Rotational diffusion of a tracer colloid particle

Alavi, F.N.; Jones, Robert B.

doi:10.1016/0378-4371(90)90190-4

Cited by 3 publications

(4 citation statements)

References 8 publications

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“…The dynamics of the orientational relaxation, on the other hand, now depends critically on the detailed shape of the external potential V (u). For the case of permanent dipoles in an external field, well-known from Debye relaxation [2] in polar fluids, the experimentally accessible time auto-correlation functions of u(t) can be calculated analytically for small field strengths [3]. They show significant departures from exponential behavior, eventually approaching a finite non-zero value at long times which reflects the non-isotropic orientational distribution in thermal equilibrium.…”

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“…If the colloids possess optical anisotropy, e.g., due to intrinsic birefringence or shape birefringence, these orientational fluctuations can be probed by depolarized quasielastic light scattering [1]. For isolated, freely rotating spherical particles in the limit of high solvent viscosity η, the rotational part of the field auto-correlation function g (1) VH (t) = E * VH (0)E VH (t) / |E VH | 2 of the scattered depolarized electric field E VH (t) decays exponentially with time t; the corresponding decay rate is proportional to the rotational diffusion constant D r = k B T /(8πηR 3 ), where k B T is the thermal energy and R is the particle radius.…”

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“…This unexpected decrease is indeed predicted by the second-order perturbation theory for |m| = 1 in eq. (3).…”

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Rotational diffusion in a bistable potential

et al. 2002

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Abstract. -Using depolarized quasielastic light scattering, we have investigated the rotational diffusion of optically anisotropic colloidal particles in a dilute suspension subject to external electric and magnetic fields (E0, B0). The particles were produced by the polymerization of nematic liquid crystal droplets, leading to birefringent colloidal spheres whose frozen orientational order is rigidly coupled to the particle orientation. The torque on the droplet director u(t) originating from the coupling of E0 and B0 to the particles' anisotropy in the refractive index and in the diamagnetic susceptibility, respectively, leads to a suppression of the orientational fluctuations about the direction of the external field. We observe a strong dependence of the measured relaxation rates on the field strength and on the orientation of the field relative to the scattering plane. We explain our findings by a solution of the Smoluchowski equation describing rotational diffusion in a bistable potential V (u) which has two equivalent minima separated by a potential barrier whose height is proportional to (E0, B0) 2 .Colloidal particles in a solvent do not only experience random forces due to the collisions with the surrounding molecules, but are also imparted random torques that lead to fluctuating particle orientations described by a unit vector u(t) also called particle director. If the colloids possess optical anisotropy, e.g., due to intrinsic birefringence or shape birefringence, these orientational fluctuations can be probed by depolarized quasielastic light scattering [1]. For isolated, freely rotating spherical particles in the limit of high solvent viscosity η, the rotational part of the field auto-correlation function g 2 of the scattered depolarized electric field E VH (t) decays exponentially with time t; the corresponding decay rate is proportional to the rotational diffusion constant D r = k B T /(8πηR 3 ), where k B T is the thermal energy and R is the particle radius.This simple situation changes completely when the rotational symmetry is broken by an external field (such as an electric or magnetic field) that couples to permanent or induced (electric or magnetic) dipoles localized on the particle. The orientational distribution then develops a peak around the direction of the external field, and, consequently, the amplitudes

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Rotational diffusion in a bistable potential

et al. 2002

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“…The orientational correlation function is usually fitted by a Kohlrausch–Williams–Watt (KWW) function − with the stretching parameter β = 1. For interacting dipoles, , this function can be analyzed using a double relaxation time approximation, which contains the one-body (self) and the two-body (pair interaction) parts C ( t ) = A C normals ( t ) + B C normalp ( t ) …”

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Temperature-Dependent Rotational Dipole Mobility and Devitrification of the Rigid Amorphous Fraction in Unpoled and Poled Biaxially Oriented Poly(vinylidene fluoride)

et al. 2022

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In addition to the pronounced ferroelectric property from polar crystalline phases, poly(vinylidene fluoride) (PVDF) and its random copolymers also exhibit high dielectric permittivities as a result of highly mobile dipoles in the amorphous phase. In this study, we developed a new theoretical approach to determine the dipole concentration, dipole moment, dipole−dipole interaction, and rotational dipole mobility for PVDF by means of broadband dielectric spectroscopy. From the permittivity of molten PVDF, the Kirkwood−Froḧlich g-factor and its temperature dependence were determined and used as global parameters for the simulation of unpoled and highly poled biaxially oriented PVDF (BOPVDF). It was found that the concentration of active dipoles substantially increased as the temperature was increased from −30 to 40 °C, indicative of the devitrification of the rigid amorphous fraction (RAF). Both the calculated dipole moment and the g-factor of poled BOPVDF were higher than those of unpoled BOPVDF, resulting in a higher permittivity and piezoelectric performance. In addition, the dipole−dipole interaction was found to increase substantially upon increasing the temperature from −30 to 40 °C, leading to an increase of over 4 orders of magnitude in the rotational dipole mobility. This was direct evidence for the devitrification of the RAF in both unpoled and poled BOPVDF.

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