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

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Chapter TwoThe elasticity of hairpin chainelastomersIn this chapterasimplemodel of a main chain liquid crystalline elastomeris presented. This model is based on the calculation of the partition functionfor a 1-D model of polymer chain with hairpin defects along its length.Calculation of the chain’s spring constants motivates a non-affine method forstretching the polymer network. The nominal stress-strain curves for thismodel are then calculated and discussed.2.1 Introduction2.1.1 Semi-flexible polymersMesogenic polymers can be divided into two classes: main chain and sidechain polymers. The focus here is main chain polymers. These polymersexhibit hairpin defects where the chain switches from following the nematicfield direction on average to following the nematic field in the opposite sense.The transition is achieved by bending the polymer (penalised by the bendingenergy if done rapidly) and having sections of the chain misaligned withthe nematic field (penalised by the nematic field energy if done too slowly).Hairpin defects are responsible for the transition from a rod like conformationof main chain polymers in strong nematic field, to a coil in weak nematicfield [23]. The statics and dynamics of these defects has been calculated in[24]. At low temperatures it is found that exponentially rapid growth of chaindimension occurs as a function of inverse temperature. This is confirmed bysmall angle neutron scattering measurements of the chain dimension as a functionof temperature [25]. A rigid cylinder model of the chain extent fitted tosmall angle neutron scattering is also consistent with the hairpin bendpicture.7
Page 3: iStatistical models of elasticity i
Page 7: AcknowledgementsDuring the course o
Page 10 and 11: viiiCONTENTS5 Soft elasticity of sm
Page 12 and 13: 2 CHAPTER 1. INTRODUCTION1.2 Neo-cl
Page 14 and 15: 4 CHAPTER 1. INTRODUCTIONticular in
Page 18 and 19: 8 CHAPTER 2. HAIRPIN CHAIN ELASTOME
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Page 59 and 60: Chapter ThreePolarisation of chiral
Page 61 and 62: 3.1. INTRODUCTION 51polarisation in
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Page 65 and 66: 3.1. INTRODUCTION 55where the tenso
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3.2. EQUILIBRIUM ORIENTATION OF THE
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3.3. THE POLARISATION OF A PURE LIQ
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3.4. SYSTEMS WHERE A POLARISATION R
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3.5. CONCLUSIONS 770.00-0.05Py-0.10
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Part IISmectic liquid crystalelasto
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82 CHAPTER 4. THE ELASTICITY OF SME
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100 CHAPTER 4. THE ELASTICITY OF SM
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Chapter FiveSoft elasticity of smec
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5.1. INTRODUCTION 121given byP 0 (R
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5.1. INTRODUCTION 123InSmAelastomer
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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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