Mixing Monte Carlo simulation results

When the two phases separate the distribution of the solvent molecules is inhomogeneous at the interface this gives rise to an additional contribution to the free energy, which Henderson and Schmickler treated in the square gradient approximation [36]. Using simple trial functions, they calculated the density profiles at the interface for a number of system parameters. The results show the same qualitative behavior as those obtained by Monte Carlo simulations for the lattice gas the lower the interfacial tension, the wider is the interfacial region in which the two solvents mix (see Table 3). 

In Fig. 11.3, we made a comparison between the binodals obtained from dynamic Monte Carlo simulations (data points) and from mean-field statistical thermodynamics (solid lines). First, one can see that even with zero mixing interactions B = 0, due to the contribution of Ep, the binodal curve is still located above the liquid-solid coexistence curve (dashed lines). This result implies that the phase separation of polymer blends occurs prior to the crystallization on cooUng. This is exactly the component-selective crystallizability-driven phase separation, as discussed above. Second, one can see that, far away from the liquid-solid coexistence curves (dashed lines), the simulated binodals (data points) are well consistent... 

Fig. 13 Global structure factor versus wave vector for different times for a quench from the mixed state at /N = 0.314 to X-N = 5. Lines represent Monte Carlo results, symbols dynamic SCF theory results, (a) Compares dynamic SCF theory using a local Onsager coefficient with Monte Carlo simulations. Local dynamics obviously overestimates the growth rate and shifts the wavevector that corresponds to maximal growth rate to larger values, (b) Compares dynamic SCF theory using anon-local Onsager coefficient that mimics Rouses dynamics with Monte Carlo results showing better agreement. From [29]...

Another way to obtain networks with irregularities is to mix chains end and cross-linking agent in a non-stoichiometric ratio of reactive groups The cycle rank and the topology of the resulting networks can be predicted by Monte-Carlo simulation... 

Fig. 27. Results from Monte Carlo simulations, like the data shown in fig. 14 (a) Remanent magnetization obtained by cooling in a field (TRM) or shortly applying a field at constant temperature (IRM) as a function of the initially applied field. IRM (fc) is obtained by some mixed cooling procedure. A, is measured at the temperature T = AJlAk. (b) Remanent magnetization M, as a function of time. The squares (TRM. B - AJ) and dots (IRM, B — i. - AJ) have the same initial energy, the dots and crosses (TRM, B = have the same initial magnetization (T= 0.5 dJ) (from Kinzel 1979).

To test the above results and determine maximum deliveries from carbons, grand canonical (GCMC) Monte Carlo simulations were performed here for both slit pores and carbon nanotubes, for the case of hydrogen as well as methane storage. The Lennard-Jones model was enployed for the fluid-fluid as well as fluid-solid interactions, using the Lorentz-Berthelot mixing rules, and commonly used parameters listed elsewhere [18]. Isosteric heats were estimated in the simulations following the well-known fluctuation formula [18]. 

From the results of Monte Carlo simulation, it is suggested that the 1 1/2 0 type SRO state is commonly described as a mixed state of Dla, DQn and Pt2Mo type microclusters. 

All models need some binary interaction parameters that have to be adjusted to some thermodynamic equihbriirm properties since these parameters are a priori not known (we will not discuss results from Monte Carlo simulations here). Binary parameters obtained from data of dilute polymer solutions as second virial coefficients are often different from those obtained from concentrated solutions. Distinguishing between intramolecular and intermolecular segment-segment interactions is not as important in concentrated solutions as it is in dilute solutions. Attempts to introduce local-composition and non-random-mix-ing approaches have been made for all the theories given above with more or less success. At least, they introduce additional parameters. More parameters may cause a higher flexibility of the model equations but leads often to physically senseless parameters that cause troubles when extrapolations may be necessary. Group-contribution concepts for binary interaction parameters in equation of state models can help to correlate parameter sets and also data of solutions within homologous series. 

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