Comment on the paper : Electromechanical response to white noise excitation in a ferroelectric liquid crystal

(1)

HAL Id: jpa-00211134

https://hal.archives-ouvertes.fr/jpa-00211134

Submitted on 1 Jan 1989

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Comment on the paper : Electromechanical response to white noise excitation in a ferroelectric liquid crystal

G. Por, A. Buka, B. Rapp, H. Gruler

To cite this version:

G. Por, A. Buka, B. Rapp, H. Gruler. Comment on the paper : Electromechanical response to white noise excitation in a ferroelectric liquid crystal. Journal de Physique, 1989, 50 (21), pp.3173-3174.

�10.1051/jphys:0198900500210317300�. �jpa-00211134�

(2)

3173

LE JOURNAL DE PHYSIQUE

Short Communication

Comment on the paper :

Electromechanical _response ^to white noise excitation in a ferroelec- tric liquid crystal

G. Por and A. Buka

B. Rapp ^and ^{H. Gruler}

Department of Biophysics, University of Ulm, ^D-7900 Ulm, ^ER.G.

(Reçu ^{le ler} septembre 1989, accepté ^{le 4} septembre 1989)

Tome 50 N°21 ^1er NOVEMBRE 1989

J. Phys. ^{France 50} (1989) ^3173-3174 ^1er ^NOVEMBRE ^1989,

Classification

Physics ^Abstracts

61.30 - 02.50 - 05.40

Por and Buka [1] reported ^about ^an electromechanical coupling ⁱⁿ ferroelectric liquid crystal

cells. In spite ^{of the} large ^cell spacing ^{of 50 pm} they obviously ^succeeded ⁱⁿ obtaining ^the ^so-called

"surface-stabilised" geometry [2]. They presented ^a formula for the vibrational amplitude ^{of the}

upper glass ^substrate ^{as a} function of cell-, liquid crystal- ^and driving-parameters. This formula is based on a cross effect between dielectric relaxation and viscous flow. The authors did not give

a value for the maximum vibrational amplitude ^measured ôr êstimated theoretically, however. In this letter we want to propose â simple model for the electromechanical effect and to prove îts validity ^based ôn ôur experimental findings.

We have made some experiments ^{on an} electromechanical effect in SmC* -cells, ^which ^we

believe to be the same phenomenon, ^{Por and} ^Buka reported ^{about We} used substrates coated with indium-tin-oxide as electrodes and polyimide alignment layers, ^which ^were ^rubbed antiparallel ^to

achieve planar liquid crystal alignment. ^Cells ^were fabricated with a spacing ^{of 2 pm} ^and filled with Merck ZLI-3654 in the isotropic phase. ^Slow cooling ^led ^to ^cells ^with nearly ^no zig-zag ^defects [3]

in the surface-stabilised geometry. Ôn applying â ¹⁰ Vpp ^sine ^voltage, the electromechanical effect could easily ^be ^heared, actually the cell acted as a loudspeaker. ^7b quantify ^the vibration, ône

substrate of the cell was fixed while the movement of the other one was recorded with a sensitive

microphone placed ^about ¹ ^cm apart ^{In the} frequency ^range ^from ¹ ^Hz ^to ¹⁰ ^kHz, ^we ^measured ^a

mechanical answer of the cell, which had the double frequency ^{of the} input ^sine ^wave. ^We ^did ^not

find a dependence ^{of the} vibrational amplitude ^{from the} driving voltage, except ^that ^a ^minimum voltage (about ³ Vpp) ^was ^required.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198900500210317300

(3)

3174

Next we wanted to examine amplitude ^{and mode} ^of vibration of the cell’s substrate. There- fore we employed holographic interferometry [4]. ^We ^made amplitude holograms of the cell with a

standard equipment (HeNe ^laser, Agfa Holotest 10 E 75 material), developed ^and replaced ^them,

and compared the interference patterns ^{of the} hologram ^{and of} ^{the -} ^now vibrating - ^cell. ^In ^{a sec-}

ond experiment ^we kept ^{the cell} vibrating during exposure (time average technique), developed

the plates ând êxamined ^them. ^The surprising result of all these experiments ^was, ^{that the} âm- plitude ôf vibration could not be resolved within the accuracy ^{of the} holographic technique. ^This gives ân upper limit for the amplitude of about 60 nm.

