Electrostatic torques

ICEP can also contribute to the rotation of polarizable particles with elongated shapes [2, 4, 5, 15], as illustrated in Pig. 2a. It is well known that DEP causes such particles to align with the axis of a uniform field, due to electrostatic torque on the induced dipole. At low AC... 

Electrokinetic Motion of Polarizable Particles, Fig. 3 Experiments on cylindrical silver particles (0.318 pm diameter, 6 pm length) sedimenting in deionized water by gravity alone (a) and in a 100 Hz, 100 V/cm AC field aligned with gravity (b). The experimental distribution of angles in different fields (c) agrees well with theoretical curves (solid) which take into account both ICEP rotation and electrostatic torque [14]... 

This equation can be solved for the electrostatic torque t, by differentiating the capacitance with respect to the mirror tilt angle. The mechanical... 

Since the mirror is supported by two torsion rods, the total mechanical restoring torque x would be x = 2x. The tilt angle 0q as a function of voltage can be found from equating the electrostatic torque to the total mechanical restoring torque x. The pull-in voltage can be found from setting the torques and the slopes of the torques equal, as was done for the parallel plate actuator ... 

Torque generation is a result of a change in electrostatic potential brought about by the ion gradients. 

Ah initio calculations suggest that in ozonolysis, as the two fragments formed by dissociation of the primary ozonide start to move apart, a strong electrostatic attraction builds up between newly formed dipoles.157 The torque created causes a flip of one relative to the other, with formation of a dipolar complex which converts to the secondary ozonide. Thus, the authors suggest that the carbonyl oxide and carbonyl are never actually separated to a van der Waals distance. This argument goes some way to explaining some observed experimental stereoselectivities. 

Colloidal, interparticle interactions (such as electrostatic forces) can apply additional torques to the particles and influence their motion. 

S.L. Price, A.J. Stone and M. Alderton, Explicit formulae for the electrostatic energy, forces and torques between a pair of molecules of arbitrary symmetry, Mol.Phys., 52 (1984) 987-1001. 

Equations [22]-[24] illustrate why the derivation and programming of the forces and torques, and second derivatives for all the terms up to R in the atom-atom multipole expansion of the electrostatic energy is a nontrivial exercise in classical mechanics. It has been described in detail by Popelier and Stone,and, with the additional derivatives required for modeling molecular crystal structures, by Willock et al. ... 

S. L. Price, A. J. Stone, and M. Alderton, Mol. Phys., 52, 987 (1984). Explicit Formulas for the Electrostatic Energy, Forces and Torques Between a Pair of Molecules of Arbitrary Symmetry. 

X. Wang, X-B Wang and P. R. C. Gascoyne, General expressions for dielectrophoretic force and electrorotational torque derived using the MaxweU stress tensor method, J. of Electrostat., 39, 277-295 (1997). 

The gradients (both forces and torques) of the polarization energy in a combined EFP/PCM calculation have been derived and implemented [22]. It is found that all of the energy gradient terms can be formulated as simple electrostatic forces and torques on the induced dipoles and charges as if they were permanent static dipoles and charges, in accordance with the electrostatic nature of these models. Geometry optimizations can be performed efficiently with the analytic... 

Berry, R.M. (1993). Torque and switching in the bacterial flagellar motor. An electrostatic model. Biophys. J. 64, 961-973. 

Elementary electrostatics says that if an object with dipole moment p is placed in an electric field E i), it feels a torque... 

---