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A Universal Isotherm Model to Capture Adsorption Uptake and Energy Distribution of Porous Heterogeneous Surface.

ABSTRACT: The adsorbate-adsorbent thermodynamics are complex as it is influenced by the pore size distributions, surface heterogeneity and site energy distribution, as well as the adsorbate properties. Together, these parameters defined the adsorbate uptake forming the state diagrams, known as the adsorption isotherms, when the sorption site energy on the pore surfaces are favorable. The available adsorption models for describing the vapor uptake or isotherms, hitherto, are individually defined to correlate to a certain type of isotherm patterns. There is yet a universal approach in developing these isotherm models. In this paper, we demonstrate that the characteristics of all sorption isotherm types can be succinctly unified by a revised Langmuir model when merged with the concepts of Homotattic Patch Approximation (HPA) and the availability of multiple sets of site energy accompanied by their respective fractional probability factors. The total uptake (q/q*) at assorted pressure ratios (P/P _s ) are inextricably traced to the manner the site energies are spread, either naturally or engineered by scientists, over and across the heterogeneous surfaces. An insight to the porous heterogeneous surface characteristics, in terms of adsorption site availability has been presented, describing the unique behavior of each isotherm type.

SUBMITTER: Ng KC

PROVIDER: S-EPMC5587542 | biostudies-literature | 2017 Sep

REPOSITORIES: biostudies-literature

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A Universal Isotherm Model to Capture Adsorption Uptake and Energy Distribution of Porous Heterogeneous Surface.

Ng Kim Choon KC Burhan Muhammad M Shahzad Muhammad Wakil MW Ismail Azahar Bin AB

Scientific reports 20170906 1

The adsorbate-adsorbent thermodynamics are complex as it is influenced by the pore size distributions, surface heterogeneity and site energy distribution, as well as the adsorbate properties. Together, these parameters defined the adsorbate uptake forming the state diagrams, known as the adsorption isotherms, when the sorption site energy on the pore surfaces are favorable. The available adsorption models for describing the vapor uptake or isotherms, hitherto, are individually defined to correla ...[more]

PMID: 28878385

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Project description:The long-lasting stability of nanoparticle (NP) suspensions in aqueous solution is one of the main challenges in colloidal science. The addition of surfactants is generally adopted to increase the free energy barrier between NPs and hence to ensure a more stable condition avoiding the NP sedimentation. However, a tailored prediction of surfactant concentration enabling a good dispersion of NPs is still an ambitious objective. Here, we demonstrate the efficiency of coupling steered molecular dynamics (SMD) with the Langmuir theory of adsorption in the low surfactant concentration regime, to predict the adsorption isotherm of sodium-dodecyl-sulfate (SDS) on bare α-alumina NPs suspended in aqueous solution. The resulting adsorption free energy landscapes (FELs) are also investigated by tuning the percentage of SDS molecules coating the target bare NP. Our findings shed light on the competing role of enthalpic and entropic interaction contributions. On one hand, the adsorption is highly promoted by the tail-NP and tail-tail nonbonded interaction adhesion; on the other hand, our results unveil the entropic nature of water and surfactant steric effects occurring at the NP surface and preventing the adsorption. Finally, a thorough analysis on the steering works emphasizes the role of the NP curvature in the FEL of adsorption. In particular, we show that, moving from a solid infinite flat surface to a nanoscale particle, a deviation from a Markovian dynamics of adsorption occurs in close proximity to a curved solid-liquid interface. Here, both the NP curvature effect and nanoscale morphology promote a modification of the thermodynamics state of adsorption with a consequent splitting of the free energy profiles and the identification of specific sites of adsorption. The modeling framework suggested in this Article provides physical insights in the surfactant adsorption onto spherical NPs and suggests some guidelines to rationally design stable NP suspensions in aqueous solutions.

Project description:For more than a century, monolayer adsorptions in which adsorbate molecules and adsorbing sites behave ideally have been successfully described by Langmuir's adsorption isotherm. For example, the amount of adsorbed material, as a function of concentration of the material which is not adsorbed, obeys Langmuir's equation. In this paper, we argue that this relation is valid only for macroscopic systems. However, when particle numbers of adsorbate molecules and/or adsorbing sites are small, Langmuir's model fails to describe the chemical equilibrium of the system. This is because the kinetics of forming, or the probability of observing, occupied sites arises from two-body interactions, and as such, ought to include cross-correlations between particle numbers of the adsorbate and adsorbing sites. The effect of these correlations, as reflected by deviations in predicting composition when correlations are ignored, increases with decreasing particle numbers and becomes substantial when only few adsorbate molecules, or adsorbing sites, are present in the system. In addition, any change that augments the fraction of occupied sites at equilibrium (e.g., smaller volume, lower temperature, or stronger adsorption energy) further increases the discrepancy between observed properties of small systems and those predicted by Langmuir's theory. In contrast, for large systems, these cross-correlations become negligible, and therefore when expressing properties involving two-body processes, it is possible to consider independently the concentration of each component. By applying statistical mechanics concepts, we derive a general expression of the equilibrium constant for adsorption. It is also demonstrated that in ensembles in which total numbers of particles are fixed, the magnitudes of fluctuations in particle numbers alone can predict the average chemical composition of the system. Moreover, an alternative adsorption equation, predicting the average fraction of occupied sites from the value of the equilibrium constant, is proposed. All derived relations were tested against results obtained by Monte Carlo simulations.

Dataset Information

A Universal Isotherm Model to Capture Adsorption Uptake and Energy Distribution of Porous Heterogeneous Surface.

Publications

A Universal Isotherm Model to Capture Adsorption Uptake and Energy Distribution of Porous Heterogeneous Surface.

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