Osmotic Ensemble Research Articles

Monte Carlo simulations of equilibrium solubilities and structure of water in n-alkanes and polyethylene

Gibbs ensemble Monte Carlo methods based on a force field that combines the simple point charge [Berendsen et al., in Intermolecular Forces, edited by Pullman (Reidel, Dordrecht, 1981), p. 331] and transferable potentials for phase equilibria [Martin and Siepmann, J. Phys. Chem. B 102, 2659 (1998)] models were used to study the equilibrium properties of binary systems consisting of water and n-alkanes with chain lengths from hexane to hexadecane. In addition, systems where extended linear alkane chains (up to 300 carbon units long) were used to represent amorphous polyethylene were simulated in the presence of water using a connectivity altering osmotic Gibbs ensemble. In these simulations the equilibrium between a liquid water phase and a polymer phase into which water was inserted was studied. The predicted solubilities, which were determined between 350 and 550 K, are in good agreement with experiment, where experimental results are available, and the density of water molecules in the hydrocarbons is approximately 63% as high as in saturated water vapor under the same conditions. At the lower temperatures most of the water exists as monomers; increasing the temperature leads to an increase in the density of water in the alkane phase and hence in the fraction of molecules that participate in clusters. Dimers are the most prevalent clusters in all hydrocarbons and at all temperatures studied, and the fraction of clusters of given size decrease with increasing cluster size. A large fraction of trimers, tetramers, and pentamers, which are the cluster sizes for which topologies have been studied, are cyclic at low temperatures, but at higher temperatures linear structures predominate. The same properties are observed for pure water vapor clusters in equilibrium with the liquid phase, showing that the cluster topologies are not significantly affected by the surrounding hydrocarbon.

Ethylene and 1-Hexene Sorption in LLDPE under Typical Gas Phase Reactor Conditions: A Priori Simulation and Modeling for Prediction of Experimental Observations

A detailed study has been conducted of the sorption of ethylene and 1-hexene in linear low density polyethylene (LLDPE) under typical gas phase LLDPE reactor conditions. The recently proposed osmotic ensemble hyperparallel tempering method is used to simulate ethylene and 1-hexene gas sorption in the polymer samples. Simulations are used to parametrize the PC−SAFT equation of state for calculation of gas sorption in amorphous polyethylene. A model for crystallite induced elastic constraints is adopted to modify the equation of state for description of gas sorption in polyethylene below melting point conditions. Single-component ethylene and 1-hexene gas sorption as well as ethylene/1-hexene gas co-sorption are studied in this work. It is observed that simulations provide an effective method to parametrize the PC−SAFT equation of state. In addition, since simulations and PC−SAFT assume a hypothetically amorphous polymer, a quantitative description of elastic effects for gas sorption in semicrystalline poly...

Simulation of the effects of chain architecture on the sorption of ethylene in polyethylene

An osmotic ensemble hyperparallel tempering technique has been developed to study the solubility of ethylene in amorphous linear low-density polyethylene of different chain architectures. The NERD united-atom force field (Nath, Escobedo, and de Pablo revised united-atom force field) is used in all simulations. We have investigated the effect of polyethylene chain length and branching on ethylene solubility. In this study, we have considered short-chain branching of amorphous linear low-density ethylene-1-hexene copolymers under typical polymerization reactor conditions. It is observed that, in the polymer, ethylene prefers to reside in the vicinity of polymer chain ends. This clustering causes a decrease in ethylene solubility with polymer chain length. When short-chain branches are introduced to a linear polymer chain, however, the chain-end clustering effect is counteracted by a higher density, thereby leading to an ethylene solubility almost identical to that in the linear polymer.

Molecular thermodynamic model for equilibria in solution: IV. Macroscopic partition functions

The molecular ensembles statistically distributed according to internal specific characteristics and distinguished for the different exchanges with the surroundings are represented on the macroscopic scale by appropriate partition functions. The partition function for osmotic non-reacting ensemble is a function of concentration or activity of the ligand and is suited to the definition of thermodynamic potential μ. The partition function for thermal non-reacting ensemble shows the dependence upon the temperature and that for thermo-osmotic non-reacting ensemble shows the dependence upon both concentration and temperature. The reaction partition function is suited to show the distribution of the different species over the different enthalpy levels of the reacting ensemble. The dispersion of the distributions are represented by second derivatives of the partition function. The information contained in the entropy axis of the thermodynamic space for reacting ensembles concerning the induced dilution of the bound ligand and final dilution of the free ligand can be spanned to a formation function diagram where free energy of reaction can be graphically represented.