arXiv subjects

A. D. Drozdov

Publications and source records attributed to A. D. Drozdov.

At least 19 recordsLinked to original sources

arXiv2024

Lifetime predictions for virgin and recycled high-density polyethylene under creep conditions

Recycling has become a predominant subject in industry and science due to a rising concern for the environment driven by high production volume of plastics. Replacement of virgin polymers with their recycled analogs is not always possible because recycled polymers cannot met the same property profiles as their virgin counterparts. To avoid deterioration of the mechanical properties, it is proposed to replace a virgin polymer with a recycled polymer of another grade whose characteristics (measured in tensile tests) are close to those of the virgin material. This approach opens a way for the use of recycled polymers in short-term application, but its suitability for long-term applications has not yet been assessed. A thorough experimental investigation is conducted of the mechanical response of virgin high-density polyethylene (HDPE) used for insulation of pipes and recycled HDPE manufactured from post-consumer plastic waste (their stiffness, strength and elongation to break adopt similar values). A model is presented in viscoelastoplasticity of semicrystalline polymers. Its parameters are determined by matching experimental data in short-term relaxation and creep tests. The lifetime of virgin and recycled HDPE under creep conditions is evaluated by means of numerical simulation. It is shown that the stress-time to failure diagrams for virgin and recycled HDPE practically coincide.

cond-mat.mtrl-sci↗

arXiv2022

Rheology of Polydisperse non-Spherical Graphite Particles Suspended in Mineral Oil

We study the role of filler concentration and microphysics on the rheology of polydisperse flake-graphite particles suspended in Newtonian mineral oil. Under steady shear, our samples exhibit shear thinning and yielding behaviour is observed for volume fractions $ϕ> 0.18$. Time-temperature superposition was observed using an Arrhenius-type horizontal shift factor, giving a flow activation energy that is dependent on the graphite volume fraction, suggesting concentration-dependent contributions to relaxation processes in the suspensions. The flow curves are fitted by a constraint-based model, indicating that the flow behaviour is controlled by frictional and adhesive contacts, with the model suggesting that the adhesive stress is temperature dependent.

cond-mat.soft↗

arXiv2005

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 $d$-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.

cond-mat.stat-mech↗

arXiv2004

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.

cond-mat.stat-mech↗

arXiv2004

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.

cond-mat.stat-mech↗

arXiv2004

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.

cond-mat.stat-mech↗

arXiv2004

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 $ε$ 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 $δ$ 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 $ε$). It is demonstrated that (i) the distribution function depends on $ε$ in a regular way, while its dependence on $δ$ is singular, and (ii) the leading term in the expression for the mean square end-to-end distance linearly grows with $ε$ and remains independent of $δ$.

cond-mat.stat-mech↗

arXiv2004

Networks of self-avoiding chains and Ogden-type constitutive equations for elastomers

An expression is derived for the strain energy of a polymer chain under an arbitrary three-dimensional deformation with finite strains. For a Gaussian chain, this expression is reduced to the conventional Moony--Rivlin constitutive law, while for non-Gaussian chains it implies novel constitutive relations. Based on the three-chain approximation, explicit formulas are developed for the strain energy of a chain modeled as a self-avoiding random walk. In the case of self-avoiding chains with stretched-exponential distribution function of end-to-end vectors, the strain energy density of a network is described by the Ogden law with only two material constants. For the des Cloizeaux distribution function, the constitutive equation involves three adjustable parameters. The governing equations are verified by fitting observations on uniaxial tension, uniaxial compression and biaxial tension of elastomers. Good agreement is demonstrated between the experimental data and the results of numerical analysis. An analytical formula is derived for the ratio of the Young's modulus of a self-avoiding chain to that of a Gaussian chain. It is found that the elastic modulus per chain in the Ogden network exceeds that in a Gaussian network by a factor of three, whereas the elastic modulus of a chain with the generalized stretched exponential distribution function equals about half of the modulus of a Gaussian chain.

cond-mat.mtrl-sci↗

arXiv2004

Constitutive equations for a polymer fluid based on the concept of non-affine networks

