The basic morphology of semi-crystalline PE.
The orthorhombic unit cell of the crystalline phase of polyethylene showing electrons in (a) valence band states concentrated about C-C and C-H bonds and (b) conduction band states concentrated between chains.
Positive polaron transport. (a) Positive hole conductive elements consisting of crystallites C, interphases I1 and I2 and an intervening amorphous phase A. (b) Positive polaron energies, Wc, in the crystalline phase and Wi in the two interphases, measured with respect to the valence band edge V B. The hole path is shown as ↷.
The energy bridge V(x) for tunnelling through the amorphous phase R between states I1 and I2 (Fig. 3 ) showing (a) the bridge arising from the discrete states in the amorphous phase and (b) the approximate bridge of mean energy V. The donor and acceptor hole states D and A at each end of the bridge (corresponding to sites I1 and I2) are shown for a hole transition in the presence of a field. They are shown as polaronic centres of radii R0.
Hole mobility (—) and velocity v (- - -) as functions of the field F. The parameters used in Eq. (8) are λ = 0.8 eV, V = 0.8 eV, R = 40 Å, E = 1 eV, T = 300 K.
The effect on mobility of changing parameters of the characteristic shown in Fig. 5 . (a) λ/eV: (1) 0.7, (2) 0.8, (3) 0.9. (b) R/Å: (1) 35, (2).40, (3) 45. (c) V/eV: (1) 0.7, (2) 0.8, (3) 0.9. (d) E/eV: (1) 0.9, (2) 1.0, (3) 1.1.
The hole mobility (a) at various temperatures and (b) as thermal activation plots at various fields.
(—) the field F(d,t) at the charge front and (- - -) the anode field F(0,t) up to the transit time when the charge front reaches the cathode for (a) ρ0 = 10 C m−3 and (b) ρ0 = 100 C m−3. The electrode spacing is 200 μm and the applied fields Fm/108 V m−1 are indicated.
Charge front distance-time plots x(t) for ρ0 (a) 10 C m−3 and (b) 100 C m−3. The electrode spacing is 200 μm and the applied fields Fm/108 V m−1 are indicated.
The charge distributions associated with the initial hole transient. The times in seconds since initiation are indicated. Note how the charge front is weakened or strengthened depending on ρ0 and Fm. These parameters determine whether the field at the front is lower or higher than that for the peak velocity.
Packet propagation. A Gaussian charge packet is generated and moves out from the anode. At t = 0, it is assumed to be centred at a distance 5 μm from the anode with a half-width of 2 μm and under an applied field Fm propagates as shown. Note how an increase of packet charge density from 10 to 100 C m−3 changes the characteristics of the propagating packet considerably.
Steady state current density J as a function of field Fm and temperature T K. Charge density ρ0 (—) 100 and (- - -) 10 C m−3.
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