Ion trapping by means of ferroelectric nanoparticles, and the quantification of
this process in liquid crystals
Yuriy Garbovskiy and Iryna Glushchenko
UCCS BioFrontiers Center & Department of Physics, University of Colorado
Colorado Springs, Colorado Springs, USA
ygarbovs@uccs.edu (YG)
Supplementary materials
a) DC driving of liquid crystals
Figure S1a illustrates what happens when the DC electric field is applied across a liquid crystal cell
with planar boundary conditions. The liquid crystal cell is placed between two crossed polarizers, and the
light passing through the cell is measured as a function of time with a photo-detector (a photo-diode). The
applied DC electric field reorients liquid crystals from the planar state toward the homeotropic state. This
reorientation changes the optical phase shift  , which results in changes in the transmitted light I (t )
according to (1) [1]:
2
  (t )  
I (t )  I 0  sin 
  ,
  2 
(1)
where I 0 is the intensity of the incident light, and the electrically induced  is expressed by (2):
 
2
dn ,

(2)
where  is the wavelength of the light, and n is the effective optical birefringence of liquid crystals. The
1
applied electric field changes n and this change can be measured and analysed quantitatively using
equations (1)-(2).
Figure 1
(a) The electro-optical response of a liquid crystal cell filled with nematic E7 (planar boundary conditions).
(b) Schematic representation of the liquid crystal reorientation under the action of a DC electric field. (c) Applied
electric field is screened by a field caused by the presence of ions in the liquid crystal.
Peak 1 shown in Figure 1a corresponds to the reorientation of the liquid crystal from a planar
orientation toward the homeotropic (as shown schematically in Figure 1b). In this particular case, when 2
V are applied across a 10 mkm thick cell filled with liquid crystal E7, the reorientation takes less than a
quarter of a second . At the same time, the ions present in the liquid crystal move toward the substrates
under the action of the DC electric field. These ions generate a so-called screening field, which is opposite
to the external field. As a result, the combined electric field decreases over time, and the liquid crystal
reorients back toward the initial planar state. This process is reflected by Peak 2, shown in Figure 1a, and
is schematically explained in Figure 1c. In the considered example, the screening electric field compensates
the applied electric field in less than 3 seconds, resulting in the substantial alteration of the liquid crystal
performance. Had the concentration of ions in the liquid crystals been negligibly small, this effect would
never happen.
b) The literature review
Table 1. Effect of nanoparticles on the electrical conductivity of liquid crystals.
2
Nanoparticles
Liquid
crystals
Results
Ref.
FLC
NLC
NLC
FLC
NLC
Decrease in ion concentration
Ion trapping
Increase in the conductivity
Reduced AC conductivity
Decrease in ion concentration
[2]
[3-5]
[6]
[7-8]
[9-10]
NLC
PDLC
CLC
FLC
NLC
FLC
NLC
Increase in the conductivity
Increase in the conductivity
Increase in the conductivity
Increase in the conductivity
Ion trapping
Decrease in the conductivity/dielectric losses
Both decrease and increase in the conductivity
[11-13]
[14]
[15]
[16-18]
[19-20]
[21-24]
[25-27]
FLC
NLC
CLC
ColLC
NLC
NLC
NLC
ColLC
NLC
FLC
Reduced AC conductivity
Two orders increase in the conductivity
Capture and release of ions
Five-six orders increase in the conductivity
Enhancement of the electrical conductivity
Increased dielectric losses
Increased anisotropy of the conductivity
Enhancement of the electrical conductivity
Ion trapping
Increase in the conductivity
[28-29]
[30-32]
[33]
[34-38]
[39]
[40]
[41]
[42]
[43]
[44]
NLC
Reduced ion current and improved voltage
holding ratio, decrease in ion concentration
[45-55]
FLC
Decrease in the conductivity
[56-59]
ColLC
Increase in the conductivity
[60]
NLC
Voltage-assisted ion reduction
[61]
Decrease in the concentration of ions
Decrease in the conductivity
Release of the trapped ions under the action of
