Simulating Retention in Gas−Liquid Chromatography

Efficient Combination of Environment Change and Alchemical Perturbation within the Enveloping Distribution Sampling (EDS) Scheme: Twin-System EDS and Application to the Determination of Octanol-Water Partition Coefficients

The methodology of Enveloping Distribution Sampling (EDS) is extended to probe a single-simulation alternative to the thermodynamic cycle that is standardly used for measuring the effect of a modification of a chemical compound, e.g. from a given species to a chemical derivative for a ligand or solute molecule, on the free-enthalpy change associated with a change in environment, e.g. from the unbound state to the bound state for a protein-ligand system or from one solvent to another one for a solute molecule. This alternative approach relies on the coupled simulation of two systems (computational boxes) 1 and 2, and the method is therefore referred to as twin-system EDS. Systems 1 and 2 account for the two choices of environment. The end states of the alchemical perturbation for the twin-system associate the two alternative forms X and Y of the molecule to systems 1 and 2 or 2 and 1, respectively. In this way, the processes of transforming one molecule into the other are carried out simultaneously in opposite directions in the two environments, leading to a change in free enthalpy that is smaller than for the two individual processes and to an energy-difference distribution that is more symmetric. As an illustration, the method is applied to the calculation of octanol-water partition coefficients for C4 to C8 alkanes, 1-hexanol and 1,2-dimethoxyethane. It is shown in particular that the consideration of the residual hydration of octanol leads to calculated partition coefficients that are in better agreement with reported experimental numbers.

Molecular simulations of retention in chromatographic systems: use of biased Monte Carlo techniques to access multiple time and length scales

The use of configurational-bias Monte Carlo simulations in the Gibbs ensemble allows for the sampling of phenomena that occur on vastly different time and length scales. In this review, applications of this simulation approach to probe retention in gas and reversed-phase liquid chromatographic systems are discussed. These simulations provide an unprecedented view of the retention processes at the molecular-level and show excellent agreement with experimental retention data.

Retention in gas–liquid chromatography with a polyethylene oxide stationary phase: Molecular simulation and experiment

Configurational-bias Monte Carlo simulations in the isobaric-isothermal Gibbs ensemble were carried out to investigate the partitioning of normal alkanes, primary and secondary alcohols, symmetric alkyl ethers and arenes between a helium vapor phase and a polyethylene oxide stationary phase (M(W)=382 g mol(-1)). The united-atom version of the transferable potentials for phase equilibria force field was used to model all solutes, polyethylene oxide and helium. The Gibbs free energies of transfer and Kovats retention indices of the solutes were calculated directly from the partition constants at two different temperatures, 353 and 393 K. Chromatographic experiments on a Carbowax 20M retentive phase were performed for the same set of solutes and temperatures ranging from 333 to 413 K. The predicted retention indices for alcohols, ethers and arenes are overestimated by about 120, 70 and 20 retention index units, respectively, pointing to an overestimation of the first-order electrostatic interactions in the model system. Molecular-level analysis shows that hydrogen-bonding and dipole-dipole interactions lead to orientational ordering for the alcohol and ether analytes, whereas the weaker dipole-quadrupole interactions for the arene solutes are not sufficient to induce orientational ordering. The retention indices of alcohols and ethers decrease with increasing temperature because of the large entropic cost of hydrogen-bonding and orientational ordering. In contrast, the retention indices for arenes increase with increasing temperature because the entropic cost of cavity formation is smaller for arenes than for comparable alkanes.

Probing the Nucleation Mechanism for the Binary n-Nonane/1-Alcohol Series with Atomistic Simulations

The AVUS-HR approach, which combines histogram reweighting with aggregation-volume-bias Monte Carlo nucleation simulations using self-adaptive umbrella sampling, was extended to multicomponent nucleation systems. It was applied to investigate the homogeneous vapor-liquid nucleation for the binary n-nonane/1-alcohol series, including the n-nonane/methanol, n-nonane/ethanol, n-nonane/1-propanol, n-nonane/1-butanol, n-nonane/1-hexanol, and n-nonane/1-decanol systems. The simple transferable potentials for phase equilibria-united atom force field was used in this investigation. It was found that the nucleation free energy (NFE) contour plots obtained for these binary n-nonane/1-alcohol nucleation systems exhibit rather interesting mechanistic features, some of which are distinct from other binary systems previously studied (such as water/ethanol and water/n-nonane). In addition, the NFE profiles show a subtle evolution with the increase in alcohol chain length, from a somewhat two-pathway type of shape as observed for the n-nonane/methanol system to a more normal single-pathway one for systems involving longer alcohols (1-hexanol and 1-decanol). In contrast, the NFE maps obtained for the other three binary systems involving those medium-length alcohols display the most striking feature with the saddle point stretched almost all the way from the n-nonane-enriched to the alcohol-enriched domain, implying that multiple pathways coexist on the nucleation map. These free energy profiles were shown to be consistent with the non-ideal nucleation behavior observed experimentally for this binary series, namely, a rather reluctant conucleation of the alcohols with n-nonane. In particular, this non-ideal behavior becomes more severe with a decrease in the alcohol chain length. Also, analysis of the compositions of the critical nuclei indicates a reluctant mixing behavior between these two species, i.e., depletion of the alcohol at low alcohol activity or depletion of n-nonane at low n-nonane activity, in agreement with the experimental interpretations. Furthermore, a microscopic inhomogeneity is present inside these critical nuclei, that is, alcohols aggregate via hydrogen bonds forming alcohol-enriched domains.

