Freederickz Transition and Dielectric Anisotropy - Revision history

Cmditradmin: /* Freedericksz Transition */

2009-11-24T21:58:27Z

Freedericksz Transition

← Older revision		Revision as of 14:58, 24 November 2009
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	Applying an electric field to liquid crystal can change the orientation of molecules.		Applying an electric field to liquid crystal can change the orientation of molecules.
	=== Freedericksz Transition ===		=== Freedericksz Transition ===
	[[Image:~~Freedericksz~~.~~png~~\|thumb\|~~300px\|An orthogonal~~ electric field ~~will align~~ the ~~director with~~ the ~~field~~]]		[[Image:Electropolar.gif\|thumb\|Molecular dipoles orient in the presence of an electric field. This changes the index of refraction of the material.]]

	Recall that for materials that contain electric dipoles, such as water molecules, the dipoles themselves stretch or reorient in an applied field.		Recall that for materials that contain electric dipoles, such as water molecules, the dipoles themselves stretch or reorient in an applied field.

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	An electric field can also induce a polarization in a molecule (a polarizable molecule) along the long axis which will the cause it to align to the field even though it did not have a dipole to begin with.		An electric field can also induce a polarization in a molecule (a polarizable molecule) along the long axis which will the cause it to align to the field even though it did not have a dipole to begin with.

			[[Image:Freedericksz.png\|thumb\|300px\|An orthogonal electric field will align the director with the field]]
	A liquid crystal can be placed between two substrates that have been treated with polyimide so that the molecules are aligned homogeneously and in one direction. At the surface the liquid crystal molecules are influenced by interaction with the substrate.		A liquid crystal can be placed between two substrates that have been treated with polyimide so that the molecules are aligned homogeneously and in one direction. At the surface the liquid crystal molecules are influenced by interaction with the substrate.

Cmditradmin at 23:33, 2 September 2009

2009-09-02T23:33:22Z

← Older revision		Revision as of 16:33, 2 September 2009
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	</tr>		</tr>
	</table>		</table>
			Applying an electric field to liquid crystal can change the orientation of molecules.
	=== Freedericksz Transition ===		=== Freedericksz Transition ===
	[[Image:Freedericksz.png\|thumb\|300px\|An orthogonal electric field will align the director with the field]]		[[Image:Freedericksz.png\|thumb\|300px\|An orthogonal electric field will align the director with the field]]

Cmditradmin: /* Freedericksz Transition */

2009-09-02T23:28:05Z

Freedericksz Transition

← Older revision		Revision as of 16:28, 2 September 2009
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	An electric field can also induce a polarization in a molecule (a polarizable molecule) along the long axis which will the cause it to align to the field even though it did not have a dipole to begin with.		An electric field can also induce a polarization in a molecule (a polarizable molecule) along the long axis which will the cause it to align to the field even though it did not have a dipole to begin with.

	~~If a~~ liquid crystal is placed between two substrates that have been treated with polyimide so that the molecules are aligned homogeneously and in one direction.		A liquid crystal can be placed between two substrates that have been treated with polyimide so that the molecules are aligned homogeneously and in one direction. At the surface the liquid crystal molecules are influenced by interaction with the substrate.

	At the ~~surface~~ the ~~molecules~~ are ~~influenced by~~ interaction ~~with the substrate~~.		If then an electric field is applied orthogonal to this direction the liquid crystal will tend to rotate to align the director with the electric field assuming that the director and the dipole moment (more precisely the larger component of the dielectric anisotropy) are essentially co-linear. The reorientation starts in the middle where there is little surface interaction.

	~~If then an electric field~~ is ~~applied orthogonal to this direction~~ the ~~liquid crystal will tend to rotate to align~~ the ~~director with~~ the ~~electric field assuming that~~ the director and the ~~dipole moment (more precisely the larger component~~ of the ~~dielectric anisotropy) are essentially colinear. The reorientation starts in the middle where there is little surface interaction~~.		This reorientation as depicted is called a Freedericksz transition. It should not be confused with a phase transition because the LC remains in the same LC phase. Simply, the orientation of the director is perturbed. The transition is smooth and is tunable by the amount of the electric field.

	This reorientation as depicted is called a Freedericksz transition. It should not be confused with a phase transition because the LC remains in the same LC phase. Simply, the orientation of the director is perturbed. The transition is smooth and is tunable by the amount of the electric field.
	Light that is polarized along the long axis will see anisotropic and birefringent material when the molecules are homogeneously aligned. When the molecules shift to be perpendicular to the substrate then light will see an isotropic surface.		Light that is polarized along the long axis will see anisotropic and birefringent material when the molecules are homogeneously aligned. When the molecules shift to be perpendicular to the substrate then light will see an isotropic surface.

