Download Electronic and Optical Properties of Conjugated Polymers by William Barford PDF
By William Barford
Conjugated polymers have vital technological functions, together with sunlight cells and lightweight emitting screens. also they are lively elements in lots of organic methods. in recent times, there were major advances in our figuring out of those platforms, because of either greater experimental measurements and the improvement of complicated computational suggestions. the purpose of this e-book is to explain and clarify the digital and optical homes of conjugated polymers. It specializes in the nature and vigorous ordering of the digital states and relates those homes to experimental observations in genuine platforms.
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Extra resources for Electronic and Optical Properties of Conjugated Polymers
Example text
1 Wannier States By Fourier transforming the Bloch operators, ckσ v † c obtain Wannier operators, c σ , which create electrons in Wannier states localized on the th repeat unit: v † c cσ = 1 Nu v † c ckσ exp(i2k a). 25) k To a rather good approximation,13 the valence and conduction band Wannier states are equivalent to the bonding and antibonding states, respectively, that is, v 1 † c cσ ≈ √ c†2 −1 ± c†2 . 26) 2 12 For 1/2 a general td and ts the energy spectrum is k = ± t2d + t2s + 2td ts cos(2ka) .
For polymers with alternating short and long bonds, δn = δ(−1)n , where δn is positive or negative for short or long bonds, respectively. 3 Undimerized chains We first consider undimerized chains with δ = 0 and tn ≡ t. 2) ckσ exp(−ikna). 3) k k The Bloch wavevector, k = 2πj/N a and the (angular momentum) quantum number j satisfies, −N/2 ≤ j ≤ N/2. a is the lattice parameter. 4) cnσ exp(ikna). 1) gives, H=− t N c†kσ ck σ exp(i(k − k )na) exp(−ik a) + hermitian conjugate. 8) we have that, cos(ka)c†kσ ckσ .
In the noninteracting limit these particle-hole states of opposite symmetry are degenerate. There is an important connection between particle-hole symmetry and the relative parity of the particle-hole pair. Consider a basis state created by the removal of an electron from a valence band Wannier orbital on the repeat unit at R − r/2 and the creation of an electron on a conduction band Wannier orbital at R + r/2. This is illustrated in Fig. 1. This particle-hole pair has a centre-ofmass coordinate, R, and a relative coordinate, r: 1 |R + r/2, R − r/2 = √ 2 v cc† R+r/2,σ cR−r/2,σ |GS .