Constitutive equations are developed for a polymer fluid, which is treated as a permanent network of strands bridged by junctions. The junctions are assumed to slide with respect to their reference positions under loading. Governing equations are derived by using the laws of thermodynamics under the assumption that the vorticity tensor for the flow of junctions is proportional to that for macro-deformation. Explicit expressions are developed for the steady elongational viscosity, as well as for the steady shear viscosity and normal stress functions. To verify the constitutive relations, three sets of experimental data are approximated on polystyrene solutions with various molecular weights. It is demonstrated that the model can correctly describe stress overshoot for the shear stress and first normal stress difference in start-up tests with various strain rates. Adjustable parameters in the governing equations change consistently with the strain rate, molecular weight and concentration of entanglements. To validate the constitutive equations, observations on low-density polyethylene melt in uniaxial extensional flow are compared with the results of numerical analysis when the material constants are found by matching experimental data in shear tests.

cond-mat.mtrl-sci↗

arXiv2003

Linear viscoelasticity of polyolefin melts: the effects of temperature and chain branching

Observations are reported in isothermal torsional oscillation tests on melts of isotactic polypropylene (iPP) and low-density polyethylene (LDPE) in the intervals of temperature between 190 and 250C (iPP) and between 120 and 190C (LDPE). With reference to the concept of transient networks, constitutive equations are developed for the viscoelastic response of polymer melts at three-dimensional deformations with small strains. A melt is treated as an equivalent network of strands bridged by temporary junctions (entanglements and physical cross-links whose life-times exceed the characteristic time of deformation). The time-dependent behavior of the network is modelled as detachment of active strands from their junctions and merging of dangling strands with the network. The network is assumed to be strongly heterogeneous in the sense that different junctions have different activation energies for separation of strands. The stress-strain relations involve three adjustable parameters (the plateau modulus, the average activation 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. The difference in the effects of temperature on the material constants of iPP and LDPE is associated with the difference in their molecular architecture.

cond-mat.mtrl-sci↗

arXiv2003

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.

cond-mat.mtrl-sci↗

arXiv2003

Kinetic equations for thermal degradation of polymers

Kinetic equations are analyzed for thermal degradation of polymers. The governing relations are based on the fragmentation-annihilation concept. Explicit solutions to these equations are derived in two particular cases of interest. For arbitrary values of adjustable parameters, the evolution of the number-average and mass-average molecular weights of polymers is analyzed numerically. Good agreement is demonstrated between the results of numerical simulation and experimental data. It is revealed that the model can correctly predict observations in thermo-gravimetric tests when its parameters are determined by matching experimental data for the decrease in molecular weight with exposure time.

cond-mat.mtrl-sci↗

arXiv2002

The effect of strain rate on the viscoplastic behavior of isotactic polypropylene at finite strains

Two series of uniaxial tensile tests are performed on isotactic polypropylene with the strain rates ranging from 5 to 200 mm/min. In the first series, injection-molded specimens are used without thermal pre-treatment, whereas in the other series, the samples are annealed for 51 h at 160C prior to testing. A constitutive model is developed for the viscoplastic behavior of isotactic polypropylene at finite strains. A semicrystalline polymer is treated as an equivalent heterogeneous network of chains bridged by permanent junctions (physical cross-links and entanglements). The network is thought of as an ensemble of meso-regions connected with each other by links (lamellar blocks). In the sub-yield region of deformations, junctions between chains in meso-domains slide with respect to their reference positions (which reflects sliding of nodes in the amorphous phase and fine slip of lamellar blocks). Above the yield point, sliding of nodes is accompanied by displacements of meso-domains in the ensemble with respect to each other (which reflects coarse slip and fragmentation of lamellar blocks). Stress-strain relations for a semicrystalline polymer are derived by using the laws of thermodynamics. The constitutive equations are determined by 5 adjustable parameters that are found by matching observations. Fair agreement is demonstrated between the experimental data and the results of numerical simulation.

