Non-innocent side-chains with dipole moments in organic solar cells improve charge separation

Providing sustainable energy is one of the biggest challenges nowadays. An attractive answer is the use of organic solar cells to capture solar energy. Recently a promising route to increase their efficiency has been suggested: developing new organic materials with a high dielectric constant. This solution focuses on lowering the coulomb attraction between electrons and holes, thereby increasing the yield of free charges. In here, we demonstrate from a theoretical point of view that incorporation of dipole moments in organic materials indeed lowers the coulomb attraction. A combination of molecular dynamics simulations for modelling the blend and ab initio quantum chemical calculations to study specific regions was performed. This approach gives predictive insight in the suitability of new materials for application in organic solar cells. In addition to all requirements that make conjugated polymers suitable for application in organic solar cells, this study demonstrates the importance of large dipole moments in polymer side-chains

Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagon

The raise and peel model of a one-dimensional fluctuating interface (model A) is extended by considering one source (model B) or two sources (model C) at the boundaries. The Hamiltonians describing the three processes have, in the thermodynamic limit, spectra given by conformal field theory. The probability of the different configurations in the stationary states of the three models are not only related but have interesting combinatorial properties. We show that by extending Pascal's triangle (which gives solutions to linear relations in terms of integer numbers), to an hexagon, one obtains integer solutions of bilinear relations. These solutions give not only the weights of the various configurations in the three models but also give an insight to the connections between the probability distributions in the stationary states of the three models. Interestingly enough, Pascal's hexagon also gives solutions to a Hirota's difference equation.Comment: 33 pages, an abstract and an introduction are rewritten, few references are adde

A refined Razumov-Stroganov conjecture II

We extend a previous conjecture [cond-mat/0407477] relating the Perron-Frobenius eigenvector of the monodromy matrix of the O(1) loop model to refined numbers of alternating sign matrices. By considering the O(1) loop model on a semi-infinite cylinder with dislocations, we obtain the generating function for alternating sign matrices with prescribed positions of 1's on their top and bottom rows. This seems to indicate a deep correspondence between observables in both models.Comment: 21 pages, 10 figures (3 in text), uses lanlmac, hyperbasics and epsf macro

The Multiplicity of Eigenvalues of the Hodge Laplacian on 5-Dimensional Compact Manifolds

We study multiplicity of the eigenvalues of the Hodge Laplacian on smooth, compact Riemannian manifolds of dimension five for generic families of metrics. We prove that generically the Hodge Laplacian, restricted to the subspace of co-exact two-forms, has nonzero eigenvalues of multiplicity two. The proof is based on the fact that Hodge Laplacian restricted to the subspace of co-exact two-forms is minus the square of the Beltrami operator, a first-order operator. We prove that for generic metrics the spectrum of the Beltrami operator is simple. Because the Beltrami operator in this setting is a skew-adjoint operator, this implies the main result for the Hodge Laplacian

Finite-size left-passage probability in percolation

We obtain an exact finite-size expression for the probability that a percolation hull will touch the boundary, on a strip of finite width. Our calculation is based on the q-deformed Knizhnik--Zamolodchikov approach, and the results are expressed in terms of symplectic characters. In the large size limit, we recover the scaling behaviour predicted by Schramm's left-passage formula. We also derive a general relation between the left-passage probability in the Fortuin--Kasteleyn cluster model and the magnetisation profile in the open XXZ chain with diagonal, complex boundary terms.Comment: 21 pages, 8 figure

Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries

We derive the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. For totally asymmetric diffusion we calculate the spectral gap, which characterizes the approach to stationarity at large times. We observe boundary induced crossovers in and between massive, diffusive and KPZ scaling regimes.Comment: 4 pages, 2 figures, published versio

Conformal invariance and its breaking in a stochastic model of a fluctuating interface

Using Monte-Carlo simulations on large lattices, we study the effects of changing the parameter $u$ (the ratio of the adsorption and desorption rates) of the raise and peel model. This is a nonlocal stochastic model of a fluctuating interface. We show that for $0<u<1$ the system is massive, for $u=1$ it is massless and conformal invariant. For $u>1$ the conformal invariance is broken. The system is in a scale invariant but not conformal invariant phase. As far as we know it is the first example of a system which shows such a behavior. Moreover in the broken phase, the critical exponents vary continuously with the parameter $u$. This stays true also for the critical exponent $\tau$ which characterizes the probability distribution function of avalanches (the critical exponent $D$ staying unchanged).Comment: 22 pages and 20 figure

Relaxation rate of the reverse biased asymmetric exclusion process

We compute the exact relaxation rate of the partially asymmetric exclusion process with open boundaries, with boundary rates opposing the preferred direction of flow in the bulk. This reverse bias introduces a length scale in the system, at which we find a crossover between exponential and algebraic relaxation on the coexistence line. Our results follow from a careful analysis of the Bethe ansatz root structure.Comment: 22 pages, 12 figure

Autocorrelations in the totally asymmetric simple exclusion process and Nagel-Schreckenberg model

We study via Monte Carlo simulation the dynamics of the Nagel-Schreckenberg model on a finite system of length L with open boundary conditions and parallel updates. We find numerically that in both the high and low density regimes the autocorrelation function of the system density behaves like 1-|t|/tau with a finite support [-tau,tau]. This is in contrast to the usual exponential decay typical of equilibrium systems. Furthermore, our results suggest that in fact tau=L/c, and in the special case of maximum velocity 1 (corresponding to the totally asymmetric simple exclusion process) we can identify the exact dependence of c on the input, output and hopping rates. We also emphasize that the parameter tau corresponds to the integrated autocorrelation time, which plays a fundamental role in quantifying the statistical errors in Monte Carlo simulations of these models.Comment: 7 pages, 6 figure

On the relation between local and charge-transfer exciton binding energies in organic photovoltaic materials

In organic photovoltaic devices two types of excitons can be generated for which different binding energies can be defined: the binding energy of the local exciton generated immediately after light absorption on the polymer and the binding energy of the charge-transfer exciton generated through the electron transfer from polymer to PCBM. Lowering these two binding energies is expected to improve the efficiency of the devices. Using (time-dependent) density functional theory, we studied whether a relation exists between the two different binding energies. For a series of related co-monomers, we found that the local exciton binding energy on a monomer is not directly related to that of the charge-transfer exciton on a monomer-PCBM complex because the variation in exciton binding energy depends mainly on the variation in electron affinity, which does not affect in a direct way the charge-transfer exciton binding energy. Furthermore, for the studied co-monomers and their corresponding trimers, we provide detailed information on the amount of charge transfer upon excitation and on the charge transfer excitation length. This detailed study of the excitation process reveals that the thiophene unit that links the donor and acceptor fragments of the co-monomer actively participates in the charge transfer process