Department of Physics
3 West 3.2
University of Bath
Claverton Down
Bath
BA2 7AY
01225 386437

## Clement Law

Currently a 1st year PhD student, working with [Rob Jack][rob_jack] on the theory of colloidal self-assembly in the University of Bath's [Condensed Matter Theory group](http://www.bath.ac.uk/physics/research/theory/). See this [Nature paper][sacanna] by *Sacanna et al* for an example of the current research direction in this field. My undergraduate MPhys was taken at the [University of Warwick][warwick] where my final year project, supervised by [Rudolf Roemer][rudolf], was concerned with the electrical conductance characteristics of DNA (based in part upon this important [paper][klotsa] by *Klotsa et al*). I'm also helping out in the [Maths for Scientists 4][maths_problem] problem classes. ---------------------------- ## Current Research Interests

Lock and key (and nanoparticle) with appropriate radii, r, labelled. The size and extent of the lock 'mouth' can be described as a spherical indentation of a 'cutting sphere' with radius rC.
### Depletion-driven self-assembly of lock and key colloidal fluids. Imagine a box filled with three kinds of particles. Two of these particles are called the lock and the key (approximately the same size), whilst the third is denoted the nanoparticle (approximately one tenth the radii of a lock). The lock is a sphere with a spherical indentation and the key and nanoparticle are both spherical. For the system in question, there are generally many more nanoparticles than locks or keys. The system is free to sample any (physical) configuration it likes, within the confines of the box, and in fact, favours a combined lock and key set up. Why is this? Our closed system will approach a state of minimum free energy: the more volume available to the nanoparticles, the lower the free energy. If you sat down and looked at the volumes of a separate lock and a separate key compared to a so called 'dimer', you'd find the dimer's volume is less. Therefore, the configurations in which the lock and key are 'locked' are the preferred states for the whole system. The nanoparticles 'force' the locks and keys into bound states so they can have more entropy, and hence the overall free energy of the system will reach a minimum. ### Current Work

I'm currently computing pair distribution functions of one lock, one key and many nanoparticle systems in the hope of parametrising an effective potential of a self-assembling lock and key system with no nanoparticles. Recently, I've been thinking about the partition function of this lock and key system. Through the generalised partition function below, I've been able to re-derive an important (approximate) result from [Sacanna's][sacanna] paper on lock and keys. ![Partition function for lock and key system](partition.png) ## Miscellaneous

After becoming frustrated with some of the brevity in the [original gnuplot documentation](http://www.gnuplot.info/docs_4.4/gnuplot.pdf), I've been padding it out myself. I've been doing a lot of three dimensional contour plotting recently, so the [document][gnuplot_doc] I've been writing deals in a bit more detail with this. The upshot of why it's important to know exactly what that famous command 'set pm3d map' does can be demonstrated from this [example](pm3d.pdf) (taken from some pair distribution functions I've been generating). ## Links

-------------------- Written with [Markdown][markdown] and inline HTML (view [Markdown source][markdown_source]) [bathlockandkey]: http://bathlockandkey.co.uk [detexify]: http://detexify.kirelabs.org/ [gnuplot_doc]: gnuplot.pdf [rob_jack]: http://people.bath.ac.uk/rj248/ [sacanna]: http://dx.doi.org/10.1038/nature08906 [warwick]: http://www.warwick.ac.uk [rudolf]: http://www2.warwick.ac.uk/fac/sci/csc/people/members/rudolf_roemer [klotsa]: http://arxiv.org/pdf/q-bio.GN/0504004 [maths_problem]: http://www.bath.ac.uk/catalogues/2011-2012/ph/PH20020.htm [markdown]: http://daringfireball.net/projects/markdown/ [markdown_source]: index.text [mathworld]: http://mathworld.wolfram.com