POLYMER ELECTROLYTE

Polymer electrolytes are the newest area of solid ionics for applications in electrochemical device such as batteries and electrochromic windows. Electrochromic windows are windows that can be darkened or lightened electronically. A small voltage applied to the windows will cause them to darken; reversing the voltage causes them to lighten. 

Two general types of polymer electrolytes have been investigated intensively:

1. Polymer salt-complexes

2. Polyelectrolytes

A polymer-salt complex consist of a coordinating polymer in which salt is dissolved. Both anion and cation can be mobile in this type. 

Figure 1. a polymer electrolyte containing a salt MX

Polyelectrolytes contain of charged groups, either cations or anions, covalently attached to the polymer, so only the

counter ion is mobile.

Figure 2. polyelectrolyte in which the anion is attached to the polymer

Polymer Salt Complexes

Poly(ethylene oxide) (PEO) has been the most intensively studied host polymer for polymer electrolytes. 

Figure 3. The structure of crystalline poly(ethylene oxide) showing the contents of one salt

The conductivity collected over the wide temperature range on amorphous polymer-salt complexes is more

accurately represented by a Vogel-Tamman-Fulcher (VTF) equation than a simple Arrhenius function as described

in equation (1).

       (1)

VTF equation can be derived on the assumption that the ions are transported by the semirandom motion of a 

short polymer segments. 

The polymer motions are:

- Crank-shaft torsional motion around C-C or C-O bonds

- C-C and C-H stretching vibrations

- The segmental motion could promote ION MOTION by making and breaking  the coordination sphere of the solvated ions and by providing space (free volume)  into which the ion may diffuse under the influence of the electrical field.

Figure 4. Scheme of ion motions in a polymer electrolyte

FORMATION OF POLYMER ELECTROLYTE

Salt crystal may be directly diffused in a polymer to produce a polymer-salt complex. Usually prepared in 

nonaqueous solutions of dried polymer and dry salt in a dry nitrogen atmospheres.

Analysis:

- XRD and Electron microscope

Structure:

The structures of crystalline polymer-salt complexes provide insight into the structure of the more conducting

amorphous materials.

Figure 5. The crystal structure of (PEO)3:NaI complex

There are some host polymers usually applied in polymer electrolyte, those are:

1. Poly propylene oxide, the structure is described in Figure 6.

Figure 6. Molecular structure of poly(propylene oxide)

2. Methoxy linked Poly(ethylene oxide). The structures is figured in Figure 7.

Figure 7. The molecular structure of Methoxy linked poly(ethylene oxide)

You may find the ppt file in this link

These are the supporting files:
file 1
file 2

GLASSY ELECTROLYTE_2

Ionic transport in glass transition region can be determined by equation (1):

   (1)

The electrical conductivity of an ionic liquid is inversely proportional to the shear viscosity of the liquid as described by equation (2)

  (2)

Swenson and Bojesson studied the correlation between volume expansion of the network and the ionic conductivity of the glass. The correlation is best fitted by equation (3).

(3)


Vd is volume of the doped glass, Vm is volume of the undoped glass. Thus, Vd-Vm is excess volume introduce by the dopant salt. 
The ionic transport in inorganic glasses have been often described with the classical defect transport theory for ionic crystals. As an example, the number of mobile interstitial ions for Frenkel defect is expressed by equation (4).

(4)



N is the number of stable or normal sites, N' is the number of interstitial sites, Gf is the Gibbs free energy of Frenkel defect formation, 

find the presentation file in here

GLASSY ELECTROLYTE_1

DEFINITION
Glass is a rigid disorder network of liquid phase which is cooled to below freezing temperature. The liquid becomes a disorder network due to the complex molecular configuration or slow molecular transport. Therefor, Glass is an amorphous (non crystalline) solid material, which is typically brittle and optically transparent. Figure 1 shows the images of natural glass and the oldest glass made by mouth blown.

Figure 1. Images of Meldavite and the oldest mouth blown window glass (Source: wikipedia)

The structural rearrangement of most metal and molten salt can occur relatively easily due to these materials have high fluidity at  temperature above the freezing temperature. Meanwhile, many inorganis silicates have very low fluidity at above freezing temperature, therefor these inorganic silicates form glasses upon cooling process. This glass formation is related to the high silicon-oxygen single bond energies and the directional bonding requirements imposed by sp3 hybridization of silicon, as shown by Figure 2. During glass formation, the volume may change associated with heating and cooling. The curve of volume change is described in Figure 3.

