(274b) Modeling Interfaces with Step Potential for Equilibria and Dynamics (iSPEAD)

Ahmadreza F. Ghobadi and J. Richard Elliott^*

Department of Chemical and Biomolecular Engineering, The University of Akron,

Akron OH 44325

An effective combination of Discontinuous Molecular Dynamics (DMD) simulation and second order Thermodynamic Perturbation Theory (TPT) can be employed to simulate the entire phase diagram and also to offer a rigorous procedure for evaluating the perturbation contributions of any SAFT-like equation of state (EOS). In DMD/TPT methodology, the athermal reference fluid is fused hard sphere chain and is simulated by DMD at one single temperature and several densities. The size of each site type (σ) is adjusted to reproduce experimental liquid density. Then, after the simulation, the first and second order attractive contributions of Helmholtz free energy can be isolated and rigorously computed in accordance with the Barker–Henderson (BH) formalism. To do so, Elliott and co-workers optimized and evaluated a site-base transferable step potential with four wells for more than 500 compounds comprising 30 different families. Parameters of interaction potential (ε_i, i = 1,4) were adjusted to reproduce experimental saturated liquid density and vapor pressure. Following this procedure, Elliott and Gray {Journal of Chemical Physics, 123 (2005), p. 184902} proposed SAFT-like correlations to the results of simulation known as Step Potential for Equilibria And Dynamics (SPEAD). Ghobadi and Elliott {Fluid Phase Equilibria, v. 306 i.1 (2011) p. 57} recently improved the correlation for the critical point region.

The main difference between SPEAD and SAFT-family approaches is the nature of evaluating perturbation contributions. In SAFT formalism, a segment-base continuous interaction potential is considered and adjustable parameters are fitted to the experimental data while SPEAD benefits from site-base discontinuous interactions and raw simulation results. Although site-base approach offers transferability and physical consistency, a segment-base interaction potential becomes absolutely beneficial where Renormalization Group (RG) theory or Density Functional Theory (DFT) is applied on the classical Equation of State (EOS).

In this work, a segment-base Lennard-Jones (LJ) interaction potential is developed by re-evaluating the perturbation contributions of SPEAD. The Mean Field and local density approximations are implemented to calculate first and second order perturbation terms, respectively. The first order term is computed using an average radial distribution function at an effective packing fraction. The relation between density and effective packing fraction introduces two adjustable parameters for each component. These parameters along with the minimum of the LJ potential (ε) are fitted to the BH-generated perturbation contributions of SPEAD. The number of segments (m) is regressed to the results of DMD simulation of the reference fluid. Therefore, each component is characterized by 5 parameters: σ, m, ε, c1 and c2.

Using the segment-based potential described above and SPEAD+DFT EOS (named as iSPEAD), liquid-vapor density profile and surface tension of several pure components from n-alkanes, branched alkanes, alcohols, acids, ester and so forth were calculated. It should be noted that hydrogen bonding contribution is considered by Wertheim theory. The results show satisfactory agreement with available experimental data. Also, adsorption isotherms of various mixtures were studied by iSPEAD. It is demonstrated that adsorption at the liquid-vapor interface happens when there is a noticeable difference between parameters of constituent components of the mixtures. The final aim of this work is to investigate the potential of DFT to indicate the effect of different experimentally-examined surfactant molecules on the interfacial properties. When dealing with large molecules such as amphiphiles, individual segment densities contain valuable information about the microstructure of the fluid. In such cases, a three-fluid model will be used to obtain the density profiles for hydrophilic head, hydrophobic tail and tail-end segments. The three-fluid model isolates the influence of each part on interfacial properties and provides more in-depth information such as average end-to-end distance of surfactants, surface area per surfactant, aggregation number and so forth.  

*Corresponding Author, please contact elliot1@uakron.edu, Office: (+1) 330 972 7253