Molecular biaxiality and temperature dependence of the cholesteric pitch

Meer, B.W. Van der; Vertogen, G.

doi:10.1016/0375-9601(76)90792-1

Cited by 38 publications

(4 citation statements)

References 9 publications

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“…At this stage one should also acknowledge the related studies on the link between the orientational order parameters and the elastic constants in nematics, which have been influential in shaping some of the theories of chiral phases. A mean-field treatment of particles with electrostatic chirality but no shape anisotropy has been developed 42,43,44 , as have Onsager DFT theories for anisotropic hard rod-like particles 45,46,47,48 and hard rods with attractive mean-fields 49,50 , the latter being closely related to the achiral contribution of the model employed in our study. The principal finding of this body of work is that the elastic constants are predicted to be proportional to the square of the nematic order parameter, at least for system with weak orientational order, confirming experimental observation 51 and the results of molecular simulation 52 .…”

Section: Introductionmentioning

confidence: 99%

Generalized van der Waals theory for the twist elastic modulus and helical pitch of cholesterics

Wensink

Jackson

2009

The Journal of Chemical Physics

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We present a generalized van der Waals theory for a lyotropic cholesteric system of chiral spherocylinders based on the classical Onsager theory for hard anisometric bodies. The rods consist of a hard spherocylindrical backbone surrounded with a square-well potential to account for attractive (or soft repulsive) interactions. Long-ranged chiral interactions are described by means of a simple pseudoscalar potential which is appropriate for weak chiral forces of a predominant electrostatic origin. Based on the formalism proposed by Straley [Phys. Rev. A 14, 1835 (1976)], we derive explicit algebraic expressions for the twist elastic modulus and the cholesteric pitch for rods as a function of density and temperature. The pitch varies nonmonotonically with density, with a sharp decrease at low packing fractions and a marked increase at higher packing fractions. A similar trend is found for the temperature dependence. The unwinding of the helical pitch at high densities (or low temperatures) originates from a strong enhancement of the local nematic order and the corresponding increase in the twist elastic resistance associated with near-parallel local rod configurations. This contrasts with the commonly held view that the increase in pitch with decreasing temperature as often observed in cholesterics is due to layer formation resulting from presmectic fluctuations. The increase in pitch with increasing temperature is consistent with an entropic unwinding as the chiral interaction becomes less significant than the thermal energy. The variation of the pitch with density, temperature, and contour length is in qualitative agreement with recent experimental results on colloidal fd rods.

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Section: Introductionmentioning

confidence: 99%

Generalized van der Waals theory for the twist elastic modulus and helical pitch of cholesterics

Wensink

Jackson

2009

The Journal of Chemical Physics

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“…Although both van der Meer and Vertogen [21], and Priest and Lubensky [15] had already proposed interactions between biaxial molecules similar to that expressed in Eq. ( 12), their models did not completely account for these interactions.…”

Section: A P mentioning

confidence: 97%

“…( 12), their models did not completely account for these interactions. [21], while the potential proposed by Priest and Lubensky only included some of the terms expressed in Eq. ( 12) [15].…”

Section: A P mentioning

confidence: 99%

Chiral Phases in a System of Biaxial Molecules Ⅱ：Examining the Assembly of Rod-like Molecules

Hosino¹,

Ijuin²

2021

Chemistry

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“…In 1974 Priest and Lubensky [5] found the order of the biaxial order parameter and predicted a fluctuation instability. Van der Meer and Vertogen [6] discussed the dependence of the pitch on the biaxial order parameter. They also derived expressions for the temperature dependence of the pitch and the elastic constants [7] in the case of the uniaxial cholesteric phases.…”

Section: Introductionmentioning

confidence: 99%

Statistical Theory of Elastic Constants of Cholesteric Liquid Crystals

Kapanowski

2002

Zeitschrift Für Naturforschung A

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A statistical theory of cholesteric liquid crystals composed of short rigid biaxial molecules is presented. It is derived in the thermodynamic limit at a small density and a small twist. The uniaxial (biaxial) cholesteric phase is regarded as a distorted form of the uniaxial (biaxial) nematic phase. The chirality of the interactions and the implementation of the inversion to the rotation matrix elements are discussed in detail. General microscopic expressions for the elastic constants are derived. The expressions involve the one-particle distribution function and the potential energy of two-body short-range interactions. It is shown that the elastic constants determine the twist of the phase. The stability condition for the cholesteric and nematic phases is presented.The theory is used to study unary and binary systems. The temperature and concentration dependence of the order parameters, the elastic constants and the twist of the phase are obtained. The possibility of phase separation is not investigated.

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Molecular biaxiality and temperature dependence of the cholesteric pitch

Cited by 38 publications

References 9 publications

Generalized van der Waals theory for the twist elastic modulus and helical pitch of cholesterics

Generalized van der Waals theory for the twist elastic modulus and helical pitch of cholesterics

Chiral Phases in a System of Biaxial Molecules Ⅱ：Examining the Assembly of Rod-like Molecules

Statistical Theory of Elastic Constants of Cholesteric Liquid Crystals

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