Cmditradmin: /* Anisotropic Nature of Polarizability */

2009-09-02T23:26:05Z

Anisotropic Nature of Polarizability

← Older revision		Revision as of 16:26, 2 September 2009
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	[[Image:Anis_polar.png\|thumb\|300px\|An applied filed can induce a dipole in another direction]]		[[Image:Anis_polar.png\|thumb\|300px\|An applied filed can induce a dipole in another direction]]
	In this example a field is applied along the long axis and there is large polarization. Applying a field perpendicular results in a very small polarization. If the molecule is oriented at an angle to the electric field and there is a high degree of polarizability along that axis and there is an oscillating electric field then the electrons will oscillate back and forth becoming a little antennae that will give off electromagnetic radiation. The polarization of the electromagnetic radiation has two components, one aligned along the axis of the applied field and a component along the perpendicular. If two polarizers are added and the molecule is located at an angle, then a dipole can be induced in the orthogonal direction which couples to the electric field and allows light to pass through. This induced polarization will be depend on the cosine of the angle.		In this example a field is applied along the long axis and there is large polarization. Applying a field perpendicular results in a very small polarization. If the molecule is oriented at an angle to the electric field and there is a high degree of polarizability along that axis and there is an oscillating electric field then the electrons will oscillate back and forth becoming a little antennae that will give off electromagnetic radiation. The polarization of the electromagnetic radiation has two components, one aligned along the axis of the applied field and a component along the perpendicular. If two polarizers are added and the molecule is located at an angle, then a dipole can be induced in the orthogonal direction which couples to the electric field and allows light to pass through. This induced polarization will be depend on the cosine of the angle.


			=== Summary ===


	You now have all the ingredients to make a simple display;		You now have all the ingredients to make a simple display;

Cmditradmin: /* Anisotropic Nature of Polarizability */

2009-06-29T17:57:49Z

Anisotropic Nature of Polarizability

← Older revision		Revision as of 10:57, 29 June 2009
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	You now have all the ingredients to make a simple display;		You now have all the ingredients to make a simple display;

	*You understand how liquid ~~cyrstals~~ align		*You understand how liquid crystals align
	*You can control molecular alignment with surface alignment layers		*You can control molecular alignment with surface alignment layers
	*Due to dielectric anisotropy we can ~~change~~ force the molecule to change from parallel to the surface to perpendicular to the surface		*Due to dielectric anisotropy we can force the molecule to change from parallel to the surface to perpendicular to the surface
	*Using a cross polarizer and depending on the how the molecules align, light can pass through or not.		*Using a cross polarizer and depending on the how the molecules align, light can pass through or not.

Cmditradmin: /* Threshold voltage */

2009-06-29T17:56:52Z

Threshold voltage

← Older revision		Revision as of 10:56, 29 June 2009
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	=== Threshold voltage ===		=== Threshold voltage ===
	[[Image:Splaytwistbend.png\|thumb\|300px\|Splay (K<sub>11</sub>), Twist (K<sub>22</sub>) and Bend (K<sup>33</sup>)]]		[[Image:Splaytwistbend.png\|thumb\|300px\|Splay (K<sub>11</sub>), Twist (K<sub>22</sub>) and Bend (K<sup>33</sup>)]]
	The threshold voltage (Vc) is the minimum voltage that will cause an LCD to switch. It depends on the square root of the on the elastic coefficient (~~K33~~ and ~~K22~~). The elastic coefficients refer to specific movements between molecules. The higher the elastic coefficients the harde it is to switch from one orientation to another.		The threshold voltage (Vc) is the minimum voltage that will cause an LCD to switch. It depends on the square root of the on the elastic coefficient (K<sub>33</sub> and K<sub>22</sub>). The elastic coefficients refer to specific movements between molecules. The higher the elastic coefficients the harde it is to switch from one orientation to another.

	:<math>V_c = \pi \sqrt {\frac {K_{11} + ¼ (K_{33}-2 K_{22})} {\epsilon_0 \Delta \epsilon}}\,\!</math>		:<math>V_c = \pi \sqrt {\frac {K_{11} + ¼ (K_{33}-2 K_{22})} {\epsilon_0 \Delta \epsilon}}\,\!</math>

Cmditradmin: /* Anisotropic Nature of Polarizability */

2009-06-25T21:21:54Z

Anisotropic Nature of Polarizability

← Older revision		Revision as of 14:21, 25 June 2009
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	=== Anisotropic Nature of Polarizability ===		=== Anisotropic Nature of Polarizability ===
			[[Image:Anis_polar.png\|thumb\|300px\|An applied filed can induce a dipole in another direction]]
	In this example a field is applied along the long axis and there is large polarization. Applying a field perpendicular results in a very small polarization. If the molecule is oriented at an angle to the electric field and there is a high degree of polarizability along that axis and there is an oscillating electric field then the electrons will oscillate back and forth becoming a little antennae that will give off electromagnetic radiation. The polarization of the electromagnetic radiation has two components, one aligned along the axis of the applied field and a component along the perpendicular. If two polarizers are added and the molecule is located at an angle, then a dipole can be induced in the orthogonal direction which couples to the electric field and allows light to pass through. This induced polarization will be depend on the cosine of the angle.		In this example a field is applied along the long axis and there is large polarization. Applying a field perpendicular results in a very small polarization. If the molecule is oriented at an angle to the electric field and there is a high degree of polarizability along that axis and there is an oscillating electric field then the electrons will oscillate back and forth becoming a little antennae that will give off electromagnetic radiation. The polarization of the electromagnetic radiation has two components, one aligned along the axis of the applied field and a component along the perpendicular. If two polarizers are added and the molecule is located at an angle, then a dipole can be induced in the orthogonal direction which couples to the electric field and allows light to pass through. This induced polarization will be depend on the cosine of the angle.

