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Solid State Ionics 160 (2003) 301–307

Effect of donor number of solvent on the conductivity behaviour

of nonaqueous proton-conducting polymer gel electrolytes

S.S. Sekhon*, Narinder Arora, Harinder Pal Singh

Department of Applied Physics, Guru Nanak Dev University, Amritsar 143005, India

Received 8 November 2002; received in revised form 28 February 2003; accepted 15 April 2003

Abstract

The effect of donor number of solvent on the conductivity behaviour of gel electrolytes has been studied. Liquid electrolytes

were prepared by dissolving salicylic acid in solvents based on ethylene carbonate (EC), propylene carbonate (PC) and

dimethylformamide (DMF) with different donor number and dielectric constant values. Three different polymers,

polymethylmethacrylate (PMMA), polyacrylonitrile (PAN) and polyethylene oxide (PEO), were used as the gelling polymer.

The conductivity of polymer gel electrolytes has been found to be higher than the corresponding liquid electrolytes, i.e. r(gel)>r (liquid). This has been explained to be due to an increase in carrier concentration by the dissociation of undissociated

salicylic acid/ion aggregates present in the electrolytes with the addition of polymer. However, the relative increase in

conductivity observed with the addition of different gelling polymers has been found to depend upon the donor number of the

solvent used.

D 2003 Elsevier Science B.V. All rights reserved.

Keywords: Polymer gel electrolytes; Donor number; Undissociated acid; Proton conductors; Carrier concentration

1. Introduction gels whereas the polymer provides the mechanical

Nonaqueous polymer gel electrolytes belonging to

the salt–solvent–polymer hybrid system are prepared

by immobilizing the salt solution in a suitable polymer

matrix [1–3]. These electrolytes are promising ion-

conducting materials due to their high value of con-

ductivity that is comparable to that of liquid electro-

lytes [4–10]. The high conductivity of these polymer

gel electrolytes is due to the fact that the liquid phase

still provides the channels for ion conduction in the

0167-2738/03/$ - see front matter D 2003 Elsevier Science B.V. All right

doi:10.1016/S0167-2738(03)00167-X

* Corresponding author. Tel.: +91-183-2711098; fax: +91-183-

2258820.

E-mail address: sekhon@angelfire.com (S.S. Sekhon).

support and mainly acts as a stiffener [11]. The

addition of polymer to liquid electrolytes generally

results in an increase in viscosity of the gel electro-

lytes. The viscosity of gel electrolytes can be con-

trolled by the amount and nature of the polymer used

and gels in the bulk as well as in the free standing film

form can be obtained. However, distinction must be

made between macroscopic and microscopic or local

viscosity. The experimentally measured viscosity is

macroscopic whereas it is the local viscosity, which is

related to ionic mobility and therefore affects the ion

transport. As viscosity (g) is inversely proportional to

mobility (l) by the relation l = e/6prg, so an increase

in viscosity shall result in lower mobility [12,13]. The

conductivity (r) is generally given by r = nql, where

s reserved.

S.S. Sekhon et al. / Solid State Ionics 160 (2003) 301–307302

n is the charge carrier concentration, q is the charge on

the mobile species and l is the mobility of ions. Thus

conductivity depends upon two factors—carrier con-

centration and mobility. An increase in viscosity of

the gel electrolytes with polymer addition shall result

in a decrease in mobility and, hence, conductivity

shall also decrease whereas an increase in carrier

concentration shall result in an increase in conductiv-

ity.

The conductivity of charge carriers (n) present in

an electrolyte generally depends upon the concentra-

tion of salt containing the mobile species as well as on

the extent up to which the salt is dissociated. If the salt

is completely dissociated, then nearly all ions shall be

available for conduction, but if the salt is not com-

pletely dissociated, then it will result in a decrease in

carrier concentration which shall lower conductivity.

