Theoretical Insights of Poly Ethylene Oxide to Predict the ...

Theoretical Insights of Poly Ethylene Oxide to Predict the Properties for

Dye-Sensitized Solar Cell Applications: a DFT Approach

G. Maheswari1,*, R. Victor Williams2

1PG Department of Physics, Cauvery College for Women (Autonomous), Affiliated to

Bharathidasan University, Tiruchirappalli-620 018, Tamil Nadu, India 2PG and Research Department of Physics, St. Joseph’s College (Autonomous), Affiliated to

Bharathidasan Unviersity, Tiruchirappalli-620 002, Tamil Nadu, India

*Email: [email protected]

Abstract

Dye-sensitized solar cells (DSSCs) represent one of the most promising alternatives to the

traditional inorganic semiconductor based solar cells because of their ecological and economic

features. Electrolyte is the one of the important area in DSSC which requires stabilization. To

achieve high stability, various polymer materials have been substituted in electrolyte, In this regard,

Density functional theory (DFT) was used to model the oligomers of poly ethylene oxide to

understand its suitability in electrolyte. The structure of oligomer with chain elongation (n=1-5)

was built and optimized to mimic PEO. The modeling predicts the oligomer size n=5 is the

sufficient model to predict the properties of polymers. The complete vibrational analysis for the

oligomer was also done with different solvents and the results are compared with experimental

results obtained from the FT-IR spectra. Various essential parameters such as ionization potential,

electron affinity, hardness, softness, electrochemical potential, electrophilicity, maximum charge

transfer, electron back donation, band gap were calculated by HOMO-LUMO analysis. All the

calculations were extended to infinite chain length using oligomer extrapolation method to predict

the properties of PEO. The time-dependent density functional theory (TD-DFT) has been employed

to estimate the band gap which is found to be in good agreement with the experimental results. The

electrophilic and nuclephilic sites of PEO for the interaction of electrolyte were depicted through

molecular electrostatic potential plot. Natural bond orbital analysis has been carried out to show the

intra molecular charge transfer, inter hybridization and delocalization of electron density within the

polymer.

Keywords: DFT, HOMO-LUMO, TD-DFT, FT-IR, Oligomer Extrapolation.

1. Introduction

Recently, dye-sensitized solar cells (DSSCs) have been inspired as the most promising

alternative materials compared to silicon-based solar cells [1,2] because of their mechanical flexibility,

low cost, and easy fabrication processes. Electrolytes are the promising substituents in DSSCs [3]. It

has great influence on the light-to-electric conversion efficiency and long-term stability of the devices.

The use of liquid electrolytes confines the long-term stability of DSSCs for outdoor applications

because of the evaporation and leakage of volatile solvents. To prevail over such problems caused by

liquid electrolyte a considerable research has been carried out to substitute the liquid electrolytes with

room temperature ionic liquids [4, 5] solid polymer [6, 7] and gel polymer electrolyte [8].

Journal of Information and Computational Science

Volume 9 Issue 12 - 2019

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Poly ethylene oxide(PEO) based polymer electrolytes also attracted much interest due to the

formation of most stable complexes with inorganic salts and possesses higher solvating power for salt

than any other polymers [9,10]. In recent years, PEO based polymer electrolyte has been extensively

studied from experimental methods [11], there are not many theoretical studies about them. In

connection with the experimental work above, we modeled the oligomers of PEO (n=1-5) and predicted

the properties to understand its significance in the polymer electrolyte.

The spectral investigations and ionization potentials (IPs), electron affinities (EAs) , chemical

hardness (η),softness (s), electro chemical potential (μ), electrophilicity (ω), maximum charge transfer

(∆Nmax), Electron back-donation (∆Eback-donation), the highest occupied molecular orbitals (HOMOs), the

lowest unoccupied molecular orbitals (LUMOs), HOMO-LUMO energy gap (∆EH-L) for oligomers

(n = 1-5) of PEO were calculated by density functional theory (DFT) through B3LYP (Becke-3 Lee

Yang Parr) functional using 6-311++G(d,p) basis sets in gas and solvent phase (water and acetone)

and these results have been reported and discussed in detail in this work. All these parameters for

polymer are estimated through oligomer extrapolation technique [12-14]. The results are summarized

by comparing the properties of oligomer and polymer. In addition, TD-DFT analyses were carried out

to obtain the band gap and the theoretical results are in good agreement with experimental data. A

computation of charge transfer and electron back donation indicates that PEO may be a good candidate

polymer for polymer electrolyte in DSSCs. This theoretical analysis is instructive for the

experimentalist to tune the charge transfer and electron back donation property to improve the DSSCs

performance.

2. Experimental details

The poly ethylene oxide (assay 99%) was obtained from Sigma-Aldrich Company and used

for characterization without any further purification. The FTIR spectrum of PEO was recorded in the

wave number range of 4000-400 cm-1 on infrared spectrometer (Nicolet, iS5) by KBr pellet method

with spectral resolution of 2 cm-1 and the UV-Vis absorption spectrum of PEO was recorded on UV-

Visible spectrophotometer (Perkin Elmer, Lambda 35) in the range 200-1100 nm.

3. Quantum chemical calculations

The quantum chemical calculations of the oligomers (PEO)n=1-5 were carried out using

Gaussian'09 program [15] using density functional theory (DFT) with Becke’s three-parameter hybrid

functional using the correlation functional of Lee-Yang –Parr functional (B3LYP) [16, 17] and the 6-

311++G (d, p) basis set in the gas and solvent phase. Additionally, Ultraviolet-Visible (UV–Vis) study

was made by Time-dependent density functional theory (TD–DFT) in gas phase using the oscillator

strength, in conjunction with a polarizable continuum model (PCM) to evaluate the effect of the

solvent (water and acetone) and the natural bond orbital (NBO) analysis [18] was performed in



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NBO3.1 program as implemented in the Gaussian09 package to study the intra molecular charge

transfer (ICT).

4. Results and Discussion

4.1. Molecular geometry study

The lack of enough detailed structural data is the barrier in understanding the fundamental properties

of polymers. The oligomers in their ground state were fully optimized at B3LYP/ 6-311++G (d,p)

level of theory in gas phase, water and acetone in order to determine the geometrical parameters

namely bond lengths and bond angles [19,20]. The optimized molecular structure of the oligomer

(PEO)n=1-5 is depicted in Figure 1a-e.

Figure 1. a-e Optimized structures of polyethylene oxide (PEO) n, a (PEO)n=1, C2H6O2. b (PEO)n=2,

C4H10O3. c (PEO)n=3, C6H14O4, d (PEO)n=4, C8H18O5, e (PEO)n=5, C10H22O6, by DFT-B3LYP/6-311++G(d,p)

level of theory in (water) C atoms are shown in gray, O atoms in red and H in white

The bond lengths of atoms C-H, C-C, C-O and O-H are in the range of 1.09-1.10Å, 1.51-

1.53Å, 1.41-1.43Å and 0.96Å for (PEO)n=1-5 respectively for gas phase, water and acetone are shown

in Table 1. The bond lengths of oligomers (PEO) n=1-5 are almost same and the comparison leading to a

good match between both the solvents. The bond length provides information on the mechanical and

chemical stability of the polymer structure. The shortest bonds require more energy to break, so the

structure is difficult to degrade.

According to Table 1, the arrangement of repeated chains shows longer C-C bonds and shorter

O-H bonds. besides, the optimized bond lengths do not undergo significant variation but shows very

small and systematic deviations [21-23] with different oligomer sizes of (PEO)n, which predicts that

the fundamental structure of this polymer as their oligomer structure (PEO)n=5.



