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cDFT is a Python package to implement classical Density Functional Theory (cDFT) for fluids in contact with smooth planar surfaces, smooth solutes and confined between two smooth planar walls (an infinite slit).

I was introduced to cDFT during the early stages of my PhD. Whilst I could clearly see the merits of cDFT, I found that the literature surrounding it was fairly scattered and there was limited information on how to actually implement it computationally. A lot of the numerical tricks to write a good cDFT program are typically passed by word of mouth and I personally have seen very few resources which clearly lay out the mathematics behind implementing attractive fluids. Obstacles such as these meant I found it difficult to firstly find a package that I could use and then to write my own. I therefore decided that when I wrote my own program for cDFT I would try to make it as user-friendly and freely available as possible.

As this package was written as part of my PhD research it is by no means professional or to a large extent complete. In time I plan to add notes here with instructuctions on how to add new fluid and external potentials, so that other students (or anyone else who is interested) will be able to use this package in the way that best meets their research needs.

In the meantime, this repository will consist of the package in its current state and three tutorials which I hope will help you understand how to use it. For more information on the theory behind this package, and details of underlying calculations, please see Chapter 4 and Appendices A-C of my thesis, available here.

This package is setup to deal with two fluid types and three geometries. The fluids that can be studied using this package are the hard-sphere fluid and a truncated Lennard-Jones (LJ) fluid. Note that the length of the truncation in the latter is arbitrary - you can set the truncation to be hundreds of times the size of the fluid particle. This means the package can effectively study both short-ranged and long-ranged LJ fluids.

The package gives the user the option of three systems: a fluid in contact with a smooth planar surface; a fluid in contact with a smooth solute of arbitrary radius; and a fluid confined to an infinite slit in which the walls are smooth. The use of the term 'smooth' is important here. This means that the external potential that any of these surfaces exerts on the fluid varies in only one direction. For a planar surface or a slit, this is the direction perpendicular to the wall(s). For a solute, this is along the radial axis extending from the centre of the solute. The density profile of the fluid will take the symmetry of the external potential exerted on it, hence for each of these systems the density profile varies along only one axis. The consequence of this is that the weighted density and correlation functions can be reduced to one-dimensional calculations by analytically evaluating their results in the two dimensions in which the density profile is homogeneous. This greatly reduces the computation involved and therefore makes the package fairly quick. To clarify, the systems studied are three-dimensional, we have just made the computer's job easier by doing the calculation ourselves in two of the three dimensions.

The package implements statistical mechanics sum rules. These are formally exact equations which relate microscopic and macroscopic properties of a system. Importantly, either side of these equations can be calculated independently and hence you can test the numerical consistency of asking the package to calculating either side of these equations and compare them.

This package uses two different sum rules - the Gibbs' adsorption equation and the contact sum rule. For more information, take a look at the tutorials.

Honestly, probably not. This was done as part of my PhD which I have now finished, and I am likely to move on to other challenges. However I encourage you to add your own features. In due course I'll hopefully put some notes up to explain how to add features into the package.

To find out how to use the package, take a look at the tutorials! I also provide references there to help aid your understanding of cDFT.

The package currently supports:

Fluids: Hard-Sphere, truncated Lennard-Jones

Geometries: Planar surface, solute and infinite slit.

Functionals (for implementing Fundamental Measure Theory for hard-spheres): Rosenfeld, White-Bear and White-Bear Mark II

Surface/Solute-fluid interactions: hard (planar, solute and slit), Lennard-Jones (planar and solute), shifted Lennard-Jones (planar, solute and slit), WCA Lennard-Jones (planar)

Sum-Rules: contact sum rule and (Gibbs') adsorption sum-rule for all surface/solute-fluid interactions listed above

Measures: adsorption, surface tension, contact density, density profile, local compressibility and local thermal susceptibility profiles (see tutorial 3 for an explaination of these)