Noura Dawass

4 68 S URFACE E FFECTS 3. Computing G ∞ from fitting the linear regime of the scaling of LG V with L (Eq. (4.7) ). The values of the integrals G V are computed using Eq. (1.25) . To simplify the estimation of KBIs, it would be useful to evaluate the performance of these methods in terms of accuracy and practicality. Similarly, different meth- ods are available to compute the surface term in the thermodynamic limit F ∞ : 1. Using the expression in Eq. (4.6) . 2. From the scaling of LF V with L (Eq. (4.4) ). F V is computed using Eq. (4.5) . The value of F ∞ is obtained from the slope of the scaling as LF V ( L ) = F ∞ L + C , in which C is a constant. 3. From the scaling of LG V with L (Eq. (4.4) ). The value of F ∞ is obtained from the intercept of the scaling. The objective of this chapter is to test the estimation of KBIs G ∞ and the sur- face effects F ∞ using the approaches discussed earlier. For both G ∞ and F ∞ , the effect of the size of the system is studied. These effects are investigated for both LJ and WCA fluids [130] at different densities. Finally, this work aims at quanti- fying the contributions of the surface term when computing KBIs of LJ fluid at various densities. This chapter is organized as follows. In section 4.2, the methods used to com- pute RDFs, KBIs, and the surface termof KBIs of LJ andWCA fluids are presented. Section 4.2 includes the details of the MD simulations. In section 4.3, the results are presented, which include KBIs and the surface term for WCA and LJ systems at different sizes and densities. Section 4.4 summarises the main findings of this chapter. 4.2. M ETHODS RDFs of systems of particles interacting via the LJ potential are computed us- ing MD simulations in the NV T ensemble. Systems with different densities and number of particles are studied. Also, systems of particles interacting via the WCA potential [112] , where only the repulsive part of the LJ potential is included, are considered. For each system, the computed RDF is used to compute KBIs G ∞ and the surface term F ∞ in the thermodynamic limit. For both quantities, the methods discussed in section 4.1 are used. In this section, the numerical details of computing RDFs and the required integrals are briefly discussed. For all systems studied in this work, RDFs are corrected using the Ganguly and van der Vegt correction [113] , see section 3.3.1. The corrected RDFs are nu- merically integrated to obtain G V , G 2 , F V , and F ∞ 2 . Once these quantities are ob- tained, various methods are implemented to estimate KBIs G ∞ and the surface