Nanoporous Carbon Research

Introduction Nanoporous carbons, which I define as those who contain micropores and/or mesopores as defined by IUPAC, are used across industry and beyond. Traditional applications of continuing importance include gas production, water treatment, gas masks and catalysis. Examples of newer uses include group protection against chemical agents, separations in protein, pharmaceutical and blood production, environmental remediation, rechargeable battery and fuel cell electrodes, CH4 and H2 storage, controlled drug delivery and membrane reactors. Most phenomena associated with nanoporous carbons and their applications are linked to the carbon structure. For example, storage and recovery of lithium from a carbon anode is linked to the molecular structure of the carbon whilst pore size clearly plays a pivotal role in molecular sieving. Pore surface chemistry is also often critical – water adsorption related phenomena and catalysis are well known cases in point – whilst bulk chemistry plays a role in, for example, the thermal stability of porous carbons. The critical importance of the structure has motivated our work in nanoporous carbons, which has been primarily aimed at building models that go beyond the standard graphitic slit-pore model to capture the structural (energetic) heterogenity and topology of carbons.

In the first half of the 1990s, I published the first ever computer-based complex models of nanoporous carbons (right), termed virtual porous carbons (VPCs). By providing more realistic representations of carbons, the VPC concept has allowed me to elucidate the fundamentals of fluids within nanoporous carbons in a way that is impossible with the slit-pore model - this is demonstrated below by three examples. Our carbon-related work is continuing in a number of directions including the development of VPCs that explicitly include heteroatoms, the study of phase behaviour of fluids in complex carbonaceous nanopore spaces, and adsorption of proteins on nanoporous carbons such as carbon nanotubes.

 

Elevated freezing in nanoporous carbons

There is some indirect (and therefore uncertain) experimental evidence that simple fluids can take on solid-like densities and structures in nanoporous carbons at temperatures above the bulk freezing point (i.e. where the fluid would be a liquid in the bulk phase). Although some groups have predicted elevated freezing using molecular simulation in graphitic slit-pores, it was not clear if this was a result of the symmetry of the pore model - we investigated this affect using our VPC and found that elevated freezing is indeed possible even in very complex pore spaces. This is revealed in the image above, which was used on the cover of the issue of Langmuir in which this work is reported.

 

Absolute assessment of adsorption-based characterization methods

Although adsorption is by far the most widely used means of nanoporous solid characterisation, it is not without its problems; these may be broadly described in terms of correctness, consistency (i.e. is the parameter purely related to what it purports to represent or does it 'include' more), and meaningfulness (e.g. what does 'surface area' mean in a microporous solid). Much effort has been directed towards addressing these concerns using relative assessment in which data obtained from two or more methods for a solid are compared. This approach is rarely satisfactory for a variety of reasons including, amongst others, the difficulty faced in understanding any observed differences. An alternative to relative assessment is to use a solid whose characteristics are exactly known and for which the interstitial fluid behaviour can be probed in detail. Whilst such an absolute assessment process is (perhaps) experimentally feasible for solids like zeolites, it is clearly not for ill-defined solids such as carbons, which are most in need of assessment. We have, therefore, developed and applied a molecular simulation based methodology for the absolute assessment of adsorption-based characterisation methods that is illustrated below.

Briefly, the process involves use of Grand Canonical Monte Carlo (GCMC) simulation to determine the adsorption and desorption isotherms for a model fluid in an VPC for which measures of the characteristics are known exactly. The adsorption or, if appropriate, desorption isotherm is then submitted to the method to be assessed and estimates obtained. These estimates are compared with the corresponding exactly known measures and conclusions are drawn regarding the correctness (closed loop in figure above) and, if appropriate, meaningfulness and consistency of the methods for the particular model system. Reasons for lack of correctness can be identified and assessment of meaningfulness and consistency can be made by probing the adsorption process at the molecular level; such analysis can be used to suggest improvements to the characterisation method (feedback loop in above figure) or an entirely new method that can in turn be assessed. We have applied this absolute assessment methodology to a variety of adsorption-based characterisation methods including the Gurvitsch rule, comparison methods, the SPE method, the BET method, a method for determining the pore size distribution and connectivity of the pore space, and various single and multi-isotherm methods for determining the pore surface fractal dimension (see Biggs et al. (2006) for details). As a result, we have been able to identify which methods are fundamentally flawed (e.g. the SPE method) and suggest alternative approaches (e.g. a new protocol for evaluating the pore surface fractal dimension) - many of these findings have been documented in our existing publications, whilst further publications are in preparation.

Diffusion coefficients from adsorption only
Diffusion in nanoporous carbons is important in a variety of applications including gas separation, catalysis, energy storage and controlled drug delivery. The design of carbons in such applications and associated process requires at the very least knowledge of the effective diffusion coefficients of the relevant fluids within the carbons, whilst optimization of carbons and associated processes further requires knowledge of the relationship between these coefficients and the carbon structure. Experimental methods are currently the primary means of determining effective diffusion coefficients. These experiments require, however, specialist apparatus and expertise. Even if such are available, the experiments are non-trivial and present considerable challenges as is evidenced by, for example, the very different (i.e. >1 order of magnitude) diffusion coefficients yielded by different methods for the same material. These issues mean there is a relative dearth of diffusion coefficient data for nanoporous carbons and virtually no understanding of the coefficient-structure relationship. Equilibrium measurements are far more common and straightforward to undertake. We have, therefore, developed a hybrid pore network/molecular simulation (PN/MS) approach for predicting effective diffusion coefficients for nanoporous carbons using as input adsorption isotherm data only (below).
The hybrid PN/MS model consists of four stages. In the first, molecular simulation is used to determine the transport diffusivities for the fluid of interest in a library of single pores - although in principle there is no limit to the number of different single pore models that can be used, nor their complexity, our library currently consists of graphitic slit pores only with pore widthes ranging from 0.7-3.5 nm. In the second stage, the pore size distribution (PSD) and connectivity, Z, of the solid of interest are determined from adsorption data; we use the method of López-Ramón et al. (Langmuir, 13, 4435, 1997) to do this. The third stage involves construction of a pore network (PN) model with this PSD and Z. The fourth and final stage involves determination of the effective diffusion coefficient for the fluid in the PN, Dm, assuming that diffusion in the individual pores of the network is described by the transport diffusivities embedded in the database determined in the first stage; we do this using the REMA method of Zhang and Seaton (AIChE J. 38, 1816, 1992). One of two strategies may be used to validate the hybrid PN/MS model. The first is purely experimental – compare predicted diffusion coefficients with experimental values. The problem with this is the limited capacity for resolving any observed differences. This is especially acute given that even experimental values for the same solid can vary widely depending on the experimental method used. The alternative is a model-based approach such as that illustrated below left, where a real porous solid in the laboratory is replaced by an VPC, and molecular simulation is used to obtain the adsorption isotherm and effective diffusion coefficient for the VPC. What makes this approach so attractive is the certainty we can have in the diffusion coefficient of the VPC, and the ability we have to directly probe the diffusion process at the molecular level, which should greatly aid resolving any differences between the actual diffusion coefficients and those obtained from the hybrid PN/MS model. This approach was, therefore, used here.
The figure above right shows that the predictions of the hybrid PN/MS model for methane in a VPC compares very well with the actual effective diffusion coefficient for a wide range of pressures. Similarly good predictions are found for other VPCs - this work will be reported in detail in a paper that is nearing completion.