	You now have all the ingredients to make a simple display;		You now have all the ingredients to make a simple display;
	You understand how liquid cyrstals align
	You can control molecular alignment with surface alignment layers		*You understand how liquid cyrstals align
	Due to dielectric anisotropy we can change force the molecule to change from parallel to the surface to perpendicular to the surface		*You can control molecular alignment with surface alignment layers
	Using a cross polarizer and depending on the how the molecules align, light can pass through or not.		*Due to dielectric anisotropy we can change force the molecule to change from parallel to the surface to perpendicular to the surface
			*Using a cross polarizer and depending on the how the molecules align, light can pass through or not.

	[[category:liquid crystals]]		[[category:liquid crystals]]

Cmditradmin: /* Threshold voltage */

2009-06-25T21:17:07Z

Threshold voltage

← Older revision		Revision as of 14:17, 25 June 2009
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	Where:		Where:
	K<~~sub~~>11</~~sub~~> is the elastic coefficient for splaying		:<math>K_{11}\,\!</math> is the elastic coefficient for splaying
	K<~~sub~~>22</~~sub~~> is the elastic coefficient for twisting		:<math>K_{22}\,\!</math> is the elastic coefficient for twisting
	K<~~sub~~>33</~~sub~~> is the elastic coefficient for bending		:<math>K_{33}\,\!</math> is the elastic coefficient for bending
			:<math>\epsilon_0\,\!</math> is the dielectric permittivity in free space
	~~ε~~<~~sub~~>0</~~sub~~> is the dielectric permittivity in free space		:<math>\Delta \Epsilon\,\!</math> is the dielectric anisotropy of the system
	&Delta~~; &~~Epsilon; is the dielectric anisotropy of the system

	A uniaxial birefringent system has a dielectric constant along the axis and dielectric constant perpendicular to the long axis. The dielectric anisotropy relates to the difference between these two. If there is a dipole moment along the long axis it will make it very easy for the molecule to couple to the electric field and align. If there is no dipole moment but there is very large polarizability along the long axis then the field will induce a dipole, it will couple and then realign. So the two contributors to the dielectric constant are the susceptibility (polarizability for a material) and the dipole moment. A material with a high dielectric anisotropy has either a large dipole moment along the long axis and/or a large susceptibility. With no dielectric anisotropy there is nothing that will make it more stable to change orientation.		A uniaxial birefringent system has a dielectric constant along the axis and dielectric constant perpendicular to the long axis. The dielectric anisotropy relates to the difference between these two. If there is a dipole moment along the long axis it will make it very easy for the molecule to couple to the electric field and align. If there is no dipole moment but there is very large polarizability along the long axis then the field will induce a dipole, it will couple and then realign. So the two contributors to the dielectric constant are the susceptibility (polarizability for a material) and the dipole moment. A material with a high dielectric anisotropy has either a large dipole moment along the long axis and/or a large susceptibility. With no dielectric anisotropy there is nothing that will make it more stable to change orientation.

Cmditradmin: /* Threshold voltage */

2009-06-25T21:15:52Z

Threshold voltage

← Older revision		Revision as of 14:15, 25 June 2009
Line 32:		Line 32:
	The threshold voltage (Vc) is the minimum voltage that will cause an LCD to switch. It depends on the square root of the on the elastic coefficient (K33 and K22). The elastic coefficients refer to specific movements between molecules. The higher the elastic coefficients the harde it is to switch from one orientation to another.		The threshold voltage (Vc) is the minimum voltage that will cause an LCD to switch. It depends on the square root of the on the elastic coefficient (K33 and K22). The elastic coefficients refer to specific movements between molecules. The higher the elastic coefficients the harde it is to switch from one orientation to another.

	:<math>V_c = \pi \sqrt {\frac {K_{11} + ¼ (K_{33}-2 K_{22})} {\~~Epsilon_0~~ \Delta \~~Epsilon~~}}\,\!</math>		:<math>V_c = \pi \sqrt {\frac {K_{11} + ¼ (K_{33}-2 K_{22})} {\epsilon_0 \Delta \epsilon}}\,\!</math>

	Where:		Where:

Cmditradmin: /* Threshold voltage */

2009-06-25T21:15:34Z

Threshold voltage

← Older revision		Revision as of 14:15, 25 June 2009
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	K<sub>33</sub> is the elastic coefficient for bending		K<sub>33</sub> is the elastic coefficient for bending

	&~~Epsilon~~;<sub>0</sub> is the dielectric permittivity in free space		ε<sub>0</sub> is the dielectric permittivity in free space
	Δ Ε is the dielectric anisotropy of the system		Δ Ε is the dielectric anisotropy of the system