Temperature Dependence of Dynamic Properties of Elastomers. Relaxation Distributions

1952 ◽  
Vol 25 (4) ◽  
pp. 720-729 ◽  
Author(s):  
John D. Ferry ◽  
Edwin R. Fitzgerald ◽  
Lester D. Grandine ◽  
Malcolm L. Williams
Keyword(s):  
Distribution Function ◽  
Temperature Dependence ◽  
Dynamic Properties ◽  
Relaxation Times ◽  
Dynamic Mechanical Properties ◽  
Relaxation Processes ◽  
The Real ◽  
Reduced Frequency ◽  
Dynamic Rigidity ◽  
Composite Curve

Abstract By the use of reduced variables, the temperature dependence and frequency dependence of dynamic mechanical properties of rubberlike materials can be interrelated without any arbitrary assumptions about the functional form of either The definitions of the reduced variables are based on some simple assumptions regarding the nature of relaxation processes. The real part of the reduced dynamic rigidity, plotted against the reduced frequency, gives a single composite curve for data over wide ranges of frequency and temperature; this is true also for the imaginary part of the rigidity or the dynamic viscosity. The real and imaginary parts of the rigidity, although independent measurements, are interrelated through the distribution function of relaxation times, and this relation provides a check on experimental results. First and second approximation methods of calculating the distribution function from dynamic data are given. The use of the distribution function to predict various types of time-dependent mechanical behavior is illustrated.

scholarly journals The Dynamic Properties of 5Cb Filled with Aerosil Particles Investigated by Pcs

1999 ◽  
Vol 559 ◽  
Author(s):  
F.M. Aliev ◽  
M. Kreuzer ◽  
Yu.P. Panarin
Keyword(s):  
Liquid Crystal ◽  
Temperature Dependence ◽  
Relaxation Process ◽  
Nematic Liquid Crystal ◽  
Broad Spectrum ◽  
Dynamic Properties ◽  
Relaxation Times ◽  
Correlation Spectroscopy ◽  
Relaxation Processes ◽  
Optoelectronic Application

ABSTRACTNematic liquid crystal filled with Aerosil particles, a prospective composite material for optoelectronic application, has been investigated by static light scattering and Photon Correlation Spectroscopy (PCS). The Aerosil particles in filled nematic liquid crystals (FN) form a network structure with LC domains about 2500 Å in size with a random distribution of the director orientation of each domain.We found that the properties of 5CB are considerably affected by the network. The N-I phase transition in filled 5CB was found to be smeared out and depressed. PCS experiments show that two new relaxation processes appear in filled 5CB in addition to the director fluctuation process in bulk. The slow relaxation process, with a broad spectrum of relaxation times, is somewhat similar to the slow decay, which is observed in confined nematic liquid crystal.The middle frequency process was assigned to the director fluctuations in the surface layer formed at the particle-LC interface. The decay function describing this relaxation process is a stretched exponential (β ≍ 0.7). The temperature dependence of the relaxation times of the middle frequency obeys the Vogel-Rilcher law. Such a temperature dependence, accompanied by a broad spectrum of relaxation times suggests that the dynamics of the director fluctuations near the Aerosil particle-LC interface is glass-like.

High-Temperature Dielectric Properties of Goethite From 400 to 3000 MHz

2005 ◽  
Vol 20 (1) ◽  
pp. 18-29 ◽  
Author(s):  
C.A. Pickles ◽  
J. Mouris ◽  
R.M. Hutcheon
Keyword(s):  
Dielectric Properties ◽  
Thermogravimetric Analysis ◽  
Perturbation Technique ◽  
Relaxation Times ◽  
Relaxation Processes ◽  
Heating Rates ◽  
Hydrogen Atoms ◽  
Debye Relaxation ◽  
The Real ◽  
Thermally Activated

