^{1,a)}, A. Ignacio Moreno-Ventas Bravo

^{2}, J. M. Míguez

^{3}, M. M. Piñeiro

^{3}and L. G. MacDowell

^{4}

### Abstract

We have obtained the interfacial properties of short rigid-linear chains formed from tangentially bonded Lennard-Jones monomeric units from direct simulation of the vapour-liquid interface. The full long-range tails of the potential are accounted for by means of an improved version of the inhomogeneous long-range corrections of Janeček [J. Phys. Chem. B110, 6264–6269 (2006)]10.1021/jp056344z proposed recently by MacDowell and Blas [J. Chem. Phys.131, 074705 (2009)]10.1063/1.3197009 valid for spherical as well as for rigid and flexible molecular systems. Three different model systems comprising of 3, 4, and 5 monomers per molecule are considered. The simulations are performed in the canonical ensemble, and the vapor-liquid interfacial tension is evaluated using the test-area method. In addition to the surface tension, we also obtain density profiles, coexistence densities, critical temperature and density, and interfacial thickness as functions of temperature, paying particular attention to the effect of the chain length and rigidity on these properties. According to our results, the main effect of increasing the chain length (at fixed temperature) is to sharpen the vapor-liquid interface and to increase the width of the biphasic coexistence region. As a result, the interfacial thickness decreases and the surface tension increases as the molecular chains get longer. The surface tension has been scaled by critical properties and represented as a function of the difference between coexistence densities relative to the critical density.

The authors would like to acknowledge helpful discussions with F. J. Martínez-Ruiz, E. de Miguel, C. Vega, and A. Galindo. This work was supported by Ministerio de Ciencia e Innovación (MICINN, Spain) through Grant Nos. FIS2010-14866 (F.J.B.), FIS2009-07923 (J.M.M. and M.M.P.) and FIS2010-22047-C05-05 (L.G.M.D.). J.M.M. also acknowledges Ministerio de Ciencia e Innovación for the FPU Grant with reference AP2007-02172. Further financial support from Proyecto de Excelencia from Junta de Andalucía (Grant No. P07-FQM02884), Consellería de Educacion e Ordenacion Universitaria (Xunta de Galicia), Comunidad Autónoma de Madrid (Grant No. MODELICO-P2009/EPS-1691), and Universidad de Huelva are also acknowledged.

I. INTRODUCTION

II. EFFECTIVE LONG-RANGE PAIRWISE POTENTIAL FOR MOLECULAR SYSTEMS

III. MODEL AND SIMULATION DETAILS

IV. RESULTS AND DISCUSSION

V. CONCLUSION

### Key Topics

- Surface tension
- 31.0
- Intermolecular forces
- 24.0
- Interfacial properties
- 23.0
- Polymers
- 23.0
- Intermolecular potentials
- 16.0

## Figures

Simulated equilibrium density profiles across the vapour-liquid interface of rigid-linear LJ chains formed from three (*m* = 3), four (*m* = 4), and five (*m* = 5) monomers with a monomer-monomer LJ cutoff of *r* _{ c } = 3σ and inhomogeneous LRCs at several temperatures. From top to bottom (in the liquid region): (a) *T* = 1.10, 1.20, 1.30, 1.40, 1.50, 1.60, 1.70.1.80, and 1.85; (b) *T* = 1.45, 1.50, 1.60, 1.70, 1.80, 1.85, 1.90, and 1.95; (c) *T* = 2.05, 2.10, 2.15, 2.20, 2.23, 2.25, 2.27, and 2.30.

Simulated equilibrium density profiles across the vapour-liquid interface of rigid-linear LJ chains formed from three (*m* = 3), four (*m* = 4), and five (*m* = 5) monomers with a monomer-monomer LJ cutoff of *r* _{ c } = 3σ and inhomogeneous LRCs at several temperatures. From top to bottom (in the liquid region): (a) *T* = 1.10, 1.20, 1.30, 1.40, 1.50, 1.60, 1.70.1.80, and 1.85; (b) *T* = 1.45, 1.50, 1.60, 1.70, 1.80, 1.85, 1.90, and 1.95; (c) *T* = 2.05, 2.10, 2.15, 2.20, 2.23, 2.25, 2.27, and 2.30.

