Modified method of conductometric data analysis to calculate the conductivity of surfactant ions

Methodology for simple analytical refinement of the equivalent electrical conductivities of surfactant ions and counterions was proposed in the framework of the Debye – Hückel – Onsager theory as applied to surfactant dispersions at various concentrations. The developed methodology is based on the use of the mathematical form for the concentration dependencies of the specific conductivity in the premicellar region and makes it possible to calculate the equivalent conductivities of surfactant ions both under infinite dilution conditions and near the CMC. One of the advantages of the described method is the possibility of calculating the ion conductivities in the presence of a minimum number of experimental points (formally, a straight line can be constructed and its tangent of the angle of inclination can be determined even by two points corresponding to region 0.2 CMC — 0.8 CMC). Using the values of the equivalent conductivities of surfactant ions and counterions calculated for the required concentrations, allows to determine the parameters of the solution more accurately, including the contribution of micelles to the total conductivity of the solution.

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Modified method of conductometric data analysis to calculate the degree of ionization and conductivity of micelles

E3S Web of Conferences ◽

10.1051/e3sconf/201912403008 ◽

2019 ◽

Vol 124 ◽

pp. 03008

Author(s):

O. S. Zueva

Keyword(s):

Data Analysis ◽

Micellar Solution ◽

Specific Conductance ◽

Total Conductivity ◽

Calculation Methods ◽

Degree Of Ionization ◽

Modified Method ◽

High Concentrations ◽

Onsager Theory ◽

New Formula

Methods for calculation of specific conductance of ions and micelles and the degree of micelle ionization using conductometric data in various approximations of the Debye – Hückel – Onsager theory were considered. The analysis of the existing calculation methods was carried out to identify their drawbacks and to suggest ways of their elimination. The calculation method of the micellar parameters on the basis of conductometric data using micellar size was modified, and a new formula for determining the degree of micelle ionization was obtained. All calculations using the modified method were performed in the first and the second approximations, and the newly obtained values of the micellar parameters are in greater agreement with the results of other studies. Based on the calculations performed, it was shown that the contribution of micelles to the total conductivity of micellar solution cannot be neglected, since at high concentrations the contribution of micelles exceeds the contribution of counterions and can exceed 50%.

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The Bakerian lecture —Regularities and irregularities in the ionosphere—I

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1937.0195 ◽

1937 ◽

Vol 162 (911) ◽

pp. 451-479 ◽

Cited By ~ 82

Keyword(s):

Specific Conductivity ◽

Wave Length ◽

Ground Level ◽

Short Wave ◽

The State ◽

Total Conductivity ◽

The Sun ◽

Magnetic Studies ◽

Short Wave Length ◽

Radio Measurements

Our knowledge concerning the state of the atmosphere lying above about 80 km. in height has been derived from experiments on radio wave reflexion as well as from studies of terrestrial magnetism and of the aurora. The information derived from radio experiments is, fortunately, in the nature of a supplement to, rather than a duplicate of, information derivable in other ways. As one of the best examples in this connexion may be mentioned the question of electrical conductivity. Here the magnetic studies of Schuster and Chapman yield an estimate of the total conductivity for currents travelling horizontally, whereas the radio measurements give the state of ionization at different levels from which the specific conductivity at those levels may be estimated. One of the most striking things about the ionosphere is the marked solar control. Speaking generally it may be said that the ionization increases and decreases as the sun rises and sets. Again, speaking generally, we may say that the main part of the ionization is caused by solar-violet light. The rays from the sun meet the outer layers of the atmosphere first and the short wave-length radiation is absorbed there, causing ionization. It thus comes about that the study of the ionosphere becomes the study of an interesting part of the sun's spectrum which cannot be detected at ground level. It also becomes the study of certain atomic processes such as photo-ionization, recombination of ions and attachment of electrons to neutral molecules such as cannot be investigated at very low pressure in the laboratory, because of the influence of the walls of the vessel confining the gas.

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Minimum Cell Connection in Line Segment Arrangements

International Journal of Computational Geometry & Applications ◽

10.1142/s0218195917500017 ◽

2017 ◽

Vol 27 (03) ◽

pp. 159-176

Author(s):

Helmut Alt ◽

Sergio Cabello ◽

Panos Giannopoulos ◽

Christian Knauer

Keyword(s):

Linear Time ◽

Optimal Solution ◽

Time Algorithm ◽

Linear Time Algorithm ◽

Constant Number ◽

Line Segments ◽

Straight Line ◽

Minimum Number ◽

Number Of Segments ◽

Connection Problems

We study the complexity of the following cell connection problems in segment arrangements. Given a set of straight-line segments in the plane and two points [Formula: see text] and [Formula: see text] in different cells of the induced arrangement: [(i)] compute the minimum number of segments one needs to remove so that there is a path connecting [Formula: see text] to [Formula: see text] that does not intersect any of the remaining segments; [(ii)] compute the minimum number of segments one needs to remove so that the arrangement induced by the remaining segments has a single cell. We show that problems (i) and (ii) are NP-hard and discuss some special, tractable cases. Most notably, we provide a near-linear-time algorithm for a variant of problem (i) where the path connecting [Formula: see text] to [Formula: see text] must stay inside a given polygon [Formula: see text] with a constant number of holes, the segments are contained in [Formula: see text], and the endpoints of the segments are on the boundary of [Formula: see text]. The approach for this latter result uses homotopy of paths to group the segments into clusters with the property that either all segments in a cluster or none participate in an optimal solution.

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