnitude than the diffusion coefficient of Na+ ion in water (D,). Although at 6.5 < pH < 9 D, values showed little variation in our experiments and were around 10e6 cm”/ set, at acid pH < 3.2 D, values decreased rapidly to 1O-8-1O-g cm2/sec owmg to a substantial decrease in Kd and Cx. In contrast to D,, the value of effective permeability of the CM: P,=D,cf/C*, where C* is the total concentration of the solution, changed very slightly through the whole pH range. For example, m 0 01 M NaCl solution at pH = 3.1, P,= 5 4 X 10-s cm2/sec, and at pH = 7 0, P,= 1.3~10B7 cm2/sec (cf. Fig. 3 and eqn 5) It should be noted that the analysis performed yields only average values of D,, which are a function of 0: and DE. The above method also enables the evaluation of effective values of diffusion coefficients H+ (Na+ ) (D,) and permeability P, in an mdividual PEC At a PEC swellability of around 75% m 0.01 M NaCl solution the D, coefficient was close to D,, namely 10e5 cm2/sec; the value of P, was ca. 10m6cm2/sec. The values of D, and P, testify to H+ (Na+ ) ion diffusion through PEC aqueous areas without any substantial limitations. These data conform with

153

previous reports. For example, m Ref. [ 141 the permeability of individual PEC of PAA and PEPP for NaCl showed a value of 7 x 10m7cm2/sec when measured conductometncally. Thus CMs possess ion-transport behaviour with parameters no worse than those of dialysis membranes. Acknowledgements The author would like to thank Drs. N.M. Kocherginsky and A.V. Indenbom for their useful criticism of this work List of symbols

c

C’ C, CL, CL C +, CH, C,,, CH, etc. D, g G’ G, Ke, JG

L p.2 R, %I R;,

R;

R Sin XS

capacitance of a cell with a membrane (F ) capacitance of a cell without a membrane (F ) membrane capacitance (F) capacitance components of C, (F) concentrations; see explanations in text effective diffusion coefficient ( cm2/sec ) diffusion coefficient in water ( cm2/sec ) frequency of applied voltage (Hz) conductivity of a cell with a membrane (S) conductivity of a cell without a membrane (S) membrane conductivity (S ) equilibrium and dissociation constants membrane thickness (cm) effective permeability ( cm2/sec) resistance of electrolyte layers flowmg around membrane (a-cm) effective resistance to charge transfer m the membrane (R-cm) resistance components of R, (R-cm) real part of the membrane impedance (Q-cm) operational area of membrane ( cm2 ) imaginary part of the membrane impedance (Q-cm) ql= (l+q;)-‘,

q2=G/G’;

q3=oC/G

o=Znf

References 1

Prepr 2nd All-Umon Conf on Interpolymer Complexes, Rlga, 1989, R I Kalyuzhnaya et al (Eds ), AN USSR, In.&tute of Wood Chemistry, 280 pp

154 2 3 4 5 6 7 8 9 10 11

12 13 14

L E Bromberg and B S Eltaefon, Electrlcal impedance of polyelectrolyte complexes, Prepr 2nd All-Umon Conf Interpolymer Complexes, Rlga, 1989, p 20 B Phlhpp, H Dautzenberg, K -J Lmow, J Kotz and W Dawydoff, Polyelectrolyte complexes recent developments and open problems, Prog Polym Scl ,14 (1989) 91 C Lmder, M Perry, M Nemas and R Katraro, Ion-selective transport membranes, Eur Pat Appl EP 315,510, May lo,1989 L E Bromberg and B S Eltsefon, Transport properties of composite membranes on the basis of polyelectrolyte complexes, Vysokomol Soedm , Ser A, 31A (1989) 1994 L E Bromberg, Composite membranes based on polyelectrolyte complexes, J Membrane Scl ,62 (1991) 131 L I Boguslavsky, Bloelectncal Phenomena and Interphase Surface (m Russian), Nauka, Moscow, 1978,360 pp 0 F Schanne and E R Cerettl, Impedance Measurements m Bloloecal Cells, Wiley, New York, NY, 1978, p 359 R de Levee, N G Seudah and H Morelra, Transport of ions of one kmd through thm membranes IV Admittance for membrane-soluble ions, J Membr Blol ,16 (1974) 17 R de Levee and D Vukadm, Dlplcrylamme transport across an ultrathm phosphatldylethanolamme membrane, J Electroanal Chem Interfacial Electrochem ,62 (1975) 95 D E Mathls, F S Stover and R P Buck, Ion transport m free and supported mtrobenzene Ahquat nitrate hquld membrane ion-selectlve electrodes II Interfaclal kinetics and tlmedependent phenomena, J Membrane Scl ,4 (1979) 395 B M Grafov and E A Ukshe, Alternating Current Electrochemical Clrcults (m Russian), Nauka, Moscow, 1973,120 pp F Helffench, Ion Exchange, McGraw-Hti, New York, NY, 1962,624 pp A R Rudman, N A Vengerova, R I Kalyuzhnaya, B S Eltsefon and A B Zezm, A study of low-molecular metabohtes permeablhty through membranes on the base of polyelectrolyte complexes, Khlm Farm Zh ,13 (1979) 82