수치해석적인 방법으로 규명한 정렬된 단축이방성 분자들의 질서변수와 상대 복굴절의 준선형 관계식
The Explicitly Quasi-linear Relation Between the Order Parameter and Normalized Birefringence of Aligned Uniaxially Anisotropic Molecules Determined Using a Numerical Method
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초록
액정과 같은 단축 이방성 분자들의 정렬 정도에 따라 달라지는 복굴절으로부터 상대 복굴절 ∆nrel를 구하고 ∆nrel과 방향질서변수(orientational order parameter) S의 관계를 탐색하였다. 무질서한 분포를 하고 있는 경우를 포함하여 액정의 정렬정도를 달리 표현할 수 있는 분포함수를 도입하고 이 분포함수를 사용하여 질서변수 S가 0부터 1까지 변하도록 액정분자들의 정렬정도를 달리하며 ∆nrel과 S를 수치계산 하였다. 이 계산 결과로부터 S와 ∆nrel는 S=(1+α)∆nrel-α∆n2rel와 같이 준선형적인 관계를 만족하며 α는 no∆n/4으로 근사할 수 있음을 확인하였다. 또한 복굴절으로부터 Vuks의 방법에 따라 구한 분자분극의 이방성과Neugebauer의 방법에 따라 구한 분자분극의 이방성이 각각 질서변수 S와 또 다른 준선형 관계식들을 따름을 보였다.
Abstract
The birefringence of distributed, uniaxially anisotropic molecules like liquid crystals is calculated as the degree of ordering is varied. The relation between the normalized birefringence ∆nrel and the orientational order parameter Sis investigated. The distribution function, which enables one to monitor the degree of ordering of liquid crystals including randomly distributed ones, is introduced. Using this distribution function, a series of distributed liquid crystals with order parameters ranging from 0 to 1 are generated, and ∆nrel and S of the correspondingly distributed liquid crystals are calculated. Based on the calculated data, it is revealed that ∆nrel and S satisfy the quasi-linear relation of S=(1+α)∆nrel-α∆n2rel, where αcan be approximated as no∆n/4. The anisotropy of molecular polarizability is also calculated, using the birefringence, and separately following Vuks’ method and Neugebauer’s method, and it is shown that the relations between S and the molecular-polarizability anisotropy are also quasi-linear.
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