Similarly, the presence of a large concentration of

charge carriers may also lead to ion association

resulting in the formation of ion aggregates which

do not take part in the conduction process and as a

result carrier concentration (n) and, hence, conductiv-

ity decreases.

In the case of nonaqueous polymer gel electrolytes,

the dissociation of salt shall depend upon the follow-

ing parameters:

(i) dissociation constant of the salt

(ii) donor number of the solvent

(iii) dielectric constant of the solvent and

(iv) nature of the salt.

In lithium ion-conducting polymer gel electro-

lytes, the addition of polymer to liquid electrolytes

has been reported to result in a decrease in conduc-

tivity, which has been explained to be due to lower

mobility due to an increase in viscosity [11–13].

However, the decrease in conductivity with polymer

addition is small and is by a factor only not by an

order, which suggests that the polymer does not take

active part in the conduction process and mainly acts

as a stiffener. However, in the case of proton-con-

ducting polymer gel electrolytes containing weak

carboxylic acids, the addition of polymer has been

reported to result in an increase in conductivity

which has been explained to be due to the role of

polymer in increasing the carrier concentration (n) by

dissociating the undissociated acid and ion aggre-

gates [14,15]. The donor number (DN) and dielectric

constant (e) of the solvent also play important roles

in determining the solvating ability of the solvent and

polymer [16]. Polymer gel electrolytes are being

increasingly used in solid state batteries [17,18],

supercapacitors [19], electrochromic devices [20]

and fuel cells [21], etc. Proton-conducting polymer

gel electrolytes with high conductivity can also find

potential use as proton-conducting membranes in

polymer electrolyte membrane fuel cells. The moti-

vation for the present study was to investigate the

effect of different physical properties (donor number,

dielectric constant, viscosity, etc.) on the conductivity

behaviour of polymer gel electrolytes so that gels

containing different polymers with optimum conduc-

tivity could be synthesized.

The present study has been undertaken to study the

role of donor number of the solvent on the conduc-

tivity behaviour of polymer gel electrolytes. In this

study, salicylic acid—which is a weak carboxylic acid

with dissociation constant 1.05� 10� 3 in aqueous

solution—has been used in the preparation of gel

electrolytes. Ethylene carbonate (EC), propylene car-

bonate (PC), dimethylformamide (DMF) and their

binary/ternary solvent mixtures with different values

of donor number and dielectric constant have been

used as solvents. Polyethylene oxide (PEO), polya-

crylonitrile (PAN) and polymethylmethacrylate

(PMMA) have been used as the gelling polymers.

The variation of conductivity of polymer gel electro-

lytes as a function of acid concentration, polymer

content and temperature has been studied. The mod-

ification of conductivity of gel electrolytes with the

addition of different polymers and its correlation with

the donor number of the solvent used has been

investigated.

2. Experimental details

Salicylic acid (Lancaster), EC, PC and DMF (all

Merck) and PEO (powder, average Mw 5,000,000;

Tm = 65 jC), PAN (powder, Tg = 85 jC; Tm = 317 jC)and PMMA (powder, average Mw 120,000; Tg = 114

jC) (all from Aldrich) were used as the starting

materials in the preparation of gel electrolytes. Liquid

electrolytes were prepared by dissolving salicylic acid

in different concentrations (expressed as molarity

S.S. Sekhon et al. / Solid State Ionics 160 (2003) 301–307 303

values) in different single/binary/ternary solvent mix-

tures. Gel electrolytes were prepared by adding poly-

mers in different concentrations (expressed as wt.% of

liquid electrolyte) to the liquid electrolytes along with

continuous stirring. The conductivity of liquid and gel

electrolytes was measured by using WTW LF 330

conductivity meter and HP4284A precision LCR

meter operating in the 20 Hz–1 MHz frequency range

as described earlier [8].

