Density and chain conformation profiles of square-well chains between two parallel walls were studied by using density-functional theory. The free energy of square-well chains is separated into two contributions: the hard-sphere repulsion and the attraction. The Heaviside function is used as the weighting function for both of the two parts. The equation of state of Hu et al. is used to calculate the excess free energy of the repulsive part. The equation of state of statistical associating fluid theory for chain molecules with attractive potentials of variable range [A. Gil-Villegas et al. J. Chem. Phys. 106, 4168 (1997)] is used to calculate the excess free energy of the attractive part. Because the wall is inaccessible to a mass center of a longer chain, there exists a sharp fall in the distribution of end-to-end distance near the wall as the chain length increases. When the average density of the system is not too low, the prediction of this work is in good agreement with computer simulation results for the density profiles and the chain conformation over a wide range of chain length, temperature, and attraction strength of the walls. However, when the average density and the temperature are very low, the prediction deviates to a certain degree from the computer simulation results for molecules with long chain length. A more accurate functional approximation is needed.

A density functional theory (DFT) is developed for polymer mixtures with shorted-ranged attractive interparticle interactions confined in a slit. Different weighting functions are used separately for the repulsive part and the attractive part of the excess free energy functional by applying the weighted density approximation. The predicted results by DFT are in good agreement with the corresponding simulation data indicating the reliability of the theory. Furthermore, the center-of-mass profiles and the end-to-end distance distributions are obtained by the single chain simulation; the predictions also agree well with simulation data. The results reveal that both the attraction of the slit wall and the temperature has stronger effect on longer chains than on shorter ones because the intrasegment correlation of chains increases with increasing chain length.

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The energy system of industrial process, particularly in the petrochemical industry, consumes most of the utility cost. In this paper, a superstructure of a large-scale industrial ethylene plant energy system including fuel, steam, electricity and water was studied. In this system, multitype energy is transferred by water, as the working medium, which makes it feasible for the multitype energy to be synthesized according to the heating, cooling, and phase changes of water. The unit models were developed by hybrid modeling method combining thermodynamics and least-square method (LSM). The seasonal energy system optimization based on typical day method was formulated as an mixed-integer nonlinear programming (MINLP) problem. Then, an efficient decomposition-based model solving strategy was proposed for solving this difficult problem, in which the fuel, steam, electricity, and water consumption were simultaneously optimized. The optimal operational solution was obtained by the following strategies: (1) regulating the steam flow rate in letdown valves, the condensing steam flow rate extracted from turbines, and selections of power sources for low demand mechanical users synergistically; (2) determining the cooling water temperature to balance the turbine efficiency and the electricity and water consumption; and (3) employing different numbers of cooling towers according to the seasons. The flow rate-related decisions are sensitive to uncertainty in the measurement, while the temperature-related and pressure-related ones are relatively more stable. The results showed that the total energy consumption was reduced by 14.42% in spring−autumn and 13.92% in summer, which were 1.44 and 0.89% better than these using the two-type energy optimization method in literature, respectively. Further energy structure analysis exhibiting consumption proportion of different types of energy showed that part of the fuel consumption was replaced by cheaper steam and electricity to reduce total energy cost. Finally, energy management strategies were formed on the basis of the above results.