Mobility simulation

Figure 12-18. The temperature dependencies of the mobility simulated for different nap depths. The trap concentrations were 3x1 O 2 and the field 2xl05 V em 1 (Ref. 72J).

Figure 12-17. The icmperalurc dependencies of Ihe mobility simulated lor <7=0.065 eV for different concentrations of traps. The Irap deplh was 0.25 eV and Ihe field 2x10s V cm 1. The dashed line corresponds to the absence of trap (Kef. 72 ).

Clavier, J.Y. (1995) Developpement du precede de Lit Mobile Simule avec eluant supercritique. These de doctoral INPL. 

Otlier expressions for tire diffusion coefficient are based on tire concept of free volume [57], i.e. tire amount of volume in tire sample tliat is not occupied by tire polymer molecules. Computer simulations have also been used to quantify tire mobility of small molecules in polymers [58]. In a first approach, tire partition functions of tire ground... 

With the Monte Carlo method, the sample is taken to be a cubic lattice consisting of 70 x 70 x 70 sites with intersite distance of 0.6 nm. By applying a periodic boundary condition, an effective sample size up to 8000 sites (equivalent to 4.8-p.m long) can be generated in the field direction (37,39). Carrier transport is simulated by a random walk in the test system under the action of a bias field. The simulation results successfully explain many of the experimental findings, notably the field and temperature dependence of hole mobilities (37,39). 

Figure 6 shows the field dependence of hole mobiUty for TAPC-doped bisphenol A polycarbonate at various temperatures (37). The mobilities decrease with increasing field at low fields. At high fields, a log oc relationship is observed. The experimental results can be reproduced by Monte Carlo simulation, shown by soHd lines in Figure 6. The model predicts that the high field mobiUty follows the following equation (37) where d = a/kT (p is the width of the Gaussian distribution density of states), Z is a parameter that characterizes the degree of positional disorder, E is the electric field, is a prefactor mobihty, and Cis an empirical constant given as 2.9 X lO " (cm/V). ...

Based on the Monte Carlo simulations, it is seen that the presence of positional disorder causes the mobiUty to decrease with increasing field at low fields (37). This is the case because the introduction of positional disorder into the system provides the carrier with energetically more favorable routes, which occasionally are against the field direction. These detour routes are most efficient at low fields, but are eliminated at high fields. This rationalizes the decrease of hole mobilities with increasing field. 

The concentration of salt in physiological systems is on the order of 150 mM, which corresponds to approximately 350 water molecules for each cation-anion pair. Eor this reason, investigations of salt effects in biological systems using detailed atomic models and molecular dynamic simulations become rapidly prohibitive, and mean-field treatments based on continuum electrostatics are advantageous. Such approximations, which were pioneered by Debye and Huckel [11], are valid at moderately low ionic concentration when core-core interactions between the mobile ions can be neglected. Briefly, the spatial density throughout the solvent is assumed to depend only on the local electrostatic poten-... 

Additional chronic toxicity Additional environmentally dangerous properties Toxicity to birds Long-term toxicity in water and soil Degradability simulation tests Additional abiotic degradability Mobility in water, soil and air cumulative... 

Apart from the global motions of the ehains in the film as a whole, one ean eonsider the loeal mobility as a funetion of distanee from the plates. While for e = 0 this mobility is slightly larger near the walls than in the eenter of the film, the opposite is true for large e [16]. This behavior refleets simply the strueture of the density profile for a purely repulsive wall the density is redueed near the wall whereas, for an attraetive wall, a layer of enhaneed density is found elose to the wall. These simulational results are in... 

The molecular simulations also showed that electro-osmosis is also observed in aqueous electrolyte solutions, as long as the external electric field is reversed periodically to prevent the ions from accumulating near the membrane. An example of this is shown in Fig. 10, which shows the effect of an electric field on a 4.67 mole percent aqueous LiCl solution at 25°C. It is quite clear that the mobility of the solvent molecules increases as a result of... 

It is obvious, and verified by experiment [73], that above a critical trap concentration the mobility increases with concentration. This is due to the onset of intertrap transfer that alleviates thermal detrapping of a carrier as a necessary step for charge transport. The simulation results presented in Figure 12-22 are in accord with this notion. The data for p(c) at ,=0.195 eV, i.e. EJa—T), pass through a minimum at a trap concentration c—10. Location of the minimum on a concentration scale depends, of course, on , since the competition between thermal detrapping and inter-trap transport scales exponentially with ,. The field dependence of the mobility in a trap containing system characterized by an effective width aeff is similar to that of a trap-free system with the same width of the DOS. 

Another issue that can be clarified with the aid of numerical simulations is that of the recombination profile. Mailiaras and Scott [145] have found that recombination takes place closer to the contact that injects the less mobile carrier, regardless of the injection characteristics. In Figure 13-12, the calculated recombination profiles arc shown for an OLED with an ohmic anode and an injection-limited cathode. When the two carriers have equal mobilities, despite the fact that the hole density is substantially larger than the electron density, electrons make it all the way to the anode and the recombination profile is uniform throughout the sample. 

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