Polymers stress relaxation

The observations above can be rapidly turned into a semi-quantitative theory for star-polymer stress-relaxation [24] which is amenable to more quantitative refinement [25]. The key observation is that the diffusion equation for stress-re-lease, which arises in linear polymers via the passage of free ends out of deformed tube segment, is now modified in star polymers by the potential of Eq. (16). Apart from small displacements of the end, the diffusion to any position s along the arm will now need to be activated and so is exponentially suppressed. Each position along the arm, s, will possess its own characteristic stress relaxation time T(s) given approximately by... 

The long delayed responses of the fuel cell to changes in load have been attributed to mechanical property changes in the polymer. We have initiated measurements of polymer stress relaxation. The stress relaxation and viscoelastic creep of Nafion is both temperature and water concentration dependent. Response times vary from 1 s to 10 s, which can give a wide range of characteristic response times for PEM fuel cells. 

Linear Viscoelastic Behavior of Polymers-Stress Relaxation.130... 

LINEAR VISCOELASTIC BEHAVIOR OF POLYMERS-STRESS RELAXATION... 

Normalpotentiale chem standard electrode potentials (tabular series), standard reduction potentials, electrochemical series (of metals) Spannungsrelaxation polym stress relaxation Spannungsriss stress crack... 

A partieular form of Eq. (14.10.23) that deserves special mention is the one resulting from the theory of Doi and Edwards [54] and based on the reptation idea of de Gennes [32], These authors assumed that upon deformation of the polymer, stress relaxation took place by two separate mechanisms. In the first instance there was a rapid retraction of the chain within the deformed tube (see Figure 13.15 of Chap. 13), and in the second instance, there was slow diffusion of the chain out of the original tube by the process of reptation. Within the confines of the tube, the polymer acts like a Rouse chain. This leads to the following linear stress relaxation modulus [33] ... 

Returning to the Maxwell element, suppose we rapidly deform the system to some state of strain and secure it in such a way that it retains the initial deformation. Because the material possesses the capability to flow, some internal relaxation will occur such that less force will be required with the passage of time to sustain the deformation. Our goal with the Maxwell model is to calculate how the stress varies with time, or, expressing the stress relative to the constant strain, to describe the time-dependent modulus. Such an experiment can readily be performed on a polymer sample, the results yielding a time-dependent stress relaxation modulus. In principle, the experiment could be conducted in either a tensile or shear mode measuring E(t) or G(t), respectively. We shall discuss the Maxwell model in terms of shear. 

Figure 4.17 Experimental stress relaxation moduli of polystyrene measured over about two orders of magnitude in time at the temperatures indicated. [Reprinted with permission from H. Fujita and K. Ninomiya, J. Polym. Sci. 24 233 (1957).]...

Creep, creep mpture, and stress relaxation tests are multiple-point tests requiring long periods of time (1000 h min) to generate useflil data these are standard tests for determining more fundamental polymer properties (202,203). Data for these tests are generated under several... 

The Metravib Micromecanalyser is an inverted torsional pendulum, but unlike the torsional pendulums described eadier, it can be operated as a forced-vibration instmment. It is fully computerized and automatically determines G, and tan 5 as a function of temperature at low frequencies (10 1 Hz). Stress relaxation and creep measurements are also possible. The temperature range is —170 to 400°C. The Micromecanalyser probably has been used more for the characterization of glasses and metals than for polymers, but has proved useful for determining glassy-state relaxations and microstmctures of polymer blends (285) and latex films (286). 

One example of this occurs with stress relaxation. If a polymer is deformed to a fixed strain at constant temperature the force required to maintain that strain will decay with time owing to viscous slippage of the molecules. One measure of this rate of decay or stress relaxation is the relaxation time 0, i.e. the time taken for the material to relax to 1/e of its stress on initial application of strain. 

The EMT analysis indicated that the stress relaxes in proportion to the number of bonds removed. The initial linear decrease of E/Eq with is intuitively appealing and is the basis for many linear constitutive theories of polymers. An example is the Doi-Edwards theory of viscoelasticity of linear polymer melts [49] in which... 