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Table 1. Optimized geometry parameters of polyethylene oxide by DFT-B3LYP / 6-311++G(d,p)

level of theory in gas phase, water and in acetone

Theoretical values of Polyethylene Oxide bond length (Å)

Bond

parameters

Gas

phase

Water Acetone Expt a Lit.b Bond

parameters

Gas

phase

Water Acetone Expt a Lit.b

(PEO)n=1

C3-H5

C3-H6

C4-H7

C4-H8

1.09

1.09

1.09

1.10

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.10

1.08 1.10 C3-C4 1.52 1.51 1.51 1.53 1.52

C3-O1

C4-O2

1.43

1.41

1.42

1.42

1.43

1.41

1.43 1.43

O1-H9

O2-H10

0.96

0.96

0.96

0.96

0.96

0.96

0.97 0.96

(PEO)n=2 C3-H5

C3-H6

C4-H7

C4-H8

C10-H12

C10-H13

C11-H14

C11-H15

1.09

1.09

1.09

1.10

1.10

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.08 1.10 C3-C4

C10-C11

1.52

1.52

1.52

1.52

1.52

1.52

1.53 1.52

C3-O1

C4-O2

C10-O2

C11-O16

1.42

1.41

1.42

1.42

1.43

1.42

1.42

1.43

1.42

1.42

1.42

1.43

1.43 1.43

O1-H9

O16-H17

0.96

0.96

0.96

0.96

0.96

0.96

0.97 0.96

(PEO)n=3 C2-H4

C2-H5

C3-H6

C8-H7

C8-H10

C8-H11

C9-H12

C9-H13

C17-H19

C17-H20

C18-H22

C18-H23

1.09

1.09

1.09

1.10

1.10

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.08 1.10 C2-C3

C8-C9

C17-C18

1.52

1.52

1.52

1.52

1.52

1.52

1.52

1.52

1.52

1.53 1.52

C3-O1

C8-O1

C17-O16

C2-O16

C9-O14

C18-O21

1.41

1.42

1.43

1.42

1.42

1.42

1.43

1.42

1.43

1.43

1.43

1.43

1.42

1.42

1.43

1.43

1.43

1.42

1.43 1.43

O14-H15

O21-H24

0.96

0.96

0.96

0.96

0.96

0.96

0.97 0.96

(PEO)n=4 C2-H4

C2-H5

C3-H6

C3-H7

C9-H12

C9-H13

C16-H21

C24-H26

C8-H10

C15-H17

C25-H29

C25-H28

C15-H18

C24-H27

C16-H20

C8-H11

1.09

1.09

1.09

1.10

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.08 1.10 C2-C3

C15-C16

C8-C9

C24-C25

C3-O1

C8-O1

C15-O14

C24-O23

C2-O14

C16-O19

C24-O29

C25-O30

O19-H22

O30-H31

1.52

1.52

1.52

1.53

1.41

1.42

1.43

1.42

1.42

1.42

1.42

1.42

0.96

0.96

1.52

1.52

1.52

1.53

1.42

1.42

1.43

1.42

1.43

1.43

1.42

1.43

0.96

0.96

1.52

1.52

1.52

1.53

1.42

1.42

1.43

1.42

1.43

1.43

1.42

1.43

0.96

0.96

1.53

1.43

0.97

1.52

1.43

0.96



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a experimental values taken from [21] b Theoretical values taken from [22,23]

From Table 2, it is inferred that the optimized bond angles of C-C-H, C-C-O, C-O-H, H-C-O

and H-C-H angles are in the range of 108º-115º,107º -117º, 105º -110º, 108º -112º and 107-110º for

(PEO)n=1-5 in gas phase, water and acetone respectively.

Table 2. Optimized parameters of polyethylene oxide by DFT/ B3LYP/6-311++G(d,p) level of

theory in gas phase, water and acetone

Theoretical Values of polyethylene oxide- Bond angles ( º )