Vapour-liquid coexistence densities for rigid-linear LJ chains with a monomer-monomer LJ cut-off distance of *r* _{ c } = 3σ and inhomogeneous LRCs. The open green circles, red squares, and blue diamonds correspond to the coexistence densities obtained from the analysis of the equilibrium density profiles obtained from MC *NVT* simulations for chain lengths of *m* = 3, 4, and 5, respectively. The filled green circles and blue diamonds correspond to the coexistence densities obtained from Gibbs ensemble MC and by performing isobaric-isothermal *NPT* calculations at zero pressure by Galindo *et al.* ^{36} Symbols at the highest temperatures for each of the coexistence curve represent critical points estimated from Eqs. (23) and (24) and those taken from the work by Galindo *et al.* ^{36}

Vapour-liquid coexistence densities for rigid-linear LJ chains with a monomer-monomer LJ cut-off distance of *r* _{ c } = 3σ and inhomogeneous LRCs. The open green circles, red squares, and blue diamonds correspond to the coexistence densities obtained from the analysis of the equilibrium density profiles obtained from MC *NVT* simulations for chain lengths of *m* = 3, 4, and 5, respectively. The filled green circles and blue diamonds correspond to the coexistence densities obtained from Gibbs ensemble MC and by performing isobaric-isothermal *NPT* calculations at zero pressure by Galindo *et al.* ^{36} Symbols at the highest temperatures for each of the coexistence curve represent critical points estimated from Eqs. (23) and (24) and those taken from the work by Galindo *et al.* ^{36}

The 10−90 interfacial thickness *t* as a function of the temperature for rigid-linear LJ chains with a monomer-monomer cut-off distance of *r* _{ c } = 3σ and inhomogeneous LRCs. The meaning of the symbols is the same as in Fig. 2. The curves are included as a guide to the eyes.

The 10−90 interfacial thickness *t* as a function of the temperature for rigid-linear LJ chains with a monomer-monomer cut-off distance of *r* _{ c } = 3σ and inhomogeneous LRCs. The meaning of the symbols is the same as in Fig. 2. The curves are included as a guide to the eyes.

Surface tension as a function of the temperature for rigid-linear LJ chains with a monomer-monomer LJ cut-off distance of *r* _{ c } = 3σ and inhomogeneous LRCs calculated using the TA methodology. The meaning of the symbols is the same as in Fig. 2. The curves represent the fits of the simulation data to the scaling relationship of the surface tension near the critical point given by Eq. (25) with μ = 1.258.

Surface tension as a function of the temperature for rigid-linear LJ chains with a monomer-monomer LJ cut-off distance of *r* _{ c } = 3σ and inhomogeneous LRCs calculated using the TA methodology. The meaning of the symbols is the same as in Fig. 2. The curves represent the fits of the simulation data to the scaling relationship of the surface tension near the critical point given by Eq. (25) with μ = 1.258.

Reduced surface tension as a function of the difference between the vapour and liquid coexistence densities with respect to the critical density for rigid-linear LJ chains with a monomer-monomer LJ cut-off distance of *r* _{ c } = 3σ and inhomogeneous LRCs. The blue circles, blue squares, and blue diamonds correspond to the reduced surface tension is calculated according to Eq. (26).

Reduced surface tension as a function of the difference between the vapour and liquid coexistence densities with respect to the critical density for rigid-linear LJ chains with a monomer-monomer LJ cut-off distance of *r* _{ c } = 3σ and inhomogeneous LRCs. The blue circles, blue squares, and blue diamonds correspond to the reduced surface tension is calculated according to Eq. (26).

## Tables

Liquid density ρ_{ L }, vapour density ρ_{ V }, 10−90 interfacial thickness *t*, and surface tension γ at different temperatures for systems of rigid-linear LJ chains formed from *m* monomers with a monomer-monomer LJ cut-off distance *r* _{ c } = 3σ and inhomogeneous LRCs. All quantities are expressed in the reduced units defined in Sec. III. The errors are estimated as explained in the text.

Liquid density ρ_{ L }, vapour density ρ_{ V }, 10−90 interfacial thickness *t*, and surface tension γ at different temperatures for systems of rigid-linear LJ chains formed from *m* monomers with a monomer-monomer LJ cut-off distance *r* _{ c } = 3σ and inhomogeneous LRCs. All quantities are expressed in the reduced units defined in Sec. III. The errors are estimated as explained in the text.

Critical temperature and density from the analysis of the coexistence densities. All quantities are expressed in the reduced units defined in Sec. III.

Critical temperature and density from the analysis of the coexistence densities. All quantities are expressed in the reduced units defined in Sec. III.

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