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id="ulink_4539304f-308c-5261-9425-c306294246fa">(3.33)upper E Subscript i Superscript l o c Baseline equals left-bracket 1 plus ModifyingAbove Above ModifyingAbove upper L With right harpoon with barb up With right harpoon with barb up italic i i Superscript Baseline left-parenthesis n Subscript i Superscript 2 Baseline minus 1 right-parenthesis right-bracket upper E Subscript i Superscript a p p Baseline comma i equals x comma y comma z period

      3.4.2. Equilibrium Temperature and Order Parameter Dependences of Refractive Indices

      (3.35)ModifyingAbove upper P With right harpoon with barb up equals upper N ModifyingAbove Above ModifyingAbove alpha With right harpoon with barb up With right harpoon with barb up colon left-parenthesis ModifyingAbove Above ModifyingAbove upper K With right harpoon with barb up With right harpoon with barb up colon ModifyingAbove upper E With right harpoon with barb up right-parenthesis

      where ModifyingAbove Above ModifyingAbove alpha With right harpoon with barb up With right harpoon with barb up is the polarizability tensor of the molecule, N is the number of molecules per unit volume, and the parentheses denote averaging over the orientations of all molecules.

      The dielectric constant ModifyingAbove Above ModifyingAbove epsilon With right harpoon with barb up With right harpoon with barb up (in units of ε0) is therefore given by

      (3.36)ModifyingAbove Above ModifyingAbove epsilon With right harpoon with barb up With right harpoon with barb up equals 1 plus StartFraction upper N Over epsilon 0 EndFraction ModifyingAbove Above ModifyingAbove alpha With right harpoon with barb up With right harpoon with barb up colon ModifyingAbove Above ModifyingAbove upper K With right harpoon with barb up With right harpoon with barb up

      and

      (3.37)StartLayout 1st Row normal upper Delta epsilon equals epsilon Subscript parallel-to Baseline minus epsilon Subscript up-tack Baseline 2nd Row equals StartFraction upper N Over epsilon 0 EndFraction left-parenthesis left pointing angle ModifyingAbove Above ModifyingAbove alpha With right harpoon with barb up With right harpoon with barb up colon ModifyingAbove Above ModifyingAbove upper K With right harpoon with barb up With right harpoon with barb up right pointing angle Subscript parallel-to Baseline minus left pointing angle ModifyingAbove Above ModifyingAbove alpha With right harpoon with barb up With right harpoon with barb up colon ModifyingAbove Above ModifyingAbove upper K With right harpoon with barb up With right harpoon with barb up right pointing angle Subscript up-tack Baseline right-parenthesis period EndLayout

      From these considerations and from observations by deJeu and Bordewijk [13] that

      (3.38)normal upper Delta epsilon proportional-to italic rho upper S

      (3.39)left pointing angle ModifyingAbove Above ModifyingAbove alpha With right harpoon with barb up With right harpoon with barb up colon ModifyingAbove Above ModifyingAbove upper K With right harpoon with barb up With right harpoon with barb up right pointing angle Subscript parallel-to Baseline minus left pointing angle ModifyingAbove Above ModifyingAbove alpha With right harpoon with barb up With right harpoon with barb up colon ModifyingAbove Above ModifyingAbove upper K With right harpoon with barb up With right harpoon with barb up right pointing angle Subscript up-tack Baseline proportional-to upper S comma

      we can write ε|| and ε as

      and

      respectively, where Kl and Kt are the values of Скачать книгу