Bond

Parameters

Gas

Phase

Water Acetone Exptd Lite Bond

Parameters

Gas

Phase

Water Acetone Exptd Lite

(PEO)n=1 H5-C3-H6

H7-C4-H8

C3-C4-H7

C3-C4-H8

C4-C3-H5

C4-C3-H6

108.51

107.64

110.05

109.70

110.46

109.92

108.61

108.06

109.89

109.96

110.06

110.03

108.51

107.64

110.05

109.70

110.46

109.92

110

110

107 H5- C3- O1

H8- C4- O2

C3- O1-H6

C4-O2 -H7

C3- O1-H9

C4- O2-H10

111.23

110.63

105.46

106.93

108.89

107.09

111.05

110.23

105.65

106.81

108.67

107.93

111.08

110.63

105.65

106.93

108.89

107.09

110

110

C4-C3- O2

C3-C4- O1

111.74

111.08

111.75

111.08

111.75

111.08

112 112

(PEO)n=2 H14-C11-H15

H5-C3-H6

H12-C10-H13

H7-C4-H8

C11-C10-H13

C10-C11-H14

C10-C11-H15

C3-C4-H8

C4-C3-H5

C11-C10-H12

C4-C3-H6

C3-C4-H7

107.89

107.90

108.01

107.57

110.29

109.80

109.68

110.13

108.58

109.93

109.15

108.16

108.17

108.03

108.22

107.76

110.10

110.01

109.88

110.48

108.35

109.49

109.11

107.89

108.16

108.03

108.21

107.76

110.11

110.00

109.87

110.23

108.35

109.99

109.47

107.89

110

110

107 H13-O2-C10

H12-O2-C10

H5-O1-C3

H8-O2-C4

H14-O16- C11

C4-O2 - H7

C3- O1- H6

C3-O1- H9

C11-O16-H17

C11-O16-H15

C10-C11-O2

C3-C4-O1

C3-C4-O2

111.52

109.71

110.78

110.25

111.55

105.59

105.76

108.89

108.20

106.14

107.36

114.42

114.79

111.15

109.86

110.61

110.03

110.99

105.80

105.78

108.56

108.83

106.14

107.49

114.38

114.29

111.16

109.85

110.61

110.04

111.47

106.00

105.78

108.56

108.63

106.19

107.49

114.39

114.36

110

110

112

112

(PEO)n=5

C2-H4

C2-H37

C3-H5

C3-H6

C29-H30

C23-H25

C7-H9

C7-H10

C8-H11

C8-H12

C29-H30

C14-H16

C14-H17

C15-H18

C15-H19

C23-H27

C32-H33

C32-H34

C24-H28

C23-H26

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

1.09

C2-C3

C7-C8

C14-C15

C29-C32

C23-C24

C3-O1

C14-O13

C7-O1

C23-O22

C2-O22

C32-O36

C8-O13

C29-O35

C15-O20

C24-O35

O20-H21

O36-H38

1.53

1.52

1.53

1.52

1.51

1.42

1.42

1.42

1.42

1.42

1.42

1.42

1.41

1.42

1.41

0.96

0.96

1.53

1.52

1.53

1.52

1.52

1.42

1.42

1.42

1.42

1.42

1.42

1.42

1.42

1.42

1.41

0.96

0.96

1.53

1.52

1.53

1.52

1.52

1.42

1.42

1.42

142

1.42

1.42

1.42

1.42

1.42

1.41

0.96

0.96

1.53

1.43

0.97

1.52

1.43

0.96



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C4-C10-O2

116.08 115.67

116.08

(PEO)n=3 H12-C9-H13

H4-C2-H5

H6-C3-H7

H10-C8-H11

H19-C17-H20

H22-C18-H23

C8-C9-H12

C3-C2-H4

C3-C2-H5

C2-C3-H7

C9-C8-H10

C9-C8-H11

C17-C18-H22

C18-C17-H20

C17-C18-H23

C2-C3-H6

C8-C9-H7

C8-C17-H19

107.87

107.92

107.70

107.98

108.44

107.68

109.84

109.12

108.86

110.58

110.02

110.20

109.77

109.67

110.19

108.05

109.66

110.56

108.17

107.88

107.70

108.26

108.30

107.97

110.05

108.87

109.19

111.16

110.05

110.20

109.97

109.86

110.19

107.76

109.84

110.24

108.15

107.35

107.76

108.19

108.32

109.76

110.05

108.87

109.19

111.02

110.07

110.11

109.76

109.87

110.51

107.83

109.83

110.27

110 107 H4-C2-O16

H12-C9-O14

H19-C17-O16

H11-C8-O1

H7-C3-O1

H10-C8-O1

H23-C18-O21

H15-C9-O14

C3-O1-H6

C2-O16-H5

C9-O14-H13

C18-O21-H24

C18-O21-H22

C17-O16-H20

C17-C18-O21

C8-C9-O14

C3-C2-O16

C8-C9-O1

C3-C2-O1

C17-C18-O16

C3-C8-O1

C2-C17-O16

110.76

111.56

111.30

111.50

110.32

109.74

110.65

108.86

105.65

106.01

106.16

106.01

106.85

106.10

111.54

111.58

113.61

107.38

114.17

110.61

116.00

115.51

110.85

110.99

111.42

111.10

110.01

109.82

110.18

108.42

105.11

106.53

106.17

106.74

106.88

106.07

111.43

111.46

113.81

107.50

113.74

110.80

116.60

115.38

110.79

111.01

111.41

111.14

109.99

109.83

110.20

108.67

105.92

106.10

106.17

106.74

106.89

106.08

111.42

111.48

113.76

107.49

113.96

110.75

116.60

115.36

110

110

112

112

(PEO)n=4 H4-C2-H5

H6-C3-H7

H10-C8-H11

H17-C15-H18

H20-C16-H21

H12-C9-H13

H26-C24-H27

H28-C25-H29

107.95

107.70

108.29

108.39

107.97

108.08

107.84

107.91

107.85

107.79

108.34

108.32

107.97

108.24

108.12

108.17

107.85

107.79

108.34

108.32

107.97

108.24

108.12

108.17

109.5 107 H4-C2-O14

H12-C9-O23

H7-C3- O1

H13-C9-O23

H28-C25-O30

H10-C8- O1

H17-C15- O14

H21-C16- O19

H11-C8- O1

H27-C24- O23

110.78

111.73

110.27

110.41

111.55

110.25

111.33

110.64

111.35

110.92

110.79

111.41

109.99

110.05

111.04

110.11

111.40

110.16

111.06

110.51

110.79

111.41

109.99

110.05

111.04

110.11

111.40

110.16

111.06

110.51

110

C3-C2-H4

C3-C2-H5

C2-C3-H6

C2-C3-H7

C8-C9-H12

C8-C9-H13

C16-C15-H17

C16-C15-H18

C9-C8-H11

C15-C16-H20

C15-C16-H21

C25-C24-H26

C25-C24-H27

C24-C25-H28

C24-C25-H29

C24-C25- H23

C9-C8-H10

C9-H23-C24

109.10

108.86

107.98

110.66

109.45

109.88

110.58

109.73

110.38

109.78

110.20

109.39

109.69

109.45

110.86

112.91

109.60

114.89

108.84

109.20

107.82

111.03

109.62

110.02

110.22

109.86

110.32

109.68

110.54

109.47

109.86

109.73

110.87

112.63

109.91

114.61

108.84

109.20

107.82

111.03

109.62

110.02

110.22

109.86

110.32

109.68

110.54

109.47

109.86

109.73

110.87

112.63

109.91

114.61

110 C2-O14- H5

C3- O1-H6

C15- O14-H18

C16- O19-H20

C24- O23-H26

C16- O19-H22

C3-C2- O1

C8-C9- O1

C3-C8- O1

C3-C2-O14

106.25

105.76

106.10

106.88

105.87

106.97

114.10

106.94

115.75

113.68

106.15

105.85

106.09

106.87

106.06

106.77

113.99

107.07

115.54

113.79

106.15

105.85

106.09

106.87

106.06

106.77

113.99

107.07

115.54

113.79

110

112

112



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(PEO)n=5 H4-C2-H37

H18-C15-H19

H16-C14-H17

H5-C3-H6

H27-C24-H28

H9-C7-H10

H30-C29-H31

H11-C8-H12

H33-C32-H34

H25-C23-H26

108.06

108.08

107.89

108.04

107.99

108.11

107.72

108.08

108.89

108.05

108.22

108.08

108.08

108.20

108.32

108.33

108.05

108.28

108.21

108.32

108.22

108.17

108.08

108.23

108.32

108.33

108.05

108.28

108.21

108.32

110 107 H4-C2-O22

H11-C8-O13

H12-C8-O13

H18-C15-O20

H27-C24-O35

H31-C29-O35

H28-C24-O35

H30-C29-O35

H34-C32-O36

H12-C8-O13

H25-C23- O22

110.86

111.82

110.49

111.57

110.75

110.26

110.81

110.91

111.60

110.14

111.87

110.47

111.47

110.14

111.02

110.42

110.17

110.46

110.50

111.03

111.03

111.49

110.47

111.47

110.14

111.02

110.42

110.17

110.40

111.50

111.03

110.14

111.49

110

C3-C2-H4

C8-C7-H10

C15-C14-H17

C24-C23-H26

C8-C7-H9

C15-C14-H17

C3-C2-H37

C7-C8-H11

C14-C15-H19

C23-C24-H27

C15-C14-H16

C2-C3-H5

C7-C8-H12

C24-C23-H25

C29-C32- H30

C29-C32- H31

C29-C32-H33

C23-C24-H28

C2-C3-H6

C14-C15-H18

C29-C32-H34

C15-C14-H16

109.61

109.30

109.73

109.83

109.84

109.99

110.39

109.39

110.81

109.86

109.46

110.17

109.76

109.38

106.69

110.14

109.67

109.77

109.54

109.46

109.72

109.05

109.81

109.53

109.99

110.02

110.06

109.99

110.40

109.59

110.89

110.02

109.46

110.33

109.95

109.59

109.94

110.18

109.86

109.99

109.77

109.66

109.92

109.48

109.81

109.53

109.99

110.02

110.06

109.99

110.40

109.59

110.89

110.07

109.48

110.33

109.95

109.59

109.94

110.18

109.86

109.99

109.77

109.66

109.92

109.48

110 C15-O20- H19

C15-O20-H21

C32-O36-H38

C32-O36- H33

C2- O22-H37

C23- O22-H26

C3-C2- O1

C3- C7- O1

C7-C8- O1

C7-C8-O13

C23-C25- O22

C23-C26- O22

C14-C15- O13

C3-C2-O22

C2-C23- O22

C23-C29-O35

C8-C14- O13

C29-C32-O35

C24-O35-C29

C14-C15-O20

C32-C29-O35

C23-C24- O22

105.59

108.87

108.94

106.23

105.90

110.47

112.42

115.11

107.17

107.27

111.49

110.15

112.69

111.87

114.90

108.10

114.79

111.56

113.56

111.39

107.98

107.20

105.80

108.64

108.67

106.27

105.76

110.02

112.22

114.93

107.23

107.37

111.49

110.15

112.39

112.02

114.86

108.10

114.55

111.56

113.17

111.18

107.98

107.24

105.80

108.64

108.67

106.27

105.76

110.02

112.22

114.93

107.23

107.37

111.49

110.15

112.39

111.02

114.86

108.10

114.55

111.56

113.17

111.18

107.98

107.24

110

110

d experimental values taken from [25,26,27] e Theoretical values taken from [28,29]

The optimized geometry parameters are in good agreement with X-ray data also [24]. The

bond angles of oligomers (PEO) n=1-5 are almost same, While comparison, good match is observed

between both the solvents. From the theoretical data, the majority of the optimized bond lengths and

bond angles show very small deviations with the experimental and literature values [25-29].

