Torques, dipole

The K quantum number ean not ehange beeause the dipole moment lies along the moleeule s C3 axis and the light s eleetrie field thus ean exert no torque that twists the moleeule about this axis. As a result, the light ean not induee transitions that exeite the moleeule s spinning motion about this axis. 

Taylor series 260 torque, correlation functions 28 transfer time, rotational relaxation 51 transitions dipole moment 30 forbidden 30 non-adiabatic 130 translational velocity v 6... 

Strong nonresonant laser fields affect molecular rotation by exerting an angle-dependent torque on the field-induced molecular dipole [15-20]. The interaction is described by the potential... 

The three-state RIS model of conformer statistics is used to analyze the 16 independent dipole coupling constants measured in a proton NMR study of n-hexane in a nematic liquid crystal solvent. The orientational ordering of the n-hexane molecule is treated in the context of the modular formulation of the potential of mean torque. This formulation gives an accurate description of alkane solute orientational order and conformer probabilities in the nematic solvent. Consequently, substantially more accurate calculated diplar couplings are obtained, and this is achieved without the need to resort to unconventionally high values of the trans-gauche energy difference E(g) in the RIS model. 

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. 

OO distance and the covalent OH bond length, denoted r, are assumed to be fixed. We also assume that a dipole moment p is rigidly connected with a molecule, so its turn on the angle (3 is accompanied by the same turn of the dipole-moment vector from the position p to p (see Fig. 56b). For simplicity we consider rotation of a molecule OBB in a plane. Then the equation of motion under the torque due to stipulated by this force is given by... 

We account for only the torque proportional to the string s expansion AL, which produces the main effect considered in this work. For calculation we employ the spectral function (SF) Lstr(Z), which is linearly connected with the spectrum of the dipolar ACF (see Section II), with Z x Y being the reduced complex frequency. Its imaginary part Y is in inverse proportion to the lifetime tstr of the dipoles exerting restricted rotation. The dimensionless absorption Astr is related to the SF Lstr as... 

Translational motion, i.e. secondary flow lateral to the flow direction, can be achieved by spatially homogeneous or inhomogeneous fields, respectively termed electrophoresis and dielectrophoresis. Rotational motion can be achieved as well, when a dipole is induced and a torque is exerted on that dipole. Then, the rotating entity may be a solid object, e.g. a microsphere, which actively mixes and is not the fluid to be mixed. Such rotating objects generates secondary flow in their vicinity and are described in Section 1.2.2. 

Objects having a dipole can be set into rotational motion by applying a torque by means of an electric field [95], Electrorotation is the rotation of particles as a consequence of the induction of dipole moments and torque exertion by a rotating electric field. Coupled electrorotation (CER) uses static external fields which are spatially fixed to induce dipoles in two or more adjacent particles. This creates oscillating components of the electric field, finally resulting in a rotating electric field (for more details, refer to the original literature [95]). 

Ferraro and coll, used canonical transformation of the Hamiltonian to resolve the average optical rotatory power of a molecule into atomic contributions, based on the acceleration gauge for the electric dipole, and/or the torque formalism [151], This method has been applied to the study of the conformational profile of the optical rotatory poser of hydrogen peroxide and hydrazine [152]. 

Debye obtained his result by solving a forced diffusion equation Ci.e., with torque of the applied field included) for the distribution of dipole coordinate p - pcosS, with 6 the polar angle between the dipole axis and tSe field, and the same result for the model follows very simply from equation (3) using the time dependent distribution function in the absence of the field (5). The relaxation time is given by td = 1/2D, which for a molecular sphere of volume v rotating in fluid of viscosity n becomes... 

In these equations, D is the appropriate rotational diffusion coefficient and 3 = 1/kT results from thermal averaging. The asymmetry of the two responses, given by the second term of the field on expression, clearly results from permanent dipole torques but involves both dipole relaxation with e 1/2 D and polarizability with relaxation time t = 1/6 D = x /3, botE for rotational diffusion. a r... 

The first order effect of L (t) is obtained exactly as in linear response theory and generates the counterpart of terms in (Aa) in eqs 11 and 12. The new problem comes in obtaining the second order effect of the dipole torque operator L (t) for terms in E, as one must then evaluate the consequences of operations of the form... 

A dipole is acted on not only by a force, but also by a torque, in an external field, and this torque is proportional to the field strength rather than to its rate of change with position. The x component of this torque, regarded as a vector, is seen to be... 

Fio. XXII-2.—Illustrating the torque on a dipole in an external force field. 

Any dipolar magnetic field pattern is symmetric with respect to rotations around a particular axis. Hence, it is customary to describe the magnetic dipole moment that creates such a field as a vector with a direction along that axis. The SI units of magnetic moments are thus A m. From Eq. 8.2, the torque experienced by the magnetic moment in the external field is given by the cross product of the magnetic moment and... 

The fonn of y to be used in Nee and Zwanzigfs equation is the true y in the material, and itself depends on e through the viscous torque experienced by a dipole rotating close to a lossy material. The torque N is related to the angular velocity Q either by... 

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