Chapter Iii.docx

CHAPTER III THEORETICAL INVESTIGATION 3.1 INTRODUCTION: Polyethylene Oxides based polymer electrolytes have been widely investigated for use in lithium batteries. In 2000, network polymer electrolytes containing PEO chain synthesized by a crosslinking reaction, quasi solid-state DSSC containing PEO gel network polymer electrolytes were fabricated and shown efficiency as high as 36% PEO segments is important for the ionic conductivity, and thus for the overall efficiency of solar cell will be improved. The assignment of band in the vibrational spectra of molecules are an essential step in the application of vibrational spectroscopy for solving various structural chemical problems. In the present study, the detailed vibrational spectral analysis of the PEO was performed by combining the experimental and theoretical calculation using density functional theory (DFT) with B3LYP function and 6311++G(d,p) basis set to derive information about electronic effects and intra molecular charge transfer. The calculated values of chemical hardness(ƞ),softness(S),electronegativity(x),ionization potential(IP) and electron affinity (EA), electrochemical potential(  ),electrophilicity(  ),charge transfer(  Nmax) and electron back-donator(  Eback-donator) were computed using orbital energies of the HOMO(Highest Occupied Molecular Orbital’s) and the LUMO(Lowest Unoccupied Molecular Orbitals) at the B3LYP/6311++G(d,p) level of theory.This method predicts relatively accurate molecular structures and vibrational spectra with moderate computational effort.Finally,FT-IR spectra were measured for PEO in gas phase,water and acetone.Furthermore UV-Visible study was done by TD-DFT calculation.

3.2.Computational details: The molecular geometry optimizations, energy and vibrations frequency calculations were carried out for PEO with the GAUSSIAN-09W software package using the B3LYP functional with 6311++G(d, p) basis set. The systematic comparison of the results from DFT theory with results of the experiments have shown that the method using B3LYP functional is the most promising in providing correct vibrational wave numbers.

3.3 Global Reactivity Descriptors: The global indices of reactivity have been determined from the values of the energies of HOMO and LUMO. The HOMO and LUMO energy gap (∆Eg) has wider importance in understanding the static molecular reactivity and helps in characterizing the chemical reactivity and

kinetic stability of the polymer. A polymer with a small energy gap is more polarizable and is generally correlated with a high chemical reactivity and low kinetic stability. The energy gap (Eg) estimated from HOMO-LUMO energies and reactive descriptors such as ionization potential (IP),electron affinity (EA), electron negativity

(x),hardness (ƞ),softness

(s),electrochemical potential (µ), electrophilicity index (  ) and charge transfer (∆Nmax) of five units of PEO calculated by DFT/6-311++G(d,p) basis set in gas phase and solvent phase namely water and acetone.

3.4 Ionization potential (IP) & Electron Affinity (EA): From Koopmans’s theorem, the ionization potential and electron affinity have been calculated by the subsequent equations, IP=-EHOMO

----- (1)

EA=-ELUMO

----- (2)

The ionization potential is well defined as the amount of energy required to remove an electron from the polymer. Ionization energy is a fundamental descriptor of the chemical reactivity of polymer.High ionization energy indicates high reactivity of the polymer.According to the various basis set calculations,the ionization potential moderately decreases from the monomer of Peo to pentamer of PEO.The electron affinity is the energy released when an electron is added to the polymer. There are fluctuations observed in the values of electron affinity with various basis set. As a result, the ionization potential of polymer is greater than the electron affinity of different units of polymer.

3.5 Chemical Hardness (ƞ) & Softness(S): The chemical hardness of the polymer has been principally calculated from the difference of HOMO and LUMO energy as, Ƞ= (ELUMO -EHOMO)/2

----- (3)

The softness of the polymer can be determined as follows, S=1/2ƞ

----- (4)

Absolute hardness and softness are important properties to measure the molecular stability, reactivity and resist the electron transfer. The most significant candidate chemical hardness fundamentally signifies the resistance towards the deformation or polarization of the electron cloud of the polymer under a small perturbation of chemical reaction.

