Daniel W. Siderius

Predicting gas adsorption in complex microporous and mesoporous materials using a new density functional theory of finely discretized lattice fluids.

We introduce a nonlocal on-lattice version of density functional theory (DFT) that allows for efficient modeling of fluids in complex inhomogeneous materials. In its previous implementations, classical DFT has required fine discretization of the fluid density. As a result, in studies of gas adsorption it has been used only in idealized pore models with high symmetry. Our new lattice DFT dramatically reduces the computational demand required to model simple fluids and hence can be efficiently applied to complex materials with multiple directions of asymmetry. We apply our new lattice DFT to study nitrogen adsorption in a slit pore with open ends and directly obtain the correct desorption hysteresis. We also apply our DFT to predict hydrogen adsorption accurately in an atomistic model of a metal-organic framework.

Extension of the Steele 10-4-3 potential for adsorption calculations in cylindrical, spherical, and other pore geometries

Simplified fluid-substrate interaction models derived from the Lennard-Jones potential are widely used in the simulation of gas physisorption phenomena. In this paper, we reinterpret the well known Steele 10-4-3 potential for a gas molecule interacting with a planar surface, and use the resultant scheme to derive new potentials for cylindrical and spherical pore geometries. These new potentials correctly recover the Steele result in the limit of infinite pore radius, a useful improvement over existing models. We demonstrate the new cylindrical Steele 10-4-3 potential in calculations of argon adsorption via fluid density functional theory. This potential yields markedly different adsorption behavior than existing cylindrical potentials, which follow from small but significant differences in both the strength and the shape of the fluid-surface interaction. These differences cannot be fully reconciled simply by reparameterizing (scaling) the existing models; the new potential is more realistic in design, and is especially to be preferred in studies where comparison with planar substrates is made. Finally, we discuss extensions of this approach to more complicated pore geometries, yielding a family of Steele-like potentials that all satisfy the correct planar limit.

On the generalized equipartition theorem in molecular dynamics ensembles and the microcanonical thermodynamics of small systems

We consider various ensemble averages within the molecular dynamics (MD) ensemble, corresponding to those states sampled during a MD simulation in which the application of periodic boundary conditions imposes a constraint on the momentum of the center of mass. As noted by Shirts et al. [J. Chem. Phys. 125, 164102 (2006)] for an isolated system, we find that the principle of equipartition is not satisfied within such simulations, i.e., the total kinetic energy of the system is not shared equally among all the translational degrees of freedom. Nevertheless, we derive two different versions of Tolmans generalized equipartition theorem, one appropriate for the canonical ensemble and the other relevant to the microcanonical ensemble. In both cases, the breakdown of the principle of equipartition immediately follows from Tolmans result. The translational degrees of freedom are, however, still equivalent, being coupled to the same bulk property in an identical manner. We also show that the temperature of an isolated system is not directly proportional to the average of the total kinetic energy (in contrast to the direct proportionality that arises between the temperature of the external bath and the kinetic energy within the canonical ensemble). Consequently, the system temperature does not appear within Tolmans generalized equipartition theorem for the microcanonical ensemble (unlike the immediate appearance of the temperature of the external bath within the canonical ensemble). Both of these results serve to highlight the flaws in the argument put forth by Hertz [Ann. Phys. 33, 225 (1910); 33, 537 (1910)] for defining the entropy of an isolated system via the integral of the phase space volume. Only the Boltzmann-Planck entropy definition, which connects entropy to the integral of the phase space density, leads to the correct description of the properties of a finite, isolated system. We demonstrate that the use of the integral of the phase space volume leads to unphysical results, indicating that the property of adiabatic invariance has little to do with the behavior of small systems.

Relation Between Pore Size and the Compressibility of a Confined Fluid

When a fluid is confined to a nanopore, its thermodynamic properties differ from the properties of a bulk fluid, so measuring such properties of the confined fluid can provide information about the pore sizes. Here, we report a simple relation between the pore size and isothermal compressibility of argon confined in such pores. Compressibility is calculated from the fluctuations of the number of particles in the grand canonical ensemble using two different simulation techniques: conventional grand-canonical Monte Carlo and grand-canonical ensemble transition-matrix Monte Carlo. Our results provide a theoretical framework for extracting the information on the pore sizes of fluid-saturated samples by measuring the compressibility from ultrasonic experiments.

