1,721,015 research outputs found
A memory-function approach to the angular correlation functions in anisotropic liquids
No full textA memory-function approach based on the Mori theory is used to test the validity of the extended diffusion equation commonly adopted to calculate angular correlation functions in partially oriented liquids. It is shown that the two methods give the same results, under the assumption of no correlation between angular variables and angular velocities, as far as the long-range terms of the intermolecular potential responsible for the orientational order are significantly smaller than the short-range terms which determine the magnitude of the friction tensor in the isotropic phase. This implies that the extended diffusion equation can give a reasonably accurate description of the rotational motion of the molecules in liquid crystals even at moderately high values of the orientational torque
On the assessment of molecular chirality
No full textA property termed helicity tensor, defined on the basis of the molecular shape, is proposed to quantify the chirality of arbitrary molecules. Numerical implementation of the model can be easily done, once the molecular geometry is known. The principal components of the tensor represent helicities of the molecular surface as viewed along the three perpendicular axes. Results are presented for a number of systems, going from asymmetrically substituted methane derivatives to complex helicoidal structures. Although originally derived to predict the twisting power of chiral probes dissolved in liquid crystal solvents, the concept of helicity tensor provides a useful tool for many applications of molecular engineering
Rotational diffusion in cubic fields
No full textThe method of the localized functions, introduced to relate the results of the full diffusional problems to those of phenomenologic random jump models, is adapted to the case of rotational diffusion in environments of cubic symmetry. Applications of the method to the description of dynamical effects occurring in orientationally disordered molecules in crystal lattices are also discussed
Diffusion between inequivalent sites
No full textThe use of localized functions is extended to obtain master equations for random walk processes among non equivalent sites, starting from a diffusional equation that includes a mean force potential. As a numerical application, the kinetic parameters are calculated for a collection of rotors in asymmetric double-minimum potentials, and for the trans-gauche isomerization of butane. These examples show that the transition rates and their Arrhenius behaviour are computed by projecting the diffusion operator onto a function set whose dimension is equal to the number of potential minima
Diffusion models for the dynamics of flexible molecules
No full textA theoretical analysis based on a multivariate diffusion equation is developed to study the rotational and internal dynamics of molecules undergoing conformational changes in liquid and liquid-crystalline phases. Numerically exact solutions are obtained for the case of a single degree of freedom, while for more complex systems a rotational isomeric state approximation, in connection with a Kramers procedure generalized to multidimensional problems, is adopted to treat the torsional variables. Hydrodynamic models including interactions between centres of frictional resistance are used to compute diffusion tensors, and 'size and shape' models are derived to account for the torques exerted by anisotropic environments on the flexible molecules. Torsional potential profiles are selected from experimental data or structural calculations. The effects resulting from coupling between internal and rotational motions and from recoils following configurational jumps, as well as the features of the saddle-point crossings, are discussed in detail. The analysis is applied to molecular systems exhibiting conformational processes in the ground or in the excited state, to typical mesogenic moieties characterized by flexible chains, and to phospholipid model membranes
Dynamical behavior of solutes in smectics
No full textThe full diffusion equation is solved for solutes in smectic phases, subjected to McMillan-type potentials. We then discuss the effects of the roto-translational coupling induced by the potential on the diffusion parameters measured by field gradient NMR and on the spectral density functions inferred from magnetic resonance relaxation experiments
Charge transfer dynamics in photophysical systems: A case of saddle point avoidance
No full textThe simple bidimensional model of a reactive coordinate coupled to a harmonic mode is known to display varied dynamical behaviour, due to the interplay of energetic and frictional factors. Molecular systems which exhibit the photophysical process of intramolecular charge transfer generally are characterized by an internal coordinate coupled to the solvent polarization. They therefore provide an appealing application of the dynamic model, by identifying a solute variable with an intrinsic timescale tau(R), and a macroscopic solvent variable with relaxation time tau(S). In this paper, a theoretical analysis based on a bidimensional diffusion equation suggests that time-dependent Stokes shifts observed in system undergoing intramolecular charge transfer processes may provide evidence of a kinetic pathway which implies saddle point avoidance
Diffusive and jump description of hindered motions
No full textSite jump models are often used to interpret spectroscopic effects of molecular motions occurring in the presence of potential wells. Continuous diffusion equations, albeit complex to handle, are expected to give a more detailed picture of the dynamics and to provide molecular interpretation of the kinetic parameters. In the paper we show how the results of random walk models can be recovered from the correct solutions of the diffusion equations. To this purpose, two routes are followed. First, a procedure is developed for the exact calculation of the time integral of pertinent correlation functions, to be compared with the time constant for the kinetic process of interest. Secondly, the asymptotic solutions of the diffusion equations, valid in the limit of high potential gradients, are used to derive ‘localized functions’, which lead quite naturally to master equations for jumps among discrete sites. Rotational diffusion in uniaxial liquid crystals, translational motions across smectic layers, hindered internal motions and conformational changes are considered as physical examples of relevant experimental interest
Orientation-Dependent Friction in Liquid Crystals
No full textThe meaning of the rotational friction and diffusion tensor in Liquid crystalline phases characterized by anisotropic viscosities is discussed, by generalizing the hydrodynamic Stokes-Einstein relationships. Corrections due to the viscosity anisotropy effects to the rotational correlation times, relevant for the interpretation of magnetic and dielectric relaxation experiments, have been computed by solving the appropriate Fokker-Planck equation
Extended Fokker-Planck model for molecular rotations in liquids
No full textExtended Fokker-Planck (FP) equations are generalized stochastic equations which describe the evolution of a set of coordinates, loosely referred to as solute, coupled with a relevant set of solvent variables. The applicational range of multidimensional stochastic operators is wide. In this paper we focus attention on model ''liquid'' systems. We discuss the effect of various kinds of cage degrees of freedom on the relaxation of orientational and angular momentum correlation functions of a probe molecule, for a model liquid composed of planar rotating dipoles interacting via a cosine potential. The results of numerically exact and asymptotic solutions of FP equations are used to interpret the dynamic behaviour of polar liquids in the frequency regions of dielectric relaxation and far-infrared absorption
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