Vibration analysis of a disordered polymer chain

A variational method is used to make a numerical calculation of the vibrations of a disordered polymer chain. A curve is constructed for the square of the frequency and the parameters of the trial function as functions of the mean phase difference between neighboring atoms. The results are compared for three forms of the distribution function for the force constants and, moreover, for two variants of the variational method and the direct calculation for a finite chain.Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 771–776, September–October, 1971.     

Free vibrations of a cantilevered plate with a polymer coating

The article considers some of the special characteristics of the free vibrations of a steel cantilevered plate, with the formation of a polymer coating on the plate. It compares the results of an experimental investigation of the effect of internal stresses in the coating on the vibrations and on the static bending of the plate. It demonstrates the possibility of determining the internal stresses in the coating from the change in the frequency of the natural vibrations of a plate with a coating.Institute for the Mechanics of Metal-Polymer Systems, Academy of Sciences of the Belorussian SSR, Gomel'. Translated from Mehanika Polimerov, No. 3, pp. 541–544, May–June, 1970.     

Dynamic method of determining the mechanical characteristics of the surface layer of polymers

A thin polymer film is treated as a three-layered plate, the inner layer being characterized by the bulk and the outer layers by the surface properties of the polymer. Using the equations describing the vibrations of a cantilever element of rectangular section, the authors propose formulas for the thickness, modulus of elasticity, and mechanical loss factor of the surface layer. The mechanical characteristics of the surface layers of PMM and nitrocellulose have been determined by electromagnetically exciting and photometrically recording vibrations in film specimens of varying thickness.Institute of the Chemistry of High-Molecular Compounds, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 3, pp. 548–550, May–June, 1969.     

A new method of measuring the viscoelastic properties of polymer systems in fluid and highly elastic states using forced vibrations in the ultralow-frequency region

A method is considered for measuring the dynamic mechanical characteristics of polyer systems using forced vibrations in the ultralow-frequency region down to 10^–6 Hz. The essence of this method lies in the fact that during the measurement process the motion of the polymer sample is controlled with a set amplitude and frequency, and the dynamic characteristics of the polymer are determined from the controlling mechanical stress. The method is illustrated using the results of measurements of the components of the complex modulus for polybutadiene over a wide range of temperatures and frequencies without making use of superimposition.The Central Constructional Bureau for Prototype Instrument Construction, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 344–347, March–April, 1976.     

Investigation of the natural vibrations of plates made of composite materials with the help of the finite-element method

The modes and frequencies of small natural vibrations in a cavity of thin plates are investigated on the basis of the method of finite elements in displacements. The effect of the rigidity characteristics of a material on the natural frequencies and modes of vibrations of flat cantilever vanes whose tapered edge is restrained is studied. An example is given of the use of the finite-element method to determine the natural vibrations of an orthotropic plate in the shape of an airplane wing. Quadrangular and modified triangular bending finite elements are used to simulate a continuous system. A mass-element matrix is constructed on the basis of a four-term ("contracted") polynomial determining the deflection that permits a significant reduction of the order of the solving system.Translated from Mekhanika Polimerov, No. 2, pp. 284–288, March–April, 1976.     

Multiphoton transitions of a bound electron interacting with anN-dimensional oscillator

Multiphoton transitions of a bound electron interacting with anN-dimensional oscillator are considered. Allowance is made for excitation of the oscillator by an external electromagnetic field and for the mixing of the molecular normal vibrations when a quantum transition occurs (Dushinsky effect). An exponential dependence of electron transition rate on the parameters of the mixing of the molecular vibrations is established. The theory is compared with experiment for the example of the SO₂ molecule.Institute of Applied Physics, Moldavian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 1, pp. 138–147, January, 1992.     

Electronic-mechanical equipment for investigating polymer vibrocreep

Equipment built at the Institute of Polymer Mechanics, AS Latvian SSR, for investigating the effect of vibrations on the creep of unreinforced polymer materials is described. The equipment can be used to conduct creep tests on tubular specimens in biaxial tension with the vibration superimposed in the direction of the longitudinal axis of the test piece.Mekhanika Polimerov, Vol. 4, No. 2, pp. 372–375, 1968     

Estimation of the length distribution of through polymer chains

The contributions of entropy and elastic forces to the tensile modulus of a polymer chain are estimated. The chain length-distribution function in the amorphous region of highly oriented Lavsan is approximately determined from macroscopic stress-strain dependence. It is found that the length distribution has a width of the order of several percent of the length of the amorphous region of the fibril.A. F. Ioffe Physicotechnical Institute, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 922–925, September–October, 1974.     