the electric field
[62-63]
[64]
Carbon-based nanomaterials
Fullerenes
Graphene
Carbon nanotubes
Diamond nanoparticles
Metal nanoparticles
Gold
Gold and Aerosil
Palladium
Silver
Copper
Nickel
Oxides
ZnO , TiO2 , Al2O3 , ZrO2 ,
Y2O3 , Co3O4
TiO2 , Al2O3 , ZrO2 , MgO
ZnO
SiO2
Semiconductor quantum dots and nanorods
FLC
CdSe
FLC
CdS
CdSe / ZnS
NLC
[65]
Ferroelectric nanoparticles
LiNbO3
FLC
Ion trapping
[66]
Sn2 P2 S 6
NLC
Increase in the conductivity
[67]
BaTiO 3
NLC
Decrease in the concentration of ions
[68]
Other materials
Nanoclay (montmorillonite)
NLC
Conducting nanofiber
Polymeric nanoparticles
NLC
FLC
FLC
ZnO1 x S x
Ion trapping, time dependent properties, and
aggregation
Increase I n the conductivity
Decrease in dielectric losses
Increase in the conductivity
[69-75]
[76-77]
[78]
[79-80]
3
FLC – ferroelectric liquid crystals
NLC – nematic liquid crystals
CLC – cholesteric liquid crystals
ColLC – columnar liquid crystals
PDLC – polymer dispersed liquid crystals
c) The model of a reversible second order reaction applied to ferroelectric nanoparticles
We will estimate n NP ,eff by applying the simplest model of a reversible second order reaction to our system
(this oversimplification is meant only to highlight the importance of the aggregation factor in the
quantitative way) [81]. In this model, we will consider only two-particle collisions. These collisions,
described by the rate constant k A , lead to the formation of the aggregate made of two particles. The
concentration of the formed aggregates is n A . The aggregate can dissociate and form two particles. This
process is described by the rate constant k D and can be facilitated by applying external perturbing factors,
such as continuous mechanical shaking and/or sonication, to the system. The following rate equation (3)
and the particle conservation equation (4) describe the above-mentioned processes:
dnNP ,eff
dt
 k A nNP ,eff   2k D n A ,
2
nNP  nNP ,eff  2n A ,
Assuming that equilibrium is reached (
dnNP ,eff
dt
(3)
(4)
 0 ), we can find the following equation (5) for the nNP ,eff
:
nNP ,eff  k D
kA
nNP ,
(5)
4
References
[1] V G Chigrinov, Liquid crystal devices: physics and applications, Artech House, Boston 360 p ., 1999.
[2] R. K. Shukla, K. K. Raina, and W. Haase, Liq. Cryst. 41(12), 1726 417 (2014).
[3] W. Lee, C.-Yu. Wang, and Yu.-C. Shih, Appl. Phys. Lett. 85, 513 (2004).
[4] C. Y. Huang and H. C. Pan, Appl. Phys. Lett. 89, 056101 (2006).
[5] S. Y. Jeon, S. H. Lee, and Y. H. Lee, Appl. Phys. Lett. 89, 056102 (2006).
[6] V. E. Vovk, A. V. Koval’chuk, and N. Lebovka, Liq. Cryst. 39(1), 77 (2012).
[7] D. P. Singh, S. K. Gupta, T. Vimal, and R. Manohar, Phys. Rev. E 90, 022501 (2014).
[8] R. Basu, Appl. Phys. Lett. 105, 112905 (2014).
[9] Po.-C. Wu and W. Lee, Appl. Phys. Lett. 102, 162904 (2013).
[10] R. Basu, A. Garvey, and D. Kinnamon, J. Appl. Phys. 117, 074301 (2015).
[11] O. Yaroshchuk, S. Tomylko, O. Kovalchuk, and N. Lebovka, Carbon 68, 389 (2014).
[12] T. Vimal, S. Pandey, S. K. Gupta, D. P. Singh, and R. Manohar, J. Mol. Liq. 204, 21 (2015).
[13] L. N. Lisetski, S. S. Minenko, V. V. Ponevchinsky, M. S. Soskin, A. I. Goncharuk, and N. I. Lebovka,
Materialwiss. Werkstofftech. 42(1), 5 436 (2011).
[14] G. De Filpo, S. Siprova, G. Chidichimo, A. I. Mashin, F. P. Nicoletta, and D. Cupelli, Liq. Cryst. 39, 359
(2012).
[15] O. K€oysal, Synth. Met. 160(9–10), 1097 (2010).
[16] R. K. Shukla, K. K. Raina, V. Hamplova, M. Kaspar, and A. Bubnov, Phase Transitions 84(9–10), 850 (2011).
[17] J. Prakash, A. Choudhary, D. S. Mehta, and A. M. Biradar, Phys. Rev. E 80, 012701 (2009).
[18] Neeraj and K. K. Raina, Physica B 434, 1 (2014).
[19] C.-W. Lee and W.-P. Shih, Mater. Lett. 64(3), 466 (2010).
[20] Bo.-Ru. Jian, C.-Yu. Tang, and W. Lee, Carbon 49(3), 910 (2011).
[21] A. Malik, J. Prakash, A. Kumar, A. Dhar, and A. M. Biradar, J. Appl. Phys. 112, 054309 (2012).
[22] P. Arora, A. Mikulko, F. Podgornov, and W. Haase, Mol. Cryst. Liq. Cryst. 502(1), 1 (2009).
[23] P. Ganguly, A. Kumar, S. Tripathi, D. Haranath, and A. M. Biradar, Liq. Cryst. 41(6), 793 (2014).
