(670f) Is the Tolman Length for Water Droplets Entropic or Enthalpic?
AIChE Annual Meeting
2015 AIChE Annual Meeting Proceedings
Engineering Sciences and Fundamentals
Thermodynamics at the Nanoscale I
Thursday, November 12, 2015 - 10:20am to 10:40am
The structure of molecules at the interface of highly curved, nanometer-sized water droplets differs significantly from that of a planar interface . As a result, the surface free energy, γ, is size-dependent as suggested Tolman, who derived an expression wherein γ is sensitive to the Tolman length, δ, a system-specific parameter . The Tolman length is a critical parameter in nucleation theories as small δ values (i.e. <1 Å) can alter the predicted nucleation rate by many orders of magnitude compared to assuming δ=0 . Numerous studies on water have confirmed a size-dependent γ [3-5], but there is no consensus on the Tolman length. Moreover, it is unknown whether the changes in surface free energy are entropic or enthalpic in origin.
In this work, we determine the size dependent surface free energy of mW water by employing the mitosis method  for droplets ranging in size from 0.7 to 1.6 nm (48 to 560 molecules, respectively). Within a δ-CNT framework , we find that δ=-0.57 ± 0.07 Å at 300 K, in agreement with a previous study on TIP4P/2005 water  and an experimental study . A negative Tolman length indicates that γ increases as droplets become smaller, which in turn hinders nucleation. By separating the Tolman length into entropic and enthalpic contributions, we find that entropy dominates the change in surface free energy. We propose that this is due to structural correlations. Moreover, our findings indicate that the number of “broken bonds” per area is nearly insensitive to the droplet size. We anticipate that our deconvolution of the entropic and enthalpic contributions to a size-dependent γ may also be applicable to the hydrophobic drying transition.
 A. Malijevksý, G. Jackson, J. Phys.-Condens. Mat., 2012, 24, 464121.
 R.C. Tolman, J. Chem. Phys. 1949, 17, 333-337.
 M.N. Joswiak, N. Duff, M.F. Doherty, B. Peters, J. Phys. Chem. Lett. 2013, 4, 4267-4272.
 G.V. Lau, I.J. Ford, P.A. Hunt, E.A. Müller, G. Jackson, J. Chem. Phys. 2015, 142, 114701.
 V. Holten, D.G. Labetski, M.E.H. van Dongen, J. Chem. Phys. 2005, 123, 104505.
 N. Duff, B. Peters, Mol. Simulat. 2010, 36, 498-504.
 M.E.M. Azouzi, C. Ramboz, J.F. Lenain, F. Caupin, Nat. Phys. 2013, 9, 38-41.