3. Results and discussion

Fig. 1 shows the variation of conductivity of

liquid electrolytes prepared by dissolving salicylic

acid in dimethylformamide as a function of acid

concentration. The conductivity increases with an

increase in acid concentration at low molarity values,

reaches a maximum and then reaches saturation and

even shows a small decrease at higher concentrations

of acid. The initial increase in conductivity is

explained to be due to the availability of mobile

ions provided by the acid whereas the small decrease

in conductivity at higher concentrations of acid is

due to the formation of ion aggregates, which do not

take part in conduction. Some undissociated acid

shall also be present in these electrolytes due to

lower value of the dissociation constant of the acid

used. The presence of ion aggregates at higher acid

concentrations can also be checked by mass action

Fig. 1. Variation of conductivity of liquid electrolytes (DMF+

salicylic acid) as a function of acid concentration.

considerations [22], according to which, the salt MX

dissociates as follows:

MXVMþ þ X�

with equilibrium constant K=[M+][X�]/[MX].

If we replace activities by concentrations and

consider that for weak dissociation ciM+, then

K ¼ ðc� cÞ=ðC � cÞ ¼ c2=C � cic2=C

u c ¼ MKC

If the acid is strongly dissociated, then ciC and a

plot of log r vs. log C should be a straight line. Any

deviation from straight-line behaviour shall indicate

ion association.

Fig. 2 shows the variation of log r vs. log C for

electrolytes containing salicylic acid in DMF. It has

been observed from Fig. 2 that the plot between log rvs. log C shows straight-line behaviour at low acid

concentrations whereas it shows deviation from

straight-line behaviour at higher acid concentra-

tions—which suggests the formation/presence of ion

aggregates at higher acid concentrations.

PEO- and PAN-based gel electrolytes were prepared

by adding polymers in different concentrations to the 1

M solution of salicylic acid in DMF, which is a solvent

with high donor number. The variation of conductivity

of gel electrolytes as a function of polymer concen-

tration (expressed as wt.% of liquid electrolyte) is given

in Fig. 3. The conductivity of liquid electrolytes has

been observed to increase with the addition of polymer

in PEO- and PAN-based gel electrolytes and r (gel)>r(liquid) at all concentrations of polymers. The increase

in conductivity with polymer addition is higher with

PEO than with PAN, and in the case of PEO-based gel

electrolytes, the conductivity of liquid electrolytes

(f 10� 5 S/cm) increases by two orders of magnitude

to f 10� 3 S/cm with the addition of PAN. This large

increase in conductivity with polymer addition could

be explained as follows.

The conductivity (r) generally depends upon

carrier concentration (n) and mobility (l) of charge

carriers. The change in conductivity could also be

explained in terms of n and l. The addition of

polymer increases the viscosity of gel electrolytes,

which shall lower mobility and, as a result, conduc-

Fig. 2. Plot of log r vs. log C for (DMF+ salicylic acid) liquid

electrolytes.

Fig. 3. Variation of conductivity of gel electrolytes containing 1 M

salicylic acid in DMF as a function of PAN (5) and PEO (E)

concentrations.

S.S. Sekhon et al. / Solid State Ionics 160 (2003) 301–307304

tivity shall decrease. Increase in conductivity with

polymer addition can be explained only if n shows

an increase with polymer addition and, secondly, the

magnitude of increase in n is more than the decrease

in l with polymer addition. How does n increases

with polymer addition? Salicylic acid used in the

present study is a weak carboxylic acid with disso-

ciation constant 1.05� 10� 3 which is less than 1. As

a result, this acid shall not be fully dissociated in the

electrolyte. In addition to undissociated acid, some

ion aggregates may also be present at higher acid

concentrations as discussed in Figs. 1 and 2. The

addition of polymer thus helps in the dissociation of

undissociated acid as well as in the dissociation of

ion aggregates which shall result in an increase in

the number of free charge carriers n and, hence,

conductivity increases. The increase in conductivity

of liquid electrolytes with the addition of polymer,

i.e. r (gel)>r (liquid), has also been reported for

polymer gel electrolytes containing various carbox-

ylic and dicarboxylic acids and with different gelling

polymers [7,9,10,15]. Thus the role of polymer in

these gel electrolytes is not passive but helps in the

dissociation of undissociated acid and ion aggre-

gates.