Osmotic virial coefficients for model protein and colloidal solutions: Importance of ensemble constraints in the analysis of light scattering data

Protein-protein interactions in solution may be quantified by the osmotic second virial coefficient (OSVC), which can be measured by various experimental techniques including light scattering. Analysis of Rayleigh light scattering measurements from such experiments requires identification of a scattering volume and the thermodynamic constraints imposed on that volume, i.e., the statistical mechanical ensemble in which light scattering occurs. Depending on the set of constraints imposed on the scattering volume, one can obtain either an apparent OSVC, A(2,app), or the true thermodynamic OSVC, B(22)(osm), that is rigorously defined in solution theory [M. A. Blanco, E. Sahin, Y. Li, and C. J. Roberts, J. Chem. Phys. 134, 225103 (2011)]. However, it is unclear to what extent A(2,app) and B(22)(osm) differ, which may have implications on the physical interpretation of OSVC measurements from light scattering experiments. In this paper, we use the multicomponent hard-sphere model and a well-known equation of state to directly compare A(2,app) and B(22)(osm). Our results from the hard-sphere equation of state indicate that A(2,app) underestimates B(22)(osm), but in a systematic manner that may be explained using fundamental thermodynamic expressions for the two OSVCs. The difference between A(2,app) and B(22)(osm) may be quantitatively significant, but may also be obscured in experimental application by statistical uncertainty or non-steric interactions. Consequently, the two OSVCs that arise in the analysis of light scattering measurements do formally differ, but in a manner that may not be detectable in actual application.

On the use of multiple interpolation functions in scaled particle theory to improve the predictions of the properties of the hard-sphere fluid.

We present a modification to a previously proposed method of adapting scaled particle theory (SPT) to an arbitrary hard-sphere equation of state that satisfies a large number of exact SPT conditions, including thermodynamic consistency. By introducing a set of functions to interpolate the density of hard-spheres centers at the cavity surface, a broad range of hard-sphere properties, in particular the planar surface tension and related properties, are predicted with high accuracy as compared to simulation data. Similarly accurate results are obtained when this modified interpolation scheme is incorporated into a self-consistent version of SPT, i.e., an equation of state is a predicted output of the method. Hence, SPT is now able to closely match the surface thermodynamic properties of the hard-sphere fluid either without using any adjustable parameters or by simply setting the pressure and chemical potential via a reliable equation of state. We also consider other interpolation schemes, some of which better represent certain exact relations that can be derived within SPT. The limited success of these more rigorous approaches provides insights into the various trade-offs between the simplicity and rigor of the chosen interpolation method, as well as the accuracy of the results, that arise in any (inexact) version of SPT.

Modulus–pressure equation for confined fluids

Ultrasonic experiments allow one to measure the elastic modulus of bulk solid or fluid samples. Recently such experiments have been carried out on fluid-saturated nanoporous glass to probe the modulus of a confined fluid. In our previous work [G. Y. Gor et al., J. Chem. Phys., 143, 194506 (2015)], using Monte Carlo simulations we showed that the elastic modulus K of a fluid confined in a mesopore is a function of the pore size. Here we focus on the modulus-pressure dependence K(P), which is linear for bulk materials, a relation known as the Tait-Murnaghan equation. Using transition-matrix Monte Carlo simulations we calculated the elastic modulus of bulk argon as a function of pressure and argon confined in silica mesopores as a function of Laplace pressure. Our calculations show that while the elastic modulus is strongly affected by confinement and temperature, the slope of the modulus versus pressure is not. Moreover, the calculated slope is in a good agreement with the reference data for bulk argon and experimental data for confined argon derived from ultrasonic experiments. We propose to use the value of the slope of K(P) to estimate the elastic moduli of an unknown porous medium.

