1,264 research outputs found
Enthalpy recovery in semicrystalline polymers
Constitutive equations are derived for enthalpy recovery in polymeric glasses
after thermal jumps. The model is based on the theory of cooperative relaxation
in a version of the trapping concept. It is demonstrated that some critical
temperature and some critical degree of crystallinity exist above which the
energy landscape becomes homogeneous and structural relaxation ceases.Comment: 13 pages, 5 figures, LATE
Modelling structural relaxation in polymeric glasses using the aggregation-fragmentation concept
Governing equations are derived for the kinetics of physical aging in
polymeric glasses. An amorphous polymer is treated as an ensemble of
cooperatively rearranged regions (CRR). Any CRR is thought of as a string of
elementary clusters (EC). Fragmentation of the string may occur at random time
at any border between ECs. Two string can aggregate at random time to produce a
new string. The processes of aggregation and fragmentation are treated as
thermally activated, and the rate of fragmentation is assumed to grow with
temperature more rapidly than that for coalescence. This implies that only
elementary clusters are stable at the glass transition temperature, whereas
below this temperature, CRRs containing several ECs remain stable as well. A
nonlinear differential equation is developed for the distribution of CRRs with
various numbers of ECs. Adjustable parameters of the model are found by fitting
experimental data in calorimetric tests for polycarbonate, poly(methyl
methacrylate), polystyrene and poly(vinyl acetate). For all materials, fair
agreement is established between observations and results of numerical
simulation. For PVAc, the relaxation spectrum found by matching data in a
calorimetric test is successfully employed to predict experimental data in a
shear relaxation test.Comment: 25 pages, 15 figure
Modeling the viscoelastoplastic response of amorphous glassy polymers
Constitutive equations are derived for the viscoelastoplastic response of
amorphous glassy polymers at isothermal loading with small strains. A polymer
is treated as an ensemble of cooperatively relaxing regions (CRR) which
rearrange at random times as they are thermally agitated. Rearrangement of CRRs
reflects the viscoelastic response of the bulk medium. At low stresses, CRRs
are connected with each other, which implies that the macro-strain in a
specimen coincides with micro-strains in individual relaxing regions. When the
average stress exceeds some threshold level, links between CRRs break and
relaxing domains begin to slide one with respect to another. Sliding of
micro-domains is associated with the viscoplastic behavior of polymers. Kinetic
equations are proposed for viscoplastic strains and for the evolution of the
threshold stress. These equations are validated by comparison with experimental
data in tensile relaxation tests and in tests with constant strain rates. Fair
agreement is demonstrated between results of numerical simulation and
observations for a polyurethane resin and poly(methyl methacrylate).Comment: 19 pages, 12 figure
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
A tube concept in rubber viscoelasticity
A constitutive model is derived for the time-dependent response of
particle-reinforced elastomers at finite strains. An amorphous rubbery polymer
is treated as a network of long chains linked by permanent junctions (chemical
crosslinks, entanglements and filler particles). A strand between two
neighboring junctions is thought of as a sequence of mers whose motion is
restricted to some tube by surrounding macromolecules. Unlike the conventional
approach that presumes the cross-section of the tube to be constant, we
postulate that its radius strongly depends on the longitudinal coordinate. This
implies that a strand may be modeled as a sequence of segments whose thermal
motion is totally frozen by the environment (bottle-neck points of the tube)
bridged by threads of mers which go through all possible configurations during
the characteristic time of a test. Thermal fluctuations affect the tube's
radius, which results in freezing and activation of regions with high molecular
mobility (RHMs). The viscoelastic response of an elastomer is associated with
thermally activated changes in the number of RHMs in strands. Stress-strain
relations for a rubbery polymer at finite strains and kinetic equations for the
concentrations of RHMs are developed by using the laws of thermodynamics. At
small strains these relations are reduced to the conventional integral
constitutive equation in linear viscoelasticity with a novel scaling law for
relaxation times. The governing equation is determined by 5 adjustable
parameters which are found by fitting experimental data in tensile dynamic
tests on a carbon black filled natural rubber vulcanizate.Comment: 28 pages, 14 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
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