Figure 2. sp3 hybridization of silica network

Figure 3. Volume change curve as the function of temperature

The glass transition, Tg, is the temperature at which a supercooled liquid becomes a glass.
The production process of glasses is listed below:
1. The melting of quartz sand, quartz sand is the main raw material of glass, as it described in Figure 4.
2. The shaping of glass while in viscous state
3. the control cooling of the shaped article

Figure 4. The quartz sand, the main raw material of glass (source: wikipedia)

There are three basic constituents present in ionically conducting glasses, e.g:

1. network former

2. network modifier

3. ionic salts

Network formers are compounds of a covalent nature such as SiO2, P2O5, GeS2 etc. They form macromolecular chains which are strongly cross-linked by an assembly consisting of tetrahedra (SiO4, PO4, BO4...) or triangle (BO3)which combine to form macro molecular chains by sharing corners or edges (Bruce, 1995).

Network modifiers include oxides or sulphides (e.g. Ag2O, Li2O, Ag2S, etc) which interact strongly with the structure of network formers. A chemical reaction leading to the breaking of the oxygen or sulphur bridge linking two network former cations with reaction as listed in equation (1) and (2)

          (1)

    (2)(Kawamura et al., 2006)


The scheme of primary network formers and network modifier are described in Figure 5.

Figure 5. Scheme of primary network former and network modifier

The mixing of network formers and modifiers often result in the enhancement of ionic conductivity and is called as mixed anion effect or mixed former effect. “It is mainly due to the change in the binding energy between the oxide and mobile cations caused by the network structure modifications”

Other example of network modifier reaction is listed in equation (3)

  (3)


see my publications in these links:
paper 1
paper 2
paper 3
paper 4 (it is free now)
book 1

DEFECT REACTION

The defect formation may occur internally in solids during synthesis or through reaction with external species added into the solid.
In order to understand the defect formation process we need to write the defect reactions. A solid containing defect can be analoged to a liquid solution in which the solid is considered as solvent and the defects as the solutes.
Here is the rules for writing defect reaction:
1. Mass balance
    The defect reaction must balance with respect to the mass, i.e the number of and types of atoms involved in the defect reaction must be the same before and after the defect formation. Vacancies have zero mass
2. Electroneutrality
    the compounds are and should remain electrically neutral
3. Ratios of regular lattice site
    The ratio(s) of the number of regular cation and anion lattice sites in a crystalline compound is constant

Kroger-Vink notation is convenient for describing a defect and the effective electrical charge relative to the surrounding lattice (Moulson and Herbert, 2003). These are the Kroger-Vink notation concepts:
1. a defect that carries an effective single positive charge bears a superscript dot (.)
2. a defect that carries an effective negative charge bears a superscript prime (')
3. neutral defect have no superscript
If an atom or ion A occupying  a site normally occupied by an atom or ion B is written AB. Meanwhile the interstitial ion is denoted as AI.
examples:
VO --> VO. + e'
VO. --> VO.. + e'
VM --> VM. + h*



READ MY PUBLICATIONS ON:
-http://www.springerlink.com/content/306457515121276g/
-http://www.amazon.com/s/ref=ntt_athr_dp_sr_1?_encoding=UTF8&sort=relevancerank&search-alias=books&ie=UTF8&field-author=Fitria%20Rahmawati
-http://link.springer.com/article/10.2478%2Fs11696-010-0036-4?LI=true
-http://www.tandfonline.com/doi/full/10.1080/02772248.2011.604322
-http://proceedings.itb.ac.id/index.php?li=article_detail&id=468

IMPERFECTION OF SOLID & ATOM MOVEMENT

You may find the discussion about this topic in:

https://docs.google.com/file/d/0B3OOiHwWphGWcHdfLVdJTVN0Z1E/edit

Below (in Figure 1)  you can watch the mechanism of vacancies formation

Figure 1. The mechanism of vacancies formation due to doping of higher oxidation state ions into the crystallite structure. It can be seen in here that an Ag+ ion must be released then produce a vacancy in order to keep the nett charge of crystal in neutral

There are 3 mechanisms of ionic migration, i.e :
1. vacancy mechanism ( mekanisme kekosongan)
2. interstitial mechanism (mekanisme selitan)
3. the combination of vacancy and interstitial mechanism (mekanisme kekosongan dan selitan)

for better understanding on that mechanisms, please watch the animations below (Figure 2, Figure 3 and Figure 4).

