Multicomponent adsorption in mesoporous flexible materials with flat-histogram Monte Carlo methods

Abstract

We demonstrate an extensible flat-histogram Monte Carlo simulation methodology for studying the adsorption of multicomponent fluids in flexible porous solids. This methodology allows us to easily obtain the complete free energy landscape for the confined fluid-solid system in equilibrium with a bulk fluid of any arbitrary composition. We use this approach to study the adsorption of a prototypical coarse-grained binary fluid in “Hookean” solids, where the free energy of the solid may be described as a simple spring. However, our approach is fully extensible to solids with arbitrarily complex free energy profiles. We demonstrate that by tuning the fluid-solid interaction ranges, the inhomogeneous fluid structure inside the pore can give rise to enhanced selective capture of a larger species through cooperative adsorption with a smaller one. The maximum enhancement in selectivity is observed at low to intermediate pressures and is especially pronounced when the larger species is very dilute in the bulk. This suggest a mechanism by which the selective capture of a minor component from a bulk fluid may be enhanced.

Relationship between pore-size distribution and flexibility of adsorbent materials: statistical mechanics and future material characterization techniques

“…We resume our discussion at Eq. 16 and then use three bridge functions that relate the semigrand and osmotic partition functions to their associated free energy potentials [24, 35]: $$-k_{\mathrm{B}}T\text{ ln }\mathrm{normal\Xi }false({\mu }_1,N_2,V_w,Tfalse)=Ffalse(V_{w}false)-{\mu }_1{false\langle N_{1}false\rangle }_{\mathit{\text{sg}}}false(V_{w}false)$$ $$-k_{\mathrm{B}}T\text{ ln }{\mathrm{\Xi }}_{1}false({\mu }_1,N_2,V_w,Tfalse)=F_{2}false(N_2,V_w,Tfalse)-k_{\mathrm{B}}T\text{ ln }\mathrm{normal\Xi }false({\mu }_1,N_2,V_w,Tfalse)$$ $$-k_{\mathrm{B}}T\text{ ln }{\mathrm{\Gamma }}_{\mathit{\text{os}}}false({\mu }_1,N_2,p,Tfalse)={false\langle {\mu }_2{N}_{2}false\rangle }_{\mathit{\text{os}}}false(pfalse)$$In the above, F is the Helmholtz free energy and, as noted in the appendix, may be decomposed as F = F 1 + F 2 , where F 1 contains all contributions to that free energy involving the fluid-fluid and fluid-solid interactions. To simplify the above and following expressions, we drop the dependencies on μ 1 , N 2 , and T and use subscripts “ sg ” and “ os ” to identify averages in the semigrand and osmotic ensembles, respectively.…”

“…Thus, we may write the total potential energy for a particular state ( r N 1 ; w ) as $$Ufalse({\mathbf{r}}^{N_1};wfalse)=U_{11}false({\mathbf{r}}^{N_1}false)+U_{12}false({\mathbf{r}}^{N_1};wfalse)+U_{22}false(wfalse)$$where U 11 , U 12 , and U 22 are the fluid-fluid, fluid-solid, and solid-solid contributions to the potential energy, respectively. Equation 27 may be rewritten as $$Qfalse(N_1,N_2,V_w,Tfalse)=\frac{1}{{\mathrm{\Lambda }}_2^{3N_2}{N}_2!}{\int }_{V_w}{\mathbf{\text{dr}}}^{N_2}\text{ exp }false[-\beta U_{22}false(wfalse)false]\times \frac{1}{{\mathrm{\Lambda }}_1^{3N_1}{N}_1!}{\int }_{V_w}{\mathbf{\text{dr}}}^{N_1}\text{ exp }false[-\beta false(U_{11}false({\mathbf{r}}^{N_1}false)+U_{12}false({\mathbf{r}}^{N_1};wfalse)false)false]$$We now make the following definitions (following Mahynski and Shen [24]): $$Q_{1}false(N_1,N_2,V_w,Tfalse)=\frac{1}{{\mathrm{\Lambda }}_1^{3N_1}{N}_1!}\times {\int }_{V_w}{\mathbf{\text{dr}}}^{N_1}\text{ exp }false[-\beta false(U_{11}false({\mathbf{r}}^{N_1}false)+U_{12}false({\mathbf{r}}^{N_1};wfalse)false)false]$$ $$Q_{2}false(N_2,V_w,Tfalse)=\frac{1}{{\mathrm{\Lambda }}_{}^{}}$$…”

“…In a rigid adsorbent, the natural ensemble for studying gas adsorption is a semigrand canonical ensemble [24, 35]. Adsorption is typically presented using a grand canonical ensemble but, strictly speaking, adsorption by a rigid material is better represented by a semigrand canonical ensemble in which the amount of adsorbate (species 1) fluctuates and the amount adsorbent (species 2) is fixed.…”

“…of Ref. [24], Eqs. 3–5 in particular), as these descriptors are reflective of the underlying adsorbent-adsorbent interactions in U .…”

Controlling relative polymorph stability in soft porous crystals with a barostat

“…The specific shape of this landscape is determined by the organic linkers between metal centers in the SPC and may be engineered simply by changing the chemistry of these linkers. 10,11 SPCs are expected to have not only mechanical utility as nanosprings and dampers 10 but are also candidates for performing efficient selective chemical separations, 12–15 catalysis, 16 and as pharmaceutical delivery systems. 17 Consequently, both theoretical 7,13,18 and computational investigations 11,15,19 have been undertaken to understand the thermodynamic stability of these polymorphs.…”