Updates on all things van der Waals - London Dispersion for Single and Multiwall Carbon Nanotubes. Rick Rajter - MIT

Review of Overall Goals for NIRT Project 2.1 Controlled Placement of Carbon Nanotubes on a Substrate Experimental and theoretical mapping of parameters that control 2D patterns; A) Different electrode geometries and materials B) Control of surface patterns by electric fields: C) Direct measurement of the 2D nematic phase: D) Development of theory 2.2 Solution-based sorting of carbon nanotubes Understanding and improving the separation mechanism 2.3 DNA-CNT Structure Measurement of chemical composition Counter-ion characterization Measurement of DNA-CNT structure (TEM / CD) Detailed molecular modeling of DNA-CNT structures 2.4 Electrostatics and van derWaals interactions: Theory Electrostatics (with application to structure, sorting, and placement) Band structure of DNA-CNT hybrids van derWaals forces My research has primarily been involved in sections and This talk will be focused more so on the latter.

General Overview of the Stages of Research Introduction to anisotropic optical properties of SWCNTs J. Appl. Phys. 101, New anisotropic solid cylinder equations for the Lifshitz formulation Phys. Rev B 76, New Perspectives on van der Waals – London Dispersion Interactions of Materials: Wetting, Graded Interfaces and Carbon Nanotubes eMRS Presentation and Proceedings 3 future topics currently being finalized for publication Mixing paper to address optical properties of the core + surfactant for SWCNT and MWCNT considerations. Datamining papers I & II to specifically analyze the trends from SWCNT structure, to optical properties, to vdW-Ld forces. For the sake of brevity (for your benefit as well as mine!), I’ll just pull relevant slides from the eMRS talk given by Roger, and then go over current progress in the future work.

But First… Motivation! In the Zheng ssDNA/SWCNT hybrid elution method, it is believe that the differences in dielectric properties are the key factor in dictating the relative binding strength. Initially this was only between metals vs semiconductors. In experiments done by scientists at Rice, separation was demonstrated via DEP, which is directly linked to the optical properties. The seperation was believed to be as a function of diameter. For separation between the [9,1,s] and [6,5,s], there are only minor differences in the electronic band gap and diameter… yet they are clearly separable. Optical properties depend on all transitions, even up to transitions as strong as 40 eV or higher. Thus we cannot make guesses from band gap data as to which one will be stronger or weaker with a given material.

Switch to the eMRS Presentation…

And we’re back!

Next Stage — Mixing Although the current formulations are a big leap forward, they currently lack the ability to account for retardation and multi-layer effects. Unfortunately, SWCNTs are notoriously hollow! An analytical formulation appears to not be tractable. Fortunately, at the two extreme limits (near contact and far away), we can adequately approximate using mixing rules.

Applications of Mixing SWCNTs + Hollow Core + Surfactant MWCNTs + Hollow Inner Core + Surfactant

Mixing SWCNTs vs a MWCNT The major difference occurs at low frequencies. Although subtle, they do have an impact on the overall vdW-Ld spectra.

Mixing SWCNTs vs a MWCNT To test our ability to use the mixing rules, we took optical properties from two SWCNTs, added them together, and compared them to an optical property calculation from a MWCNT system.

Mixing SWCNTs vs a MWCNT Result: Discrepancies exist, but the overall behavior is largely captured. Further analysis is needed to figure out just if these changes are systematic enough to be accounted for within the mixing formulation.

MWCNT Mixing Rules — Predicted Effects So far, we know that in the far limit, the optical properties are averaged. But in the near limit, it is the outer term that dominates. This could lead to situations where a particular MWCNT pair absorbs better than another despite being equally attractive far away. Obviously this remains to be seen experimentally, but there is a wealth of information that can

Next Step — Datamining I & II Here we are trying to understand the relationship of vdW-Ld back through all the levels of abstraction.

Analyzing the Links All van Hove singularities shift in eV as ~ 1/r, causing shift in e” positions. Shifting a unit area of e” causes a systematica distortion in the resulting vdW-Ld spectra. Changes in the cutting lines with n,m also affect upper band transition strengths at high eV. Changes in e” area raise or lower the vdW-Ld spectra as a whole.

A Diverse Cast of Characters Although some scaling issues remain, the resulting vdW-Ld spectra are very diverse and don’t necessarily follow trends as closely as one would expect. On the bright side, the wide range of values means that there is definitely room to separate all kinds of chirality pairs from one another.

Comparing the [6,5,s] and [9,1,s] Same diameter, both semiconductors, different wrapping angles, separable.

In Summary Introduced anisotropic vdW-Ld properties. New solid anisotropic cylinder formulations which accurately takes into account the properties of both directions simultaneously. Mixing allows for use of the solid cylinder equations for more complex multi- layer SWCNTs. Paper is currently in the preliminary draft phase. Datamining papers of 60 SWCNTs MWCNTs will follow thereafter to finally get a total picture of how these energies vary in systems equivalent to experiments.

Acknowledgments Steve-o Lustig, Roger French, Wai-Yim Ching, Rudi Podgornik, Adrian Parsegian, Craig Carter, Yet-Ming Chiang, DMA+NIRT.

Thank you for your time? Questions?