Further considerations of non symmetrical dielectric relaxation behaviour arising from a simple empirical decay function

The segmental dynamics of a model miscible blend, C 24 H 50 and C 6 D 14 , were investigated as a function of temperature and composition. The segmental dynamics of the C 24 H 50 component were measured with 13 C nuclear magnetic resonance T 1 and nuclear Overhauser effect measurements, while 2 H T 1 measurements were utilized for the C 6 D 14 component. Use of low molecular weight alkanes provides a monodisperse system in both components and allows differentiation of dynamics near the chain ends. From these measurements, correlation times can be calculated for the C-H and C-D bond reorientation as a function of component, position along the chain backbone, temperature, and composition. At 337 K, the segmental dynamics of both molecules change by a factor of 2 to 4 across the composition range, with the central C-H vectors of tetracosane showing a stronger composition dependence than other C-H or C-D vectors. Molecular simulations in the canonical and isobaric-isothermal ensembles were conducted with a united-atom force field that is known to reproduce the thermodynamic properties of pure alkanes and their mixtures with good accuracy. With a minor change to the torsion parameters, the correlation times for pure tetracosane are in good agreement with experiment. For pure hexane and its mixtures with tetracosane, the simulated dynamics are faster than experiment.

show abstract

“…͑3͔͒, the G(t) function is fit to a modified Kohlrasch-Williams-Watts ͑mKWW͒ equation 26 G͑t ͒ϭAe Ϫ͑t/ KWW ͒ ␤ ϩ͑1ϪA ͒e Ϫt/ 0 , ͑11͒…”

Section: Theory and Simulation Methodsmentioning

confidence: 99%

Segmental dynamics in a blend of alkanes: Nuclear magnetic resonance experiments and molecular dynamics simulation

Budzien

Raphael

Ediger

et al. 2002

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…The coefficients {an} and {ca} appearing in these formulae are to be found in the book by Luke [25]. The accuracy of formula [14] increases as x-0, while the accuracy of formula (15) increases as x-+oo. For x = 3.21, both formulas yield the same accuracy.…”

Section: Ga(z) = Om(a)mentioning

confidence: 99%

“…They originated in a study of observation errors by Cauchy []', and many of their mathematical proper-in terms of stable laws has been inspired by experiments performed by Williams and Watts on polymers [13,14]. Many other examples of such applications to polymers and glasses occur in the literature, cf., for example, the work of Moynihan, Boesch, and Laberge [15] and Bendler [16].…”

Section: Introductionmentioning

confidence: 99%

Stable law densities and linear relaxation phenomena

Dishon¹,

Weiss²,

Bendler³

1985

J. RES. NATL. BUR. STAN.

View full text Add to dashboard Cite

Stable law distributions occur in the description of the linear dielectric behavior of polymers, the motion of carriers in semi-conductors, the statistical behavior of neurons, and many other phenomena. No accurate tables of these distributions or algorithms for estimating the parameters in these relaxation models exist. In this paper we present tables of the functions Q.(Z)= J rea cos(zu)duVa()= e sin(zu)du together with related functional properties of zQa(z). These are useful in the estimation of the parameters in relaxation models for polymers and related materials. Values of the integral Qa(z) are given for a=0.01, 0.02(0.02)0.1(0.1)1.0(0.2)2.0 and those of V(z) are given for a=0.0(0.01)0.l(0.1)2.0. A variety of methods was used to obtain six place accuracy. The tables can be used to sequentially estimate the three parameters appearing in the Williams-Watts model of relaxation. An illustration of this method applied to data in the literature is given.

show abstract

“…1,2 In elastomers and gels, additional viscous dissipation enters due to the network. [3][4][5] As is common for liquid-crystal polymer light-scattering studies, 8,9 correlation functions from homopolymer solutions were fitted to the empirical Williams-Watts function, 10,11 exp(2tC) b where C is the relaxation rate and 0 , b , 1 is a stretching exponent equal to one for purely exponential relaxation. If b is assumed to result from a spectrum of relaxation times, the average relaxation rate ,C. may be calculated 12 from bC/[C 1 (b 21 )], where C 1 denotes the Gamma function.…”

Section: Ps 140 Kg Molmentioning

confidence: 99%

Director dynamics in liquid-crystal physical gels

et al. 2007

View full text Add to dashboard Cite

Nematic liquid-crystal (LC) elastomers and gels have a rubbery polymer network coupled to the nematic director. While LC elastomers show a single, non-hydrodynamic relaxation mode, dynamic light-scattering studies of self-assembled liquid-crystal gels reveal orientational fluctuations that relax over a broad time scale. At short times, the relaxation dynamics exhibit hydrodynamic behavior. In contrast, the relaxation dynamics at long times are nonhydrodynamic, highly anisotropic, and increase in amplitude at small scattering angles. We argue that the slower dynamics arise from coupling between the director and the physically associated network, which prevents director orientational fluctuations from decaying completely at short times. At long enough times the network restructures, allowing the orientational fluctuations to fully decay. Director dynamics in the self-assembled gels are thus quite distinct from those observed in LC elastomers in two respects: they display soft orientational fluctuations at short times, and they exhibit at least two qualitatively distinct relaxation processes.

show abstract

Further considerations of non symmetrical dielectric relaxation behaviour arising from a simple empirical decay function

Cited by 477 publications

References 2 publications

Segmental dynamics in a blend of alkanes: Nuclear magnetic resonance experiments and molecular dynamics simulation

Segmental dynamics in a blend of alkanes: Nuclear magnetic resonance experiments and molecular dynamics simulation

Stable law densities and linear relaxation phenomena

Director dynamics in liquid-crystal physical gels

Contact Info

Product

Resources

About