Molecular simulation study of the bonded-phase structure in reversed-phase liquid chromatography with neat aqueous solvent

The dramatic loss of retention in reversed-phase liquid chromatography when switching to 100% aqueous solvent and stopping flow (depressurizing) has long intrigued separation scientists. Recent experimental evidence suggests that the observed loss of retention is due to the loss of pore wetting with subsequent loss of solvent penetration in the porous matrix. One of the prevalent explanations of this phenomenon has been that the bonded phase chains, typically octadecyl silane bound to porous silica, would undergo significant conformational changes, viz. collapse, under pure aqueous conditions. As a definitive means toward elucidating the conformation of bonded-phase chains under pure aqueous conditions, configurational-bias Monte Carlo simulations in the Gibbs ensemble were carried out for a system of dimethyl octadecyl silane of intermediate coverage bound to the (111) face of beta-cristobalite and immersed in pure water. The results of two sets of simulations, which were started from two entirely different starting configurations as a validity check toward reaching the same equilibrium distribution of states, show that chains are neither clustering together nor laying on the surface but rather have a broad distribution of orientations and of conformational states. The interface between the bonded and solvent phases is rough on a molecular level, and clusters of water molecules are sometimes found to adsorb at the silica surface. This computational study lends further evidence that the driving force for the loss of retention when switching to pure aqueous conditions and depressurizing is not the collapse of bonded-phase chains.

Simulation Studies on the Effects of Mobile-Phase Modification on Partitioning in Liquid Chromatography

Various driving forces have been suggested to explain retention and selectivity in reversed-phase liquid chromatography (RPLC). To provide molecular-level information on the retention mechanism in RPLC, configurational-bias Monte Carlo simulations in the Gibbs ensemble were carried out for model systems consisting of three phases: an n-hexadecane retentive phase, a mobile phase with varying water-methanol composition, and a helium vapor phase as reference state. Liquid n-hexadecane functions as a model of a hydrophobic stationary phase, and a wealth of experimental data exists for this system. Gibbs free energies for solute transfers from gas to retentive phase, from gas to mobile phase, and from mobile to retentive phase were determined for a series of short linear alkanes and primary alcohols. Although the magnitude of the incremental Gibbs free energy of transfer for a methylene segment is always larger for the gas- to retentive-phase transfer than the gas- to mobile-phase transfer, it is found that the partitioning of alkanes and alkyl tail groups is mostly affected by the changes in the aqueous mobile phase that occur when methanol modifiers are added. In contrast, the partitioning of the alcohol headgroup is sensitive to changes in both the n-hexadecane and the mobile phases. In particular, it is found that hydrogen-bonded aggregates of methanol are present in the n-hexadecane phase for higher methanol concentrations in the mobile phase. These aggregates strongly increase alcohol partitioning into the retentive phase. The simulation data clearly demonstrate that due to modification of the retentive-phase hydrocarbons by solvent components, neither the solvophobic theory of RPLC, advocated by Horvath and co-workers, nor the lipophilic theory of RPLC, advocated by Carr and co-workers, can adequately describe the separation mechanism of the hexadecane model system of a retentive phase studied here nor the more complex situation present in actual RPLC systems.

Temperature effects on the retention of n-alkanes and arenes in helium-squalane gas-liquid chromatography. Experiment and molecular simulation

Experiments and molecular simulations were carried out to study temperature effects (in the range of 323 to 383 K) on the absolute and relative retention of n-hexane, n-heptane, n-octane, benzene, toluene and the three xylene isomers in gas-liquid chromatography. Helium and squalane were used as the carrier gas and retentive phase, respectively. Both the experiments and the simulations show a markedly different temperature dependence of the retention for the n-alkanes compared to the arenes. For example, over the 60 K temperature range studied, the Kovats retention index of benzene is found to increase by about 16 or 18+/-10 retention index units determined from the experiments or simulations, respectively. For toluene and the xylenes, the experimentally measured increases are similar in magnitude and range from 14 to 17 retention index units for m-xylene to o-xylene. The molecular simulation data provide an independent method of obtaining the transfer enthalpies and entropies. The change in retention indices is shown to be the result of the larger entropic penalty and the larger heat capacity for the transfer of the alkane molecules.