Monte Carlo simulations orientational ordering

Figure 15.9 Spectrum for an elongated network (A, = 3.41, N = 51, Q = 0°) obtained by Monte-Carlo simulation. The abscissa scale denotes the reduced interaction A/vq, i.e. the orientational order parameter S. Ordinates are in linear arbitrary units...

Preliminary results of Monte Carlo simulation [183] have also demonstrated the usefulness of the bond - orientational order parameters in determining the inner structure of films adsorbed on the (100) face of an fee crystal. 

The Pauli Master equation approach to calculating RET rates is particularly useful for simulating time-resolved anisotropy decay that results from RET within aggregates of molecules. In that case the orientation of the aggregate in the laboratory frame is also randomly selected at each Monte Carlo iteration in order to account for the rotational averaging properly. 

Figure 21. Orientational order-disorder (squares) and translational melting (circles) transition temperatures for N2 monolayers on graphite as a function of the island size N from Monte Carlo simulations with free boundary conditions. The arrows with the corresponding symbols at the end mark the infinite system size estimates for these quantities within the same model. (Adapted from Fig. 1 of Ref. 185.)...

Figure 33. Herringbone orientational correlation functions F (3.15) in the inset and the logarithmic derivatives 62 In (3.18) as a function of distance I in units of the lattice constant a - 4.26 A in the disordered phase of the anisotropic-planar-rotor model (2.5) from Monte Carlo simulations at 7" = 25.5 K and a linear system size of L = 180. The different symbols distinguish the three symmetty axes a, and the dashed line marks the plateau 2/. In the inset all three F fall on top of each other and the different symbols denote here the two oscillating parts of the antiferromagnetic-like ordering pattern. (Adapted from Fig. 1 of Ref. 273.)...

The grand canonical Monte Carlo simulation of O2 adsorption by a graphite slit at 100 K showed that O2 molecules are orientationally ordered on the micropore walls [72]. If O2 molecules have an orientationally ordered structure in the micropore as suggested by the simulation work, such an ordered structure coincides with the cluster and the organized assembly formation. Thus magnetic measurements are quite effective for identifying the weakly interacting molecular states in micropores. 

Capillary waves do not only broaden the width of the interface but they can also destroy the orientational order in highly swollen lamellar phases (see Fig. 1 for a phase diagram extracted from Monte Carlo Simulations). Those phases occur in mixtures of diblock-copolymers and homopolymers. The addition of homopolymers swells the distance between the lamellae, and the self-consistent field theory predicts that this distance diverges at Lifshitz points. However, general considerations show that mean-field approximations are bound to break down in the vicinity of lifshitz points [61]. (The upper critical dimension is du = 8). This can be quantified by a Ginzburg criterion. Fluctuations are important if... 

We have described lattice spin models for the simulation of polymer-dispersed liquid crystals. The biggest advantage of Monte Carlo simulations is the possibility of investigating the system at a microscopic level, and to calculate thermodynamic properties and their specific order parameters suitable for different types of PDLC. Molecular organizations can be investigated by calculating the order parameters point by point across the droplet. Moreover, it is possible to calculate experimental observables like optical textures and, as discussed here, NMR line shapes. We have given an overview of the method and some applications to models of PDLC with radial and bipolar boundary conditions, and considered the effect of orientational and translational diffusion on the spectra. We have examined in particular under what conditions the NMR spectra of the deuterated nematic can provide reliable information on the actual boundaries present in these submicron size droplets. 

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