Improved synthesis and crystal structure of the flexible pillared layer porous coordination polymer: Ni(1,2-bis(4-pyridyl)ethylene)[Ni(CN)4]

This paper reports our synthesis of flexible coordination polymer, Ni(L)[Ni(CN)4], (L = 1,2-bis(4-pyridyl)ethylene (nicknamed bpene)), and its structural characterization using synchrotron single crystal X-ray diffraction. The structure of the purplish crystals has been determined to be monoclinic, space group P21/m, a = 13.5941(12) A, b = 14.3621(12) A, c = 14.2561(12) A, β = 96.141(2)°, V = 2767.4(4) A3, Z = 4, Dc = 1.46 g cm−1. Ni(bpene)[Ni(CN)4] assumes a pillared layer structure with layers defined by Ni[Ni(CN)4]n nets and bpene ligands acting as pillars. With the present crystallization technique which involves the use of concentrated ammonium hydroxide solution and dimethyl sulfoxide (DMSO), disordered free bpene ligands and solvents of crystallization (DMSO and water molecules) occupy the pores, resulting in a formula of Ni(bpene)[Ni(CN)4]·½bpene·DMSO·2H2O, or Ni2N7C24H25SO3. Without the inclusion of free bpene ligands and solvent molecules, the free volume is approximately 61% of the total volume; this free volume fraction is reduced to 50% with the free ligands present. Pores without the free ligands were found to have a local diameter of 5.7 A and a main aperture of 3.5 A. Based on the successful crystal synthesis, we also devised a new bulk synthetic technique which yielded a polycrystalline material with a significantly improved CO2 uptake as compared to the originally reported powder material. The improved synthetic technique yielded a polycrystalline material with 40% higher CO2 uptake compared to the previously reported powder material. An estimated 14.4 molecules of CO2 per unit cell was obtained.

Connection Between Thermodynamics and Dynamics of Simple Fluids in Pores: Impact of Fluid–Fluid Interaction Range and Fluid–Solid Interaction Strength

Using molecular simulations, we investigate how the range of fluid-fluid (adsorbate-adsorbate) interactions and the strength of fluid-solid (adsorbate-adsorbent) interactions impact the strong connection between distinct adsorptive regimes and distinct self-diffusivity regimes reported in [Krekelberg, W. P.; Siderius, D. W.; Shen, V. K.; Truskett, T. M.; Errington, J. R. Langmuir2013, 29, 14527-14535]. Although increasing the fluid-fluid interaction range changes both the thermodynamics and the dynamic properties of adsorbed fluids, the previously reported connection between adsorptive filling regimes and self-diffusivity regimes remains. Increasing the fluid-fluid interaction range leads to enhanced layering and decreased self-diffusivity in the multilayer-formation regime but has little effect on the properties within film-formation and pore-filling regimes. We also find that weakly attractive adsorbents, which do not display distinct multilayer formation, are hard-sphere-like at super- and subcritical temperatures. In this case, the self-diffusivity of the confined and bulk fluid has a nearly identical scaling-relationship with effective density.

On the line tension of curved boundary layers. I. boundary thermodynamics.

We present a formally exact thermodynamic treatment of curved boundary layers. Specifically, we extend the boundary layer analysis of Mandell and Reiss [ J. Stat. Phys. 1975 , 13 , 107 ] for a spherical cavity located within a uniform bulk fluid to the case of a cavity intersecting a hard, structureless wall. We derive various expressions for the line tension of an intersecting cavity, all of which can be evaluated for a hard-sphere fluid using existing versions of scaled particle theory. Since the analysis is similar to the standard approach for describing curved interfacial layers, several boundary analogues to conventional interfacial relations appear. In some instances, we obtain results that apparently have not yet been derived either for boundary layers or for their parallel relations in interfacial thermodynamics. Several results offer interesting insights into the behavior of the line tension of a cavity when the cavity approaches macroscopic sizes or in the specific limit where the cavity no longer intersects the wall.