Our measurements led us to a simple mechanical model, which is based on director reorien- tation during switching ^from ône ^state (e.g. Up) ^to ^{the other} (Down) ôr ^vice ^versa. During ^this reorientation, ^the liquid crystal ^molecules ^rotate ^{on a cone} ^with â ^certain angle, ^the cone-angle

9. 8 is a material parameter, ^{which is} only temperature dependent, ^but kept ^constant ^{inside the}

celL The position ôf â molecule is therefore fully ^described by ^the âzimuthal angle ^0, ^which equals

0° in the ideal Up-state ^and ^180° in the ideal Down-state. During reorientation the smectic lay-

ers expand ^{until 0} equals ^{90° and} ^therefore lift the movable substrate. The maximum increase bd in cell thickness d thus equals - neglecting ^resonance phenomena - ^l.sin (0) , ^where 1 stands for the molecular length. Choosing typical ^values (1

⁼

³ nm, 8

⁼

22.5° ) bd becomes about 1.1 nm.

Even if a resonance quality ^of ^{10 is} assumed, ^the increase in cell thickness is just ¹¹ ^nm. ^{The model} predicts ^the experimental findings quite satisfying :

1) the estimated maximum amplitude ^{of 11} ^nm ^is ^far beyond ^the light-holographic ^resolution (about ⁶⁰ nm) ^{and thus} explains ^our failure in recording ^the vibration of the cell holographically ; 2) the acoustic answer must have the double frequency of the electric driving signal, ^{since the}

molecules reorient every halfwave of the driving signal ;

3) the vibrational amplitude ^must ^be independent ^{from the} applied voltage, ensured that it is larger

than a certain threshold voltage.

In conclusion, ^we ^have presented ^a simple explanation ^{for the} electromechanical effect in surface-stabilised ferroelectric liquid crystal cells observed by Por and Buka.

Acknowledgments.

This work was supported by ^the "Bundesministerium für Forschung ^und Technologie ^BMFT",

"Fonds der chemischen Industrie" and ’AEG". We want to thank E. Merck for supplying ^us ^with liquid crystals.

References

[1] ^POR ^G., ^BUKA ^{A., J.} Phys. ^{France 50} (1989) ^783.

[2] CLARK N.A., LAGERWALL S.T, Appl. Phys. ^Lett. 36 (1980) ^899.

[3] ÎSHIKAWA ^K., ÔUCHI ^Y., ÛEMURA ^T, ^TSUCHIYA ^T, ^TAKEZOE ^H., ^FUKUDA Â., ^Mol. Cryst. Liq.

Cryst. ¹²² (1985) ^175.

[4] ^OSTROVSKY B., Interferometry by Holography (Springer) ^1980.

Comment on the paper : Electromechanical response to white noise excitation in a ferroelectric liquid crystal

HAL Id: jpa-00211134

https://hal.archives-ouvertes.fr/jpa-00211134

Submitted on 1 Jan 1989

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Comment on the paper : Electromechanical response to white noise excitation in a ferroelectric liquid crystal

G. Por, A. Buka, B. Rapp, H. Gruler

To cite this version:

G. Por, A. Buka, B. Rapp, H. Gruler. Comment on the paper : Electromechanical response to white noise excitation in a ferroelectric liquid crystal. Journal de Physique, 1989, 50 (21), pp.3173-3174.

�10.1051/jphys:0198900500210317300�. �jpa-00211134�

3173

LE JOURNAL DE PHYSIQUE

Short Communication

Comment on the paper :

Electromechanical response to white noise excitation in a ferroelec- tric liquid crystal

G. Por and A. Buka

B. Rapp and H. Gruler

Department of Biophysics, University of Ulm, D-7900 Ulm, ER.G.

(Reçu le ler septembre 1989, accepté le 4 septembre 1989)

Tome 50 N°21 1er NOVEMBRE 1989

J. Phys. France 50 (1989) 3173-3174 1er NOVEMBRE 1989,

Classification

Physics Abstracts

61.30 - 02.50 - 05.40

Por and Buka [1] reported about an electromechanical coupling in ferroelectric liquid crystal

cells. In spite of the large cell spacing of 50 pm they obviously succeeded in obtaining the so-called

"surface-stabilised" geometry [2]. They presented a formula for the vibrational amplitude of the

upper glass substrate as a function of cell-, liquid crystal- and driving-parameters. This formula is based on a cross effect between dielectric relaxation and viscous flow. The authors did not give

a value for the maximum vibrational amplitude measured or estimated theoretically, however. In this letter we want to propose a simple model for the electromechanical effect and to prove its validity based on our experimental findings.