cond-mat.mtrl-sci↗

arXiv2002

A model for anomalous moisture diffusion through a polymer-clay nanocomposite

Experimental data are reported on moisture diffusion and the elastoplastic response of an intercalated nanocomposite with vinyl ester resin matrix and montmorillonite clay filler at room temperature. Observations in diffusion tests show that water transport in the neat resin is Fickian, whereas it becomes anomalous (non-Fickian) with the growth of the clay content. This transition is attributed to immobilization of penetrant molecules on the surfaces of hydrophilic clay layers. Observations in uniaxial tensile tests demonstrate that the response of vinyl ester resin is strongly elastoplastic, whereas an increase in the clay content results in a severe decrease of plastic strains observed as a noticeable reduction of curvatures of the stress--strain diagrams. This is explained by slowing down of molecular mobility in the host matrix driven by confinement of chains in galleries between platelets. Constitutive equations are developed for the anomalous moisture diffusion through and the elastoplastic behavior of a nanocomposite. Adjustable parameters in these relations are found by fitting the experimental data. Fair agreement is demonstrated between the observations and the results of numerical simulation. A striking similarity is revealed between changes in diffusivity, ultimate water uptake and the rate of plastic flow with an increase in the clay content.

cond-mat.mtrl-sci↗

arXiv2002

The elastoplastic response of and moisture diffusion through a vinyl ester resin-clay nanocomposite

Experimental data are reported on the elastoplastic response of and moisture diffusion through a vinyl ester resin-montmorillonite clay nanocomposite with various amounts of filler. Two simple models are developed for the elastoplastic behavior of a nanocomposite and for the anomalous diffusion of penetrant molecules. Adjustable parameters in the constitutive equations are found by fitting the observations. It is revealed that some critical concentration of filler exists (about 1 wt.-%): in the sub-critical region of concentrations, molecular mobility of the host polymer strongly decreases with the clay content, whereas in the post-critical domain, the filler fraction weakly affects mobility of chains.

cond-mat.mtrl-sci↗

arXiv2002

The effect of annealing on the elastoplastic response of isotactic polypropylene

Four series of tensile loading-unloading tests are performed on isotactic polypropylene in the sub-yield domain of deformations at room temperature. In the first series, injection-molded specimens are used as produced, whereas in the other series the samples are annealed for 24 h at 120, 140 and 160 C, which covers the low-temperature region and an initial part of the high-temperature region of annealing temperatures. A constitutive model is developed for the elastoplastic behavior of a semicrystalline polymer. The stress-strain relations are determined by five adjustable parameters that are found by fitting the experimental data. The effect of annealing is analyzed on the material constants.

cond-mat.mtrl-sci↗

arXiv2002

Modelling the linear viscoelastic behavior of silicate glasses near the glass transition point

A model is derived for the viscoelastic response of glasses at isothermal uniaxial deformation with small strains. A glass is treated as an ensemble of relaxing units with various activation energies for rearrangement. With reference to the energy-landscape concept, the rearrangement process is thought of as a series of hops of relaxing units (trapped in their potential wells on the energy landscape) to higher energy levels. Stress-strain relations are developed by using the laws of thermodynamics. Adjustable parameters are found by fitting experimental data in torsional dynamic tests on a multicomponent silicate glass at several temperatures near the glass transition point.

cond-mat.mtrl-sci↗

arXiv2002

The effect of annealing on the elastoplastic and viscoelastic responses of isotactic polypropylene

Observations are reported on isotactic polypropylene (i) in a series of tensile tests with a constant strain rate on specimens annealed for 24 h at various temperatures in the range from 110 to 150 C and (ii) in two series of creep tests in the sub-yield region of deformation on samples not subjected to thermal treatment and on specimens annealed at 140 C. A model is developed for the elastoplastic and nonlinear viscoelastic responses of semicrystalline polymers. A polymer is treated an equivalent transient network of macromolecules bridged by junctions (physical cross-links, entanglements and lamellar blocks). The network is assumed to be highly heterogeneous, and it is thought of as an ensemble of meso-regions with different activation energies for separation of strands from temporary nodes. The elastoplastic behavior is modelled as sliding of meso-domains with respect to each other driven by mechanical factors. The viscoelastic response is attributed to detachment of active strands from temporary junctions and attachment of dangling chains to the network. Constitutive equations for isothermal uniaxial deformation are derived by using the laws of thermodynamics. Adjustable parameters in the stress-strain relations are found by fitting the experimental data.

cond-mat.mtrl-sci↗