Double-layer interaction of two charged colloidal spherical particles of a concentrated dispersion in a medium of low dielectric constant. Part 2.—A cell model

1975 ◽  
Vol 71 (0) ◽  
pp. 102-118 ◽  
Author(s):  
Gérard R. Féat ◽  
Samuel Levine
Keyword(s):  
Dielectric Constant ◽  
Double Layer ◽  
Cell Model ◽  
Spherical Particles ◽  
Low Dielectric Constant ◽  
Layer Interaction ◽  
Low Dielectric ◽  
A Cell ◽  
Constant Part ◽  
Concentrated Dispersion

scholarly journals Debye-Hückel Free Energy of an Electric Double Layer with Discrete Charges Located at a Dielectric Interface

Membranes ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 129
Author(s):  
Guilherme Volpe Bossa ◽  
Sylvio May
Keyword(s):  
Free Energy ◽  
Double Layer ◽  
Electric Double Layer ◽  
Low Dielectric Constant ◽  
Surface Charges ◽  
Dielectric Interface ◽  
Charge Densities ◽  
Low Dielectric ◽  
Poisson Boltzmann ◽  
The Continuum

Poisson–Boltzmann theory provides an established framework to calculate properties and free energies of an electric double layer, especially for simple geometries and interfaces that carry continuous charge densities. At sufficiently small length scales, however, the discreteness of the surface charges cannot be neglected. We consider a planar dielectric interface that separates a salt-containing aqueous phase from a medium of low dielectric constant and carries discrete surface charges of fixed density. Within the linear Debye-Hückel limit of Poisson–Boltzmann theory, we calculate the surface potential inside a Wigner–Seitz cell that is produced by all surface charges outside the cell using a Fourier-Bessel series and a Hankel transformation. From the surface potential, we obtain the Debye-Hückel free energy of the electric double layer, which we compare with the corresponding expression in the continuum limit. Differences arise for sufficiently small charge densities, where we show that the dominating interaction is dipolar, arising from the dipoles formed by the surface charges and associated counterions. This interaction propagates through the medium of a low dielectric constant and alters the continuum power of two dependence of the free energy on the surface charge density to a power of 2.5 law.

Structire, Properties, and Process Characteristics of Low-K Materials Prepared by PECVD

1999 ◽  
Vol 565 ◽  
Author(s):  
Y. Shimogaki ◽  
S. W. Lim ◽  
E. G. Loh ◽  
Y. Nakano ◽  
K. Tada ◽  
...  
Keyword(s):  
Growth Rate ◽  
Dielectric Constant ◽  
Gas Flow ◽  
Structural Changes ◽  
Silicon Oxide ◽  
Reactive Species ◽  
Low Dielectric Constant ◽  
Low Dielectric ◽  
Step Coverage ◽  
Low K

AbstractLow dielectric constant F-doped silicon oxide films (SiO:F) can be prepared by adding fluorine source, like as CF4 to the conventional PECVD processes. We could obtain SiO:F films with dielectric constant as low as 2.6 from the reaction mixture of SiH4/N2 O/CF4. The structural changes of the oxides were sensitively detected by Raman spectroscopy. The three-fold ring and network structure of the silicon oxides were selectively decreased by adding fluorine into the film. These structural changes contribute to the decrease ionic polarization of the film, but it was not the major factor for the low dielectric constant. The addition of fluorine was very effective to eliminate the Si-OH in the film and the disappearance of the Si-OH was the key factor to obtain low dielectric constant. A kinetic analysis of the process was also performed to investigate the reaction mechanism. We focused on the effect of gas flow rate, i.e. the residence time of the precursors in the reactor, on growth rate and step coverage of SiO:F films. It revealed that there exists two species to form SiO:F films. One is the reactive species which contributes to increase the growth rate and the other one is the less reactive species which contributes to have uniform step coverage. The same approach was made on the PECVD process to produce low-k C:F films from C2F4, and we found ionic species is the main precursor to form C:F films.

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