P. Terech, P. Maldivi, C. Dammer. Living polymers in organic solvents Stress relaxation in bicopper tetracarboxylate/tert-butyl cyclohexane solutions. J Phys II (France) 4 1799-1811, 1994. 

R. Granek. Stress relaxation in polymer melts and solutions Bridging between the breathing and reptation regimes. Macromolecules 2<5 5370-5371, 1995. 

There are two further related sets of tests that can be used to give information on the mechanical properties of viscoelastic polymers, namely creep and stress relaxation. In a creep test, a constant load is applied to the specimen and the elongation is measured as a function of time. In a stress relaxation test, the specimen is strained quickly to a fixed amount and the stress needed to maintain this strain is also measured as a function of time. 

Stress relaxation tests are alternative ways of measuring the same basic phenomenon in viscoelastic polymers as creep tests, Le. the time-dependent nature of their response to an applied stress. As such, they have also been of value in understanding the behaviour of these materials. The essence of stress relaxation tests is that strain increases with time for a given stress, so that if stress is decreased with time in a controlled manner ( relaxed ), a state... 

The effect of oxidative irradiation on mechanical properties on the foams of E-plastomers has been investigated. In this study, stress relaxation and dynamic rheological experiments are used to probe the effects of oxidative irradiation on the stmcture and final properties of these polymeric foams. Experiments conducted on irradiated E-plastomer (octene comonomer) foams of two different densities reveal significantly different behavior. Gamma irradiation of the lighter foam causes stmctural degradation due to chain scission reactions. This is manifested in faster stress-relaxation rates and lower values of elastic modulus and gel fraction in the irradiated samples. The incorporation of O2 into the polymer backbone, verified by IR analysis, conftrms the hypothesis of... 

Gillen, K.T., M. Celina, and R. Bernstein, Validation of improved methods for predicting long-term elastomeric seal lifetimes from compression stress-relaxation and oxygen consumption techniques. Polymer Degradation and Stability, 82(1), 25-35, 2003. 

A8. The Helmholtz elastic free energy relation of the composite network contains a separate term for each of the two networks as in eq. 5. However, the precise mathematical form of the strain dependence is not critical at small deformations. Although all the assumptions seem to be reasonably fulfilled, a simpler method, which would require fewer assumptions, would obviously be desirable. A simpler method can be used if we just want to compare the equilibrium contribution from chain engangling in the cross-linked polymer to the stress-relaxation modulus of the uncross-linked polymer. The new method is described in Part 3. 

A new stress-relaxation two-network method is used for a more direct measurement of the equilibrium elastic contribution of chain entangling in highly cross-linked 1,2-polybutadiene. The new method shows clearly, without the need of any theory, that the equilibrium contribution is equal to the non-equilibrium stress-relaxation modulus of the uncross-linked polymer immediately prior to cross-linking. The new method also directly confirms six of the eight assumptions required for the original two-network method. 

Creep and stress-relaxation tests measure the dimensional stability of a material, and because the tests can be of long duration, such tests are of great practical importance. Creep measurements, especially, are of interest to engineers in any application where the polymer must sustain loads for long periods. Creep and stress relaxation are also of major importance to anyone interested in the theory of or molecular origins of Viscoelasticity. 

Very simple models can illustrate the general creep and stress-relaxation behavior of polymers except that the time scales are greatly collapsed in the models compared to actual materials. In the models most of the in-... 

The longest relaxation time. t,. corresponds to p = 1. The important characteristics of the polymer are its steady-state viscosity > at zero rate of shear, molecular weight A/, and its density p at temperature 7" R is the gas constant, and N is the number of statistical segments in the polymer chain. For vinyl polymers N contains about 10 to 20 monomer units. This equation holds only for the longer relaxation times (i.e., in the terminal zone). In this region the stress-relaxation curve is now given by a sum of exponential terms just as in equation (10), but the number of terms in the sum and the relationship between the T S of each term is specified completely. Thus... 

Thus (he time scale / at /, divided by an is equivalent to the scale at On a log scale, log a, is thus the horizontal shift factor required for superposition. An important consequence of equation (22) is that a, or log (ii is the same for a given polymer (or solution) no matter what experiment is being employed. Thai is. creep and stress-relaxation curves are shifted by the same amount. 

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