Scission of Nanotubes in Sonication

PITTSBURGH - July 4, 2016 - PRLog -- .
Introduction
The ultrasonic modification of chemicals in liquids by high temperatures > 5000 K during bubble collapse has recently been extended to modifying the molecular weight of polymers. However, the effect is thought not to arise from the high temperatures in the collapse of cavitation bubbles, but rather by high strain rates of 10⁹/s generated in the surrounding liquid, the accompanying viscous friction causing bond fracture by stretching the polymer, e.g., graphene oxide sheets can be cut into nanoscale fragments in < 10 min of sonication time.

Similarly, sonication based on viscous friction forces is thought [1-3] to sort liquid-suspended SWNTs by diameter dependent scission giving rise to shorter SWNT fractions with large diameter while smaller diameters characterize longer SWNTs. SWNTs stand for single-walled nanotubes. Like polymers, SWNTs always break near their center, the shortening being limited to a length of about 120 nm, below which no further shortening occurs.

Problem
Despite the long-standing history of sonication, the mechanism by which polymers and SWNTs undergo scission is still not understood. However, the stretching of SWNTs by viscous drag forces to scission SWNTs by tensile fracture is considered unlikely as the viscosity of water most likely does not exist at extreme strain rates.

Proposal
Ultrasound induced scission is proposed caused by photoelectric charging of SWNTs from QED induced non-thermal EM radiation at UV frequencies produced in collapsing bubbles. QED stands for quantum electrodynamics, EM for electromagnetic, and UV for ultraviolet. Here, QED is a far simpler form of the light-matter intraction advanced by Feynman and others. SWNT scission occurs as the UV radiation charges the SWNTs to produce electrostatic repulsion between the atoms with scission occurring by tensile fracture.

Theory
QED induced scission is a consequence of QM that denies the water molecule during bubble collapse the heat capacity to conserve heat by the usual increase in temperature. QM stands for quantum mechanics. Consistent with the Planck law of QM at ambient temperature, water molecules on the surface of a collapsing bubble have thermal kT energy in the IR provided the bubble is macroscopic. Here k is Boltzmann's constant, T absolute temperature, and IR infrared. But as the bubble collapses to nanoscale dimensions, the long wavelength IR radiation from surface water molecules is suppressed by the EM confinement provided by the bubble wall. By QM, the suppressed IR heat cannot be conserved by an increase in temperature of surface water molecules, and therefore QED conserves the heat by creating EM radiation at half-wavelength  λ/2 = d, where d is the bubble diameter. Indeed, the minimum SWNT shortening observed to be about 120 nm occurs because the background UV radiation shown in {Fig. 4(a) of [1]} peaks at λ of about 240 nm, after which the UV ceases and further scissioning does not occur. See diverse QED applications at http://www.nanoqed.org/, 2010 - 2016.

Summary
The QED induced force F and the time τ to scission SWNTs as a function of the interatomic spacing, designated a, between groups of Ncir atoms along the length L of the SWNT is summarized in the inset of the thumbnail.

Tensile Force The groups Ncir are the number of carbon atoms around the tube circumference of diameter d, i.e., Ncir = πd/a. The charge on each atom is ηq, where η < 4 and q the unit charge. For a charged SWNT, each group Ncir of atoms to the right and left of the SWNT center contributes to the central electrostatic force by the Basal series sum, Σ( 1 + 1/4 + 1/9 + ) = π²/6. Hence, SWNTs always fracture near their center. For SWNTs, the isotropic dielectric constant κ = 10 gives the tensile force of about 20 nN for η = 1.29 in order to be consistent with [1].

Sonication Time The time τ in minutes to scission SWNTs depends on their number Nswnt and the number Natoms of atoms per SWNT, the charge energy ηq per atom, and the ultrasonic power P. Here, Nswnt = W/ALρ, where W is the weight of SWNT material, A and ρ are the cross-section area and density of  the SWNTs. In terms of the SWNT wall thickness w, A = π[d²-(d-2w)²)]/4, where d and w are 1.2 and 0.34 nm. But Natoms = Ncir(L/a) and therefore τ is independent of the SWNT length L. Indeed, SWNT length shortening [1,2] is given by power laws of sonication time τ ^-m , where m = 0.2 to 0.5. Contrarily, {Fig. 9 of [1]} showing SWNT length to decrease linearly from 800 to 250 nm in about 10 minutes suggests m = 1. For W = 1 mg and P = 20 W, QED scission is consistent with tensile forces 20 nN having a sonication time τ of about 10 minutes as shown in the thumbnail. At times τ > 10 minutes, there is essentially no additional decrease in SWNT length.

Conclusions
SWNTs scission in sonication because collapsing bubbles produce UV radiation that charges the SWNTs to produce electrostatic repulsion between atoms, tensile fracture occurring at the SWNT center coinciding with the position of maximum electrostatic force. At collapse, charged carbon atoms recombine with the electrons lost in charging.

Length dependent scission rates are artifacts of viscous drag forces that scale with the second or fourth power of SWNT length do not occur.

QED induced scission does not predict diameter dependent SWNT lengths. Increased SWMT diameter gives higher forces but tensile stress is not increased as the cross-section area also increases. More study is required.

References
[1] F. Hennrich, et al., "The Mechanism of Cavitation-Induced Scission of Single-Walled Carbon Nanotubes," J. Phys. Chem. B, 111, 1932-1937, 2007.
[2] G. Pagani, et al., "Competing mechanisms and scaling laws for carbon nanotube scission by ultrasonication," PNAS, 109, 11599-11604, 2012.
[3] J. Stegen, "Mechanics of carbon nanotube scission under sonication," J. Chem. Phys., 140, 244908, 2014.