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Electric Field Poled Polymeric Nonlinear Optical Systems: Molecular Dynamics Simulations of Poly(methyl methacrylate) Doped with Disperse Red Chromophores Yaoquan Tu,† Qiong Zhang,†,‡ and Hans Ågren*,† Theoretical Chemistry, Royal Institute of Technology, AlbaNoVa UniVersity Center, S-106 91 Stockholm, Sweden, and Laboratory for AdVanced Materials and Institute of Fine Chemicals, East China UniVersity of Science and Technology, Shanghai 200237, P. R. China ReceiVed: NoVember 8, 2006; In Final Form: January 12, 2007
We demonstrate a complete procedure for simulations of electric field poled polymeric nonlinear optical systems with the purpose to evaluate the macroscopic electro-optic coefficients. The simulations cover the electric field poling effects on the chromophore order at the liquid state, the cooling procedure from the liquid to the solid state in the presence of the poling field, and the back-relaxation of the system after the removal of the field. We use Disperse Red chromophore molecules doped in a poly(methyl methacrylate) matrix for a numerical demonstration of the total procedure. On the basis of the simulation results, the polymer mobility and the static properties of the dopant chromophores are derived. In the liquid state, the chromophore molecules are closer to the side chains than to the backbones of the polymer matrix, and after the simulated annealing, the polymer matrix tends to be closely packed, leading to a significant change in the polymer structure around the chromophore molecules. Besides predicting the absolute macroscopic electro-optic coefficient values, the results are used to derive the microscopic origin of these values in terms of geometric and electronic structure, loading, poling, and back-relaxation effects, thereby aiding to establish design principles for optimum guest-host configurations.
1. Introduction Organic polymeric nonlinear optical (NLO) materials have great potential for applications within photonics, such as ultrafast optical switches, efficient electro-optic modulators, and highly packed photostorage discs. Such NLO materials, with organic NLO chromophores either doped in or covalently bonded to host polymers, are often associated with large NLO responses, ultrafast response times, and exceptional bandwidths and have therefore been the subject of intensive studies in recent years.1-7 The macroscopic NLO response of a polymeric NLO material is closely related to the properties of the contained organic chromophores, in particular their hyperpolarizabilities. Organic conjugate systems with highly polarizable π electron bridges and donor-acceptor end groups show large hyperpolarizabilities and have therefore often been employed as useful NLO chromophores.1,3,8,9 In order to obtain the macroscopic NLO response of a polymeric material, it is also crucial that the chromophores be arranged in a noncentrosymmetrical order. There are several ways to achieve such noncentrosymmetrical arrangements of organic chromophores. The most commonly used method is the electric field poling technique,2,3,6 which, for a polymeric material with dipolar chromophores, is accomplished by applying an external electric field to rearrange the chromophores at a temperature above the glass transition temperature, Tg, of the material. The interaction of the field with the dipole moment of a chromophore tends to align the dipole moment along the field, leading to ordered arrangements of the chromophores. The order of the chromophores can be maintained by gradually cooling the system from the liquid to the * Corresponding author. E-mail:
[email protected]. † Theoretical Chemistry. ‡ Laboratory for Advanced Materials and Institute of Fine Chemicals.
glass state in the presence of the poling field. One would expect that the NLO response of a bulk material could increase with the chromophore concentration. However, experimental measurements of the macroscopic electro-optic coefficients, r33, of polymeric materials show that this is the case only for moderate chromophore concentrations. At higher concentrations, r33 reaches saturation or a maximum.4 Such observations have been attributed to strong chromophore-chromophore interactions, which result in a poor poling efficiency. Obviously, the interactions between chromophores and the host matrix, and the structure of the host matrix, could also have a large influence on the local field felt by the chromophores and therefore affect the poling efficiency. Such interactions can even play important roles in the back-relaxation of the chromophore order after the removal of the poling field. In understanding and predicting the macroscopic nonlinearity from the microscopic nonlinear property of a chromophore, theoretical modeling can play an essential role. To model and design the NLO response at an individual chromophore level, structure-function relationships as well as quantitative quantum chemistry calculations have occasionally been used.1,3,8,9 In modeling the chromophore behavior of an interaction system, the conventional Onsager cavity model has commonly been adopted,2,3 in which the organic chromophore occupies a cavity and its surrounding is simply approximated as a uniform dielectric continuum. Although the Onsager model could be used satisfactorily in describing the behavior of a molecular chromophore in a uniform medium, such as a solution, it is generally difficult to use the model to describe how the chromophorechromophore and chromophore-host matrix interactions, and the structure of the host matrix, affect the macroscopic NLO properties. This is because the Onsager model neglects any
10.1021/jp067384l CCC: $37.00 © 2007 American Chemical Society Published on Web 03/21/2007
3592 J. Phys. Chem. B, Vol. 111, No. 14, 2007
Tu et al. interactions are modeled by a class I molecular mechanical force field with the form:
E)
Vn
kr(r - req)2 + ∑ kθ(θ - θeq)2 + ∑ [1 + ∑ bonds angles dihedrals 2 cos(nφ - γ)] +
Figure 1. Structure of Disperse Red (DR) molecule and the PMMA unit.
detailed description of the microscopic structure, which is essential for understanding and deriving the macroscopic NLO properties. The rapid development in recent years in molecular simulation techniques has provided powerful tools to model the detailed structure of an interaction system at the microscopic level. By using modern simulation techniques, especially those based on molecular dynamics (MD) algorithms, one can estimate the macroscopic properties of a system and study the microscopic origin behind them. Applications of MD simulation techniques to the study of NLO molecular chromophores in organic solutions and polymeric materials have recently been reported in the literature.10-14,18-20 For example, by using MD simulations, Kim and Hayden10 studied the electric field poling effects of poly(methyl methacrylate) (PMMA) doped with the NLO chromophore N,N-dimethyl-p-nitroaniline (DPNA). MakowskaJanusik et al.13 carried out MD simulations on three electric field poled host-guest systems. On the basis of the structures from MD simulations, Reis et al.14 proposed an approach to the calculation of linear and nonlinear optical susceptibilities of poled guest-host polymer systems. By using Monte Carlo statistical mechanical simulations, Robinson et al. have studied saturation effect at higher loadings.15,16 So far, the reported MD simulations of electric field poled guest-host polymeric NLO systems have mainly been carried out with applied fields much higher than those that can be implemented in experiments. In the work of Leahy-Hoppa et al.,17 the poling fields were indeed as low as 0.18 kV/µm, which are experimentally accessible. However, the densities used in the simulations were much lower than those for real polymeric systems. Although simulations under such conditions could be useful for the study of a system with limited computer resources, it is evidently more desirable to simulate a polymeric NLO system at conditions close to those in experiments and to explore the results for practical applications, such as for modeling the NLO response of a bulk material. In this paper, we report an effort in studying an electric field poled guest-host system under conditions close to experiment. The system we studied contains PMMA as host polymer matrix doped with Disperse Red (DR) molecules as guest NLO chromophores (see Figure 1 for the structures of a DR molecule and a PMMA unit). The simulations cover the electric field poling effects on the chromophore order at a temperature above Tg, the cooling procedure from the liquid to the glass state in the presence of the poling field, and the back-relaxation of the system after the removal of the field. On the basis of the simulation results, the macroscopic NLO responses, such as the electro-optic coefficients, were evaluated and the interactions between the chromophore molecules and host matrix were analyzed. 2. Computational Details The main tool we used in this work is the MD simulation technique. In these simulations, the intra- and intermolecular
∑ i
