Viscoelastic Properties of Rubber Networks

1975 ◽  
Vol 48 (5) ◽  
pp. 981-994 ◽  
Author(s):  
P. Thirion
Keyword(s):  
Viscoelastic Properties ◽  
Dynamic Properties ◽  
Mechanical Energy ◽  
Filler Particle ◽  
Polymer Networks ◽  
Relaxation Times ◽  
Low Frequency ◽  
Linear Polymers ◽  
Approach To Equilibrium ◽  
Sinusoidal Vibration

Abstract The molecular theory of Rouse, Zimm, and Bueche correctly accounts for the viscoelastic properties of polymers in very dilute solution and, to a large extent, for those of polymers in bulk or in concentrated solution, as long as their mean molecular weight is below about 20 000. Above this MW limit, relaxation times appear which are longer than those provided for in this theory. The “viscoelastic plateau”, which then appears in the long relaxation time region of the dynamic spectrum, is ascribed to entanglements of molecular chains which behave like temporary crosslinks. An analogous phenomenon occurs in the same way in permanent polymer networks, such as rubber vulcanizates. In this case one finds abnormally slow relaxation or creep rates during the approach to equilibrium, as well as increased low-frequency mechanical energy losses under forced sinusoidal vibration. The presence of colloidal fillers, such as carbon blacks used to reinforce rubbers, also seems to increase this hysteresis within the polymer matrix, independent of thixotropic effects which result from the reversible rupture of filler particle aggregates under large-amplitude cyclic deformations. We propose to analyze here the results (obtained jointly at the Institut Français du Caoutchouc and at the laboratory of Professor J. D. Ferry, University of Wisconsin) of measurements over the entire rubbery spectrum of the dynamic properties and of stress relaxation on vulcanizates of natural rubber, cis-polybutadiene, and styrene-butadiene copolymer (SBR) in the absence of secondary crystallization or aging phenomena. Then we examine the interpretation of the behavior of these materials, both at low frequency and during the approach to equilibrium, by analogy with the theories of the “viscoelastic plateau” of linear polymers.

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.

Dielectric Relaxation Studies of Silver Nanoparticles dispersed Liquid Crystal

2015 ◽  
Vol 8 (3) ◽  
pp. 2176-2188 ◽  
Author(s):  
Keisham Nanao Singh
Keyword(s):  
Activation Energy ◽  
Silver Nanoparticles ◽  
Liquid Crystal ◽  
Dielectric Relaxation ◽  
Relaxation Process ◽  
Relaxation Times ◽  
Low Frequency ◽  
Bulk Liquid ◽  
Molecular Rearrangement ◽  
Relaxation Studies

This article reports on the Dielectric Relaxation Studies of two Liquid Crystalline compounds - 7O.4 and 7O.6 - doped with dodecanethiol capped Silver Nanoparticles. The liquid crystal molecules are aligned homeotropically using CTAB. The low frequency relaxation process occurring above 1 MHz is fitted to Cole-Cole formula using the software Dielectric Spectra fit. The effect of the Silver Nanoparticles on the molecular dipole dynamics are discussed in terms of the fitted relaxation times, Cole-Cole distribution parameter and activation energy. The study indicate a local molecular rearrangement of the liquid crystal molecules without affecting the order of the bulk liquid crystal molecules but these local molecules surrounding the Silver Nanoparticles do not contribute to the relaxation process in the studied frequency range. The observed effect on activation energy suggests a change in interaction between the nanoparticles/liquid crystal molecules.

scholarly journals Determination of the Distribution of Relaxation Times by Means of Pulse Evaluation for Offline and Online Diagnosis of Lithium-Ion Batteries

Batteries ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 36
Author(s):  
Erik Goldammer ◽  
Julia Kowal
Keyword(s):  
Lithium Ion Batteries ◽  
Electrochemical Impedance ◽  
Sampling Rate ◽  
Relaxation Times ◽  
Low Frequency ◽  
Lithium Ion ◽  
Battery Management ◽  
Time Constants ◽  
Time Domain Data ◽  
Aging Study

The distribution of relaxation times (DRT) analysis of impedance spectra is a proven method to determine the number of occurring polarization processes in lithium-ion batteries (LIBs), their polarization contributions and characteristic time constants. Direct measurement of a spectrum by means of electrochemical impedance spectroscopy (EIS), however, suffers from a high expenditure of time for low-frequency impedances and a lack of general availability in most online applications. In this study, a method is presented to derive the DRT by evaluating the relaxation voltage after a current pulse. The method was experimentally validated using both EIS and the proposed pulse evaluation to determine the DRT of automotive pouch-cells and an aging study was carried out. The DRT derived from time domain data provided improved resolution of processes with large time constants and therefore enabled changes in low-frequency impedance and the correlated degradation mechanisms to be identified. One of the polarization contributions identified could be determined as an indicator for the potential risk of plating. The novel, general approach for batteries was tested with a sampling rate of 10 Hz and only requires relaxation periods. Therefore, the method is applicable in battery management systems and contributes to improving the reliability and safety of LIBs.

