Thrust Area B: Molecular Thermodynamics and Computer Simulations

Accomplishments for 11/1/99-7/31/00

Tasks during the last nine months include such preliminary work as recruiting graduate students and post-docs, ordering and installing equipment, developing computer facilities, developing codes for computer simulations, etc. Most of the research programs have been initiated. Currently there are too few interactions between the research programs. During the next year, considerable effort will be made to coordinate the research activities of Thrust Area B. Common materials will be identified for studies in all the programs. The materials will be selected according to the needs of the other thrust areas. The principal investigators, graduate students, and post-docs of all the programs will meet regularly to exchange ideas and to ensure maximum cooperation between programs. These efforts are expected to yield positive results as far as the progress of research in this thrust area as well as other thrust areas. The current progress of each of the six research programs is reported below.

Molecular Dynamics Simulations of Multicomponent Systems in CO2 (6) The Beowulf Cluster of 17 Alpha-DEC workstations (described in detail under Shared Experimental Facilities Section) was purchased, assembled and tested. Molecular dynamics suite of programs DL_POLY was adjusted for simulations of both sub-critical and super-critical CO2 and tested. Molecular dynamics of CO2 represented by different potential models was performed. Preliminary simulations of alkanes and fluoroalkanes in low density CO2 were performed

Molecular Structure and Dynamics at the CO₂/Water Interface (7) During the first nine months, Rossky has made considerable progress on the initial project of characterizing the supercritical CO₂/liquid water interface at the molecular level. Simulations are executed with ~1000 molecules with a number of important technical elements implemented, including full treatment of long range electrostatic forces via Ewald sums and equilibration of the interfacial system at constant pressure. Simulations are executed at the equilibrated volume with molecular dynamics, so that dynamical information is accessible in addition to structure. Simulations have revealed a realistic interface between a water-rich phase and an essentially pure CO₂ phase. Preliminary values for the interfacial tension support the usefulness of the pair of solvent molecular models, each of which is a good model for the respective neat fluid. A key element in the analysis is the characterization of the interface both in terms of the large length scale dividing surface, corresponding to the macroscopic interface, and a local, molecular scale, interface. The latter analysis reveals the molecular character on the scale relevant to the interactions with surfactant molecules. Of most interest, results reveal a distinct difference in “wetting” behavior when the interface is viewed from the water-rich or CO₂ sides. Significant effects of electrostatic interactions, associated with the polarity of a realistic model of CO₂, are evident for water that is in contact with CO₂ molecules at the interface and in the bulk aqueous phase.

Molecular Simulations and Thermodynamics for CO₂-Surfactant Systems (8) Gubbins and Hall have focussed on developing computer simulation and analytical models that enhance our understanding of and ability to predict phase equilibria and properties of binary and ternary mixtures containing CO₂, including the self assembly and transformations of micellar structures. Over the past nine months work has proceeded on three fronts. First, we have been working on adapting the SAFT (Statistical Associating Fluid Theory) equation of state to polyFOA/CO₂ systems. This has involved the development of a code for these systems, parameter sets for the species involved, and tests of the predictions vs. experiment. Our initial tests show that good agreement with experiment will be achieved. Second, we have completed preliminary runs of a discontinuous molecular dynamics (DMD) simulation of a CO₂/surfactant system modeled as square well chains (surfactant molecules) and square well spheres (CO₂ molecules). Because DMD is extremely fast, we are able to access time scales that are long enough to allow us to monitor the formation of model micelles and the exchange of surfactant molecules between them. Third, we have been trying to invent ways to use SAFT (or any equation of state approach) to treat the self-assembly of micelles. While equations of state can handle liquid/vapor and liquid/liquid transitions they cannot handle transitions which involve a change in symmetry such as liquid /solid transitions or liquid/micelle transitions. We are hopeful that a combination of the SAFT equation with density functional theory (DFT) will provide a route to solving this problem, since DFT provides an accurate description of highly inhomogeneous systems.

Thermodynamic Measurements and Models for CO₂ containing Systems (9) Kabadi’s efforts have been in three areas: (1) Thermodynamic data compilation for CO₂ systems, (2) Design and construction of apparatus for VLE measurements of CO₂ systems, (3) Design and construction of apparatus for enthalpy measurements for CO₂ systems. Data compilation includes VLE, enthalpy, and density data. Excellent literature reviews for VLE data are available until year 1992. A complete literature search has been carried out for data published after 1992. Complete tables of all literature data with references will be available at the end of summer, 2000. Literature searches have also been conducted for enthalpy and density data. Tables for these data will be completed by the end of year 2000.

Two different VLE apparatuses have been designed. The first one is a semi-continuous flow apparatus that is for measurements of equilibria of CO₂ with relatively heavy liquids. A known amount of liquid is placed in the VLE cell, and CO₂ is bubbled through the liquid at a low rate. Temperature and pressure inside the cell are maintained at desired values. When equilibrium is attained, samples of liquid and vapor are analyzed by an on-line gas chromatographic system. The second apparatus is a continuous flow and feed recirculation apparatus. This is designed for measurement of VLE of CO₂ with components of comparable volatility. A liquid mixture of CO₂ and components of known composition is maintained in a feed tank under helium pressure. The mixture is pumped into the VLE cell where desired conditions of temperature and pressure are maintained such that the mixture separates into vapor and liquid phases. Vapor and liquid exit the VLE cell through separate ports. Pressure in the cell is controlled by manipulating vapor flow rate, and a constant liquid level is maintained by manipulating the liquid flow rate. The vapor and the liquid streams are combined and pumped back into the feed tank. When equilibrium conditions are attained and maintained for sufficient time, vapor and liquid streams are sampled and analyzed by an on-line gas chromatographic system. Design of both the apparatuses has been completed. Equipment lists are being finalized. All equipment will be installed by September 2000.