[24] R. Basu, Appl. Phys. Lett. 103, 241906 (2013).
5
[25] P.-S. Chen, C.-C. Huang, Y.-W. Liu, and C.-Yu. Chao, Appl. Phys. Lett. 90, 211111 (2007).
[26] S. Tomylko, O. Yaroshchuk, O. Kovalchuk, U. Maschke, and R. Yamaguchi, Ukr. J. Phys. 57(2), 239 (2012).
[27] S. Tomylko, O. Yaroshchuk, O. Kovalchuk, U. Maschke, and R. Yamaguchi, Mol. Cryst. Liq. Cryst. 541(1), 35
(2011).
[28] R. K. Shukla, X. Feng, S. Umadevi, T. Hegmann, and W. Haase, Chem. Phys. Lett. 599, 80 (2014).
[29] F. V. Podgornov, A. V. Ryzhkova, and W. Haase, Appl. Phys. Lett. 97, 212903 (2010).
[30] S. Sridevi, S. K. Prasad, G. G. Nair, V. D’Britto, and B. L. V. Prasad, Appl. Phys. Lett. 97, 151913 (2010).
[31] S. K. Prasad, M. V. Kumar, T. Shilpa, and C. V. Yelamaggad, RSC Adv. 4, 4453 (2014).
[32] S. K. Prasad, K. L. Sandhya, G. G. Nair, U. S. Hiremath, C. V. Yelamaggad, and S. Sampath, Liq. Cryst.
33(10), 1121 (2006).
[33] M. Infusino, A. De Luca, F. Ciuchi, A. Ionescu, N. Scaramuzza, and G. Strangi, J. Mater. Sci. 49(4), 1805
(2014).
[34] M. Mishra, S. Kumar, and R. Dhar, RSC Adv. 4, 62404 (2014).
[35] Supreet, R. Pratibha, S. Kumar, and K. K. Raina, Liq. Cryst. 41(7), 933 (2014).
[36] L. A. Holt, R. J. Bushby, S. D. Evans, A. Burgess, and G. Seeley, J. Appl. Phys. 103, 063712 (2008).
[37] B. S. Avinash, V. Lakshminarayanan, S. Kumar, and J. K. Vij, Chem. Commun. 49, 978 (2013).
[38] S. Kumar, Liq. Cryst. 41(3), 353 (2014).
[39] B. Kamaliya, M. V. Kumar, C. V. Yelamaggad, and S. K. Prasad, Appl. Phys. Lett. 106, 083110 (2015).
[40] 1S. Kobayashi, Y. Sakai, T. Miyama, N. Nishida, and N. Toshima, J. Nanomater. 2012, 460658.
[41] U. B. Singh, R. Dhar, R. Dabrowski, and M. B. Pandey, Liq. Cryst. 40(6), 774 (2013).
[42] P. Yaduvanshi, S. Kumar, and R. Dhar, Effects of copper nanoparticles on the thermodynamic, electrical and
optical properties of a disc-shaped liquid crystalline material showing columnar phase, Phase Transitions: A
Multinational Journal, DOI: 10.1080/01411594.2014.984710
[43] H. M. Lee, H.-K. Chung, H.-G. Park, H.-C. Jeong, J.-J. Han, M.-J. Cho, J.-W. Lee, and D.-S. Seo, Liq. Cryst.
41(2), 247 (2014).
[44] Neeraj and K. K. Raina, Opt. Mater. 35(3), 531 (2013).
[45] W.-T. Chen, P.-S. Chen, and C.-Y. Chao, Jpn. J. Appl. Phys., Part 1 48, 015006 (2009).
[46] W.-T. Chen, P.-S. Chen, and C.-Yu. Chao, Mol. Cryst. Liq. Cryst. 507(1), 253 (2009).
6
[47] P.-S. Chen, C.-C. Huang, Y.-W. Liu, and C.-Yu. Chao, Mol. Cryst. Liq. Cryst. 507(1), 202 (2009).
[48] T.-R. Chou, J. Hsieh, W.-T. Chen, and C.-Yu. Chao, Jpn. J. Appl. Phys., Part 1 53(7), 071701 (2014).
[49] B.-Jy. Liang, D.-G. Liu, W.-Yi. Shie, and Sy.-R. Huang, Jpn. J. Appl. Phys., Part 1 49, 025004 (2010).
[50] C.-Yu. Tang, S.-M. Huang, and W. Lee, J. Phys. D: Appl. Phys. 44(35), 355102 (2011).
[51] Y.-S. Ha, H.-J. Kim, H.-G. Park, and D.-S. Seo, Opt. Express 20(6), 6448 (2012).