Propagation of large-amplitude low-frequency vibrations in polymer melt flows

The propagation of low-frequency periodic pressure pulses along an isothermal stationary flow of various polymer melts in a flat channel of finite length has been experimentally and theoretically investigated. It is shown that as a result of the wave character of the process there is a phase shift between the pressure vibrations at various points along the length of the channel, while the amplitudes of the pressure vibrations decrease along the flow in accordance with a nonlinear law. Analysis of the problem leads to the establishment of a relation between the characteristics of the wave process, the properties of the medium, and the channel geometry.Moscow Institute of Chemical Machine Building. Institute of Problems of Mechanics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 493–500, May–June, 1976.     

Effect of small vibrations on cracking kinetics in polymethyl methacrylate. Concept of a rate-dependent cracking resistance. Possible thermal mechanism

Conclusions 1. Small vibrations superposed on the main static component of an external load cause the cracking rate in polymethyl methacrylate to increase appreciably. Within the range of low cracking rates (<10^–4 cm/sec), evidently most important from the practical standpoint, the cracking resistance of this material is also found to decrease.2. The concept of a rate-dependent cracking resistance applies to conditions under a vibration load, over a wide range of vibrations at low or intermediate cracking rates.3. The effect of small vibrations is local in nature. It may have to be taken into account, if cracks or similar defects already exist in a structure or appear in it during service.4. The thermal mechanism is not adequate for quantitatively describing the experimentally observed effect of vibration.Paper presented at the Third All-Union of Conference on Polymer Mechanics in Riga, 1976.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 5, pp. 846–853, September–October, 1977.     

Mechanics of the static tension of a through chain in amorphous crystalline polymers

The displacements and tensions of the points on a through chain lying inside one crystallite of an oriented amorphous crystalline polymer are analyzed theoretically for various degrees of withdrawal of the chain from the crystallite. The tension of the chain in the amorphous region is examined as a function of its contour length and the length of the amorphous region. The nature and efficiency of the stoppers (obstacles) retaining the through chain inside the crystallites are considered. Specific results are calculated for polyethylene and polypropylene.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 771–778, September–October, 1973.     

Origin of laser damage in transparent dielectrics of the plexiglas type

A gasification mechanism is proposed. This mechanism is based on multiphoton photodegradation of the polymer molecules and the resulting formation of free radicals which trigger a chain reaction and the subsequent formation of gas molecules. The kinetics of this process, in which an important part is played by the microstructure of the material, are examined.Institute of Problems of Mechanics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 232–238, March–April, 1973.     

Solution of some dynamic problems of viscoelasticity theory by the averaging method

Damping of longitudinal vibrations of a viscoelastic bar and transverse vibrations of a freely supported orthotropic plate is investigated by the averaging method. The problem of the forced movement of a viscoelastic cylinder enclosed in a thin elastic shell under the effect of an arbitrarily time-varying internal pressure is studied.Institute of Cybernetics at the Computer Center Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Mekhanika Polimerov, No. 2, pp. 246–252, March–April, 1970.     

Study of the role of intermolecular interactions (hydrogen bonds) in the initial stage of orientation of polyvinyl alcohol and vinyl alcohol copolymers

The effect of hydrogen bond rupture on the process of destruction of the starting crystallite structure of polyvinyl alcohol and copolymers of vinyl alcohol and N-vinylpyrrolidone and -vinylcaprolactam has been investigated. The differential spectrum method is used to establish the frequency (3200 cm^–1) of the band corresponding to the vibrations of the bound hydroxyl groups; the temperature dependence of the optical density of the 3200 cm^–1 band has been recorded. The strength of the starting structure is calculated from the stress-strain diagram and its temperature dependence is plotted. It is concluded that the strength of the starting structure is chiefly determined by the presence of hydrogen bonds between the polymer macromolecules.Leningrad Kirov Institute of Textile and Light Industry. Translated from Mekhanika Polimerov, No. 2, pp. 327–329, March–April, 1971.     

