Sociopsychological Foundations of Intractable Conflicts
Summary (2 min read)
1 Introduction
- Interfacial phenomena play a key role not only in many scientific fields, such as nucleation, nanotechnology or the dynamics of phase transitions, but also in a great number of practical applications1.
- This allows to implement more elaborated and complex theories that in a second stage could be apply to predict the thermodynamic and interfacial behaviour of real models.
- As the authors have mentioned previously in this Section, it is possible to determine the interfacial properties of molecular model systems, not only from computer simulation but also using a molecular theory based on Statistical Mechanics.
- In particular, the theoretical formalism uses a Helmholtz free-energy functional which reduces to the SAFT-VR83,84 free energy of the homogeneous fluid in the limit of constant density.
2 Model and Theory
- The molecular model and theory used to determine the bulk phase behaviour and the interfacial properties of TSWC are briefly described in this section before presenting the results.
- The molecular chains considered in this work are formed from m spherical segments tangentially bonded that interact through the SW intermolecular potential, which is characterised by a diameter σ , a dispersive energy ε, and a potential range λ .
- This contribution is treated within a Local Density Approximation (LDA)1,39, which implies that the hard-sphere contribution to the free energy of the inhomogeneous system is approximated by that of an equivalent homogeneous system of hard spheres evaluated at the local density ρ(r).
- The term Fchain in Eq. (5) corresponds to the contribution to the free energy due to the formation of chains of m square-well segments, according to the standard Wertheim’s first-order thermodynamic perturbation theory (TPT1) of association86.
- As in their previous papers72,72,82, a numerical integration of Eq. (3) is performed by starting from a trial density profile ρold with limiting densities which correspond to the vapour and liquid equilibrium bulk densities (obtained as described in reference83).
3 Simulation Details
- The authors determine the phase equilibrium and interfacial properties of chain molecules formed from spherical monomers that interact through the SW intermolecular potential from Monte Carlo simulation.
- The authors consider a system of N molecules at a temperature T in a volume V = Lx Ly Lz, where Lx, Ly and Lz are the dimensions of the rectangular simulation box.
- Each type of move is chosen with a probability of 20%, 40%, and 40% for centre of mass displacements, partial configurational bias chain regrowth, and Grand–Canonical configurational bias chain insertion/deletion, respectively.
- The residual chemical potential, as a function of density, was then fitted to a polynomial of 2nd up to 5th order and integrated up to the coexistence vapour density.
- This is achieved by introducing a new MC move, which consists of an attempt to deform the box by changing the interfacial area of the system at constant volume.
4 Results
- The authors apply the SAFT-VR DFT approach outlined in the Introduction to study the vapour-liquid interfacial properties of fully-flexible TSWC with potential range λ = 1.5σ and varying chain length.
- Differences between both results can be observed at temperatures close to the critical temperature of each chain length.
- The SAFT-VR approach, as in the case of the vapour-liquid coexistence envelopes, provides a qualitative description of the vapour pressure of chains formed from several SW monomeric units.
- At low temperatures and particularly for the cases m = 4 and m = 8, the SAFT-VR DFT formalism underestimates the surface tension values obtained from Monte Carlo simulation.
- The authors have also included the scaling relation given by Eq. (12) using the simulation data presented in Table 1.
5 Conclusions
- The authors have determined the interfacial properties of the vapourliquid interface of fully-flexible chains formed from tangentially bonded SW monomers (TSCW model) with potential range λ = 1.5 using the Statistical Associating Fluid Theory for Variable Range (SAFT-VR) density functional theory (DFT).
- Chains formed by four, eight, twelve, and sixteen monomers are considered.
- The effect of the chain length on the density profiles, coexistence densities, vapour pressures, critical temperature and density, and surface tension has been investigated.
- In the case of the coexistence densities and vapour pressures, agreement between their simulation results and those taken from the literature for both models (TSWC and VSWC) are excellent in all cases.
- Whereas in the TSWC model the authors use here the segments forming the fully flexible chains are strictly tangent, in the VSWC model the intramolecular distance between consecutive segments is 0.97 (and not 1.0) in reduced units.
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