We have made some experiments on an electromechanical effect in SmC* -cells, which we

believe to be the same phenomenon, Por and Buka reported about We used substrates coated with indium-tin-oxide as electrodes and polyimide alignment layers, which were rubbed antiparallel to

achieve planar liquid crystal alignment. Cells were fabricated with a spacing of 2 pm and filled with Merck ZLI-3654 in the isotropic phase. Slow cooling led to cells with nearly no zig-zag defects [3]

in the surface-stabilised geometry. On applying a 10 Vpp sine voltage, the electromechanical effect could easily be heared, actually the cell acted as a loudspeaker. 7b quantify the vibration, one

substrate of the cell was fixed while the movement of the other one was recorded with a sensitive

microphone placed about 1 cm apart In the frequency range from 1 Hz to 10 kHz, we measured a

mechanical answer of the cell, which had the double frequency of the input sine wave. We did not

find a dependence of the vibrational amplitude from the driving voltage, except that a minimum voltage (about 3 Vpp) was required.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198900500210317300

3174

Next we wanted to examine amplitude and mode of vibration of the cell’s substrate. There- fore we employed holographic interferometry [4]. We made amplitude holograms of the cell with a

standard equipment (HeNe laser, Agfa Holotest 10 E 75 material), developed and replaced them,

and compared the interference patterns of the hologram and of the - now vibrating - cell. In a sec-

ond experiment we kept the cell vibrating during exposure (time average technique), developed

the plates and examined them. The surprising result of all these experiments was, that the am- plitude of vibration could not be resolved within the accuracy of the holographic technique. This gives an upper limit for the amplitude of about 60 nm.

Our measurements led us to a simple mechanical model, which is based on director reorien- tation during switching from one state (e.g. Up) to the other (Down) or vice versa. During this reorientation, the liquid crystal molecules rotate on a cone with a certain angle, the cone-angle

9. 8 is a material parameter, which is only temperature dependent, but kept constant inside the

celL The position of a molecule is therefore fully described by the azimuthal angle 0, which equals

0° in the ideal Up-state and 180° in the ideal Down-state. During reorientation the smectic lay-

ers expand until 0 equals 90° and therefore lift the movable substrate. The maximum increase bd in cell thickness d thus equals - neglecting resonance phenomena - l.sin (0) , where 1 stands for the molecular length. Choosing typical values (1

3 nm, 8

22.5° ) bd becomes about 1.1 nm.

Even if a resonance quality of 10 is assumed, the increase in cell thickness is just 11 nm. The model predicts the experimental findings quite satisfying :

1) the estimated maximum amplitude of 11 nm is far beyond the light-holographic resolution (about 60 nm) and thus explains our failure in recording the vibration of the cell holographically ; 2) the acoustic answer must have the double frequency of the electric driving signal, since the

molecules reorient every halfwave of the driving signal ;

3) the vibrational amplitude must be independent from the applied voltage, ensured that it is larger

than a certain threshold voltage.

In conclusion, we have presented a simple explanation for the electromechanical effect in surface-stabilised ferroelectric liquid crystal cells observed by Por and Buka.

Acknowledgments.

This work was supported by the "Bundesministerium für Forschung und Technologie BMFT",

"Fonds der chemischen Industrie" and ’AEG". We want to thank E. Merck for supplying us with liquid crystals.

References

[1] POR G., BUKA A., J. Phys. France 50 (1989) 783.

[2] CLARK N.A., LAGERWALL S.T, Appl. Phys. Lett. 36 (1980) 899.

[3] ISHIKAWA K., OUCHI Y., UEMURA T, TSUCHIYA T, TAKEZOE H., FUKUDA A., Mol. Cryst. Liq.

Cryst. 122 (1985) 175.

[4] OSTROVSKY B., Interferometry by Holography (Springer) 1980.

Electromechanical _response ^to white noise excitation in a ferroelec- tric liquid crystal

B. Rapp ^and ^{H. Gruler}

Department of Biophysics, University of Ulm, ^D-7900 Ulm, ^ER.G.