4.2. Spectral analysis

The functional group analysis of (PEO)n=2 is performed at DFT/B3LYP level with 6-

311++G(d,p) basis set in gas phase, acetone and water and are summarized in Table 3. The calculated

vibrational wave numbers corresponding to the different normal modes are used for identifying the

vibrational modes explicitly. Comparison between the calculated and the observed vibrational spectra

helps us to realize the observed spectral features. For visual assessment, the observed and simulated

Fourier transform infrared (FTIR) spectrum of (PEO)n=2 is shown in Figure 2 a &b.



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Figure 2 a. Theoretical FTIR Spectrum computed for (PEO)n=2 acquired by DFT-B3LYP/6-311++G(d,p)

level of theory in Water a scaling factor of 0.9673, b. experimental FTIR spectrum of PEO( a range of

4000-400 cm-1) in Water

Table 3. Vibrational assignment of (PEO)n=2 at DFT/B3LYP/6-311++G(d, p) level of theory

Experimental

Wavenumber (cm-1)

Theoretical wavenumber (cm-1)

(scaled)a

Vibrational assignment

Gas phase water Acetone

3707 3711 3726 OH stretching

3113 3705 3703 3711 OH stretching

2992 2958 2952 CH stretching

2963 2933 2951 CH stretching

3001 2976 2916 CH2 asymmetric stretching

2956 2912 2913 CH2 asymmetric stretching

2856 2883 2888 CH2 symmetric stretching

2338 2846 2873 2882 CH2 symmetric stretching

1478 1473 1479 CC stretching

1458 1460 1458 1474 CC stretching

1438 1439 1427 CH2 scissoring

1377 1389 1421 1409 CH2 scissoring

1331 1339 1330 1355 CO stretching

1330 1274 1316 CO stretching

1305 1264 1207 CH in plane bending

1266 1271 1269 1268 CH2 wagging

1259 1258 1258 CH2 wagging

1176 1177 1192 1190 CH2 twisting

1165 1189 1188 CH2 twisting

1080 1116 1113 1109 OH in plane bending

926 1041 1053 1031 CH2 rocking

888 1021 1020 1017 OH in plane bending

880 944 967 CH2 rocking

810 788 810 CC in plane bending

649 791 805 800 CC in plane bending

444 511 512 517 CO in plane bending



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430 477 443 CO in plane bending

375 369 311 OH out of plane bending

287 230 206 CC out of plane bending

251 275 264 OH out of plane bending

197 206 199 CC out of plane bending

131 119 125 CO out of plane bending

44 41 52 CO out of plane bending

aScaling factor: 0.9673 for DFT/B3LYP/6-311++G(d,p) level of theory

4.2.1. O-H Vibrations

The polymer under investigation shows strong band at 3707, 3705 cm-1 (gas phase) 3726, 3711

cm-1 (acetone) and 3711, 3703 cm-1 (water) which are assigned to O-H stretching vibrations which

indicates the presence of intra-molecular hydrogen bonding [30]. In view of that, the O-H in-plane

bending vibrations occurred at 1116, 1147 cm-1 (gas phase) 1109, 1017 cm-1 (water) and 1021, 1051

cm-1 (acetone). The out-of-plane bending vibrations are observed at 375, 251 cm-1 (gas phase) 369,

275cm-1 (water) and 311,264 cm-1 (acetone). The experimental value for the CH2 asymmetric

stretching vibrations is found at 3113cm-1. All these wave numbers are in good agreement with

literature [31].

4.2.2. CH2 Vibrations

The methylene group of the polyethylene oxide normally appeared in four stretching modes

and a couple of scissoring, wagging, twisting and rocking modes. The asymmetric stretching mode is

observed at 3001, 2956 cm-1 (gas phase), 2976, 2912 cm-1 (water) and 2916, 2913 cm-1 (acetone). The

bands at 2856, 2846 cm-1 (gas phase) 2883, 2873 cm-1 (water) and 2888, 2882 cm-1 (acetone) are

designed as symmetric stretching modes. The CH2 scissoring occurred at 1438, 1389 cm-1(gas phase)

1439, 1421 cm-1(water) and 1427, 1409 cm-1 (acetone). The CH2 wagging vibrations observed at 1271,

1259 cm-1 (gas phase), 1269 and 1258 cm-1 (water) and 1268, 1258 cm-1 (acetone). The bands at 1177,

1165 (gas phase) cm-1, 1192 and 1189 cm-1 (water), 1190, 1188 cm-1 (acetone) are ascribed to twisting

vibrations. The peaks displayed at 1041, 880 cm-1 (gas phase), 1053 and 944 cm-1 (water) and 1031,

967 (acetone) cm-1 for CH2 rocking vibrations. They agreed well with the literature [32].

4.2.3. C-C vibrations

Basically, the C-C stretching vibrations are observed in the region at 1600-1400 cm-1 [33]. In

the FTIR spectra, the values at 1478, 1460,1479,1474,1473 and 1458 cm-1 correspond to C-C

stretching vibrations. The weak in-plane bending vibration has given across to the low-frequency

region below at 1000 cm-1 [34]. These C-C in-plane bending vibrations are observed at 810,791 (gas

phase) 788, 805 cm-1 (water) and 810,800 (acetone). The bands at 287,206 cm-1 (gas phase) 230, and

203 cm-1 (water) and 197,199 cm-1 (acetone) are attributed to C-C out of plane bending vibrations. All

these values are in good agreement with literature one [35]



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4.2.4. C-H Vibrations

The polymer structure shows the presence of C-H stretching vibrations in the region 3000-

2850 cm-1 which are the characteristic region for the ready identification of C-H stretching vibrations.

There are four expected C-H Stretching vibrations corresponds to stretching modes of PEO. The

bands observed at 2992,2963,1339,1330 cm-1 (gas phase) , 2958,2933,1274,1330 cm-1 (water) and

2952,2951,1355,1316 cm-1 (acetone) are assigned to C-H stretching vibration, In addition, C-H

stretching vibrations calculated theoretically are in good agreement with the experimentally reported

values [36].

The C-H in-plane bending modes are observed in the region 1300-1000 cm-1 [37]. The

vibrations at 1305cm-1 (gas phase) , 1264 cm-1 (water) and 1207 cm-1 (acetone) correspond to C-H in-

plane bending. All the vibrations coincide satisfactorily with the experimentally observed values [38].

4.2.5. C-O vibrations

The C-O stretching vibrations are found in the region 1380-1000 cm-1 [39]. The wave numbers

at 1339, 1330 cm-1 (gas phase), 1330, 1274 cm-1 (water) and 1335, 1316 cm-1 (acetone) refers to C-O

stretching vibration. This is in agreement with the very strong experimental wave numbers at 1331

cm-1. The in-plane C-O bending vibrations are observed at 511,430 cm-1 (gas phase), 512,477 (water)

and 517,443 (acetone) cm-1. The out -of- plane C-O bending vibration modes are observed in the

wave numbers at 131, 44 cm-1 (gas phase) 119, 41 cm-1 (water) and 125, 52 cm-1 (acetone). All these

vibrations are in good agreement with the literature [40].

