Nonlinear dynamics and the problem of polymer fracture

Abstract

SynopsisThe results of the experimental and molecular-dynamics study of the process of mechanical degradation of polymer chain, testifying to the essential role of nonthermal channels of dissipation of elastic energy accumulated during deformation, have been discussed. High-energy molecular products of mechanical degradation, which are able to induce a chain branching process leading to "explosive" formation of submicrocracks, have been discovered. It has been noted that a considerable part of polymer chain energy is concentrated in localized excitations of a soliton type, which play the determining role at all the stages of mechanical degradation under consideration.Deformation and fracture of polymers as well as of other solids are accompanied by complex and little-studied physicochemical processes. One may assume that, a t the stage going immediately after the first act of macromolecule breaking, the elastic energy stored in the macromolecule during its stretching dissipates in the following way:-It leads to electronic excitation and ionization and is carried away by electrons, photons, and ions. -It is spent on the fragmentation of chains and transforms into translational, rotatory, and vibratory energy of molecular products of mechanical degradation.--It transforms into heat including infrared (IR) radiation.Ultimately, the energy of molecular products of mechanical degradation, electrons, ions, and photons also transforms into heat. This may lead to additional IR radiation, thermal degradation, and plastic flow.Theoretical interpretation of mechanical degradation is based on a model of thermal fluctuations,' which takes into account only thermal processes. These characteristic times of elastic energy thermalization are practically assumed to be small so that direct influence of nonthermal effects on mechanical degradation can be neglected. Both experimental data and the results of computer simulation of mechanical degradation of polymer chain by the method of molecular dynamics are discussed in terms of thermal fluctuations.2 At the present time the consistent molecular theory of mechanical degradation has not been available.Two principal questions arise in connection with the development of such a theory. Speaking about thermal fluctuations in solids, one usually bears in mind phonons, which are determined in a harmonic approximation and

Transformations of organic compounds under the action of mechanical stress

“…46,48,49 The decrease in the ionisation potential of molecules subjected to mechanical stresses has been described by quantum-chemical methods. 27,30 Figure 4 shows the calculated plot for the variation of the ionisation potential I as a function of bond angles in the propane molecule. 27 It can be seen that an increase in the deformation of the molecule results in lower I values.…”

Nonlinear dynamics of zigzag molecular chains

“…Although the problem of the linear dynamics of the polyethylene molecule was studied by Kirkwood [43] over half a century ago, its nonlinear extension has only recently become the subject of theoretical analysis [36,37]. The interest was evoked by the recognition of the importance of localized soliton-type nonlinear excitations for the process of mechanical destruction of one-dimensional crystals [44,45]. It turned out that the transition from the rectilinear chain to the transzigzag conformation leads to a qualitative change in the type of the soliton solutions: instead of compression solitons, the role of nonlinear elementary excitations is now played by extension solitons [36,37].…”

Energy exchange, localization, and transfer in nanoscale systems (weak-coupling approximation)

“…The mobility of localized excitations in molecular and polymeric chains determines the microscopic mechanisms of various physical processes, such as structural transitions and fracture [1,2], dielectric and mechanical relaxation [3,4], thermal conduction [5], charge transport in polymers with conjugated bonds [6], and topochemical polymerization [7]. Although the physical nature of these processes is assumed to be different and they are usually treated independently of each other, an asymptotic analysis reveals the underly ing nonlinear elementary excitations of continuous (in the reasonable approximation) nonlinear fields (in the case of polymeric macromolecules) or discrete oscilla tor chains (in the case of oligomers and other nano structures).…”