A density-functional approach and canonical Monte Carlo simulations are presented for describing the ionic microscopic structure around the DNA molecule immersed in mixed-size counterion solutions. In the density-functional approach, the hard-sphere contribution to the Helmholtz energy functional is obtained from the modified fundamental measure theory [Y.-X. Yu and J. Z. Wu, J. Chem. Phys. 117, 10156 (2002)], and the electrostatic contribution is evaluated through a quadratic functional Taylor expansion. The new theory is suitable to the systems containing ions of arbitrary sizes and valences. In the established canonical Monte Carlo simulation, an iterative self-consistent method is used to evaluate the long-range energy, and another iterative algorithm is adopted to obtain desired bulk ionic concentrations. The ion distributions from the density-functional theory (DFT) are in good agreement with those from the corresponding Monte Carlo (MC) simulations. It is found that the ratio of the bulk concentrations of two species of counterions (cations) makes significant contribution to the ion distributions in the vicinity of DNA. Comparisons with the electrostatic potential profiles from the MC simulations show that the accuracy of the DFT becomes low when a small divalent cation exists. Both the DFT and MC simulation results illustrate that the electrostatic potential at the surface of DNA increases as the anion diameter or the total cation concentration is increased and decreases as the diameter of one cation species is increased. The calculation of electrostatic potential using real ion diameters shows that the accuracy of DFT predictions for divalent ions is also acceptable.

In substitution of path integral isomorphism of the quantum particle, an effective polymer ring model is proposed in the density functional calculation for hydrogen adsorption in single-walled carbon nanotubes. The excess intrinsic Helmholtz energy for quantum particles includes contributions from hard-sphere repulsion, interatomic bonding and soft attraction. The first two contributions are considered through the method developed by Yu and Wu [J. Chem. Phys. 117, 2368 (2002)], and the last contribution is obtained from mean field approximation using Weeks–Chandler–Anderson potential. The theoretical predictions are in good agreement with Monte Carlo simulation data for the density distributions of the hydrogen molecule inside the tube. In addition, the proposed model is applied to the calculation of the adsorption isotherms of hydrogen at 100 and 150 K. The present model is simpler than the current existing theories for quantum fluids.

Boiling points have been determined at 101.33 kPa for the binary mixtures of sulfolane+o-xylene, sulfolane+m-xylene, sulfolane+p-xylene, sulfolane+ethylbenzene and sulfolane+1,2,4-trimethylbenzene. Calculations of the non-ideality of the vapor phase were made with the second virial coefficients evaluated from the Hayden-O'Connell method. The binary parameters for five activity coefficient models (Margules, van Laar, Wilson, NRTL and UNIQUAC) have been fitted with the experimental boiling points measured in this work. A comparison of model performances has been carried out using the criterion of the average absolute deviations in boiling point. The activity coefficient of the component in the liquid phase is discussed based on the UNIFAC model with the consideration of the dipole–dipole interactions.