Continuous time random walk model polymers

Abstract This topic reviews random walk Monte Carlo simulation models of charge transport in DSSC. The main electrmi transport approaches used are covered. Monte Carlo methods and results are explained, addressing the continuous time random walk model developed for transport in disordered materials in the context of the large number of trap states present in the electron transporting material. Multiple timescale MC models developed to look at the morphology dependence of electron transport are described. The concluding section looks at future applications of these methods and the related MC models for polymer blend cells. 

This chapter provides an overview of the most frequently applied numerical methods for the simulation of polymerization processes, that is, die calculation of the polymer microstructure as a function of monomer conversion and process conditions such as the temperature and initial concentrations. It is important to note that such simulations allow one to optimize the macroscopic polymer properties and to influence the polymer processability and final polymer product application range. Both deterministic and stochastic modeling techniques are discussed. In deterministic modeling techniques, time variation is seen as a continuous and predictable process, whereas in stochastic modeling techniques, a random-walk process is assumed instead. 

Models of Brownian motion and of the geometry of ideal polymer chains are based on the concept of a random walk. Let us start at time t = 0 and flip a coin. If heads, we take a step to the right of length /. If tails, we take a step to the left. We continue to do this, taking n steps, and measure the net displacements (our final position) (Figure 7.7). 

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