The dielectric properties of goethite and, in particular, the changes during the topotactic conversion of goethite to hematite were studied from room temperature to about 800 °C in the frequency range of 400 to 3000 MHz using the cavity perturbation technique. The complex permittivity, that is, both the real and the imaginary or absorptive parts (έ and ἕ), were measured under various heating regimens. In addition, thermogravimetric analysis (TGA) was performed to characterize the transformation of goethite to hematite. The Debye relaxation formalism was applied to the processes occurring both during and after the main dehydroxylation reaction to calculate the relaxation times. The Arrhenius equation for thermally activated relaxation times was used to determine the activation energies. Both the real and the absorptive parts of the permittivity exhibited a significant peak during the main part of the goethite to hematite decomposition reaction. Above the transformation, there was another, less dramatic, thermally activated increase in the permittivity values. The increase in the permittivities during the goethite to hematite transformation was attributed to the formation of quasi-free migrating radicals, for example, hydroxyl ions, oxygen ions, or hydrogen atoms, during the dehydroxylation of goethite. The derivative thermogravimetric analysis (DTGA) curve was found to be directly related to the transient values of the real and the imaginary permittivities. Higher heating rates resulted in an accelerated rate of dehydroxylation and therefore higher values of the transient permittivities. In the temperature range of 400 °C to 500 °C (i.e., just above the dehydroxylation peak), the real permittivity exhibited a varying frequency dependence, which suggested that changes were occurring in the newly formed, highly defected hematite structure, which is referred to as hydrohematite. During the reaction there were multiple relaxation processes and thus the Debye relationship could not be applied. However, at temperatures above about 500 °C, the structure stabilized, the Debye relationship was more closely followed, and the relaxation times could be determined as a function of temperature. The activation energy for the relaxation process above 500 °C was determined to be 0.47 kJ/mol.

scholarly journals On relaxation processes in a completely ionized plasma

2020 ◽  
Keyword(s):  
Distribution Function ◽  
Electric Field ◽  
External Electric Field ◽  
Electron Distribution ◽  
Electron Distribution Function ◽  
Relaxation Times ◽  
Relaxation Processes ◽  
Energy And Momentum ◽  
Energy And Momentum Densities ◽  
Relaxation Coefficients

Relaxation of the electron energy and momentum densities is investigated in spatially uniform states of completely ionized plasma in the presence of small constant and spatially homogeneous external electric field. The plasma is considered in a generalized Lorentz model which contrary to standard one assumes that ions form an equilibrium system. Following to Lorentz it is neglected by electron-electron and ion-ion interactions. The investigation is based on linear kinetic equation obtained by us early from the Landau kinetic equation. Therefore long-range electron-ion Coulomb interaction is consequentially described. The research of the model is based on spectral theory of the collision integral operator. This operator is symmetric and positively defined one. Its eigenvectors are chosen in the form of symmetric irreducible tensors which describe kinetic modes of the system. The corresponding eigenvalues are relaxation coefficients and define the relaxation times of the system. It is established that scalar and vector eigenfunctions describe evolution of electron energy and momentum densities (vector and scalar system modes). By this way in the present paper exact close set of equations for the densities valid for all times is obtained. Further, it is assumed that their relaxation times are much more than relaxation times of all other modes. In this case there exists a characteristic time such that at corresponding larger times the evolution of the system is reduced described by asymptotic values of the densities. At the reduced description electron distribution function depends on time only through asymptotic densities and they satisfy a closed set of equations. In our previous paper this result was proved in the absence of an external electric field and exact nonequilibrium distribution function was found. Here it is proved that this reduced description takes also place for small homogeneous external electric field. This can be considered as a justification of the Bogolyubov idea of the functional hypothesis for the relaxation processes in the plasma. The proof is done in the first approximation of the perturbation theory in the field. However, its idea is true in all orders in the field. Electron mobility in the plasma, its conductivity and phenomenon of equilibrium temperature difference of electrons and ions are discussed in exact theory and approximately analyzed. With this end in view, following our previous paper, approximate solution of the spectral problem is discussed by the method of truncated expansion of the eigenfunctions in series of the Sonine polynomials. In one-polynomial approximation it is shown that nonequilibrium electron distribution function at the end of relaxation processes can be approximated by the Maxwell distribution function. This result is a justification of Lorentz–Landau assumption in their theory of nonequilibrium processes in plasma. The temperature and velocity relaxation coefficients were calculated by us early in one- and two-polynomial approximation.