Investigation of the mechanical properties of polymer surface layers using surface waves

It is possible to excite ultrasonic surface waves at the surface of polymer materials and to determine the dependence of the wave parameters on the mechanical properties of the surface. The nature of the variation of the surface wave characteristics with material, temperature, and the frequency of the exciting vibrations has been established.Mekhanika Polimerov, Vol. 3, No. 5, pp. 933–939, 1967     

Effect of a mechanical field on polymer crystallization morphology

Crystallization carried out in the presence of shear or tensile stresses in the melt or solution leads to the formation of unusual morphological forms — flattened spherulites, structures of the shish kebab type, "skew" crystals, etc. A thermodynamic analysis of the kinetics and morphology of spherulite growth makes it possible to explain the spherulite flattening effect and obtain an expression relating the shape of the spherulite and the stress characteristics. By taking into account the changes in the configuration entropy of the deformed polymer chain during the formation of a folded-chain crystal it is possible to gain a better understanding of the spherulite flattening effect and describe the mechanism of skew crystal formation. A relation is obtained between the optimum angle of orientation of the c axis relative to the direction of the applied stress and such macroscopic parameters as the crystallinity. A general picture of the effect of a mechanical field on the morphology of crystallizing polymers in various stages of extension is proposed.Institute of Macromolecular Compounds, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 6, pp. 963–970, November–December, 1970.     

Molecular mechanism of orientation in polymers

On the basis of calculations in which the behavior of the chain under load is investigated, it is suggested that, apart from the rotational isomerism mechanism, at low temperatures and high stresses the instability of the folded configuration may play an important part in polymer orientation. A distinctive feature of the proposed mechanism is the high rate of orientation, which for an isolated chain is of the order of the speed of sound.T. G. Shevchenko Kiev State University. Translated from Mekhanika Polimerov, No. 3, pp. 525–528, May–June, 1976.     

Calculation of damage and of force relaxation in amorpho-crystalline polymers

The dynamics of damage and of the relaxing force in amorpho-crystalline polymers under constant strain are calculated using the formulas for the probability of rupture of a deformed polymer molecule and a model representation of amorphous interlayers. The main parameters of the model are the maximum and minimum possible deformations of molecular chains, the energy of rupture activation, the function of the chain length distribution, the temperature, the macroscopic strain, and the relative dimensions of the amorphous interlayer. The conformity of the theoretical model and the association of the relaxation spectrum with the internal molecular and structural characteristics of the material are established.Zhambyl Technical Institute of Light and Food Industry, Taraz, Kazakhstan. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 499–508, July–August, 1999.     

An infrared spectroscopic study of the breakdown of polymers under load

It has been found that when a uniaxial tension is applied to highly oriented polymer films of polypropylene, polyvinyl alcohol, or polyethylene, an increase in the intensity of the absorption bands corresponding to the vibrations of the C=O carbonyl groups is observed. These groups are produced by the oxidation of the free radicals formed on the rupture of the chemical bonds under the influence of mechanical stress. The composition of the products has been studied, and their concentration has been estimated. Curves giving the accumulation of C=O groups with time at constant load and with increase in stress for a fixed period of time under load have been studied. It is suggested that the rate of accumulation of C=O groups in both cases is determined chiefly by the rate of rupture of the molecular chains under load.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 433–436, May–June 1970.     

Effect of external pressure on the physicochemical and mechanical properties of polymers

The behavior of crystalline polymers obtained by molding at high pressures has been investigated. External pressure can promote or retard polymer crystallization processes, depending on its intensity. Comparison of various physicochemical and mechanical properties of specimens obtained at different external pressures shows that the corresponding curves have two maxima: one at 200–800 kgf/cm² and another on the narrower interval between 1300 and 1500 kgf/cm². The position of the first maximum is associated with the molecular weight distribution and the flexibility of the polymer chain, and position of the second is determined by the chemical nature of the polymer. The data obtained help to make possible a rational choice of polymer processing methods in which pressure is involved.Mekhanika Polimerov, Vol. 4, No. 2, pp. 200–204, 1968