Thomson equation revisited in light of ion-clustering experiments

Abstract

there are initial concentration gradients in both phases at the beginning of the ripple experiments. We, therefore, first solved eq 10, 12,13, 17, 20, and 21, respectively, for a flat interface starting with a fresh interface at t = 0, i.e., Ci(x,y,0) = C0 and C2(x,y,0) = 0. We then assumed that quantities like C^Cy.t), which now depend on time and location because of evaporation, do not change significantly on the time scale of ripples and calculated the perturbed concentration profile by an appropriate linearization procedure. So we determined Ct(1) from the equation [see (12)] dCi(1)(x,y,0 _ Dll 77 + 77 |c1(1)(x,y,t) -v{x,y,t)^-Cxm{y,te) (22) \ dx2 dy2 4J oy where te is the time of observation.For all practical situations, the initial concentration gradients lead to negligible deviations from the equilibrium results presented above. This can easily be understood: according to ( 14), perturbations of solute concentration decay on a length scale ^ * 1 1~( 1/ )1/2 while Cif0)(t0) changes on a length scale of ^)1/2. Hence, initial gradients are of little importance for ( ^)1/2 » 1 which holds for all experimental situations. ConclusionsOur main result is expression 19 for the dilational index e. We have shown that diffusion in the liquid dominates evporation as the mechanism for restoring gradients in solute concentration. But even diffusion is of minor importance: Lucassen and Hansen5 6have shown that it is already difficult to determine the diffusion coefficient from ripple experiments. Hence, our results suggest that it will be almost impossible to get reliable data on evaporation from studies of the ripple spectrum.Similar equations can be applied to ripples at a liquidliquid interface when discussing transfer of surfactant between the liquids. In that case, the additional terms in the expression for the dilational modulus will probably be more important, and the effect may be larger.

From molecular clusters to nanoparticles: second-generation ion-mediated nucleation model

“…The predictions based on traditional CKT equation (Holland and Castleman, 1982) are shown in Fig. 3a only. pressure, etc.)…”

“…Figure 3 Fig. 3a are predictions based on traditional CKT equation (Holland and Castleman, 1982) and MKT equation (Yu, 2005a) with f − =1, f − =r 0 /r n , f − =(r 0 /r n ) 2 , respectively. For the un-hydrated negative H 2 SO 4 ions, measured G 0 n,n−1 at smaller n are up to ∼10 kcal/mol larger than those predicted by CKT equation.…”

The role of atmospheric ions in aerosol nucleation – a review

“…Nadykto and Yu (2004) discussed the modelling of the dipole further, and their calculations compared well with experimental nucleation measurements. Thomsons's charged liquid drop model, employed in the determination of δ G i , was tested experimentally for various clusters (Holland and Castlemann Jr., 1982) with a positive core ion. The results compared favourably for water clusters but not for the other ligands tested.…”

Effects of electron kinetic energy and ion-electron inelastic collisions in electron capture dissociation measured using ion nanocalorimetry

“…To obtain the RE, the threshold dissociation energy for the loss of each water molecule from the reduced precursor must be known. Values for clusters of the size typically investigated have not been measured, but these values can be obtained from the Thomson liquid drop model [28,29]. Various implementations of this model have been recently evaluated by comparison to experimental data for both monovalent and divalent ions [29].…”