Relaxation processes of some simple aliphatic molecules in dilute solutions

1977 ◽  
Vol 55 (4) ◽  
pp. 297-301 ◽  
Author(s):  
M. P. Madan
Keyword(s):  
Carbon Tetrachloride ◽  
Dielectric Relaxation ◽  
Thermodynamic Parameters ◽  
Relaxation Times ◽  
Relaxation Processes ◽  
Dilute Solutions ◽  
Microwave Region ◽  
Nonpolar Solvents ◽  
Dielectric Data ◽  
Intramolecular Rotation

The dielectric relaxation processes of acetone, cyclohexanone, 4-methyl-2-pentanone, and 4-heptanone in dilute nonpolar solvents, n-heptane, cyclohexane, benzene, and carbon tetrachloride have been studied in the microwave region over a temperature range 10 to 60 °C. The relaxation times and the thermodynamic parameters for the activated states have been determined using the measured dielectric data. The results have been discussed in terms of dipole reorientation by molecular and intramolecular rotation and compared, wherever possible, with other similar studies on aliphatic molecules.

Relaxation processes of quinoline, isoquinoline, and their mixtures

1980 ◽  
Vol 58 (1) ◽  
pp. 20-24 ◽  
Author(s):  
M. P. Madan
Keyword(s):  
Thermodynamic Parameters ◽  
Molecular Motion ◽  
Polar Solvent ◽  
Relaxation Times ◽  
Relaxation Processes ◽  
Polar Components ◽  
Dielectric Absorption ◽  
System A ◽  
Dielectric Data ◽  
Activated State

The dielectric absorption of quinoline, isoquinoline, and their binary mixtures has been studied in the microwave region over a range of temperatures in dilute benzene and n-heptane solutions. The relaxation times and the thermodynamic parameters for the activated state have been determined using the measured dielectric data. The results obtained have been discussed in terms of the molecular motion of the system. A relation has been proposed to represent the relaxation behavior of a system of two Debye-type polar components in a non-polar solvent. The relation has been tested by comparing the calculated values with those determined experimentally for a few systems consisting of similar, simple rigid polar molecules.

Bonded Hydrogen and Trapped H2 in a-Si1−xGex:H Alloys

1989 ◽  
Vol 149 ◽  
Author(s):  
E. J. Vanderheiden ◽  
G. A. Williams ◽  
P. C. Taylor ◽  
F. Finger ◽  
W. Fuhs
Keyword(s):  
Temperature Dependence ◽  
Molecular Hydrogen ◽  
Relaxation Times ◽  
Lattice Relaxation ◽  
Spin Lattice Relaxation ◽  
Spin Lattice ◽  
H Nmr ◽  
Local Environments

ABSTRACT1H NMR has been employed to study the local environments of bonded hydrogen and trapped molecular hydrogen (H2) in a series of a-Si1−xGex:H alloys. There is a monotonic decrease of bonded hydrogen with increasing x from ≈ 10 at. % at x = 0 (a-Si:H) to ≈ 1 at. % at x = 1 (a-Ge:H). The amplitude of the broad 1H NMR line, which is attributed to clustered bonded hydrogen, decreases continuously across the system. The amplitude of the narrow 1H NMR line, which is attributed to bonded hydrogen essentially randomly distributed in the films, decreases as x increases from 0 to ≈ 0.2. From x = 0.2 to x ≈ 0.6 the amplitude of the narrow 1H NMR line is essentially constant, and for x ≥ 0.6 the amplitude decreases once again. The existence of trapped H2 molecules is inferred indirectly by their influence on the temperature dependence of the spin-lattice relaxation times, T1. Through T1, measurements it is determined that the trapped H2 concentration drops precipitously between x = 0.1 and x = 0.2, but is fairly constant for 0.2 ≤ x ≤ 0.6. For a-Si:H (x = 0) the H2 concentration is ≈ 0.1 at. %, while for x ≥ 0.2 the concentration of H2 is ≤ 0.02 at. %.