(Reçu ^{le ler} septembre 1989, accepté ^{le 4} septembre 1989)

Tome 50 N°21 ^1er NOVEMBRE 1989

J. Phys. ^{France 50} (1989) ^3173-3174 ^1er ^NOVEMBRE ^1989,

Physics ^Abstracts

Por and Buka [1] reported ^about ^an electromechanical coupling ⁱⁿ ferroelectric liquid crystal

cells. In spite ^{of the} large ^cell spacing ^{of 50 pm} they obviously ^succeeded ⁱⁿ obtaining ^the ^so-called

"surface-stabilised" geometry [2]. They presented ^a formula for the vibrational amplitude ^{of the}

upper glass ^substrate ^{as a} function of cell-, liquid crystal- ^and driving-parameters. This formula is based on a cross effect between dielectric relaxation and viscous flow. The authors did not give

a value for the maximum vibrational amplitude ^measured ôr êstimated theoretically, however. In this letter we want to propose â simple model for the electromechanical effect and to prove îts validity ^based ôn ôur experimental findings.

We have made some experiments ^{on an} electromechanical effect in SmC* -cells, ^which ^we

believe to be the same phenomenon, ^{Por and} ^Buka reported ^{about We} used substrates coated with indium-tin-oxide as electrodes and polyimide alignment layers, ^which ^were ^rubbed antiparallel ^to

achieve planar liquid crystal alignment. ^Cells ^were fabricated with a spacing ^{of 2 pm} ^and filled with Merck ZLI-3654 in the isotropic phase. ^Slow cooling ^led ^to ^cells ^with nearly ^no zig-zag ^defects [3]

in the surface-stabilised geometry. Ôn applying â ¹⁰ Vpp ^sine ^voltage, the electromechanical effect could easily ^be ^heared, actually the cell acted as a loudspeaker. ^7b quantify ^the vibration, ône

microphone placed ^about ¹ ^cm apart ^{In the} frequency ^range ^from ¹ ^Hz ^to ¹⁰ ^kHz, ^we ^measured ^a

mechanical answer of the cell, which had the double frequency ^{of the} input ^sine ^wave. ^We ^did ^not

find a dependence ^{of the} vibrational amplitude ^{from the} driving voltage, except ^that ^a ^minimum voltage (about ³ Vpp) ^was ^required.

Next we wanted to examine amplitude ^{and mode} ^of vibration of the cell’s substrate. There- fore we employed holographic interferometry [4]. ^We ^made amplitude holograms of the cell with a

standard equipment (HeNe ^laser, Agfa Holotest 10 E 75 material), developed ^and replaced ^them,

and compared the interference patterns ^{of the} hologram ^{and of} ^{the -} ^now vibrating - ^cell. ^In ^{a sec-}

ond experiment ^we kept ^{the cell} vibrating during exposure (time average technique), developed

the plates ând êxamined ^them. ^The surprising result of all these experiments ^was, ^{that the} âm- plitude ôf vibration could not be resolved within the accuracy ^{of the} holographic technique. ^This gives ân upper limit for the amplitude of about 60 nm.

9. 8 is a material parameter, ^{which is} only temperature dependent, ^but kept ^constant ^{inside the}

celL The position ôf â molecule is therefore fully ^described by ^the âzimuthal angle ^0, ^which equals

0° in the ideal Up-state ^and ^180° in the ideal Down-state. During reorientation the smectic lay-

ers expand ^{until 0} equals ^{90° and} ^therefore lift the movable substrate. The maximum increase bd in cell thickness d thus equals - neglecting ^resonance phenomena - ^l.sin (0) , ^where 1 stands for the molecular length. Choosing typical ^values (1

³ nm, 8

Even if a resonance quality ^of ^{10 is} assumed, ^the increase in cell thickness is just ¹¹ ^nm. ^{The model} predicts ^the experimental findings quite satisfying :

3) the vibrational amplitude ^must ^be independent ^{from the} applied voltage, ensured that it is larger

In conclusion, ^we ^have presented ^a simple explanation ^{for the} electromechanical effect in surface-stabilised ferroelectric liquid crystal cells observed by Por and Buka.

This work was supported by ^the "Bundesministerium für Forschung ^und Technologie ^BMFT",

"Fonds der chemischen Industrie" and ’AEG". We want to thank E. Merck for supplying ^us ^with liquid crystals.

[1] ^POR ^G., ^BUKA ^{A., J.} Phys. ^{France 50} (1989) ^783.

[2] CLARK N.A., LAGERWALL S.T, Appl. Phys. ^Lett. 36 (1980) ^899.

[3] ÎSHIKAWA ^K., ÔUCHI ^Y., ÛEMURA ^T, ^TSUCHIYA ^T, ^TAKEZOE ^H., ^FUKUDA Â., ^Mol. Cryst. Liq.

Cryst. ¹²² (1985) ^175.

[4] ^OSTROVSKY B., Interferometry by Holography (Springer) ^1980.