The increase in conductivity of liquid electrolytes

containing different aromatic carboxylic acids and

aliphatic dicarboxylic acids has been explained on

the basis of Breathing Polymeric Chain Model [15],

according to which the polymer gel electrolyte is

supposed to consist of free ions, ion aggregates,

undissociated acid and polymer chains dispersed in

the gel. The polymer is supposed to breathe in and out

by folding and unfolding (fully/partially) up of its

loops/chains. This leads to density or pressure fluctu-

ations at the microscopic level which assists in the

motion of ions as well in the dissociation of ion

aggregates/undissociated acid leading to an effect

which increases conductivity. Similar studies have

also been reported on other polymer gel electrolytes

where the polymer effects the dissociation degree of

salt in gel electrolytes [5,16,23,24]. If the addition of

polymer enhances the dissociation of acid, then the

number of H+ ions should increase and this should

change the pH of the electrolyte. Preliminary results

on the measurement of pH in a representative case

shows that pH of DMF is 12.0 and when 1 M solution

of salicylic acid is prepared in DMF, the pH changes

to 3.60, which shows the acidic nature of the electro-

lyte or the presence of free H+ ions in the electrolyte.

When PMMA is added to the above liquid electrolyte,

its pH has been observed to decrease to 3.22, which

indicates an increase in acidity or an increase in the

concentrations of free H+ ions. This is in agreement

with the above argument that the polymer enhances

the dissociation of undissociated acid and ion aggre-

gates resulting in an increase in concentration of free

Fig. 4. Variation of conductivity of gel electrolytes containing 1 M

salicylic acid in EC/PC as a function of PAN (E) and PEO (5)

concentrations.

Table 1

Physical properties of the solvents used

Solvent Dielectric

constant,

e (at 25 jC)

Donor

number

(DN)

Single Ethylene

carbonate (EC)

89.1a 16.4

Propylene

carbonate (PC)

64.9 15.1

Dimethylformamide

(DMF)

36.1 26.6

Binary EC/PC

(in equal volume ratio)

77b 15.75b

Ternary EC/PC/DMF

(in equal volume ratio)

63.36b 19.36b

a At 40 jC.b Estimated values (approximates) only.

S.S. Sekhon et al. / Solid State Ionics 160 (2003) 301–307 305

ions. However, further detailed studies on the varia-

tion of pH with acid and polymer concentration shall

be undertaken.

The physical properties of the solvent used, namely

donor number and dielectric constant, shall also affect

the dissociation of acid in these electrolytes. DMF

used as a solvent in the synthesis of PAN- and PEO-

based polymer gel electrolytes has higher donor

number (26.6). The effect of the donor number of

the solvent on the conductivity behaviour of polymer

gel electrolytes was studied by using a binary solvent

mixture of EC and PC taken in equal volume ratio

with donor number (15.75) lower than that of DMF

but having higher dielectric constant value than DMF.

The variation of conductivity of polymer gel electro-

lytes containing 1 M salicylic acid in the binary

solvent mixture of EC and PC was studied as a

function of polymer (PAN, PEO) concentration and

the results are given in Fig. 4. Except for the solvent,

all other constituents of polymer gel electrolytes are

the same. The results of Fig. 4 also shows that the

conductivity of liquid electrolytes increases with the

addition of PEO and PAN and r (gel)>r (liquid) at all

polymer concentrations. The increase in conductivity

observed with polymer addition is small as compared

with the results of Fig. 3, and the increase in con-

ductivity is by a factor only not by an order. Secondly,

the increase in conductivity with PEO addition is

more than with PAN addition and r (PEO)>r

(PAN), which is opposite to the trend observed for

DMF-based polymer gel electrolytes, i.e. r (PAN)>r(PEO).

