Balance Laws and Constitutive Equations of Microscopic Rigid Bodies: A Model for Biaxial Liquid Crystals

Ehrentraut, H.; Muschik, W.

doi:10.1080/10587259508033558

Cited by 13 publications

(9 citation statements)

References 5 publications

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“…A constraint between these two directors is the fixed angle between them, usually chosen to be π/2. Therefore the orientation of a biaxial molecule is fixed by three parameters, two for the orientation of the first director, a third one for that of the second director [16]. Because of this constraint a two-director theory [51,52] is clumsy to handle, and therefore in our work [53,54] we replace it by another representation of orthogonal transformations using quaternions, because in this case no constraints appear.…”

Section: Remarks On Liquid Crystals Of Biaxial Moleculesmentioning

confidence: 98%

“…All relations derived for uniaxial molecules are formally valid for biaxial molecules by the above mentioned replacement. More details concerning liquid crystals consisting of biaxial molecules can be found in [16].…”

Section: Remarks On Liquid Crystals Of Biaxial Moleculesmentioning

confidence: 99%

“…These three components correspond to a unit vector n 0 ∈ R 4 in the four-dimensional Euclidean space. Because also the orientation of a biaxial molecule is described by three independent components, it can be proved [16,53] that n 0 is the microscopic director for liquid crystals of biaxial molecules.…”

Section: Remarks On Liquid Crystals Of Biaxial Moleculesmentioning

confidence: 99%

“…The domain on which these balances are defined is different from the usual one, because it contains the microscopic director as a variable. This so-called mesoscopic concept-which is discussed in more detail below-is valid for uniaxial as well as for biaxial molecules [16]. Also two-dimensional liquid crystals as films and interfaces can be treated mesoscopically [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Sketch of the mesoscopic description of nematic liquid crystals

Muschik

Papenfuß

Ehrentraut

2004

Journal of Non-Newtonian Fluid Mechanics

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Section: Remarks On Liquid Crystals Of Biaxial Moleculesmentioning

confidence: 98%

Section: Remarks On Liquid Crystals Of Biaxial Moleculesmentioning

confidence: 99%

Section: Remarks On Liquid Crystals Of Biaxial Moleculesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Sketch of the mesoscopic description of nematic liquid crystals

Muschik

Papenfuß

Ehrentraut

2004

Journal of Non-Newtonian Fluid Mechanics

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“…The anisotropic fluid is formally treated as a mixture by regarding all particles of a volume element of the same orientation as one component of the fluid [9][10][11][12][13]. This so-called mesoscopic concept, which is discussed in more detail below, is valid for uniaxial as well as for biaxial molecules [16]. Because mixture theories are well developed [14,15], balance equations for liquid crystals can be written down very easily by using this method.…”

Section: Introductionmentioning

confidence: 99%

Mesoscopic theory of liquid crystals

Muschik¹,

Papenfuß²,

Ehrentraut³

2004

Journal of Non-Equilibrium Thermodynamics

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Mesoscopic Theory of Liquid Crystals

Muschik

Papenfuß

Ehrentraut

Entropy and Entropy Generation

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Liquid crystals of uniaxial and biaxial molecules are considered in the framework of the mesoscopic description which is a general tool of continuum theory. A mesoscopic theory introduces the fields beyond hydrodynamics as additional variables of a configuration space, called mesoscopic space, on which the fields appearing in balances are defined. Besides the mesoscopic space, a mesoscopic distribution function is introduced which describes the distribution of the additional variables at each time and position. It is demonstrated, how the mesoscopic theory can be applied to liquid crystals, and how the Ericksen-Leslie theory and the alignment tensor theory of liquid crystals fit into the mesoscopic framework. general case in constitutive theory. As the following examples show, the additional fields describing complex materials are of various kinds: internal variables ! memory alloys order parameters ! phase transitions damage parameters ! fatigue problems Cosserat triads ! steel, microcrystallites, granular media conformation tensors ! polymers fabric tensors ! composite materials directors, alignment tensors ! liquid crystals.The orientational order in liquid crystals can be di¤erently characterized. Because of thermal fluctuations the molecules are not totally aligned, but have a certain distribution around a ''mean orientation'' which can be described by a normalized macroscopic director field. The name ''macroscopic'' originates from the fact that the macroscopic director field belongs to all molecules of a volume element, whereas a special molecule may be aligned di¤erently. So it is obvious to introduce a microscopic director which describes the alignment of a single molecule and which is different from the local macroscopic director in general.Besides the microscopic and the macroscopic director, other descriptions for alignment are in use which can be found in the following synopsis. Up to now there are five di¤erent phenomenological concepts suitable to describe liquid crystals nonmicroscopically. The first one is the well known Ericksen-Leslie theory [1, 2] whose balance equations are formulated by use of the macroscopic director mentioned above. But in fact this theory is not able to represent a change in the degree of orientational order [3]. In general we need at each point and time a distribution function for describing the macroscopic orientation of the fluid. Therefore the macroscopic director has to be redefined statistically.The second concept describes liquid crystals as micropolar media in the frame of a 3-director theory [4]. Instead of a balance equation for the macroscopic director, the spin balance is taken into account, but no microscopic concepts are introduced.The third concept [5] introduces besides the balance equations of a micropolar medium an additional field, called microinertia tensor field. This field, satisfying its own balance equation, is coupled to the spin balance. The form of this coupling causes all needle-shaped molecules of a volume element to always have the same angul...

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Balance Laws and Constitutive Equations of Microscopic Rigid Bodies: A Model for Biaxial Liquid Crystals

Cited by 13 publications

References 5 publications

Sketch of the mesoscopic description of nematic liquid crystals

Sketch of the mesoscopic description of nematic liquid crystals

Mesoscopic theory of liquid crystals

Mesoscopic Theory of Liquid Crystals

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