1,771 research outputs found
Non-entropic theory of rubber elasticity: flexible chains grafted on a rigid surface
The elastic response is studied of a single flexible chain grafted on a rigid
plane and an ensemble of non-interacting tethered chains. It is demonstrated
that the entropic theory of rubber elasticity leads to conclusions that
disagree with experimental data. A modification of the conventional approach is
proposed, where the end-to-end distribution function (treated as the governing
parameter) is replaced by the average energy of a chain. It is revealed that
this refinement ensures an adequate description of the mechanical behavior of
flexible chains. Results of numerical simulation are compared with observations
on uniaxial compression of a layer of grafted chains, and an acceptable
agreement is shown between the model predictions and the experimental data.
Based on the analysis of combined compression and shear, a novel
micro-mechanism is proposed for the reduction of friction of polymer melts at
rigid walls.Comment: 16 pages, 2 figure
Stiffness of polymer chains
A formula is derived for stiffness of a polymer chain in terms of the
distribution function of end-to-end vectors. This relationship is applied to
calculate the stiffness of Gaussian chains (neutral and carrying electric
charges at the ends), chains modeled as self-avoiding random walks, as well as
semi-flexible (worm-like and Dirac) chains. The effects of persistence length
and Bjerrum's length on the chain stiffness are analyzed numerically. An
explicit expression is developed for the radial distribution function of a
chain with the maximum stiffness.Comment: 21 pages, 6 figure
Non-entropic theory of rubber elasticity: flexible chains with weak excluded-volume interactions
Strain energy density is calculated for a network of flexible chains with
weak excluded-volume interactions (whose energy is small compared with thermal
energy). Constitutive equations are developed for an incompressible network of
chains with segment interactions at finite deformations. These relations are
applied to the study of uniaxial and equi-biaxial tension (compression), where
the stress--strain diagrams are analyzed numerically. It is demonstrated that
intra-chain interactions (i) cause an increase in the Young's modulus of the
network and (ii) induce the growth of stresses (compared to an appropriate
network of Gaussian chains), which becomes substantial at relatively large
elongation ratios. The effect of excluded-volume interactions on the elastic
response strongly depends on the deformation mode, in particular, it is more
pronounced at equi-biaxial tension than at uniaxial elongation.Comment: 21 pages, 3 figure
Scattering function for a self-avoiding polymer chain
An explicit expression is derived for the scattering function of a
self-avoiding polymer chain in a -dimensional space. The effect of strength
of segment interactions on the shape of the scattering function and the radius
of gyration of the chain is studied numerically. Good agreement is demonstrated
between experimental data on dilute solutions of several polymers and results
of numerical simulation.Comment: 16 pages, 7 figure
The end-to-end distribution function for a flexible chain with weak excluded-volume interactions
An explicit expression is derived for the distribution function of end-to-end
vectors and for the mean square end-to-end distance of a flexible chain with
excluded-volume interactions. The Hamiltonian for a flexible chain with weak
intra-chain interactions is determined by two small parameters: the ratio
of the energy of interaction between segments (within a sphere whose
radius coincides with the cut-off length for the potential) to the thermal
energy, and the ratio of the cut-off length to the radius of gyration
for a Gaussian chain. Unlike conventional approaches grounded on the mean-field
evaluation of the end-to-end distance, the Green function is found explicitly
(in the first approximation with respect to ). It is demonstrated
that (i) the distribution function depends on in a regular way,
while its dependence on is singular, and (ii) the leading term in the
expression for the mean square end-to-end distance linearly grows with
and remains independent of .Comment: 39 pages, 1 figur
Thermal degradation and viscoelasticity of polypropylene-clay nanocomposites
Results of torsional oscillation tests are reported that were performed at
the temperature T=230C on melts of a hybrid nanocomposite consisting of
isotactic polypropylene reinforced with 5 wt.% of montmorillonite clay. Prior
to mechanical testing, specimens were annealed at temperatures ranging from 250
to 310C for various amounts of time (from 15 to 420 min). Thermal treatment
induced degradation of the matrix and a pronounced decrease in its molecular
weight. An integro-differential equation is derived for the evolution of
molecular weight based on the fragmentation-aggregation concept. This relation
involves two adjustable parameters that are found by fitting observations. With
reference to the theory of transient networks, constitutive equations are
developed for the viscoelastic response of nanocomposite melts. The
stress-strain relations are characterized by three material constants (the
shear modulus, the average energy for rearrangement of strands and the standard
deviation of activation energies) that are determined by matching the
dependencies of storage and loss moduli on frequency of oscillations. Good
agreement is demonstrated between the experimental data and the results of
numerical simulation. It is revealed that the average energy for separation of
strands from temporary junctions is independent of molecular weight, whereas
the elastic modulus and the standard deviation of activation energies linearly
increase with mass-average molecular weight.Comment: 24 pages and 18 figure
How Long Is a Photon?
An interpretation of an electromagnetic quantum as a single pulse is
suggested. In this context the Planck formula is shown to be equivalent to the
Heisenberg time-energy uncertainty relation. This allows to treat the photon
frequency as an inverse time of emission. Such an ansatz avoids the inherent
problems of the conventional approach.Comment: 6 page
Local Energy Velocity of Classical Fields
It is proposed to apply a recently developed concept of local wave velocities
to the dynamical field characteristics, especially for the canonical field
energy density. It is shown that local energy velocities can be derived from
the lagrangian directly. The local velocities of zero- and first- order for
energy propagation has been obtained for special cases of scalar and vector
fields. Some important special cases of these results are discussed.Comment: 8 Page
A Local Concept of Wave Velocities
The classical characterization of \wp, as a typical concept for far field
phenomena, has been successfully applied to many \w phenomena in past decades.
The recent reports of superluminal tunnelling times and negative group
velocities challenged this concept. A new local approach for the definition of
\wvs avoiding these difficulties while including the classical definitions as
particular cases is proposed here. This generalisation of the conventional
non-local approach can be applied to arbitrary \w forms and propagation media.
Some applications of the formalism are presented and basic properties of the
concept are summarized.Comment: 18 pages 5 figure
Two- and Three-dimensional Generalisation of Lower Order Local Wave Velocities
A general local approach for the definition of velocities and especially
phase velocities for waves recently proposed for one-dimensional waves is
generalized for 2 and 3 dimensional scalar wave. A geometrically consistent
generalization has been found for the local wave velocities of order zero and
one.Comment: 5 page
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