4.3. UV- Vis absorption spectra

In order to identify the electronic transition of the title polymer, UV-visible absorption

spectrum in gas phase and solvent phase (water, acetone) was obtained by DFT/B3LYP/6-

311++G(d,p) level of theory using TD-DFT method for three excited states. To account solvent effect

polarized continuum Model (CPCM) was used. The observed and experimental UV-Vis spectrum of

(PEO)n=5 in gas phase and solvent phase(water and acetone) are shown in Figure 3a -e.

The maximum absorption wavelength (λ max), the oscillator strength (f), excitation energy (E )

and frontier orbitals involved in each transition are listed in Tables 4 and 5.The TD-DFT method is

able to detect accurate absorption wavelength at a relatively small computing time, which corresponds

to electronic transition computed on the ground state geometry (figure 3 a-c ).

From table 4 it is inferred that the oligomer (PEO)n=5 exhibit significant absorption peak

between 207.50 and 207.55 nm for S0—S1 transition for different solvents (water and acetone) are

giving a considerable blue-shifting absorption wavelength relatively.



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Figure 3. Simulated (a-in gas phase, b-in water and c-in acetone ) d- Experimental (in water)

and e-Experimental indirect band gap by Tauc-plot (in water) by UV-Visible absorption

spectrum of PEO

The experimental absorption spectrum of the title polymer (Fig 3d) has a wide absorption at

about 350-485 nm which is characterized by maximum at 399 nm and calculated spectrum in water

and acetone (Figure 3 b-c) show the highest oscillation in 208 nm at f = 0.016 (Table 5) .The strong

peak at 208 nm is due to the charge-transfer (CT) excited state. The other peaks are local excited states

corresponding to electrons giving into anti-bonding orbitals associated with the head of the polymer

(CH2 units). Excitation of one electron at 208 nm belonged to the transition into the excited singlet

state S0S1 and describes by a wave function corresponding to configuration for one-electron

excitation 53 (HOMO) 54 (LUMO ). The other excited states have very small intensity (f<0.016).

These transitions are nearly forbidden by orbital symmetry considerations.

Table 4 Singlet computed excitation energies, oscillator strength, configuration and wavelength

of (PEO) n =5 using TD- DFT/B3LYP/6-311++G(d,p) level of theory gas and solvent phase

Phase excited

state

excitation

energy

(eV)

oscillator

strength

(f)

configuration wavelength

(nm)

Gas 1 5.82 0.0128 53→54 213

2 5.96 0.0058 52→55 208

3 6.17 0.0051 53→56 201

Water 1 5.97 0.0160 53→54 208

2 6.24 0.0067 52→55 198

3 6.29 0.0030 53→55 197

Acetone 1 5.97 0.0162 53→54 208

2 6.23 0.0068 52→55 199

3 6.28 0.0030 53→55 197



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The most intense peak (table 5) at 213 nm with f = 0.013 is due to HOMO → LUMO

transition for gas phase and 208 nm with f =0.016 which corresponds to HOMO → LUMO transition

for water and acetone.

Table 5. The UV-Vis band gap energy E (eV), Wavelength 𝝀max (nm) and oscillator strength (f) for (PEO)n=5

by TD-DFT/B3LYP/6-311++G(d,p) level of theory in gas phase, water, acetone

Gas phase Assignment Water Assignment Acetone Assignment

𝜆max

f E

𝜆max

f E

𝜆max

f E

212.74 0.013 5.827 HOMO→ LUMO

207.50 0.016 5.975b HOMO→LUMO

207.55 0.016 5.974b HOMO→ LUMO

207.72 0.006 5.969 HOMO-1→LUMO+1

198.46 0.007 6.247 HOMO-1→ LUMO 198.77 0.007 6.237 HOMO-1→ LUMO+1

200.69 0.005 6.178

HOMO→LUMO+2 196.98 0.003 6.294 HOMO→LUMO+1

197.17 0.003 6.288 HOMO→LUMO+1

a experimental band gap (Tauc plot) b theoretical band gap in acetone and water

5.56a

5.97b

In this view, we can observe that the intense wavelengths are all made up of orbital transitions

of HOMO→ LUMO. It is observed that the indirect energy gap determined by Tauc’s plot (Figure 3 e)

is 5.56 eV, which agrees with the calculated value (5.97 eV).

4.4. HOMO – LUMO analysis

The highest occupied molecular orbitals (HOMO) and the lowest unoccupied

molecular orbitals (LUMO) are useful for understanding more details on optical and electronic

properties. The HOMO and LUMO picture of (PEO)n=5 in the solvent phase (water) is shown in the

figure 4.

Figure 4. Form of the Molecular Orbital (MO) involved in the pattern of absorption spectrum

of (PEO)n=5 in water at λmax = 208 nm.

The localization of charges is predominantly observed either in the head or in the tail of the

polymer for the HOMO orbitals. Whereas for LUMO orbitals the charges are localized more on the

tail than the head of the polymer for (PEO)n= 5. This indicates the charge transfer within the polymer.

The HOMO and LUMO energy levels, as well as the energy gaps of (PEO) n=1-5 were computed and

extrapolated to the infinite chain length of (PEO) n=∞ by oligomer extrapolation method [41, 42]. For

(PEO)n=5 the important molecular orbitals (MO) namely HOMO, HOMO-1, HOMO-2, LUMO,

LUMO+1 and LUMO+2 were examined as seen in figure 6.



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Figure 5. The HOMO and LUMO orbitals plots of (PEO)n=5 by DFT-B3LYP/6-311++G(d,p)

level of theory in gas phase and solvent phase(water and acetone)



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Figure 6. Three-dimensional plots of the HOMO, HOMO-1, HOMO-2, LUMO, LUMO+1 and

LUMO+2 of (PEO)n=5 by DFT- B3LYP/6-311++G(d,p) level of theory in water.

Table 6 shows the energy gap Eg of (PEO)n=1 is higher than those of (PEO)n =2-∞ by 0.70, 0.88,

0.93, 1.12 and 1.18 eV respectively for the gas phase in 6-311++G(d,p) basis set. As the chain length

increases, the separation energies between the frontier occupied or unoccupied molecular orbitals

(FMOs) get gradually smaller and the HOMO and LUMO energy level decrease. Hence, their energy

gaps get smaller.

Table 6. HOMO – LUMO values of polyethylene oxide by DFT/B3LYP/6-311++G (d,p) level of theory

Also, the energy gap (Table 6) of (PEO)n =2-∞ for water in the same basis set shows 0.60, 0.84,

0.89, 1.12 and 1.11 eV lesser than (PEO) n=1 respectively and in acetone the energy gap for

(PEO) n = 2-∞ is lesser than (PEO) n = 1 by an amount of 0.8, 0.86, 0.93, 1.19 and 1.20 eV respectively.

On the whole, energy gap of the polymer accords with the particular sequence (PEO)n=1 >(PEO)n=2

>(PEO)n=3 >(PEO)n=4 >(PEO)n=5 >(PEO)n=∞

The above analysis indicates the feasibility of charge transfer within the polymer network.

4.5.Chemical reactivity descriptors

The chemical reactivity parameters have been determined from the values of the energies of

HOMO and LUMO. The HOMO and LUMO energy gap has wider importance in understanding the

static molecular reactivity and helps in characterizing the chemical reactivity and kinetic stability of

the polymer.

The energy gaps (Eg) and reactive descriptors such as ionization potential (IP), electron

affinity (EA), electronegativity (χ), hardness (η), softness (s), chemical potential (μ), softness (S),

charge transfer (ΔNmax), back donation (∆Eback-donation), of (PEO)n=1-5 have been calculated by DFT/6-

311++G(d,p) level of theory in gas and solution phase and are presented in Table 7. The extrapolated

values for infinite chain length of the title polymer are shown in the Figure 7a-7l.