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 Recent Observations on the Mechanical Properties of Polymer Networks

1971 ◽  
Vol 44 (5) ◽  
pp. 1256-1272 ◽  
Author(s):  
P. Thirion ◽  
R. Chasset
Keyword(s):  
Crosslink Density ◽  
Room Temperature ◽  
Dynamic Properties ◽  
Polymer Networks ◽  
The Other ◽  
Dilution Ratio ◽  
Chain Entanglement ◽  
Influence Of Temperature ◽  
Terminal Zone ◽  
Crosslinking Agents

Abstract The influence of temperature, elongation, swelling or dilution ratio, crosslink density, nature of the polymers, and crosslinking agents on the dynamic properties, creep and relaxation of polymer networks is surveyed in the terminal region of the spectrum. Whereas the deformation does not change the relaxation kinetics in large ranges of extension, the crosslink density acts as a reduced variable apparently accelerating uniformly the viscoelastic processes beyond the glass transition. The other possible reductions ‘time-temperature’ and ‘time—swelling’ do not necessarily seem related to the variations of free volume. From the viewpoint of the explanation of the relaxation mechanisms in the terminal zone, the fact that the equilibrium of loosely crosslinked elastomers would only virtually be reached after several years at room temperature seem in better agreement with chain entanglement effects, either trapped or not by the permanent network, than with the dissociation of secondary linkages.

On the Measurement of Dynamic Properties of Lubricants under E. H. L. Conditions Using a Disc Machine

1974 ◽  
Vol 16 (5) ◽  
pp. 331-338 ◽  
Author(s):  
J. M. Davies ◽  
K. Walters
Keyword(s):  
Viscoelastic Properties ◽  
Dynamic Properties ◽  
Elastohydrodynamic Lubrication ◽  
Deborah Number ◽  
Theoretical Treatment

Johnson and Roberts (1)‡ have recently shown how a simple adaptation of the conventional disc machine can be used to measure the viscoelastic properties of lubricants under conditions of elastohydrodynamic lubrication. The present paper contains a theoretical treatment of the problem and derives operating formulae pertinent to conditions of low, finite and high Deborah number.

scholarly journals Dynamics and Protein–Solvent Interactions of Hemoglobin in T and R Quaternary Conformation

2002 ◽  
Vol 16 (3-4) ◽  
pp. 227-233 ◽  
Author(s):  
Chiara Caronna ◽  
Antonio Cupane
Keyword(s):  
Quaternary Structure ◽  
Dynamic Properties ◽  
Low Frequency ◽  
Helical Structure ◽  
Blue Shift ◽  
Peak Frequency ◽  
The Other ◽  
Solvent Interactions ◽  
Reported Data ◽  
Increasing Temperature

In this work we report the thermal behaviour of the amide I′ band of carbonmonoxy and deoxy hemoglobin in 65% v/v glycerolD8/D2O solutions and in the temperature interval 10–295 K. Following recent suggestions in the literature, we analyze the amide I′ band in terms of two components, one at about 1630 cm−1and the other at about 1650 cm−1, that are assigned to solvent‒exposed and buried α‒helical regions, respectively.For deoxy hemoglobin (in T quaternary structure) both components are narrower with respect to carbonmonoxy hemoglobin (in R quaternary structure), while the peak frequency blue shift observed, upon increasing temperature, for the component at about 1630 cm−1is smaller. The reported data provide evidence of the dependence of hemoglobin dynamic properties upon the protein quaternary structure and suggest a more compact α‒helical structure of hemoglobin in T conformation, with reduced population of low‒frequency modes involving the solvent and protein.

scholarly journals Study of Mechanical Energy Dissipation by Normal and Decalcified Animals Bones

2019 ◽  
Vol 16 (1) ◽  
pp. 113-119
Author(s):  
Abdul Rauf ◽  
Syed Ismail Ahmad
Keyword(s):  
Energy Dissipation ◽  
Viscoelastic Properties ◽  
Applied Load ◽  
Mechanical Energy ◽  
Maximum Energy ◽  
Hysteresis Curve ◽  
Normal Bone ◽  
Dissipation Of Energy ◽  
Mechanical Energy Dissipation ◽  
Energy Dissipated

The energy dissipated properties of normal and decalcified femur, rib and scapula bones of animals ox and camel have been studied by uniform bending technique. A hysteresis curve has been observed between the elevation in bone and load applied. It is observed that the energy dissipated as calculated from the hysteresis loop for rib is more than that of femur and scapula of ox and camel. It has been observed that the dissipation of energy in normal bone is less than that of decalcified bone under the same condition of applied load. The highest energy dissipation was observed in case of rib bone of camel compared to that of any other bone, rib of camel and scapula of ox dissipates maximum energy than femur bones. The study suggests that this technique is simple, elegant and inexpensive besides accurate in determining viscoelastic properties of bone.

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.

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