Chemistry Reference
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CHAPTER 3
Dividing Planes of Hexagonal H
II
Mesophase
VESSELIN KOLEV
Casali Institute of Applied Chemistry, The Institute of Chemistry, The Hebrew University of
Jerusalem, Jerusalem, Israel
Department of Chemical Engineering, Faculty of Chemistry, Sofi a University, Sofi a, Bulgaria
ABRAHAM ASERIN and NISSIM GARTI
Casali Institute of Applied Chemistry, The Institute of Chemistry, The Hebrew University of
Jerusalem, Jerusalem, Israel
Abstract
Presented is a brief review of the cylindrical dividing surfaces (planes) of the hexagonal
inverse H
II
phase—Luzzati, pivotal, and neutral. They are presented as interrelated
surfaces through the general expression of elastic energy per molecule valid for the
corresponding surface. For each of the planes, the routine for deriving the plane
parameters—radius, area, and volume per molecule, as well as their role in terms of
mechanical description the of H
II
phase—is described in detail. Special attention is paid
to the numerical routines for parameter calculations from experimental data, using
least-squares routines and the related methods of merit function optimization (mini-
mization). In addition, cases of error estimation are presented along with discussions
about the accuracy of used numerical routines.
3.1
Introduction
80
3.2
Determination and Role of the Planes
81
3.2.1
Luzzati Plane
82
3.2.2
Pivotal Plane
85
3.2.3
Neutral Plane
91
3.3
Concluding Remarks
94
References
95
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