A calorimeter for the enthalpy measurements for CO₂ systems between –40C to +80C has been ordered. The instrument provides for simultaneous measurement of three samples. Sample cells are being designed to handle binary systems containing liquid and SCCO2.

Models of Polymeric Surfactants (10) A molecular dynamics program for simulation of both sub-critical and super-critical CO₂ and one for simulation of short polymeric chains in CO₂ were tested. A Monte Carlo program for simulation of Lennard-Jones polymeric chains was developed, optimized and tested. And a Monte Carlo program for simulation of Lennard-Jones polymeric chains in a Lennard-Jones solvent was developed, optimized and tested. Working with E. Zhulina, UNC-CH, we have developed a scaling model of block copolymers associating in a selective solvent. Special attention was devoted to the stability of micelles of various shapes (spherical, cylindrical, etc.). Critical parameters controlling the shape of the micelles (molecular weight and solvent quality of the corresponding block) were identified. Preliminary results were discussed with experimentalists M. Adam and S. Wells, working on the complimentary project.

Molecular Simulations of the Solubility of Organic Compounds in CO₂ (11) Excellent thermal, mechanical and gas-transport properties make fluorine-containing polyimides interesting in the application as gas separation membranes. We chose to investigate the two isomeric polyimides formed from hexafluoro dianhydride and para and meta isomers of a hexafluoro diamine: poly-6FDA-6FmDA (meta) and poly-6FDA-6FpDA (para). Although chemically identical, they display major differences in physical properties. For example glass transition temperature, T_g = 598 K for the para isomer and 532 K for the meta isomer. Gas permeation of small molecules through films of these isomers also differs significantly. Gas permeation is faster at room temperature through the para isomer, even though it has the higher glass temperature.

Molecular dynamics (MD) simulations were performed with the Cerius2 package to obtain the cavity size distributions and carbon dioxide diffusion coefficients in both the meta and para isomer. In both cases the simulated polymers consisted of one 20 repeat unit strand. The applied COMPASS force field models each molecule in an atomistic way. The initial states were generated at the experimental densities at 308 K for meta (1.493 g/cc) and para (1.466 g/cc) isomer. The Cerius2 package uses an amorphous state builder, which is capable of folding a polymer onto itself at these densities by use of its mirror images. Minimization is required after an amorphous state is formed in order for MD simulations to be run on an initial state. The cavity size distributions were determined for each isomer by generating 50 initial states and equilibrating them over 60 ps, followed by application of our cavity-sizing algorithm. Diffusion coefficients were determined at these experimental conditions by adding 10 carbon dioxide molecules to 20 independent states: 10 states per isomer. After each state was equilibrated for 60 ps, the diffusion constants were calculated by center of mass displacement over a 120 ps interval.

Comparison of experimental with simulated diffusion constants show excellent agreement. This is remarkable bearing in mind that an atomistic model without any adjustable parameters represents polymer and carbon dioxide molecules. Diffusion constant results support the outcome of the cavity size distribution simulations (Monte Carlo method), which indicate a higher probability of large cavities in the para isomer (see Figure II.B in Appendix G). The average cavity size reflects this trend: 5.0 Å for the meta and 5.4 Å for the para isomer.

Plans for 8/1/00-7/31/01

We anticipate no major changes in plans for the coming year. Rossky’s group will complete analysis of the SC CO₂/water interface, including the effect of pressure on interfacial densities. They will then focus on the exploration of the impact of surfactant molecules on the interfacial behavior, emphasizing surfactant-induced structural effects and the analysis of energetic contributions to surfactant solvation. Gubbins and Hall will initiate a new project on Monte Carlo simulation of micellar CO₂ solvent systems in collaboration with Professor A. Z. Panagiotopoulos of Princeton University. The objective of the work will be to map out the phase diagrams for a range of ternary mixtures involving CO₂, a surfactant, and a solute. Calculations will be made using a highly successful lattice MC method applied recently by the Panagiotopoulos group to other micellar systems.

Kabadi will stay the course. He plans to (1) finish the construction of the VLE and enthalpy apparatuses; (2) initiate VLE and enthalpy measurements for selected systems; (3) complete data compilation and data tables for VLE, enthalpy and density data for CO2 systems; and (4) initiate thermodynamic model review for CO2-containing systems

Rubenstein will systematically investigate conformations of polymer in a compressible solvent using Monte Carlo computer simulations and compare the results with scattering data on polymers in CO₂. A Monte Carlo program will also be developed to study a phase diagram of polymer/compressible solvent binary system. Finally, the Monte Carlo code will be extended to the study self-assembly properties of block copolymer/compressible solvent binary system. Initially we will simulate micelles with different aggregation numbers in order to find out the optimal shape and size of these aggregates. Phase diagrams for block copolymers will then be constructed as functions of the polymer concentration, polymer molecular weight, strength of the CO2-phobic and -philic interactions, polymer architecture and CO2 pressure and temperature.

Outstanding Achievement

The nearly completed simulations of the supercritical CO2/water interface are the first ever carried out for this system, to the best of our knowledge.