Electric potential.

The potential /(r) at a place r is defined as the reversible electrical work, at constant p and T, to transport a unit charge from infinity to r, 

This definition is theoretically adequate, but may give rise to confusion when measurements are to be interpreted. In electrolyte solutions and the solution side of electrical double layers, the ions are the carriers of charge. However, in ions, charge is always linked to matter so that transport of the charge can only be achieved by simultaneously transporting matter. Consequently, the total work of ion transport includes an electrical and a chemical contribution. 

In the inner part of the electrical double layer, adjacent to the (solid) surface, the structure of the hydration water differs from that in the bulk solution, and at the surface the environment is even more different. Hence, the surface potential /o cannot be established as the work of charging the surface. 

For some substances, such as oxides and other inorganic materials, there may be a way out of this problem, namely if an electrode can be made of the solid phase. In that case an electrical cell can be set up consisting of that electrode and a reference electrode (e.g., a calomel electrode) in a solution containing the cdi, and then the potential difference between the two electrodes can be measured. Examples of such electrodes are the glass electrode and the Ag/Agl electrode which respond according to Nernst s law (cf. Section 14.3)  

p(x) must be known to derive /(x). In Section 9.4, the most current models for charge distributions in the electrical double layer are presented. 

After the qualitative discussion exemplified with the electric plate condenser, we can explain the electric potential. 

Coulomb invented a torsion balance, which could measure electrostatic forces in relationship to their distance. We start with Coulomb s law that describes the relationship between force, charge, and distance. He is most famous for his discovery in electrostatics. His other fields of interest were friction phenomena. 

The particle (1) builds up an electric field in the space surrounding this particle. The field is there, even if the particle (2) is not there. However, to measure the field, it is necessary to probe it by another particle (2). But particle (2) exerts itself a field that disturbs the field of particle (1). Therefore, to probe the field of field strength of particle (1), the charge must be made as small as possible. We can define the field of particle (1) as the specific force S2 acting on particle (2), at the limit of zero charge of particle (2)  

Now the specific force of Eq. (5.8) is no longer dependent on the charge of particle (2). 

The energy of the electric system is obtained by placing the particle from a site of zero force, infinitely far away from the other in a distinct position. So 

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A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

The mathematics is completed by one additional theorem relating the divergence of the gradient of the electrical potential at a given point to the charge density at that point through Poisson s equation... 

The electrochemical potentials pi, may now be expressed in terms of the chemical potentials pt, and the electrical potentials (see Section V-9) ... 

A special example of electrical work occurs when work is done on an electrochemical cell or by such a cell on the surroundings -w in the convention of this article). Themiodynamics applies to such a cell when it is at equilibrium with its surroundings, i.e. when the electrical potential (electromotive force emi) of the cell is... 

In these equations the electrostatic potential i might be thought to be the potential at the actual electrodes, the platinum on the left and the silver on the right. However, electrons are not the hypothetical test particles of physics, and the electrostatic potential difference at a junction between two metals is nnmeasurable. Wliat is measurable is the difference in the electrochemical potential p of the electron, which at equilibrium must be the same in any two wires that are in electrical contact. One assumes that the electrochemical potential can be written as the combination of two tenns, a chemical potential minus the electrical potential (- / because of the negative charge on the electron). Wlien two copper wires are connected to the two electrodes, the... 

Migration is the movement of ions due to a potential gradient. In an electrochemical cell the external electric field at the electrode/solution interface due to the drop in electrical potential between the two phases exerts an electrostatic force on the charged species present in the interfacial region, thus inducing movement of ions to or from the electrode. The magnitude is proportional to the concentration of the ion, the electric field and the ionic mobility. 

There are otlier teclmiques for mass separation such as tire quadmpole mass filter and Wien filter. Anotlier mass spectrometry teclmique is based on ion chromatography, which is also capable of measuring tire shapes of clusters [30, 31]. In tills metliod, cluster ions of a given mass are injected into a drift tube witli well-defined entrance and exit slits and filled witli an inert gas. The clusters drift tlirough tills tube under a weak electric potential. Since the... 

I l. isson s equation relates the second derivative of the electric potential to the charge density ... 

Williams D E 1991. Net Atomic Charge and Multipole Models for the Ah Initio Molecula Electric Potential. In Lipkowitz K B and D B Boyd (Editors). Reviews in Computational Chemistr Volume 2. New York, VCH Publishers, pp. 219-271. 

Electric potential difference U, AV Eermi, unit of length f... 

Gap energy (solid state) E, Inner electric potential 4>... 

The measurement of mass using a quartz crystal microbalance is based on the piezoelectric effect.When a piezoelectric material, such as a quartz crystal, experiences a mechanical stress, it generates an electrical potential whose magnitude is proportional to the applied stress. Gonversely, when an alternating electrical field is... 

An electric potential placed across a needle and a flat (plate) electrode. The lines of equipotential in the resulting electric field are focused around the tip of the needle, where the electric field becomes very large. 

If a gas such as argon is held in a glass envelope that has two electrodes set into it (Figure 6.4), application of an electric potential across the electrodes leads to changes in the gas as the electrons flow from the cathode (negative electrode) to the anode (positive electrode). This passage of electrons... 

For the chromatographic column, flow of solution from the narrow inlet tube into the ionization/desolvation region is measured in terms of only a few microliters per minute. Under these circumstances, spraying becomes very easy by application of a high electrical potential of about 3-4 kV to the end of the nanotube. Similarly, spraying from any narrow capillary is also possible. The ions formed as part of the spraying process follow Z-shaped trajectories, as discussed below. 

A common liquid chromatography column is somewhat larger in diameter than a nanocolumn. Consequently, the flow of solution along such a column is measured in terms of one or two milliliters per minute, and spraying requires the aid of a gas flowing concentrically around the end of the inlet tube (Figure 10.2c). An electrical potential is still applied to the end of this tube to ensure adequate electrical chaiging of the droplets. 

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