1,721,094 research outputs found
A Stochastic Model for Crankshaft Transitions
No full textThe model of three coupled rotors is analyzed by solving the corresponding Fokker-Plank equation of Smoluchowski type. From the numerical eigenvalues of the Fokker-Planck operator, the kinetic coefficients for conformational transitions are derived in the presence of bistable potentials for the torsional angles. Besides single-bond transitions through a saddle point of the internal potential, this procedure allows the identification of an anomalous type of kinetic processes, described as transitions of the inner rotor when the outer ones remain almost immobile (or rotate together). Their anomalous character derives from the absence of a saddle point crossing. Because of the localization within the chain, they can be assigned to transitions of crankshaft type. As expected on a qualitative ground, the increase of the friction of the outer rotors favors crankshaft transitions with respect to single-bond transitions. The implications of the model for the observation of crankshaft transitions in molecular systems are discussed in the conclusion
Non-orthogonal basis functions in the solution of diffusional problems
No full textThe diffusion equation in presence of strong potential gradients can be conveniently solved by means of a suitable set of non-orthogonal basis functions that mimic the asymptotic behaviour of the eigensolutions of the time evolution operator. This method is discussed in the context of the calculation of spectroscopic observables by means of the Lanczos algorithm, that is by representing the spectral density as a continued fraction. The modified Lanczos algorithm, which takes into account the non-orthogonality of the basis functions, is analysed in detail. In order to test the performance of the new procedure, the planar rotor subject to a cosine potential is considered, and the set of non-orthogonal functions having the correct asymptotic behaviour is derived in both cases of single and double minimum. The results of the numerical calculations clearly show the advantages of the proposed method when dealing with systems characterized by hindered motions
Coupling of the overall molecular motion with the conformational transitions. II. The full rotational problem
No full textThe method proposed in the companion paper for analysing the coupling between overall and internal dynamics is applied to the study of the full rotational motion of a molecule with one internal degree of freedom. For systems characterized by a finite set of stable conformers determined by the minima of the intramolecular potential, a simplified time evolution operator of mixed type is derived, with the continuous diffusion equation and the generalized random walk operator representing the overall rotation and the internal dynamics, respectively. The dependence on the conformational state of the rotational diffusion tensor is one source of coupling between these two types of motion. Another source is represented by the recoil rotations acting on each subunit during a conformational transition. Both conformational-dependent rotational diffusion tensors and recoil rotations can be calculated from a model for the friction exerted by the solvent. Some applications of the theory are presented in relation to the butane molecule and the molecules having the structure of biphenyl, with particular emphasis on the calculation of the experimental observables in NMR and dielectric relaxation measurements
Typicality in Ensembles of Quantum States: Monte Carlo Sampling versus Analytical Approximations
No full textpeer reviewe
Spectral densities from asymptotic solutions of the Fokker-Planck equation
No full textBy considering Fokker-Planck equation in the asymptotic limit, that is when strong potential act on the particles, a simplified description of its solutions is achievable. The asymptotic behaviour of the Fokker-Planck equation is analyzed for one-dimensional motions in the context of the correlation functions formalism. Much emphasis is placed on the single-minimum potential and analytical relations are derived in all the range of friction, from the zero-friction limit where the process of velocity relaxation is absent, to the diffusional regime. The planar rotator is used as a test case for comparing the asymptotic form of the spectral densities with the numerical solution of the Fokker-Planck operator. By incorporating known results of the theory of activated rate processes, the analysis is extended to multiminima potential
Coupling of the overall molecular motion with the conformational transitions. I. The model sysstem of two coupled rotors
No full textModels based on the neglect of the coupling of the overall molecular rotations with the conformational transitions are normally used to interpret spectroscopic data, like NMR relaxation times or dielectric relaxation spectra of flexible molecules. However, when the mobile parts of the molecule have a comparable size, the effects of such coupling cannot be ignored. A theoretical analysis of the problem is presented for the model system of two coupled rotors whose time evolution is given by a diffusion equation under the influence of the intramolecular potential. When the potential is steep enough to determine stable conformers, an approximate description of the system is obtained in terms of a time evolution operator of mixed type: diffusion motion for the rotation of the overall system and generalized random walk among sites for the internal degree of freedom. The localized functions formalism allows one to generate the approximate time evolution operator without neglect of the coupling, so recovering two important effects: the dependence of the diffusion coefficient for the overall motion on the conformational state, and the recoil rotations of the rods during a conformational transition. The results of the approximate model have been compared with the numerical solutions of the complete diffusion equation, and small deviations on the spectral densities have been found with potential barriers typical of alkyl chains at room temperature
Director reorientation due to dye photoabsorption
No full textThe addition of small quantities of an absorbing dye can modify the optical properties of liquid crystals, in particular by producing a photo-induced torque reorienting the director. Such an effect is modelled by including in the free energy the contribution of dye-solvent electrostatic interactions between the molecular charges and the solvent polarisation. The system evolution is described through the torque acting on the director and the diffusion equations for the orientational distributions of the dye in the ground and the excited states. In the presence of a time scale separation between molecular variables (orientation) and collective properties (director), an explicit relation is derived for the dye photo-induced torque, which appears to be compatible with the experimental findings
Transverse Nuclear Spin Relaxation in Nematic Liquid Crystals. Angular Dependence of the Relaxation Rate in Pulsed Experiments
No full textThe theory underlying the slow-motional description of transverse relaxation in 2H-NMR pulsed experiments, sensitive to order director fluctuations in nematic liquid crystals, is outlined in a comprehensive way in order to highlight the physical parameters which enter the expressions elsewhere derived, to stress the limits of their applicability, and to address those experimental situations which may be more (or less) appealing from the point of view of the extent of information achievable from the analysis of the data. A comparison between fast-motional and slow-motional results is made here, for the first time, in relation to measures performed on samples aligned by the magnetic field
A stochastic model for crankshaft transitions. II Analysis of transition dynamics
No full textThe three-rotor model introduced in part I (J. Phys. Chem. 1996, 100, 16419) displays transitions of crankshaft type between stable states that are not connected by saddle points of the potential. The method of site localizing functions is employed for characterizing the crankshaft process. We show that its rate is controlled by the torsional dynamics near the bifurcations of separatrices originating from the potential maximum. From the analysis of the probability flux, the picture of crankshaft transitions as sequential and concerted crossings of the barrier by two torsional angles is recovered, like in the concerted torsional transitions found in the simulations of polymers. The identification of the separatrix bifurcations leads to an analytical estimate of the crankshaft transition rate. Moreover, it is shown how such an estimate can be generalized to multidimensional stochastic problems, so opening the possibility of analyzing similar types of transitions from realistic models of torsional dynamics in polymers
Roto-translational diffusion in smectic-C liquid crystals
No full textRoto-translational diffusion of uniaxial molecules has been investigated in smectic-C (Sm-C) phases. A modified version of the McMillan mean-field potential has been adopted to describe the tilted monoclinic symmetry of the Sm-C domains with respect to the Sm-A. The roto-translational dynamics have been modeled as a diffusive stochastic process, and the relevant first- and second-rank rotational correlation functions used to describe spectroscopic experiments (dielectric relaxation and magnetic resonance respectively) have been calculated. The model calculations show that some peculiar features of the relaxation processes in Sm-C phases emerge in the comparison of the same observables evaluated for phases with different symmetry, and this could suggest new and specific methods of analysis for the experiments on biaxial smectics
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