[52] H.-J. Kim, Y.-Gu. Kang, H.-G. Park, K.-M. Lee, S. Yang, H.-Y. Jung, and D.-S. Seo, Liq. Cryst. 38(7), 871
(2011).
[53] H.-Y. Jung, H.-J. Kim, S. Yang, Y.-Gu. Kang, B.-Y. Oh, H.-G. Park, and D.-S. Seo, Liq. Cryst. 39(7), 789
(2012).
[54] H.-K. Chung, H.-G. Park, Y.-S. Ha, J.-M. Han, J.-W. Lee, and D.-S. Seo, Liq. Cryst. 40(5), 632 (2013).
[55] N. Yadav, R. Dabrowski, and R. Dhar, Liq. Cryst. 41(12), 1803 (2014).
[56] T. Joshi, J. Prakash, A. Kumar, J. Gangwar, A. K Srivastava, S. Singh, and A. M. Biradar, J. Phys. D: Appl.
Phys. 44, 315404 (2011).
[57] A. Chandran, J. Prakash, P. Ganguly, and A. M. Biradar, RSC Adv. 3, 17166 (2013).
[58] S. K. Gupta, D. P. Singh, and R. Manohar, Adv. Mater. Lett. 6(1), 68 (2015).
[59] A. Chandran, J. Prakash, K. K. Naik, A. K. Srivastava, R. Da˛browski, M. Czerwinski, and A. M. Biradar, J.
Mater. Chem. C 2, 1844 (2014).
[60] Supreet, S. Kumar, K. K. Raina, and R. Pratibha, Liq. Cryst. 40(2), 228 (2013).
[61] S.-W. Liao, C.-T. Hsieh, C.-C. Kuo, and C.-Y. Huang, Appl. Phys. Lett. 101, 161906 (2012).
[62] R. K. Shukla, Y. G. Galyametdinov, R. R. Shamilov, and W. Haase, Liq. Crys. 41(12), 1889 (2014).
[63] D. P. Singh, S. K. Gupta, P. Tripathi, M. C. Varia, S. Kumar, and R. Manohar, Liq. Cryst. 41(9), 1356 (2014).
[64] P. Malik, A. Chaudhary, R. Mehra, and K. K. Raina, Adv. Condens. Matter Phys. 2012, 853160.
[65] E. A. Konshina, I. F. Galin, and E. O. Gavrish, Univers. J. Mater. Sci. 2(1), 1 (2014).
[66] R. K. Shukla, C. M. Liebig, D. R. Evans, and W. Haase, RSC Adv. 4, 18529 (2014).
[67] E. Ouskova, O. Buchnev, V. Reshetnyak, Yu. Reznikov, and H. Kresse, Liq. Cryst. 30(10), 1235 (2003).
[68] R. Basu and A. Garvey, Appl. Phys. Lett. 105, 151905 (2014).
[69] Y.-M. Chang, T.-Y. Tsai, Y.-P. Huang, W.-S. Chen, and W. Lee, Jpn. J. Appl. Phys., Part 1 46(11), 7368
(2007).
7
[70] T.-Y. Tsai, Y.-P. Huang, H.-Yu. Chen, W. Lee, Y.-M. Chang, and W.-K. Chin, Nanotechnology 16(8), 1053
(2005).
[71] H.-H. Liu and W. Lee, Appl. Phys. Lett. 97, 023510 (2010).
[72] H.-H. Liu and W. Lee, Appl. Phys. Lett. 97, 173501 (2010).
[73] Y.-P. Huang, H.-Yu. Chen, W. Lee, T.-Y. Tsai, and W.-K. Chin, Nanotechnology 16(4), 590 (2005).
[74] N. Lebovka, A. Goncharuk, T. Bezrodna, I. Chashechnikova, and V. Nesprava, Liq. Cryst. 39(5), 531 (2012).
[75] Y. Shaydyuk, G. Puchkovska, A. Goncharuk, and N. Lebovka, Liq. Cryst. 38(2), 155 (2011).
[76] R. Manda, V. Dasari, P. Sathyanarayana, M. V. Rasna, P. Paik, and S. Dhara, Appl. Phys. Lett. 103, 141910
(2013).
[77] M. V. Rasna, K. P. Zuhail, R. Manda, P. Paik, W. Haase, and S. Dhara, Phys. Rev. E 89, 052503 (2014).
[78] A. Kumar, P. Silotia, and A. M. Biradar, J. Appl. Phys. 108, 024107 (2010).
[79] D. P. Singh, S. K. Gupta, A. C. Pandey, and R. Manohar, Adv. Mater. Lett. 4(7), 556 (2013).
[80] D. P. Singh, S. K. Gupta, and R. Manohar, Adv. Condens. Matter Phys. 2013, 250301.
[81] N I Lebovka, Adv. Polym Sci, 255, 57-96 (2014).
8