3.6 Chemical Potential(µ): The chemical potential (µ) describes the escaping tendency of electrons from an equilibrium system. The greater the electronic chemical potential, the less stable or more reactive is the compound. The chemical potential of the polymer with 6-311++G(d,p) basis sets are calculated by, µ=-(ELUMO+EHOMO)/2

----- (5)

3.7 Electrophilicity (  ) & Charge transfer (∆Nmax): The electrophilicity index has been described as a structural depictor of the analysis of the chemical reactivity of molecules. It measures the tendency of the species to accept electrons. A good, more reactive, nucleophile has a lower value of (  ), in opposite a good electrophile has a high value of (

 ). The global electrophilicity index measures the stabilization in energy when the system acquires an additional electronic charge ∆N from the environment which has been given by the following expression.

 = µ2/2ƞ

--- (6)

The electrophilicity index (  ) is associated with the energy lowering for maximal electron flow. The electrophilicity index encompasses both the propensity of the electrophile to acquire an additional electronic charge driven by µ2 and the resistance of the system to exchange electronic charge with the environment described by ƞ. The maximum amount of electronic charge that an electrophile system may accept is given by the following equation. ∆Nmax=-µ/ƞ

--- (7)

The maximum charge transfer ∆Nmax in the direction of the electrophile was predicted using equation (7).Thus, while the quantity defined by equation (7) describes the tendency of the molecule to acquire an additional electronic charge from the environment, the quantity defined in equation (6) describes the charge capacity of the molecule.

3.8 Inhibition efficiency through back donation (∆Eback donation): According to Gomez et al an electronic process might be occurring governing the interaction between the inhibitor molecule and the metal surface. The concept establishes that if both processes occur, namely charge transfer to the molecule and back – donation from the molecule, the energy change is directly proportional to the hardness of the molecule, as indicated in the following expression: ∆Eback-donation= - ƞ/4

---- (8)

The ∆Eback-donation suggests that when ƞ>0 and ∆Eback-donation <0 the charge transfer to a molecule is actively favoured followed by a back – donation from the molecule.In this environment, it is possible to balance the stabilization among inhibiting molecules. The maximum charge transfer ∆Nmax is also used

to predict the inhibitor efficiency. The values of ∆Nmax indicate the trend within a set of molecules and the highest values of ∆Nmax is related to high inhibitor efficiency.

CHAPTER IV RESULTS AND DISCUSSION 4.1 MOLECULAR GEOMETRY: The optimized structure parameters of polyethylene oxide calculated by DFT/B3LYP function with the 6-311(++)G(d,p) with water and acetone basis sets are listed in the table 1,2.The optimized structures are shown in figure 1. It is inferred that bond length and bond angle show small deviations in the basis sets 6-311(++)G(d,p) with the solvent namely water and acetone.The bond lengths of C-H, C-C, C-O and O-H are in the range of 1.09-1.10 Ao, 1.51-1.52 Ao, 1.41-1.43 Ao and 0.96 Ao for (PEO)n=1-5 respectively are shown in table1.From table 2 it is inferred that the optimized bond angles of C-C-H, H-C-H, O-C-H, O-C-C and C-O-H are in the range of 109.89-110.46,107.64-108.51,106.93-111.23,111.08-111.74 and 107.09-108.89.The increase in repeated units of polymers exhibits same bond length and bond angle.The observed optimized parameters reveals the basis structure of the polymer is the oligomer structure.

4.2 HOMO-LUMO BAND GAP: The electronic absorption corresponds to the transition from the ground to the first excited state and is mainly described by one electron excitation from the highest occupied molecular orbital (HOMO) to lowest unoccupied molecular orbitals (LUMO). The HOMO-LUMO energy gap of polyethylene oxide is calculated at B3LYP/6311(++)G(d,p) with water and acetone level is shown in the figure 4-7.The energy gap reflects the chemical activity of the polymer.The LUMO represents the ability to obtain an electron and HOMO represents the ability to donate an electron.HOMO of (PEO)5 is localized on the core of the polymer but in LUMO of (PEO)5 is localized on the starting of the polymer. The HOMO of (PEO)5 is more localized on the core of the polymer network in gas phase whereas it is more localized on entire chain of the polymer in water than in the acetone.

