Velocity of an ion

In TOF-SIMS, the source of primary ions is pulsed at a rate of a few kHz. The pulse width is on the order of 1 ns. Secondary ions ejected from the sample surface are accelerated through a potential V and then drift through a field-free TOF analyzer with different velocities, depending on their masses. The drift velocity of an ion with charge-to-mass ratio zjm can be determined from the expression ... 

The absolute ionic mobility or the absolute velocity of an ion represents its velocity in centimeters per second under a potential gradient of one volt per centimeter (potential gradient = applied emf/distance between the electrodes). For example, if the velocity of the ion at infinite dilution is U cm per second when the distance between the electrodes is 25 cm and voltage is 125, the potential gradient is 125/25, i.e., 5 volts per cm and the absolute mobility is U/5 cm s 1. 

All ions leaving the ion source have the same kinetic energy E, but the velocity v of a particular ion will depend on its mass. The velocity of an ion is given by rearranging the above ... 

In a TOP mass analyzer, ions of different mIz ratios are determined by the time they take to travel through a field-free path of known length between the source and the detector. The ions are accelerated by application of an electrical potential. The velocity of an ion is inversely proportional to its mass therefore, each m/z has a characteristic TOP (de Hoffman and Stroobant, 2001). 

Ionic mobility refers to the velocity of an ion moving toward an oppositely charged electrode when a 1-volt potential is applied across a 1-centimeter electrochemical cell, strongly hydrated molecular cluster, such as [H-(OH2)4], is probably a more realistic representation (M. Eigen (1964) Angew. Chem. (Int. Eng. Edn.) 3, 1). 

Diffusion is due to random motion of particles. Conduction is due to motion of ions under an electric field. Ionic diffusivity and conductivity are hence related. Under an electric field, the velocity of an ion is proportional to the electric... 

The diffusion equation with inter-reactant potential energy contribution included, eqn. (141), has been used so far in this analysis of the recombination probability of ion-pairs. It was derived in Chap. 3, Sect. 1.1 with the aid of thermodynamic considerations. The velocity of an ion (number 1) was shown to be [eqn. (41)]... 

IONIC MOBILITY. I. The ratio nf the average drift velocity of an ion in solution to the electric licld. it is expressed hy the relationship... 

Here D, is the diffusion coefficient of species i, and Ej is the liquid junction potential that develops along the channel. The electrolytic mobility n, is the limiting velocity of an ion in the electric field of unit strength. It has dimensions of cm2 s 1 V 1 and... 

In the case of one-dimensional motion the time dependence of oscillating velocity of an ion can be expressed by a series, containing only odd harmonics ... 

Ionic mobility — Quantity defined by the velocity of an ion moving in a unit electric field (SI unit m2 V-1 s-1). The ionic mobility of ion i (uf) is related to its molar ionic conductivity (A ) by A = zfFui, where Z is the charge number of the ion. The ionic mobility is also related to the -> diffusion coefficient (A) by the Nernst-Einstein... 

Mobility — The (ionic or electric) mobility u of an ion is given by the drift velocity v (the velocity of an ion at equilibrium between the accelerating effect of the electric field and the decelerating effect of the viscous medium (Stokes friction)) of an ion and the effective electric field E v... 

Does this concern ions in solution and electrochemistry It does indeed concern some approaches to diffusion and hence the related properties of conduction and viscous flow. It has been found that the autocorrelation function for the velocity of an ion diffusing in solution decays to zero very quickly, i.e., in about the same time as that of the random force due to collisions between the ion and the solvent. This is awkward because it is not consistent with one of the approximations used to derive analytical expressions for the autocorrelation function. The result of this is that instead of an analytical expression, one has to deal with molecular dynamics simulations. 

The average value of that component of the velocity of an ion picked up from the externally applied force is the product of the acceleration due to this force and the average time between collisions. Hence, the drift velocity Vj is given by... 

The next step is to evaluate the electrophoretic and relaxation components of the net drift velocity of an ion. 

The electrophoretic component Vg of the drift velocity of an ion is equal to the electrophoretic velocity of its ionic cloud because the central ion shares in the motion of its cloud. If one ignores the asymmetry of the ionic cloud, a simple calculation of the electrophoretic velocity Vg can be made. 

Velocity = Absolute mobility x force it is clear that the relaxation component of the drift velocity of an ion can be obtained... 

There are several ways of expressing ionic mobility. According to one of them, the absolute mobility, is the velocity of an ion under an applied force of 1 dyne. The conventional mobility, on the other hand, is the velocity under the force exerted on an ion by its interaction with an electric field of 1 V cm . Deduce the relation between and... 

The subject of drift velocities, particularly as it pertains to inert gas systems, was discussed by Hornbeck (5S) (experimental results) and Holstein (57) (theoretical) as part of the program for a symposium on Electron Transfer Processes in general, held at Notre Dame in 1952. The significant observation is that the drift velocity of an ion such as He+-is much less than is expected if account is taken only of the usual processes for energy transfer, including polarization of He by the positive ion. Similar effects are noted for the other inert gas ions and have been recorded also for N2+ in N2 (50). The effective collision cross section is increased by symmetry effects which include electron transfer as a component. Table I... 

V = velocity of an ion after acceleration through the electric potential (V). 

Hiickel proposed an equation taking account of the influence of these factors upon the electrophoretic velocity of an ion considered as a sphere of radius r. 

The velocity at which an ion moves under the influence of an external field is proportional to the field, with the constant of proportionality being the mobihty of the ion. Provided this strict simple proportionality remains for large fields and, provided the mobihty is known, the velocity of an ion can be calculated. 5 x 10 cm s V is a typical value for an ionic mobility. 

The theoretical principles of capillary electrophoresis are closely related to those of electrophoresis. In electrophoresis the velocity of an ion is related to its electrophoretic mobility (Me) as follows ... 

Note that in a fixed field, the cyclotron frequency depends only on the inverse of the m/z value. Increases in the velocity of an ion will be accompanied by a corresponding increusc in the radius of rotation of the ion. A measurement of can provide an accurate indication of zim and thus the mass-io-chargc ratio of the ion. 

In the presence of electroosmosis. the velocity of an ion is the sum of its migration velocity ahi the elec-troosmolic flow velocity. Thus,... 

The velocity of an ion depends on its mass the velocity is inversely proportional to the square root of the mass of the ion. 

A TOF analyzer does not use an external force to separate ions of different m/z values. Instead, pulses of ions are accelerated into an evacuated held free region called a drift tube. If aU ions have the same kinetic energy, then the velocity of an ion depends on its mass-to-charge ratio, or on its mass, if all ions have the same charge. Lighter ions will travel faster along the drift tube than heavier ions and are detected hrst. The process is shown schematically in Fig. 9.19. 

Ions are separated in the drift tube according to their velocities. The velocity of an ion, V, can be expressed as ... 

The mobility of an ion,is defined as the limiting velocity of an ion moving in an electric field of unit strength. The minus sign arises because the direction of flux opposes the direction of increasing Q. 

In an increase in sample ion concentration occurs due to a local decrease in the magnitude of the drift velocity of an ion. For drift velocity vector field Vd, stacking occurs when... 

Solutions to the Mathieu equation completely describe the trajectory of an ion in terms of each ion s initial conditions. Without any force acting along the z axis, the position and velocity of an ion along its z axis is unaffected by any potential applied to the rods. The use of rods of a... 

---