A comparison of counterion effects in surfactant and classical colloid systems

Abstract

Macrocyclic compounds are used to complex metal counterions and thereby change the interfacial properties of anionic micelles and mica. Macrocyclic cryptate ligands (C221 or C222) or the crown ether (18-crown-6) were added to surfactant solutions of lithium, sodium, potassium, calcium, or barium dodecyl sulfate. This resulted in lower critical micelle concentrations, decreased aggregation numbers, which are insensitive to added salt, and larger interfacial areas per molecule. Surface forces measurements show that the mica counterion complexation effects are less dramatic. Addition of C222 to potassium or barium salt solutions results in significant increase in the separation of the mica surfaces at "contact", but almost no change in the surface potential. These results provide a basis for comparing counterion effects for colloidal interfaces with fixed and labile surface charges.

Unified Octonionic Representation of the 10–13 Dimensional Clifford Algebra

“…For quaternions, being non commutative, one should dierentiate between right and left multiplication, (our quaternionic algebra is given by e i :e j = ij + ijk e k ; and i; j; k = 1; 2; 3), q = q 0 + q 1 e 1 + q 2 e 2 + q 3 1 C C C C C C C C C C A ; (22) and so on for the dierent (e 2 ; e 3 ; 1 j e 2 ; 1 j e 3 ) …”

“…H ( n ); (2) R(8n) ! O ( n ) : (3) The aim of the paper is to illustrate how this structural isomorphism 1 works and to construct dierent Cliord algebra over quaternions and octonions. The paper is organized as follows: In section II.…”

Supermembranes: An Introduction

“…Since the numbers 1, 2, 4 and 8 are also the dimension of the four division algebras, these four types of solution are referred to as real, complex, quaternion and octonion respectively. The connection with the division algebras can in fact be made more precise [40,41].…”

Effect of lithium encapsulation by a macrocyclic aza cage in micellar solutions of lithium dodecyl sulfate

“…In ionie micellar solutions the counterion properties have been the object of many experimental and theoretical studies [1][2][3][4][5][6][7][8][9][10]. In most of these, electrostatic interactions have been studied by changing the ionie strength of the micellar solution (mainly by adding a salt), or by changing the counterion.…”