Article pubs.acs.org/Langmuir
Electric-Field-Induced Phase Separation and Homogenization Dynamics in Colloidal Suspensions of Dichroic Rod-Shaped Pigment Particles Kathrin May,† Ralf Stannarius,† Susanne Klein,‡ and Alexey Eremin*,† †
Otto von Guericke University, Institute for Experimental Physics, Department for Nonlinear Phenomena, 39106 Magdeburg, Germany ‡ HP Laboratories, Long Down Avenue, Stoke Gifford, Bristol BS34 8QZ, U.K. ABSTRACT: We report a reversible phase separation phenomenon in nonpolar colloidal suspensions of rod-shaped dichroic pigment particles in an electric field. The voltage− frequency phase diagram features a variety of phases with different morphologies. Single static particle-rich islands, chains of islands, and dynamic patterns were found in this system. We demonstrate that those patterns exhibit complex relaxation dynamics toward the homogeneous field-free state once the external field is removed.
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ray.14,15 Such materials, formed by anisometric dichroic particles, are good candidates for development of display applications. At lower volume fractions ( 0.1 μm−1. Only slow relaxation was found for the island pattern designated as Islands 2, created in a strong low-frequency electric field (Figure 9). This pattern consists of two features: large islands and small ripples. Both features populate in different areas of the reciprocal space and exhibit different relaxation behaviors. Whereas the islands exhibit a linear dispersion relation for 0.1 7072
dx.doi.org/10.1021/la501120k | Langmuir 2014, 30, 7070−7076
Langmuir
Article
Figure 7. Pattern relaxation: (a) Initial pattern of the islands formed in an electric field ( f = 800 Hz, Epp = 6.0 V/μm); (b) Fourier transform of the concentration distribution from part a; (c) radial distributions of concentration u(q) at consecutive times (t = 0 s corresponds to switching the field off).
Figure 8. Relaxation rates Γ(q) as functions of scattering vector measured in 5 wt % samples with different initial states on the E−f diagramm. The pattern created at f = 40 Hz and E = 1.1 V/μm exhibits two relaxation branches.
μm−1 < q < 0.5 μm−1, the relaxation rate of the ripples is proportional to the square of the wavenumber for 1.4 μm−1 < q < 3.7 μm−1. The diffusion constants extracted from the slopes of the Γ(q2) curves are listed in Table 1. Another way to estimate the rate of the homogenization process without using an electric field is to create a heterogeneous particle distribution using a tightly focused IR laser beam. This creates an area of reduced particle concentration in the shape of a circular disc (Figure 10a). The minimal concentration in the center of the disc depends on the exposure time. The radial concentration profile is nearly Gaussian (Figure 10b). ⎛ r2 ⎞ c(r ) = c0 − A exp⎜ − 2 ⎟ ⎝ 2w ⎠
Figure 9. Relaxation rates Γ(q) as functions of scattering vector measured in 5 wt % samples in the phase Islands 2 created at Epp = 12 V/μm and f = 70 Hz: (a) a long-wave linear branch of the relaxation rate Γ(q); (b) both long- and short-wavelength branches Γ(q2). Please note the difference in dependence on q. The straight lines are linear fits of the data.
where c0 is the nonperturbed concentration, w = w(t) is the width of the distribution, and A is the amplitude.
(1) 7073
dx.doi.org/10.1021/la501120k | Langmuir 2014, 30, 7070−7076
Langmuir
Article
w0 2(c0 − cmin(t ) − A) = 4D(c)t (cmin(t ) − c0)
Table 1. Constants of Diffusion for Various Patterns pattern 1. Disordered dynamic (40 Hz, 1.1 V μm−1) 2. Labyrinths (100 Hz, 1.1 V μm−1) 3. Dynamic islands (300 Hz, 2.2 V μm−1) 4a. Islands 2 (70 Hz, 6.0 V μm−1) 4b. Islands 2 (Ripples) (70 Hz, 6.0 V μm−1)
Dfast (μm2 s−1) 1.8 1.5 2.0
Dslow (μm2 s−1)
(2)
The experimental graph of s(t) is shown in Figure 10c. It exhibits a nearly linear dependence with the slope D = 1.89 ± 0.02 μm/s2. This also shows no indication of the dependence if D(c) is in the range of low volume fractions
Electric-Field-Induced Phase Separation and Homogenization Dynamics in Colloidal Suspensions of Dichroic Rod-Shaped Pigment Particles Kathrin May,† Ralf Stannarius,† Susanne Klein,‡ and Alexey Eremin*,† †
Otto von Guericke University, Institute for Experimental Physics, Department for Nonlinear Phenomena, 39106 Magdeburg, Germany ‡ HP Laboratories, Long Down Avenue, Stoke Gifford, Bristol BS34 8QZ, U.K. ABSTRACT: We report a reversible phase separation phenomenon in nonpolar colloidal suspensions of rod-shaped dichroic pigment particles in an electric field. The voltage− frequency phase diagram features a variety of phases with different morphologies. Single static particle-rich islands, chains of islands, and dynamic patterns were found in this system. We demonstrate that those patterns exhibit complex relaxation dynamics toward the homogeneous field-free state once the external field is removed.
