Polymer density functional theory approach based on scaling second-order direct correlation function

A second-order direct correlation function (DCF) from solving the polymer-RISM integral equation is scaled up or down by an equation of state for bulk polymer, the resultant scaling second-order DCF is in better agreement with corresponding simulation results than the un-scaling second-order DCF. When the scaling second-order DCF is imported into a recently proposed LTDFA-based polymer DFT approach, an originally associated adjustable but mathematically meaningless parameter now becomes mathematically meaningful, i.e., the numerical value lies now between 0 and 1. When the adjustable parameter-free version of the LTDFA is used instead of the LTDFA, i.e., the adjustable parameter is fixed at 0.5, the resultant parameter-free version of the scaling LTDFA-based polymer DFT is also in good agreement with the corresponding simulation data for density profiles. The parameter-free version of the scaling LTDFA-based polymer DFT is employed to investigate the density profiles of a freely jointed tangent hard sphere chain near a variable sized central hard sphere, again the predictions reproduce accurately the simulational results. Importance of the present adjustable parameter-free version lies in its combination with a recently proposed universal theoretical way, in the resultant formalism, the contact theorem is still met by the adjustable parameter associated with the theoretical way.

Graphical abstractThe reduced site packing fraction profile G(z)=ρ(z)(π/6)/ηaveG(z)=ρ(z)(π/6)/ηave with ηave=π6∫0Hσρ(z)dz/Hσ for a coexistence bulk state point of a 20-mers with η=ρbσ3π6=0.2 and H=16σH=16σ. The symbols are for simulation data [S. Zhou, J. Chem. Phys. (2005), submitted for publication].Figure optionsDownload full-size imageDownload high-quality image (38 K)Download as PowerPoint slide