Mechanisms of ionic transport in ionically conducting polymers

Summary

• 2. Mechanisms of ionic transport in ionically conducting polymers

• 2.1. Interaction between polymer and salt• 2.1.1.Ion solvatation by the polymer• 2.1.2.Hard - soft acid -base principle• 2.1.3.Anions• 2.1.4.Complex formation• 2.2. Transport theory and models• 2.2.1.Arrhenius model• 2.2.2.VTF and WLF models

Liquid-solid electrolytes diferences

• The essential feature that distinguishes a polymer electrolyte from low-molecular weight solvent-based systems is that net ionic motion in polymer electrolytes takes place without long-range displacement of the solvent.

• Gel electrolytes (i.e. polymers containing a low-molecular-weight fraction) and polyelectrolytes again rely on an incorporated low-molecular-weight solvent medium to assist ionic transport.

• In a polymer electrolytes no low-molecular-weight solvent is present and ion transport relies on local relaxation process in the polymer chain which may provide liquidlike degrees of freedom, giving the polymer properties similar to those of molecular liquid.

• The macroscopic properties that are similar to those of a solid are the result of chain entanglements and possibly crosslink.

• Ion transport in polymer electrolytes is considered to take place by a combination of ion motion coupled to the local motion of polymer segments and inter- and intrapolymer transition between ion coordinating sites

Intra polymer180º bond rotation at C-O bond A-B

Inter

Fiona M. Gray “Solid Polymer Electrolytes, Fundamentals and technological applications”VCH Publishers, 1991.

Interaction between polymer and saltIon solvatation by the polymer

• Salt dissolve in a solvent only if the associated energy and entropy changes produce an overall reduction in free energy of the system

• In polymer exist polar groups and it can be expected that polymers behave as solvents and dissolve salts to form stable ion-polymer complexes

• It is possible when the interaction between the ionic species and the coordinating groups on the polymer chain compensate for the loss of salt lattice energy

• Polymers are macromolecules

– Deformation of the polymer structure and destruction of lattice structure – gain of entropy

– Localized ordering of the polymer host by the anions – decrease of entropy

– The distance of the apart of the coordinating groups and the polymer´s ability to adopt conformations that allow multiple inter- and intramolecular coordination are important

• No polymer electrolytes: poly(methylen oxide) [(CH2O)n] nor poly(trimethylene oxide) [(CH2CH2CH2O)n]

– Rigidity of the chain– Inability to adopt low-energy conformations to maximize

polymer-cation coordination– PPO – difficult due to the steric hindrance of the CH3 groups

Solubility of salts in PEO

Hard - soft acid - base principle• Principle suggested by Pearson as a means of accounting for and

predicting the stability of complexes formed between Lewis acids and bases

– Small acid and bases (termed HARD) are• highly electronegative,• of low polarizability • Hard to oxidize• They tend to hold their electrons tightly

– SOFT acid or bases are• Low electronegativity• Tend to be large• Highly polarizable• Easy to oxidize• They hold their valance electronce loosely

• Preference for complexes between hard acids and bases or soft acid and bases• PEO can be considered as a hard base

R.G. Pearson J.Am.Chem.Soc. 85 (1963) 3533R.G. Pearson J.Chem.Ed. 45 (1968) 581, 643

Classification of hard and soft acids and bases

PEO complexes

• The data suggest that Mg2+ (hard) would be expected to form very stable complexes with PEO, whereas Hg2+ (soft) would show only a weak interaction

• Complexes with both cations are readily formed transference number measurements showed that:– Mg2+ ions are immobile

– Hg2+ ions are mobile in PEO

• Relationship between complex formation and the consequential effects on cation mobility

Anions

• In polar solvents as water or methanol, hydrogen bonding is important for specific anion solvatation, whereas aprotic liquids (no hydrogen bonding) and solvating polymers have negligible anion stabilization energies

• Differences in the general solvatation energies of anions do occur as the dielectric constant of the solvents varies.

• On passing from a polar, protic medium trough to a less polar one, most anions are destabilized, the destabilization being greatest when the charge density and basicity of the ions are low:

F->>Cl->Br->I- ~SCN->ClO4- ~CF3SO3

->BF4- ~AsF6

-

Most suitable choices of anions for aproticLow-dielectric-constant dipolar polymer-based SPE

Anions

• Large anions

• With delocalized charge

• Weak bases

• Posses low ion-dipol stabilization energies

• Have low lattice energies i.e. little tendency to form tight ion pairs (I- or ClO4

-)

Anions

• Formation of polymer electrolytes is controlled by the cation solvatation energy in opposition to the salt lattice energy

• i.e. strongly solvated ions such a Li+ can be complexated by PEO, even when the counter ion is relatively small, like Cl- and there is associated high energy lattice.

