# Molecular Conformational Manifolds between Gas-Liquid Interface and Multiphasic

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mass Evaporation Coefficient and Quantum/Statistical Mechanics Methods

_{g}) can be derived from the terms of thermodynamic potentials [1] and SAFT [5,6]. SAFT is a molecular-based equation of state that can be applied to predict the interfacial layer thickness of fluids. It incorporates the effects of chain length, molecular association, and other interactions such as long-range dipolar forces and dispersions. While the interfacial layer effects did not explicitly future in References [1,2], we consider these effects in this study to estimate the evaporation/condensation coefficient to find out whether this thermodynamics-based approach can be suitable for modelling interfacial flows. To set up an equation including interfacial width, δ, a standard state has to be defined for the evaporation/condensation process. With this thickness, the relationship between the free energy of evaporation/condensation ($\Delta {G}_{g\leftrightarrow l}$) and the coefficient of β

_{g}becomes:

^{−10}m; a = 1.16 m and υ = 0.5 are constants; and T

_{c}= 658.2 K is the critical temperature for n-dodecane. The results of DFT calculations are based on multi-structural torsional (MS-T) method and continuum solvation model of SMD [8], in which the conformer temperature Gibbs free energies in the gas (${G}_{g}^{j}(T)$) and the interface of droplets (${G}_{i}^{j}(T)$) are computed. The temperature dependence of the surface tension can be included using the following formula [9]:

^{−3}kcal/(mol × Å

^{2}), n = 1.3325, and T

_{c}is the critical temperature of n-dodecane (658.2 K). The temperature dependency of the interfacial density of n-dodecane is also computed with the self-consistent reaction field (SCRF) method, implemented in the Gaussian 09 suite [10]. The interfacial density, ρ(z), can be expressed as a hyperbolic tangent function:

_{0}is the position of the Gibbs dividing surface located at z

_{0}= 0 that is given by:

_{0}) is the pressure in the center of the interfacial layer and ρ(z

_{0}) is the experimental interfacial density of n-dodecane changing from 372.8 kg/m

^{3}at 298.15 K to 117.5 kg/m

^{3}at 648.15 K [10]. Taking all of the aforementioned parameters and correction terms into consideration, this leads to the same results as reported in Reference [1]. One question raised was whether or not adding the interfacial layer using SAFT has an effect on the evaporation/condensation coefficient of n-dodecane. The answer is no, since SAFT, being a thermodynamics-based approach, cannot model properly transient processes such as internal activation dynamics effects [3].

## 3. Evaporation Rate of Fuel Droplets and Hybrid Kinetics Method

**x**and speed

**v**at time t using a distribution function f(

**x**,

**v**, t). We estimated this distribution function in the evaporation process based on the molecular theory of solvation for systems consisting of long-chain molecules, and concluded that “internal molecular dynamic” effects are important in this function rather than intermolecular interactions [3,4]. In order to understand the importance of transient internal activation dynamics during the evaporation process on hydrocarbon molecules, we calculated the evaporation rate, ${k}_{i,jk}$, using a QTST-based expression ${k}_{i}^{TST}$(T) = ${\kappa}_{i}\frac{{k}_{B}T}{h}\mathrm{exp}(-\frac{{G}_{i}^{{[{R}_{i}-{P}_{i}]}^{\#}}}{{k}_{B}T})$ which is eventually incorporated as a correction term in the CKGT-based equation ${k}_{i,jk}^{KGT}$(T) = $(\frac{p}{{n}_{0}{k}_{B}T}){\Omega}_{jk}\mathrm{exp}(\frac{\Delta {G}_{i}^{[g\leftrightarrow l]}}{RT})$ [3]:

_{i}is the magnitude of the transition-state imaginary frequency (see References [3,4] for more detail). While CKGT describes the collision effects among surrounding gases, vapor molecules, clusters, and droplets, assuming those are in the thermodynamic equilibrium states, QTST presents some kinetic quasi-equilibrium phenomena at an atomic level in the vicinity of fuel droplets. This novel hybrid method bridges micro/macro-scale modelling with atomistic-scale modelling to unravel the kinetic effects at the surface of fuel droplets and elucidate the role of equilibrium thermodynamics in the liquid and gas phases and of transient kinetics in the interfacial flows during the evaporation/condensation process (see Figure 1).

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Nasiri, R.; Luo, K.H.
Molecular Conformational Manifolds between Gas-Liquid Interface and Multiphasic. *Entropy* **2017**, *19*, 695.
https://doi.org/10.3390/e19120695

**AMA Style**

Nasiri R, Luo KH.
Molecular Conformational Manifolds between Gas-Liquid Interface and Multiphasic. *Entropy*. 2017; 19(12):695.
https://doi.org/10.3390/e19120695

**Chicago/Turabian Style**

Nasiri, Rasoul, and Kai Hong Luo.
2017. "Molecular Conformational Manifolds between Gas-Liquid Interface and Multiphasic" *Entropy* 19, no. 12: 695.
https://doi.org/10.3390/e19120695