175 research outputs found
Elastic models for the non-Arrhenius viscosity of glass-forming liquids
This paper first reviews the shoving model for the non-Arrhenius viscosity of
viscous liquids. According to this model the main contribution to the
activation energy of a flow event is the energy needed for molecules to shove
aside the surrounding, an energy which is proportional to the instantaneous
shear modulus of the liquid. Data are presented supporting the model. It is
shown that the fractional Debye-Stokes-Einstein relation, that quantitatively
expresses the frequently observed decoupling of, e.g., conductivity from
viscous flow, may be understood within the model. The paper goes on to review
several related explanations for the non-Arrhenius viscosity. Most of these are
also "elastic models," i.e., they express the viscosity activation energy in
terms of short-time elastic properties of the liquid. Finally, two new
arguments for elastic models are given, a general solid-state defect argument
and an Occam's razor type argument
Beta relaxation in the shear mechanics of equilibrium viscous liquids: Phenomenology and network modeling of the alpha-beta merging region
The phenomenology of the beta relaxation process in the shear-mechanical
response of glass-forming liquids is summarized and compared to that of the
dielectric beta process. Furthermore, we discuss how to model the observations
by means of standard viscoelastic modeling elements. Necessary physical
requirements to such a model are outlined, and it is argued that physically
relevant models must be additive in the shear compliance of the alpha and beta
parts. A model based on these considerations is proposed and fitted to data for
Polyisobutylene 680.Comment: 8 pages, 6 figures, Minor correction
The mixed convolved action
A series of stationary principles are developed for dynamical systems by
formulating the concept of mixed convolved action, which is written in terms of
mixed variables, using temporal convolutions and fractional derivatives.
Dynamical systems with discrete and continuous spatial representations are
considered as initial applications. In each case, a single scalar functional
provides the governing differential equations, along with all the pertinent
initial and boundary conditions, as the Euler-Lagrange equations emanating from
the stationarity of this mixed convolved action. Both conservative and
non-conservative processes can be considered within a common framework, thus
resolving a long-standing limitation of variational approaches for dynamical
systems. Several results in fractional calculus also are developed
Dielectric and thermal relaxation in the energy landscape
We derive an energy landscape interpretation of dielectric relaxation times
in undercooled liquids, comparing it to the traditional Debye and
Gemant-DiMarzio-Bishop pictures. The interaction between different local
structural rearrangements in the energy landscape explains qualitatively the
recently observed splitting of the flow process into an initial and a final
stage. The initial mechanical relaxation stage is attributed to hopping
processes, the final thermal or structural relaxation stage to the decay of the
local double-well potentials. The energy landscape concept provides an
explanation for the equality of thermal and dielectric relaxation times. The
equality itself is once more demonstrated on the basis of literature data for
salol.Comment: 7 pages, 3 figures, 41 references, Workshop Disordered Systems,
Molveno 2006, submitted to Philosophical Magazin
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