The LUMO is localized on the monomer unit of the polymer at gas phase whereas for water it is more localized on the entire work.

4.3 U-V ANALYSIS: The TD-DFT/B3LYP/6-311(++)G(d,p) with water and acetone were empolyed to obtain the energy of the singlet-singlet electronic transition as well as transition energies ,oscillator strengths and main configurations for three singlet – excited states (PEO)5 and the results are reported in table respectively. As shown,TD-DFT method show the strongest excitation from ground state to excited state and gives a good interpretive transition to the pro-motion of an electron from HOMO to LUMO. There are two interesting trends on oscillator strength(f) in the tables.  The oscillator strengths (f) in ground state to excited state have the largest value in all series of all oligomers.  The tendency of oscillator strength(f) increase with extending the chain length.Moreover all electronic transition of each oligomer are found to be π-π* transition character.  The maximum absorption wavelength of (PEO)5 6-311(++)G(d,p) with gas,water and acetone phase from TD-DFT method are calculated to be 212, 207 and 208 nm respectively.The absorption wavelength of (PEO)5 exhibits blue shift.The absorption wavelength ground state to excited state transition is the longest among the three electronic transition in all oligomers moreover there is attend that showing that the absorption wavelength increases with extending molecular sizes as in the case of oscillator strength.Furthermore,we found that oscillator strength (f) at ground state to excited state transition of each oligomer for 6-311(++)G(d,p) are bigger transition than that (PEO)4 indicating that π-π* transition of 6-311(++)G(d,p) is stronger.These results confirm again that 6-311(++)G(d,p) should have better performance than (PEO)4 based on low energy consumption and high intensity absorption.

4.4 MOLECULAR PROPERTIES: The electronic molecular properties namely ionization potential (IP),electron affinities

(EA),chemical

potential

(µ)(the

negative

of

electronegativity (χ)),hardness

(η),softness(S),electrophilic index (ω) and the max charge transfer etc were calculated.

4.4.1 Ionization potential (IP) & Electron affinity (EA): The Ionization potential (IP) is 9.51,8.86,8.63,8.83,8.70 eV and the Electron affinity (EA) is 1.51,1.56,1.66,1.71,1. 90 eV for (PEO)n=1-5

respectively in gas phase.There are

fluctuation observed in the values of ionization potential and electron affinity with various chain lengths both in water and acetone.It indicates the folding nature of the polymer.

4.4.2 Chemical Hardness (ƞ) & Softness(S): The chemical hardness and softness reflects the stability and reactivity.The chemical hardness of (PEO)n=1-5 are found to be 4,3.65,3.54,3.56 and 3.4 eV.The softness values are found to be 0.12,0.13,0.14,0.14 and 0.14 eV.However,very small deviations observed for both the phases in 6-311++G(d,p) basis set. 4.5 Chemical Potential(µ): The chemical potential obtained for (PEO)n=5 at 6-311G(d,p) basis set is-5.51,5.21,-5.09,-5.27 and -5.3 eV for water and acetone respectively.The above result predicts the high stability nature of the polymer. 4.6 Electrophilicity (w) & Charge transfer (∆Nmax): The Electrophilicity (w) of (PEO)n=1-5 are found to be 3.79,3.71,3.65,3.90 and 4.13 eV.The Charge transfer (∆Nmax) are found to be 1.37,1.42,1.43,1.48 and 1.55 eV.However,very small deviations observed for both the phases in 6-311++G(d,p) basis set.

CHAPTER V CONCLUSION: The results of the study lead to the following conclusions:  The optimized geometries of polyethylene oxide was determind and analyzed by DFT level of theories utilizing 6-311 (++) G(d,p)/6-311(++)G(d,p) with water and acetone.  HOMO

value,

LUMO

value,

Energy

gap,

Ionization

potential(IP),Electron

affinity(EA),Hardness(η),Softness(S),chemical potential(µ),electrophilicity(ω) were calculated. Using oligomer extrapolation technique, the polymer properties were calculated.  The U-V analysis and FTIR were also done.