(PEO)n B3LYP/6-311++

G(d,p)/

gas phase

Eg B3LYP/6-311++

G(d,p)/

water

Eg B3LYP/6-311++

G(d,p)/

Acetone

Eg

HOMO

(eV)

LUMO

(eV)

HOMO

(eV)

LUMO

(eV)

HOMO

(eV)

LUMO

(eV)

1 -9.51 -1.51 8.00 -9.63 -1.71 7.92 -9.64 -1.69 7.95

2 -8.86 -1.56 7.30 -8.97 -1.65 7.32 -9.00 -1.85 7.15

3 -8.83 -1.71 7.12 -8.84 -1.76 7.08 -8.84 -1.75 7.09

4 -8.63 -1.56 7.07 -8.64 -1.61 7.03 -8.95 -1.93 7.02

5 -8.70 -1.90 6.80 -8.70 -1.90 6.80 -8.71 -1.95 6.76

∞b -8.78 -1.96 6.82 -8.75 -1.94 6.81 -8.79 -2.04 6.75 bOligomer extrapolation method



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Table 7. Chemical reactivity parameters (eV) of polyethylene oxide by DFT/B3LYP/ 6-311++G (d,p) level of

theory in gas phase ,water and acetone in eV

Figure 7 Plot of polyethylene oxide – (a. Ionization Potential b. Electron affinity c. Softness d.

Electrophilicity e. Electrochemical potential f. Charge transfer g. Electron back -donation h.

Band gap i. Hardness Vs inverse chain length (1/n)) optimized at DFT-B3LYP/6311++G(d,p)

level of theory in solution phase (water) by oligomer extrapolation method.

Phase Basis set (PVA)n IP EA S µ ∆Nmax ∆Eback-donation Eg

Gas B3LYP/

6-311++

G(d,p)

n = 1 9.51 1.51 4 0.12 -5.51 3.79 1.38 -1 8.00

n = 2 8.86 1.56 3.65 0.13 -5.21 3.71 1.43 -0.91 7.30

n = 3 8.83 1.71 3.56 0.14 -5.27 3.90 1.48 -0.89 7.12

n = 4 8.63 1.56 3.54 0.14 -5.10 3.65 1.44 -0.88 7.07

n = 5 8.70 1.90 3.4 0.14 -5.30 4.13 1.56 -0.85 6.80

n = ∞b 8.78 1.96 3.41 0.15 -5.37 4.23 1.57 -0.85 6.82

Water B3LYP/

6-311++

G(d,p)

n = 1 9.63 1.71 3.96 0.12 -5.67 4.05 1.43 -0.99 7.92

n = 2 8.97 1.65 3.66 0.13 -5.31 3.85 1.45 -0.87 7.32

n = 3 8.84 1.76 3.54 0.14 -5.30 3.96 1.50 -0.88 7.08

n = 4 8.64 1.61 3.51 0.14 -5.13 3.73 1.46 -0.87 7.03

n = 5 8.70 1.90 3.40 0.14 -5.30 4.13 1.56 -0.85 6.80

n = ∞b 8.75 1.94 3.41 0.15 -5.35 4.19 1.57 -0.85 6.81

Acetone B3LYP/

6-311++

G(d,p)

n = 1 9.64 1.69 3.97 0.12 -5.67 4.03 1.42 -0.99 7.95

n = 2 9.00 1.85 3.57 0.14 -5.43 4.11 1.52 -0.89 7.15

n = 3 8.84 1.75 3.55 0.14 -5.30 3.96 1.49 -0.88 7.09

n = 4 8.95 1.93 3.51 0.14 -5.44 4.21 1.55 -0.87 7.02

n = 5 8.71 1.95 3.38 0.15 -5.33 4.20 1.58 -0.85 6.76

n = ∞b 8.79 2.04 3.38 0.15 -5.42 4.34 1.60 -0.85 6.75 bOligomer extrapolation method



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4.5.1. Ionization potential (IP) and electron affinity (EA)

From Koopman's theorem, the ionization potential and electron affinity have been calculated

by the subsequent equations [43].

IP= -EHOMO --- (1)

EA= -ELUMO --- (2)

Ionization energy is a fundamental descriptor of the chemical reactivity of the compound.

High ionization energy indicates high stability and small ionization energy indicates high reactivity of

the compound. According to the 6-311++G(d,p) basis set calculations in gas phase, the ionization

potential is 9.51, 8.86, 8.83, 8.63 and 8.70 eV and the electron affinity is 1.51, 1.56, 1.71, 1.56 and

1.90 eV for (PEO)n= 1-5 respectively. There are fluctuations observed in the values of ionization

potential and electron affinity with various chain lengths. It indicates the change in the folding nature

of polymer as compact, random and expanded coil arrangement. The predicted value of the ionization

potential for (PEO) n= ∞ are 0.08, 0.05, 0.08 eV greater than (PEO)n=5. Similarly the electron affinity for

(PEO) n= ∞ are 0.06, 0.04, 0.09 eV greater than (PEO)n=5 in gas, water and acetone phase respectively.

The above result confirms the high stability nature of the title polymer and hence prevents leakage in

the electrolyte.

4.5.2. Chemical Hardness (η) and Softness (S)

The chemical hardness of the title polymer has been principally calculated from the difference

of HOMO and LUMO energy as [44].

η = (ELUMO – EHOMO)/2 --- (3)

The softness of PEO can be determined as follows,

S = 1/2η --- (4)

Absolute hardness and softness are important properties which are reciprocal to one another

and they also measure the molecular stability, reactivity and resistance of the electron transfer. The

chemical hardness of (PEO) n=1-5 is found to be 4.0, 3.65, 3.56, 3.54 and 3.4 eV. However very small

deviations observed for both the phases in 6-311++G(d,p) basis set. Therefore, the predicted value for

(PEO)n= ∞ is 3.4 eV which is very close to the calculated value.

According to 6-311++G(d,p) basis set, the softness value is 0.14 eV which is very close to the

predicted value for (PEO) n= ∞.

4.5.3. 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 at various basis sets is calculated by,

µ = - (ELUMO + EHOMO)/2 --- (5)



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The chemical potential obtained for the (PEO) n= 5 at 6-311++G(d,p) basis set is -5.30 and

-5.33 eV for all phases which is in close agreement with the predicted value -5.37, -5.35, -5.42 eV for

infinite chain of the title polymer Thus, the above result predicts the high stability nature of the

polymer.

4.5.4. Electrophilicity(ω) and Charge transfer (ΔNmax)

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:

ω = (µ2|2 𝜂). ---(6)

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 η.

The maximum amount of electronic charge that an electrophile system may accept is given by

the following equation [45]

ΔNmax = -(𝜇|𝜂). -- (7)

The maximum charge transfer ΔNmax in the direction of the electrophile was predicted using

equation (7) and it describes the tendency of the molecule to acquire an additional electronic charge

from the environment while the quantity defined in equation (6) describes the charge capacity of the

polymer.

In this environment, it is possible to balance the stabilization among inhibiting molecule. The

maximum charge transfer ΔNmax is also used to predict the inhibitor efficiency. The highest value of

∆Nmax is related to high inhibitor efficiency. The maximum charge transfer for (PEO) n= 5 is 1.56 which

is in close agreement with the predicted value for infinite chain. While introducing the solvent acetone,

it is increased by an amount of 0.02 eV.

