Effect of Organic Ions on The Formation and Collapse of Nanometric Bubbles in Ionic Liquid/Water Solutions: A Molecular Dynamics Study

Molecular dynamics simulation is applied to investigate the effect of two ionic liquids (IL) on the nucleation and growth of (nano)cavities in water under tension and on the cavities’ collapse following the release of tension. Simulations of the same phenomena in two pure water samples of different sizes are carried out for comparison. The first IL, i.e., tetra-ethylammonium mesylate ([Tea][Ms]), is relatively hydrophilic and its addition to water at 25 wt % concentration decreases its tendency to nucleate cavities. Apart from quantitative details, cavity formation and collapse are similar to those taking place in water and qualitatively follow the Rayleigh–Plesset (RP) equation. The second IL, i.e., tetrabutyl phosphonium 2,4-dimethylbenzenesulfonate ([P4444][DMBS]), is amphiphilic and forms nanostructured solutions with water. At 25 wt % concentrations, [P4444][DMBS] favors the nucleation of bubbles that tend to form at the interface between water-rich and IL-rich domains. Cavity collapse in [P4444][DMBS]/water solutions are greatly hindered by a shell of ions decorating the interface between the solution and the vapor phase. A similar effect is observed for the equilibration of a population of bubbles of different sizes. The drastic slowing down of the bubbles’ relaxation processes suggests ways to produce long-lived nanometric cavities in the liquid phase that could be useful for nanotechnology and drug delivery.

to resist the external tension, and its volume is expanding at a rapidly increasing rate. To prevent such an unbound expansion, the analysis of bubble nucleation, growth and bubblebubble interaction have been investigated at NVT conditions. Red dots: OW atoms of water.
Blue dots: oxygen of the ghost particles inserted to identify voids in the system (see text).
Hydrogen atoms not shown. The side of the sample in the three panels is proportional to the size of the simulation cell at the times reported in the figure. in the volume of the homogeneous sample at θ = 1300 bar. The computation of the shape parameters is based on the N discrete volume elements V w0 corresponding to the N probe water molecules inserted in the sample to identify cavities in the system (see the Methods section in the main text). The gyration radius R g is defined as R g (t) = (t)/N (t). The parameters and δ 2 /3 2 are defined in the text. δ 2 /3 2 in particular is a measure of the asphericity of the cavity. shows that nucleation started about 40 ps before, with the slow ripening of the initial nucleus (identified by the gray area at t < 0). Including this initial stage, the cavity formation lasts ∼ 180 ps, i.e., three times longer than in the water sample of the same size and equal θ crit − θ. that the equilibration to the expected state consisting of a single bubble whose volume is the sum of the two initial volumes is exceedingly slow.

The nucleation and growth of cavities observed by simulation at NVT condtions
The observations on the nucleation and growth of cavities obtained through simulation at NVT conditions, can be rationalised in terms of the static Laplace equation (Eq. 5 of the main text). Let us consider a homogeneous liquid under tension θ start at volume V , whose equilibrium volume at P = 1 bar is V 0 . After its formation, the nanometric bubbles at equilibrium in the equally mesoscopic samples contain a very dilute vapour corresponding to the water vapour tension at T = 300 K. This dilute vapour has positive but negligible pressure. Hence, to estimate the order of magnitude of the different parameters, we assume p in = 0. Then, in the presence of the bubble, the residual pressure in the (no longer homogeneous) liquid phase is S17 (see Eq. 5 of the main text): where γ is the surface tension of water and R = (3Ω/4π) 1/3 is the radius of the bubble.
After the cavity formation, the liquid will occupy a volume (V −V 0 −Ω) > V 0 , with a residual tension that can be estimated as θ res ≡ θ out = B(V − V 0 − Ω)/V 0 . Therefore, the volume Ω of the equilibrium bubble has to satisfy: or: On the one hand, the volume Ω of the bubble cannot exceed V − V 0 , otherwise the residual tension would be negative (i.e., p out > 0), a condition hardly compatible with the presence of a stable cavity. On the other hand, because of the 2γ/R term, the cavity cannot be arbitrarly small otherwise this term could not be balanced in Eq. 3. Eq. 3 has been solved numerically as a function of volume V for a sample whose equilibrium size V 0 = 6000 nm 3 is comparable to No Ω > 0 solution is found for V <V , volume at which a bubble appears with a non-zero volume Ω min . At V >V the two curves cross at two Ω values, but it is immediate to verify that only the second is a minimum of the free energy. The first crossing is a maximum of free energy, and is reminiscent of the activated state for nucleation.
Needless to say, these considerations strictly depend on the NVT conditions of the simulation and of the model, and also on the mesoscopic size of the simulated sample. Nevertheless, they are useful to interpret the simulation data and could be relevant for cavitation in porous media or, in general, in confined geometries.

Considerations on the collapse of cavities in water based on the Reyleigh-Plesset equation
For what concerns the water case, the RP can therefore be used to make simple predictions that represent a benchmark for our investigation of IL effects. First, at zero pressure and considering (spherical) cavity sizes in the µm range (thus beyond the sizes considered in simulation), the time evolution is mainly determined by viscosity. Excluding the very initial and final stages of collapse, in which inertia is relevant, the RP equation can be approximated as:Ω whose solution (with boundary conditions Ω(t) = Ω 0 for t ≤ 0, and Ω(t) = 0 for t ≥T ) is: is the time required for the bubble to collapse. Sincet grows linearly on the initial radius of the bubble, the velocity of the cavity surface during collapse will be virtually the same at all sizes, and no extreme heating will take place. However, for pressure p out exceeding a few bar, the RP equation can be approximated as:Ω Ω = 3p out 4η (7) Hence, the rate of volume reduction is proportional to the volume, and the velocity of the approaching surfaces will also grow linearly with the cavity size. A simple estimate using the viscosity of water and pressures in the ∼ 10 2 range shows that for cavities of µm radius, this velocity will reach the sound velocity, generating the shock waves which play a crucial role in sonochemistry and sonoluminescence. S20