Statistical models of elasticity in main chain and smectic liquid ...

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Chapter FourThe elasticity of smectic-AelastomersAmodel of smectic elastomers is developed in this chapter, startingfrom a microscopic model that is used calculate the properties of an averagechain, and then using the affine approximation to build up the propertiesof the whole elastomer.4.1 IntroductionSmectic liquid single crystal elastomers share properties with both smecticliquid crystals and nematic elastomers. In this introduction some of the propertiesof smectic liquid crystals are discussed, aswell as methods used to describethem.InparticulartheHelfrich-Huraulteffect, observedexperimentallyin smectic A (SmA) liquid crystals by Clark and Meyer [55], is examined.Some of the experimentally measured properties of SmA elastomers are thenreviewed, and the terms used in the continuum model to describe smecticelastomers summarised.4.1.1 Smectic liquid crystal order parameterSmectic and nematic liquid crystals are both composed of rod like molecules.However in the case of smectic liquid crystals, a short range anisotropic attractiveinteraction causes a modulation in the density of the rods in additionto the alignment of the rods along a particular direction. This modulation inthe density distinguishes the smectic phase from the nematic phase and canbe used to define an order parameter for the smectic phase. The density can81
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iStatistical models of elasticity i
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AcknowledgementsDuring the course o
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viiiCONTENTS5 Soft elasticity of sm
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2 CHAPTER 1. INTRODUCTION1.2 Neo-cl
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4 CHAPTER 1. INTRODUCTIONticular in
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Chapter TwoThe elasticity of hairpi
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2.1. INTRODUCTION 9Fig. 2.1. This b
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2.2. MODEL OF HAIRPIN CHAINS 11nFig
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2.2. MODEL OF HAIRPIN CHAINS 13za)
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2.2. MODEL OF HAIRPIN CHAINS 15in
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2.2. MODEL OF HAIRPIN CHAINS 17The
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2.2. MODEL OF HAIRPIN CHAINS 1910.8
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2.2. MODEL OF HAIRPIN CHAINS 21This
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2.2. MODEL OF HAIRPIN CHAINS 23f g
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2.3. NON-AFFINE DEFORMATION MODEL 2
Page 41 and 42: 2.4. HAIRPIN CHAIN NETWORK FREE ENE
Page 43 and 44: 2.4. HAIRPIN CHAIN NETWORK FREE ENE
Page 45 and 46: 2.5. CONCLUSIONS 35to their limit
Page 47 and 48: 2.A. GEOMETRY OF A HAIRPIN AT ZERO
Page 49 and 50: 2.B. UNDULATING CHAIN STATISTICS 39
Page 51 and 52: 2.C. COUNTING CONFIGURATIONS BY IND
Page 53 and 54: 2.C. COUNTING CONFIGURATIONS BY IND
Page 55 and 56: 2.D. INTERPRETATION OF FN 452.D Int
Page 57: 2.E. SPRING CONSTANT OF AN EXTENDED
Page 60 and 61: 50 CHAPTER 3. POLARISATION OF CHIRA
Page 92 and 93: 82 CHAPTER 4. THE ELASTICITY OF SME
Page 110 and 111: 100 CHAPTER 4. THE ELASTICITY OF SM
Page 129 and 130: Chapter FiveSoft elasticity of smec
Page 131 and 132: 5.1. INTRODUCTION 121given byP 0 (R
Page 133 and 134: 5.1. INTRODUCTION 123InSmAelastomer
Page 135 and 136: 5.3. SOFT MODES OF SMECTIC C ELASTO
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5.3. SOFT MODES OF SMECTIC C ELASTO
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5.4. CONCLUSIONS 133Alternatively,
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5.A. DETAILS OF THE DEFORMATION MAT
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138 BIBLIOGRAPHY[13] S. Courty, A.
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140 BIBLIOGRAPHY[42] J. S. Patel an
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142 BIBLIOGRAPHY[72] M. J. Osborne
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144 BIBLIOGRAPHY[99] E. Gebhard and
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