■
ray.14,15 Such materials, formed by anisometric dichroic particles, are good candidates for development of display applications. At lower volume fractions ( 0.1 μm−1. Only slow relaxation was found for the island pattern designated as Islands 2, created in a strong low-frequency electric field (Figure 9). This pattern consists of two features: large islands and small ripples. Both features populate in different areas of the reciprocal space and exhibit different relaxation behaviors. Whereas the islands exhibit a linear dispersion relation for 0.1 7072
dx.doi.org/10.1021/la501120k | Langmuir 2014, 30, 7070−7076
Langmuir
Article
Figure 7. Pattern relaxation: (a) Initial pattern of the islands formed in an electric field ( f = 800 Hz, Epp = 6.0 V/μm); (b) Fourier transform of the concentration distribution from part a; (c) radial distributions of concentration u(q) at consecutive times (t = 0 s corresponds to switching the field off).
Figure 8. Relaxation rates Γ(q) as functions of scattering vector measured in 5 wt % samples with different initial states on the E−f diagramm. The pattern created at f = 40 Hz and E = 1.1 V/μm exhibits two relaxation branches.
μm−1 < q < 0.5 μm−1, the relaxation rate of the ripples is proportional to the square of the wavenumber for 1.4 μm−1 < q < 3.7 μm−1. The diffusion constants extracted from the slopes of the Γ(q2) curves are listed in Table 1. Another way to estimate the rate of the homogenization process without using an electric field is to create a heterogeneous particle distribution using a tightly focused IR laser beam. This creates an area of reduced particle concentration in the shape of a circular disc (Figure 10a). The minimal concentration in the center of the disc depends on the exposure time. The radial concentration profile is nearly Gaussian (Figure 10b). ⎛ r2 ⎞ c(r ) = c0 − A exp⎜ − 2 ⎟ ⎝ 2w ⎠
Figure 9. Relaxation rates Γ(q) as functions of scattering vector measured in 5 wt % samples in the phase Islands 2 created at Epp = 12 V/μm and f = 70 Hz: (a) a long-wave linear branch of the relaxation rate Γ(q); (b) both long- and short-wavelength branches Γ(q2). Please note the difference in dependence on q. The straight lines are linear fits of the data.
where c0 is the nonperturbed concentration, w = w(t) is the width of the distribution, and A is the amplitude.
(1) 7073
dx.doi.org/10.1021/la501120k | Langmuir 2014, 30, 7070−7076
Langmuir
Article
w0 2(c0 − cmin(t ) − A) = 4D(c)t (cmin(t ) − c0)
Table 1. Constants of Diffusion for Various Patterns pattern 1. Disordered dynamic (40 Hz, 1.1 V μm−1) 2. Labyrinths (100 Hz, 1.1 V μm−1) 3. Dynamic islands (300 Hz, 2.2 V μm−1) 4a. Islands 2 (70 Hz, 6.0 V μm−1) 4b. Islands 2 (Ripples) (70 Hz, 6.0 V μm−1)
Dfast (μm2 s−1) 1.8 1.5 2.0
Dslow (μm2 s−1)
(2)
The experimental graph of s(t) is shown in Figure 10c. It exhibits a nearly linear dependence with the slope D = 1.89 ± 0.02 μm/s2. This also shows no indication of the dependence if D(c) is in the range of low volume fractions
