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K. Xiao and C.-X. Wu
Fig. 8.10 Equilibrium position x 0 for different a radii (2.2 µm, 2.35 µm, 2.5 µm and 3.0 µm); b
densities (0.99, 1.0 and 1.04 g · cm −3 ) of a microparticle with K = 7 pN and L = 7 µm, showing
the same critical value E c of electric field triggering positional transition. The dependence of E c on
√
K /L for different c radii (2.2 µm, 2.35 µm, 2.5 µm and 3.0 µm); d densities (0.99, 1.0 and 1.04
g · cm −3 ) of the microparticle, obeying strictly a master curve which can be given by the theoretical
prediction Eq. (8.31)
suggesting that the critical electric value is independent of or negligibly depends on
microparticle size and density. To gain more insight into the dynamic behaviors of the
microparticle, we further plot the threshold value against
√
K /L in Fig. 8.10c and d,
where a Fréedericksz curve (black) is shown as well. It is interesting to find that the
critical electric field to trigger a positional transition for a microparticle suspended
in an NLC cell follows a Fréedericksz-like linear master curve with slightly different
slopes, a universal one also valid for different microparticle sizes and densities.
By comparing the numerical calculation results with the Fréedericksz transition
(π
√
4π/|
√
K /L) in Fig. 8.10c and d, we found that the slope difference between
them is by a prefactor of ∼0.915, and that enables us to propose a theoretical prediction for the critical electric field
E c 0.915F,
(8.31)
where F denotes the Fréedericksz effect. Such a prediction, as shown by straight
line (red) in Fig. 8.10c and d, agrees very well for different radii (2.2, 2.35, 2.5,
K. Xiao and C.-X. Wu
Fig. 8.10 Equilibrium position x 0 for different a radii (2.2 µm, 2.35 µm, 2.5 µm and 3.0 µm); b
densities (0.99, 1.0 and 1.04 g · cm −3 ) of a microparticle with K = 7 pN and L = 7 µm, showing
the same critical value E c of electric field triggering positional transition. The dependence of E c on
√
K /L for different c radii (2.2 µm, 2.35 µm, 2.5 µm and 3.0 µm); d densities (0.99, 1.0 and 1.04
g · cm −3 ) of the microparticle, obeying strictly a master curve which can be given by the theoretical
prediction Eq. (8.31)
suggesting that the critical electric value is independent of or negligibly depends on
microparticle size and density. To gain more insight into the dynamic behaviors of the
microparticle, we further plot the threshold value against
√
K /L in Fig. 8.10c and d,
where a Fréedericksz curve (black) is shown as well. It is interesting to find that the
critical electric field to trigger a positional transition for a microparticle suspended
in an NLC cell follows a Fréedericksz-like linear master curve with slightly different
slopes, a universal one also valid for different microparticle sizes and densities.
By comparing the numerical calculation results with the Fréedericksz transition
(π
√
4π/|
√
K /L) in Fig. 8.10c and d, we found that the slope difference between
them is by a prefactor of ∼0.915, and that enables us to propose a theoretical prediction for the critical electric field
E c 0.915F,
(8.31)
where F denotes the Fréedericksz effect. Such a prediction, as shown by straight
line (red) in Fig. 8.10c and d, agrees very well for different radii (2.2, 2.35, 2.5,