Predictions of Static and Dynamic Properties of Liquid Crystalline and Polymeric Systems in Electric Fields
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PREDICTIONS OF STATIC AND DYNAMIC PROPERTIES OF LIQUID CRYSTALLINE AND POLYMERIC SYSTEMS IN ELECTRIC FIELDS F. DOWELL Department of Chemistry, Harvard University, 12 Oxford Street, Cambridge, MA 02138 USA ABSTRACT Predictions of static and dynamic properties from a unified molecular statistical mechanics theory for complex fluids in static electric fields are summarized. Included are thermodynamic, molecular ordering, and transport properties. In this new theory, the effects of an electric field E, on the dipole moments and bond polarizabilities of tile molecules have been added to an eaxlier successful theory for complex organic molecules in condensed phases. Included are liquid crystalline (LC) and polymeric systems (including the first interlocking polymers). INTRODUCTION AND THEORETICAL SUMMARY: Static electric fields axe frequently used to align (orient) macroscopic LC samples and to pole (orient) piezoelectric polymers. In the earlier static theory (Refs. 1-10 and references therein), standard statistical mechanics have been used to derive a configurational partition function ("master equation"), from which are derived equations for the thermodynamic properties, molecular ordering properties, static mechanical properties, and other static properties of the system of molecules. The Gibbs free energy G of the system is given by G = U + PV - TS, where U is the total energy, P is the pressure, V is the volume, T is the temperature, and S is the entropy. The P11 and TS terms are determined by using DiMarzio-type [11] combinatorial statistics to count the number of ways that the molecules cani be packed into the system at a given P and T; the intermolecular energy Ur term of U is determined by counting the intermolecular interactions of the molecules having such packing (again using DiMaxzio-type combinatorial statistics). Urn is the sum of intermolecular interaction energies from repulsions and van der Waals attractions (London dispersion attractions), dipolar interactions (dipole/dipole interactions and dipole/induced dipole interactions), and hydrogen bonding. The total energy U is given by U = Ur + U,, where U, is the sum of energies arising from the interactions of an external applied electric field E, with the polarizabilibies of the bonds and the dipole moments of the molecules. In earlier papers [1-10] with the static theory, U = Urn (i.e., Ue = 0); what is new in this paper is the calculation of Ue, where Ue ? 0. Therefore, due to length constraints in this paper, please see the earlier papers for the calculation of all other parts of the partition function, other thais Ue.
From Ref. 12a, Ue
[U.,P) +Ue(d)] =-- ZNrn {[ (Ee
-!
.Ee) /2] + [zF (E- LD
I
where Ue(p) and Ue(d) are the parts of Ue that come from the Ee/polarizability interactions and the Ee/dipole interactions, respectively; Nm is the number of molecules in the system; _aj is the polarizability of chemical bond j in a molecule; and p-•9• is the permanent dipole moment n in a molecule. The theory has been derived for both (1) the case in whic
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