Viscoelastic Relaxation of Rubber Vulcanizates Between the Glass Transition and Equilibrium

1966 ◽  
Vol 39 (4) ◽  
pp. 870-880 ◽  
Author(s):  
R. Chasset ◽  
P. Thirion
Keyword(s):  
Molecular Weight ◽  
Dynamic Properties ◽  
Average Length ◽  
Linear Part ◽  
Polymer Networks ◽  
Relaxation Times ◽  
Distribution Functions ◽  
Viscoelastic Relaxation ◽  
Theoretical Understanding ◽  
Rouse Theory

Abstract In agreement with the results of dynamic experiments of Stratton and Ferry, this study of relaxation of rubber vulcanizates entirely confirms the existence of peculiar, slow, viscoelastic processes in high polymer networks. Characteristic differences with the rheological behavior of unvulcanized polymers are best reflected by the shape of the end of the distribution functions of relaxation times. The box distribution found for free chains is replaced, for crosslinked polymers, by a long incline extending during several decades of time. The slope of this linear part of the spectrum is only slightly dependent on nature of the polymer and type of vulcanizate. On the other hand, the position of the incline along the time scale is very sensitive to the mean molecular weight Mc of the vulcanizates, by far the most important factor controlling the phenomenon. The downward deviations observed at the end of the incline also occur later for larger values of Mc. A useful step towards theoretical understanding of this behavior should be a quantitative knowledge of the effect of molecular weight in a broader range of Mc than studied here. If the chain entanglements are of primary importance, as considered probable by Ferry it seems that some singularity should occur for a critical molecular weight fitting the corresponding value for the viscosity of free chains. The role of crosslink mobility might be tested by comparing the relaxation of ordinary random vulcanizates with that of eventually more regular polybutadiene networks prepared by end group crosslinking of carboxy-terminated and mono-disperse chains. In fact, the displacement of a crosslink away from its affine position requires, apart from the Brownian fluctuations, an unbalance between the forces exerted by the four radiating chains. This implies that the lengths of the strands present large differences and that the shortest chains are approaching their limit of extensibility. As the latter condition can hardly be fullfilled at small deformations, it seems doubtful that this mechanism may be predominant either for dynamic properties or the relaxation experiments reported here. Another cause sometimes invoked is the presence of free chains attached to the networks and we are presently studying their effect on viscoelastic relaxation. At this stage, it is already apparent that they do not have a large effect, as might be expected on theoretical grounds. In our opinion, special attention should be paid to the reason why the experimentally found relaxation times are so large, in spite of the relatively short average length of the network strands. If the usual notion of entanglements developed for free chains, as an extension of the Rouse theory, should fail in this respect, it would be necessary to reconsider the non-equilibrium statistics of single chains with fixed ends, taking into account the proper inter- and intramolecular forces hindering their motion. This more direct approach to the problem, already outlined by Kirkwood, ought to express mathematically the fact that the presence of crosslinks tends to prevent longitudinal slippage of large parts of the chains. The slow changes of configuration should occur therefore rather through lateral motions to which the neighboring medium opposes a much greater resistance.

Relaxation Time Spectrum, Elasticity, and Viscosity of Rubber. I

1954 ◽  
Vol 27 (1) ◽  
pp. 36-54 ◽  
Author(s):  
W. Kuhn ◽  
O. Künzle ◽  
A. Preissmann
Keyword(s):  
Relaxation Time ◽  
Relaxation Times ◽  
Time Spectrum ◽  
Test Sample ◽  
Elastic Behavior ◽  
Relaxation Processes ◽  
Relaxation Time Spectrum ◽  
Restoring Force ◽  
Constant Length ◽  
Rapid Deformation

Abstract By rapid deformation of a medium in which linear molecules are present, various changes are produced simultaneously in the latter. These changes are more or less independent of one another, and can release independently and totally or partially by rearrangement of valence distances and valence angles in the chain molecules. By virtue of such relaxation processes, a portion of the stress originating in the rapid deformation disappears, with a changing time requirement for the various portions. A relaxation time spectrum is thus formed. The relaxation time spectrum consists of a finite number of restoring force mechanisms with proper relaxation times or of a continuous spectrum. Both the creep curves (the dependence of the length of a body on time at constant load), and stress relaxation (decay of the stress observed in test sample kept at constant length after rapid deformation), as well as the total visco-elastic behavior, especially the behavior at constant periodic deformation of the test sample, are determined by the relaxation time spectrum. The appropriate Quantitative relationships were derived.

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