The maximum value of charge transfer of the investigated polymer follows the same trend as

that of the other polymers [46, 47]. The above result also suggests that the title polymer has the

potential to transfer charge when it acquires a charge from the counter electrode.

4.5.5. Inhibition efficiency through back donation (∆Eback-donation)

According to Gomez et al. [48], an electronic back-donation process might be occurring

governing the interaction between the inhibitor molecule and the metal surface. The concept

establishes that if both the 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 = - (𝜂|4). --- (8)

The ∆Eback-donation suggests that when η > 0 and ∆Eback-donation< 0 the charge transfer to a polymer

is actively favoured followed by a back-donation from the polymer. All the calculated ∆Nmax and



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∆Eback-donation of PEO in different phases are collected and shown in Table 7. In this study, the highest

value of ∆Eback-donation is -0.85 eV for both the solvents. From Table 7, the calculated chemical

reactivity descriptors shows almost the same value for the (PEO)n=5 at the 6-311++G(d,p) basis set in

gas and solution phase. The above parameter predicts that the tuning of the polymeric nature of the

title polymer starts at the oligomer size of n=5.

4.6.Molecular Electrostatic Potential Analysis

The molecular electrostatic potential (MEP) is a very valuable descriptor in understanding the

sites for electrophilic and nucleophilic reactions as well as hydrogen bonding interactions [49].

Even though there is a considerable number of an experimental finding [50] available on

qualitative description of the interaction between PEO and electrolyte molecules, no satisfactory

quantitative analysis is found to describe which part of the polymer molecule interacts with which part

of the electrolyte (cation or anion).The present study provides a quantitative description of the

polymer with its interactive site.

The electrostatic potential is considered predictive of chemical reactivity because regions of

negative potential are expected to be sites of protonation and nucleophilic attack, while regions of

positive potential may indicate electrophilic sites.To envisage reactive sites for the investigated

polymer, MEP was calculated with DFT/B3LYP/6-311++G(d,p)level of theory in the solution phase.

The charge distribution determine how molecules interact with one another. A high electrostatic

potential indicates the relative abdunance of electrons and a low electrostatic potential indicates an

absence of electrons [ 51].

The calculated molecular electrostatic potential surfaces of model oligomer (PEO)n=5 are

presented in figure 8.

Water



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Figure 8. Electron density iso-surface mapped diagram of (PEO) n=5 by DFT-B3LYP/6-311++ G

(d,p) level of theory

The yellow colour indicates the lowest electrostatic potential energy and blue indicates the

highest electrostatic potential energy. Areas of low potential, yellow are characterized by an

abundance of electrons. Areas of high potential blue are characterized by a relative absence of

electrons.Oxygen bonds would have a higher electron density around them than Carbon-Hydrogen

bonds. From the MEP of (PEO)n=5, C-H bonds have high electrostatic potential and O bonds have low

electrostatic potential. O bonds are characterized by an abundance of electrons. so, these bonds behave

like donors and C-H bonds are characterized by a relative absence of electrons, so, these bonds

behaves like acceptors. Yellow parts of the surface refer to the sites for electrophilic reactions with

negative ESP, blue parts represent nucleophilic sites with the positive ESP.

From fig.8, it is evident that the hydrogen atoms present in the modeled (PEO)n=5 are the

electrophilic sites, which tend to interact with nucleophile. Besides, oxygen atoms refer to the most

nucleophilic sites which tend to interact with the electrophilic cation of the electrolyte.

4.7. NBO analysis

The NBO analysis is the most efficient method for studying the charge transport property,

intra and intermolecular bonding nature and interaction among bonds of the molecular system. The

electron- donor orbital, electron-acceptor orbital and the overlap stabilization energy resulting from the

second –order micro disturbance theory are theoretically reported in the present manuscript.

The NBO analysis was performed on (PEO) n=5 at B3LYP/6-311++G (d, p) level of theory in

water and acetone in order to elucidate the intra-molecular, rehybridization and delocalization of

electron density within the polymeric system. The second-order Fock matrix was carried out to

evaluate the donor-acceptor interactions in the NBO analysis [52]. For each donor NBO (i) and

acceptor NBO (j), the stabilization energy E (2) associated with delocalization i, j is estimated as

E2 = ΔEij = 𝑞𝑖𝐹(𝑖,𝑗)2

𝐸(𝑖)−𝐸(𝑗) --- (9)

Acetone



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Where qi is the donor orbital occupancy, E (i) and E (j) are diagonal elements and F (i, j) is the off-

diagonal NBO Fock matrix elements. The strong intra-molecular hyperconjugation interaction of σ

bonding of C-H, C-C, C-O and σ* bonding of C-C, C-H, C-O, leads to stabilization of some part of

the polymer as evident from Table 8.

The electrons of LP(2) O14, LP(2) O7, LP (2) O8, LP(2) O30, LP(2) O30, LP(2) O7, LP(2)

O8, LP(2) O14, LP(2) O22 can be redistributed into σ*(C16-H17), σ*(C1-H3),σ*(C2-H6), σ*(C31-

C34), σ*(C27-H29), σ*(C24-C27), σ*(C9-C11), σ*(C9-C11), σ*(C19-H20) with the potential of 30.8,

30.4, 30.3, 30.1, 29.4, 29.4, 27.9, 27.7 and 26.9 kJ/mol respectively.

The strongest interaction is identified for the interaction of lone pair localised on O14 (donor)

with the adjacent σ* C16-H17 (acceptor) bonds. The electron of LP (2) O14 can be redistributed into

σ*(C16-H17) with the potential of 30.8 kJ/mol with external perturbation. The redistributed electrons

of σ* (C16-H17) can be easily transported to their neighbouring bond of σ (C19-H20) with the

interaction of 9.58 kJ/mol.

Table 8. Second-order perturbation theory analysis of Fock matrix in NBO basis for (PEO) n=5

using DFT/B3LYP/6-311++G(d,p) level of theory in Water and acetone

Donor

(i)

Type Acceptor

(j)

Type E(2)a

kJ/mol

E(j)-E(i)b

a.u

F(i,j)c

a.u.