• The larger I- anion is required for the heavier, less solvated K+ ion

Complex formation

• In the case of PE (polymer electrolytes) complexes are formed when the polymer host interact with the salt to form a new polymeric system

• At high enough temperatures or in systems where crystallization is prevented, the ions are solvated by the polymer to form a homogeneous polymer-salt solution

Complex salt-PEO

• With high-molecular-weight linear PEO the system crystallizes to form spherulites of well defined stoichiometries

• These “crystalline complexes” are often recognized by their melting points which can be well in excess of 100oC

• The amorphous regions within the spherulites of complexes material can be of a very different stoichiometry and it is somewhat inappropriate to refer to the entire system as a “complex”

Modes of solvatation of the Li+ by oxygen atoms from PEO

P.G.Bruce et al. Solid State Ionics 78 (1995) 191

Li+ coordenation

and CF3SO3

-

groups

P.G.Bruce et al. Solid State Ionics 78 (1995) 191

Anions and conductivityIt is generally accepted that anions are mobile and in some systems net cation mobility is vanishingly small (disappear)

Anions assist in cation transport

- by formation of ion pairs

- triple ions

- higher aggregates

With the assistance of polymeric chain segmental motion, the ionic cluster may itself move or it may act as transient center for the mobile species.

Aggregates formation

For higher salt concentration Ion pairs and aggregates can be formed

These species are less mobile and can promote a crosslink

a) via cation

b) via triple ion

Host polymer

To act as a successful polymer host, a polymer or the active part of a copolymer should generally have a minimum of three essential characteristics:

1) Atoms or groups of atoms with sufficient electron donor power to form coordination bonds with cations

2) Low barriers to bond rotation so that segmental motion of the polymer chain can take place readily

3) A suitable distance between coordinating centers because the formation of multiple intrapolymer ion bonds appear to be important

Polyethers• polyethers [-(CH2)nO-]

• Differences in physical properties

Differences are due to the molecular conformation and crystalline structure (not chemical)

Polyoxymethylene

and PEO

PEO crystalline structure is more open than PMO

Glass transition temp.For high Mw, Tgs are of -65 to -60oC

PEO

• Among many polymers studied no one seems

to be so good as PEO – more studied up to

now as host polymer

• Large variety of salts can be dissolved in

PEO, but more interesting are with small

atoms of Li or Na, which give SPEs for

industrial application

• Two aspects in particular govern the magnitude of the conductivity

– The degree of crystallinity– The salt concentration– Nature of salt and polymer also are important

• Interpretation of electrical conductivity difficult – more of systems studied comprise more than one phase

• Hysteresis in the conductivity is very common on thermal cycling because of slow crystallization kinetics – phase changes

• Transformations requiring the redistribution of salt between phases

• As the temperature is raised the crystalline phase progressively dissolves in the amorpouse phase, thus increasing in the concentration of charge carries

• Simultaneously the polymer dynamics are affected by the reduction in the amounth of crystalline material and

• an increase in the transient crosslink density due to the increase in the salt concentration in the conducting amorphous phase

Influence of salt concentration

• Ionic mobility is closely correlated to the relaxation modes of the polymer host

– This can be observed through the increase in the Tg of polymeric systems as salt concentration is increased

Due to the intermolecular and Due to the intermolecular and intramolecular interractions - crosslinkintramolecular interractions - crosslink

CrosslinkReduction of conductivity

for high salt concentration

• Stiffening of the polymeric matrix

• Reduced availability of coordenating sites

• Strong ion-ion interractions in the system of low permitivity (PEO) – cooperative migration of several ions

iiii μqn σ(T)

Low salt concentration

• The mobility of ions is relatively unaffected by concentration

• Transient crosslink density is low and therefore the conductivity will be controlled by the number of charge carries

• As the charge carries increase, ion pairs and mobile higher aggregates are predicted to form

• May form higher and less mobile clusters• May also act as transient crosslink species

Conductivity

Where:

ni – number of charge carriers (i)

qi - charge of each one

i - mobility

i

iii μqn σ(T)

Conductivity – impedance measurements

Z"

Z'

Z

(S/cm)AZ

lσ

'

Z’- real part and Z” – imaginary part

High frequencyLow frequency

Mass transport

Conductivity model

Cation moving via intra-polymer coordenation

Cation moving via inter-polymer coordenation

Measurements data

Typical impedance diagrams

for homogene

ous PPO-LiClO4

A.C. response

e2e1e C

1

C

1

C

1

l

AεεC 0

b

for A=1cm2 and l=1cm Cb is a dielectric constant value of polymer Generally of 5-20(o permittivity of vacuum

8,85*10-14 F/cm)

Ionic conductivity models Arrhenius

Arrhenius

Ea- activation energy - linear fitting for semi-cristaline and amorphous systems

/kT)exp(-Eσσ a0

Log = log + (-Ea / 2,303 RT)

R – ideal gas constant =8,31441 Jmol-1K-1

Vogel-Tamman-Fulcher (VTF)

Vogel-Tamman-Fulcher (VTF)

For the amorphous systems

)]TB/k(Texp[σ 00

Where B- constant, 0 - constant of T-1/2 andT0 temperature at which configurational entropy is zero (generally close to Tg) -Correlation within conductivity and visco-elastic properties of SPE.

Free volume• A small amount of unfilled volume is associated with the end of a polymer

chain. This volume is called the free volume and is schematically

represented in the diagram below.

• For a given mass of polymer the amount of free volume will depend on the number of chain ends, hence the number of chains and hence the degree of polymerisation.

Williams – Landel - Ferry (WLF)

Equivalent to VLF

viscoelastic properties also relaxation process (aT-deslocation factor)

02

01

TTC

)T(TC

010σσC1 and C2 temperature dependent constants and To – WLF temperature reference

)(

)(log

02

01T TTC

TTCa

g

gT 51,6

)17,44(log

TT

TTa

VTF and Arrhenius

Condutivity as a function of salt concentration