Rayleigh charge limit

Keywords Aerodynamic effects Charged droplets Cone jet Droplet evaporation Droplet deformation Electrohydrodynamic spray Electrospray Ion source Mass spectrometry Mass spectroscopy Rayleigh charge limit Spray modes Taylor cone... 

With a liquid droplet this maximum charge cannot be reached except in the case of extremely small droplet sizes. This is because of an additional charge limitation placed on liquid aerosols, known as the Rayleigh limit. It has been known for many years that as a highly charged droplet evaporates, a point will be reached where the outward force of the electric field at the drop surface exceeds the inward force of the droplet s surface tension. At this point, the drop will be torn apart by the close proximity of like charges and will produce a number of smaller drops in order to create more surface area for the charge. The number of electrons necessary for droplet... 

How the droplets produced upon ESI are transformed to the ions observed in the mass spectrum is not yet well xmderstood. As the solvent in the droplets evaporates, the droplets shrink and the ions contained in them accumulate at the surface to minimize coulombic repulsion between the charges. This process can continue until the Rayleigh instability limit is reached, at which the droplets disintegrate ("explode") into smaller droplets (Figure 1.15) that also shrink by solvent loss. Sequential subdivision through coulombic explosion at the Rayleigh limit may be repeated until the... 

The decrease of the droplet radius R at constant charge q leads to an increase in the electrostatic repulsion of the charges at the droplet surface until the droplet reaches the Rayleigh stability limit [28] given by ... 

In order to improve the mass spectrum analysis results, the mass spectrometer requires as many detectable gas phase ions as possible. As shown in previous sections, the electrospray produces gas phase ions from its charged droplets when the droplets reach a certain size and either the CRM of IBM model of gas phase ion formation occurs. To produce gas phase ions efficiently, an electrospray must operate in a mode where the droplets produced are relatively small, close to the Rayleigh limit, and also where the droplets are charged sufficiently. Once the droplets reach the Rayleigh stability limit at a fast pace, they can continue on to the CRM an IBM models of gas phase ion formation. 

The rival theory of Iribame and Thomson54 assumes that gas-phase ions solvated by a few solvent molecules are emitted into the gas phase by charged droplets with radii R < 10 nm, which are somewhat below the Rayleigh limit. This ion evapora-... 

There is a limit to the charge that the surface of a droplet can sustain, for the electrical stress generated by the surface charges can balance the surface tension forces. At that point the droplet becomes unstable and breaks up. Lord Rayleigh (1882) analyzed the criterion of instability for a conducting droplet using spherical harmonics to describe the modes of oscillation. The natural frequency of the nth mode of oscillation of a droplet was found to be given by... 

Here (7, is the surface tension, and Sq is the permittivity of free space. The mode n = 0 corresponds to the equilibrium sphere, and n = 1 is a purely translational mode. The first unstable mode is n = 2. The critical charge for this mode is given by setting Eq. (37) to zero, which yields the Rayleigh limit of charge,... 

---