Wat

er

Ace

ton

e

Wat

er

Ace

ton

e

Wat

er

Ace

ton

e

Wat

er

Ace

ton

e

Wat

er

Ace

ton

e

Wat

er

Ace

ton

e

Wat

er

Ace

ton

e

O 14 O14 n 2 n 2 C16-H17 C 16 -H17 σ* σ* 30.8 30.8 0.69 0.69 0.064 0.064

O 7 O 7 n 2 n 2 C1-H3 C 1- H3 σ* σ* 30.4 30.4 0.69 0.69 0.064 0.064

O 8 O 8 n 2 n 2 C2-H6 C 2 - H6 σ* σ* 30.3 30.3 0.69 0.69 0.064 0.064

O30 O30 n 2 n 2 C31-C34 C31 –C34 σ* σ* 30.1 30.1 0.67 0.67 0.063 0.063

O30 O 7 n 2 n 2 C27-H29 C24 -C27 σ* σ* 29.4 29.4 0.69 0.68 0.063 0.062

O7 O30 n 2 n 2 C24-C27 C27 -H29 σ* σ* 29.4 29.4 0.68 0.69 0.062 0.063

O8 O 8 n 2 n 2 C9 -C11 C 9- C11 σ* σ* 27.9 27.9 0.67 0.67 0.060 0.060

O 14 O14 n 2 n 2 C 9- C11 C9-C11 σ* σ* 27.7 27.7 0.67 0.67 0.060 0.060

O 22 O22 n 2 n 2 C19-H20 C19-H20 σ* σ* 26.9 27.0 0.70 0.70 0.060 0.060

O35 O35 n 2 n 2 C31-C34 C31-C34 σ* σ* 26.3 26.3 0.68 0.68 0.059 0.059

O22 O 22 n 2 n 2 C19-H21 C19-H21 σ* σ* 24.9 25.0 0.69 0.69 0.058 0.058

O14 O14 n 2 n 2 C11-H13 C11- H13 σ* σ* 24.3 24.4 0.68 0.68 0.057 0.057

O 8 O 8 n 2 n 2 C9-H10 C 9-H10 σ* σ* 23.8 23.8 0.68 0.68 0.056 0.056

O30 O30 n 2 n 2 C27-H28 C27-H28 σ* σ* 22.1 22.1 0.69 0.69 0.054 0.054

O8 O 8 n 2 n 2 C2-H5 C2-H5 σ* σ* 22.0 22.1 0.68 0.68 0.054 0.054

O14 O14 n 2 n 2 C16-H18 C16-H18 σ* σ* 21.3 21.3 0.68 0.68 0.053 0.053

O 7 O7 n 2 n 2 C1-H4 C1-H 4 σ* σ* 20.8 20.8 0.69 0.69 0.053 0.053

O35 O35 n 2 n 2 C34-H36 C34-H36 σ* σ* 19.8 19.8 0.69 0.69 0.051 0.051

C11-H13 C11 -H13 σ σ O8-C9 O8-C9 σ* σ* 19.5 19.5 0.82 0.82 0.055 0.055

C9-H10 C 9-H10 σ σ C11-O14 C11-O14 σ* σ* 19.4 19.4 0.82 0.82 0.055 0.055

O30 O30 n 2 n 2 C31-H33 C31 -H33 σ* σ* 15.4 15.4 0.69 0.69 0.045 0.045

O7 O7 n 2 n 2 C24-H26 C24-H26 σ* σ* 15.2 15.2 0.69 0.69 0.045 0.045

C9-H15 C11-H12 σ σ C2-O8 O14-C16 σ* σ* 14.4 14.4 0.81 0.82 0.047 0.047

C11-H12 C9-H15 σ σ O14-C16 C2-O8 σ* σ* 14.4 14.4 0.82 0.82 0.047 0.047

C31 - H32 C31 -H32 σ σ C27-O30 C27-O30 σ* σ* 12.9 12.9 0.81 0.81 0.045 0.045

C24 - H25 C24 - H25 σ σ C1-O7 C1-O7 σ* σ* 12.8 12.8 0.81 0.81 0.044 0.044

O 7 O7 n1 n 1 C1 C1 r* r1* 12.6 12.6 1.76 1.76 0.065 0.065

O 8 O 8 n1 n 1 C2 C2 r* r1* 12.6 12.6 1.69 1.69 0.064 0.064



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O 30 O30 n 1 n 1 C27 C27 r* r1* 11.8 11.8 1.76 1.76 0.063 0.063

O 35 O35 n 1 n 1 C34 C34 r* r1* 11.1 11.1 1.54 1.54 0.057 0.057

O 14 O8 n 1 n 1 C16 C9-H15 r* σ* 11.0 10.9 1.73 0.96 0.061 0.045

C16- C19 C16 - C19 σ σ C11-O14 C11-O14 σ* σ* 10.9 10.9 0.93 0.93 0.044 0.044

O8 O14 n1 n 1 C9-H15 C16 σ* r1* 10.9 10.9 0.96 1.73 0.045 0.060

O14 O14 n 1 n 1 C11-H12 C11-H12 σ* σ* 10.9 10.9 0.96 0.96 0.045 0.045

C1 - C2 C 1 - C2 σ σ O8-C9 O8-C9 σ* σ* 10.8 10.8 0.93 0.93 0.044 0.044

C24-H25 C24-H25 σ σ C27-H28 C27-H28 σ* σ* 10.6 10.7 0.89 0.89 0.043 0.043

O35-H38 O35-H38 σ σ C34 C34 r* r1* 10.6 10.6 1.65 1.65 0.058 0.058

C1 - C2 C 1-C2 σ σ O7-C24 O7-C24 σ* σ* 10.5 10.5 0.93 0.93 0.043 0.043

C24- C27 C 24-C27 σ σ O30-C31 O30-C31 σ* σ* 10.5 10.5 0.93 0.93 0.043 0.043

C19-H21 C 19-H21 σ σ C16-H18 C16-H18 σ* σ* 10.4 10.4 0.89 0.89 0.042 0.042

C34-H37 C 34-H37 σ σ O35-H38 O35-H 38 σ* σ* 10.3 10.3 0.95 0.95 0.043 0.043

C1 - H4 C1-H4 σ σ C2-H5 C2-H5 σ* σ* 10.2 10.2 0.89 0.89 0.042 0.042

C27-O30 C27-O30 σ σ C34-H37 C34-H37 σ* σ* 10.1 10 1.81 1.81 0.059 0.059

O35 O35 n 1 n 1 C31 C31 σ3* r3* 10.1 10.1 1.01 1.01 0.044 0.044

C27-H29 C27-H29 σ σ C24-H26 C24-H26 σ* σ* 10.0 9.96 0.89 0.89 0.041 0.041

C19-H20 C19-H20 σ σ C16-H17 C16-H17 σ* σ* 9.58 9.58 0.90 0.90 0.041 0.041 a E(2) means energy of hyper conjugative interaction (stabilization energy ) , b Ε(j)–E(i) means energy difference between donor and acceptor i and j NBO orbitals,

c F(i; j) means the Fock matrix element between i and j NBO orbitals

5. Conclusion

In this present work, density functional theory has been employed to model a series of

oligomers (PEO)n=1-5 to identify its intrinsic reason for its suitability in polymer electrolytes for DSSC

application. The optimized molecular structure and geometrical parameters namely bond length and

bond angles predict the oligomer size (PEO)n=5 is the sufficient model for understanding the

properties of the title polymer. HOMO-LUMO and other related molecular properties such as

ionization potential, electron affinity, hardness, softness, electrochemical potential and electrophilicity

obtained by HOMO-LUMO analysis are 8.70, 1.90, 3.40, 0.14, -5.30 and 4.13 eV respectively. The

extrapolated values to infinite chain lengths agree with the predicted value of (PEO) n=5 supports that it

is a sufficient model for understanding the polymer properties. The above studies show that oligomer

(n=5) gives the charge transfer value around 1.56 and an electron back-donation value of -0.85 which

follows the same trend of other polymers already utilized in polymer electrolyte in dye-sensitized solar

cells. The predicted electronic absorption spectra from the TD-DFT calculation show the optical band

gap value of 5.97 eV which agrees with the experimental value 5.56 eV. NBO analysis has provided a

detailed insight into the type of nature of bonding. The strongest donation occurs from a lone pair of

O14 to the anti-bonding acceptor C16-H17 orbitals and confirms the stabilization of the polymer arising

from hyper conjugative interaction with the potential of 30.8 KJ/mol. The molecular electrostatic

potential plot depicts the nucleophilic and electrophilic site for electrolyte interaction. On the other

hand, all the chemical reactivity parameters of (PEO)n= 5, have the same value for the solvents water

and acetone in the same basis set indicates the tuning of the polymer nature starts at the chain length of

n = 5. The ionization potential, electrochemical potential, electrophilicity, charge transfer and electron

back-donation parameter reveals that the title polymer is a good candidate for polymer electrolyte in

DSSCs application.



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6. Acknowledgement

The authors thank Cauvery College for Women(Autonomous), Annamalai Nagar, Tiruchirappalli-

620 018 for the research instruments facilities supported by DST-FIST under level ‘0’ program

Ref.no. SR/FST/College-246/2015(c).

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