Thus the conductivity of polymer gel electrolytes is

closely related to the donor number of the solvent

used. The relative increase in conductivity with the

addition of different polymers has also been found to

depend upon the donor number of the solvent used.

The addition of same amount of PAN to gel electro-

lytes containing high donor number solvent (DMF)

results in an increase in conductivity by nearly two

orders of magnitude, whereas in gel electrolytes con-

taining low donor number solvent (EC/PC), the

increase in conductivity is small and is by a factor

only. Thus the donor number of the solvent plays an

important role in the solvation of acid by the addition

of polymer.

The effect of the donor number of the solvent used

on the conductivity behaviour of polymer gel electro-

lytes was further highlighted by using three solvents,

namely DMF, EC/PC and EC/PC/DMF (in equal

volume ratio) having different donor numbers and

dielectric constants as given in Table 1. PEO was

used as the gelling polymer in each case and gel

electrolytes were prepared by adding PEO to the 1 M

solution of salicylic acid in solvents with different

donor numbers. The variation of conductivity as a

function of PEO concentration is given in Fig. 5. The

conductivity of liquid electrolytes increases with the

addition of PEO in all the three cases but the increase

Fig. 5. Variation of conductivity with PEO concentration for gel

electrolytes containing 1 M salicylic acid in DMF (5), EC/PC (o)

and EC/PC/DMF (E). Fig. 6. Dependence of conductivity on PAN concentration for gel

electrolytes containing 1 M salicylic acid in DMF (5) and EC/PC

(E).

S.S. Sekhon et al. / Solid State Ionics 160 (2003) 301–307306

is higher in DMF than with EC/PC/DMF and EC/PC

containing gel electrolytes and this trend closely

follows the donor number variation of the solvents

used, i.e.

rðDMFÞ > rðEC=PC=DMFÞ > rðEC=PCÞ

Similar studies were also carried out by using PAN

and PMMA as the gelling polymers. Different

amounts of PAN and PMMA were added to the 1 M

solution of salicylic acid in DMF, EC/PC/DMF and

EC/PC. The variation of conductivity with polymer

concentration is given in Fig. 6 for PAN-based gel

electrolytes and in Fig. 7 for PMMA-based gel elec-

trolytes. In each case, the conductivity variation with

polymer addition follows the donor number variation

of the solvent. The increase in conductivity with

different polymers (PEO, PAN, PMMA) has been

found to be higher for solvents with high donor

number. The results of Figs. 5–7 can be summarised

as follows:

r : DMF > EC=PC=DMF > EC=PC

DN : 26:6 > 19:36 > 15:75

e : 36:1 < 63:36 < 77

These results suggest that for gel electrolytes with

PEO, PAN and PMMA as the gelling polymer, the

conductivity closely follows the donor number varia-

tion of the solvents used and not the dielectric con-

stant. Solvents with high donor number have been

found to have better solvating ability.

Fig. 7. Dependence of conductivity on PMMA concentration for gel

electrolytes containing 1 M salicylic acid in DMF (5), EC/PC (o)

and EC/PC/DMF (E).

S.S. Sekhon et al. / Solid State Ionics 160 (2003) 301–307 307

4. Conclusions

Proton-conducting polymer gel electrolytes con-

taining different solvents and polymers have been

synthesized and room temperature conductivity of

2� 10� 3 S/cm has been obtained for PAN-based gel

electrolytes. The addition of polymer to liquid electro-

lytes has been found to result in an increase in

conductivity, i.e. r (gel)>r (liquid). This has been

explained to be due to the role of polymer in disso-

ciation of undissociated acid/ion aggregates and is

reflected also in the changes in pH. The conductivity

of different gel electrolytes has been found to depend

upon the donor number of the solvent used and is

higher for solvents with high donor number.

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