Density and chain conformation profiles of square-well chains confined in a slit by density-functional theory

Abstract

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 hybrid perturbed-chain SAFT density functional theory for representing fluid behavior in nanopores

“…It should be noted that the DFT models developed by Yu and Wu 8 and by Ye et al 10 can provide accurate descriptions of long chain polymers compared with simulation. However, in all these developed models, the segment number of the molecule can only be an integer, which limits their application to real substances.…”

“…32,33 Following the definition, the weighted density for square-well fluid can also be obtained by integrating the density in the range of attraction. Meanwhile, Ye et al 10 proposed another approximate method, and the weighted density was calculated by integrating the density in the range of interaction, i.e., w disp (r) = 3θ(λσ −r) 4π(λσ ) 3 . It has been systematically proved that this approximate method could provide satisfactory density profiles of square-well chain confined in a slit.…”

“…It has been systematically proved that this approximate method could provide satisfactory density profiles of square-well chain confined in a slit. 10 Therefore, in this work, the method proposed by Ye et al 10 was used for the DFT model based on PC-SAFT, i.e., the weighted density is calculated bȳ…”

“…A significant progress was the development of DFT models for representing the properties of polyatomic fluid on the basis of Wertheim's first order thermodynamic perturbation theory. [7][8][9][10][11] Compared to molecular simulation, most such DFT models accurately predict the microstructure of inhomogeneous fluid, but it is infeasible to use such models to represent properties of real substances due to the fact that most of these models were applied for model molecules with integer segment numbers. On the other hand, the bulk properties of fluids have been extensively studied in a) Electronic mail: xhlu@njut.edu.cn.…”

Density Functional Theory Study on the Structure and Capillary Phase Transition of a Polymer Melt in a Slitlike Pore: Effect of Attraction

“…Unfortunately, the latter gives a rather poor representation of the equation of state. It should be noticeable that, in the implementation of a DFT for square-well chain fluids, Ye et al 16,17 used a Heaviside step function for both repulsive and attractive weighting functions. In KR theory for chain fluids, Wertheim's first-order thermodynamic perturbation theory 18 is applied to represent the equation of state in the bulk limit.…”