Figure 2. The interstitial and vacancy mechanisms

Figure 3. The vacancy mechanism

Figure 4. The interstitial mechanism

*This blog was written by Fitria Rahmawati for Kuliah Elektrokimia Fasa Padatan
Fitria Rahmawati
Research Group of Solid State & Catalysis
Chemistry Department
Sebelas Maret University
Jl. Ir. Sutami 36 A Kentingan Surakarta 57126

BORN-HABER CYCLE

The Born-Haber cycle is an approach to analyzing reaction energies. It was developed by Max Born and Fritz Haber. This cycle is used as a means of calculating lattice energies which cannot be measured directly. The Born-Haber cycle applies Hess's Law to calculate the lattice enthalpy by comparing the standart enthalpy change of formation of the ionic compound (from the elements) to the enthalpy required to make gaseous ions from the elements.
For example is Formation of Metal Chloride: 

Figure 1. Hess's Law of Metal Chloride, MCl formation

From the Hess's Law the lattice enthalpy formation of MCl, (delta)Hf , can be calculated as:

LATTICE ENERGY_2

Crystal lattice contains of cations and anions. The interactions between them are much more complex than the interaction between two ions. This interaction is described in Figure 3, which describes the interactions inside the crystal lattice.

Figure 3. The crystal lattice of NaCl (expanded)
(Effendi, 2008)

interaction between Na+ ion in the centre of cubic di Figure 3. are:

1) Its interaction with 6 Cl- ions with distance of square root of 1.

2) Its interaction with 12 Na+ ions with distance of square root of 2

3) Its interaction with Cl- ions with distance of square root of 3

4) its interaction with 6 Na+ ions with distance of square root of 4.

The total interaction between ions inside a crystal lattice is stated by MADELUNG CONSTANT , A. In NaCl crystal, the Madelung constant of the first four stribes are:

The interaction between ions inside crystal lattice is called as geometric interaction. Due to this geometric interaction, the coulomb's electrostatic energy is become,

The electrostatic energy of 1 mol crystal which contains of N cations and N anions is,

N is the Avogadro's number

The repulsive force between electron clouds of the ions could be ignored only if the distance between ions is far. However, the repulsive force will become stronger as the distance is become smaller. In this state, the repulsion force between electron clouds of ions must be considered. Born stated that the repulsion energy, Erep is described by equation:

B is a constant and n is Born exponent.

The repulsion energy of 1 mol crystal which contains of N cations and N anions is:

The total energy of 1 mol crystal which contains of N cations and N anions is:

The value of Born exponent, n, is depend on ion type. Larger size of ions will have higher electron density than smaller ions. The Born exponent value will be higher as the ionic size become larger. 

When the repulsion force is equal to the attraction force, then the lattice energy is minimum. The condition at equilibrium condition might be stated as below,

at equilibrium condition, the lattice energy is stated as Uo and the distance between anion and cation as ro. Substitution of B into U produce the equation below,

This equation is called as Born-Lande equation. This equation can be used to calculate the  lattice energy of ionic crystal if the crystal structure and the distance of anion-cation have been known already. The crystal structure is required to calculate the Madelung constant, A. This crystal structure and also the distance of anion-cation are could be founded from crystallographic data (XRD data).

Kapustinski stated that for the ionic compounds of unknown structure, the lattice energy could be estimated from the equation below,

v is the number of ions inside a molecule of ionic compound and ro is the sum of cationic and anionic radius in pm unit. The ionic radius is calculated based on the coordination number.

READ MY PUBLICATIONS ON:

http://journal.itb.ac.id/index.php?li=article_detail&id=468

http://www.chempap.org/?id=7&paper=818

http://www.tandfonline.com/doi/full/10.1080/02772248.2011.604322