Stress-temperature coefficients

Stress-temperature coefficients are determined for cross-linked networks of PE and polyisobutylene elongated in the amorphous state. Interpretation of the indicated temperature coefficient of 0 for PE according to the three-fold potential model for rotation around the C—C bonds is consistent with an energy difference of 2.1 kJ mol-1 between gauche and trans states. The small temperature coefficient for isobutylene is due to steric interactions affecting bond rotations. 

Additional support for a value of A in the neighborhood of 1.0 10-8 is furnished by the results of our calculations of the unperturbed dimensions of a number of linear polyesters (see Section III C) which consist mainly of methylene chain units and which yield similar values of A. We should also mention an as yet unpublished calculation of Hoeve [quoted in a paper by Ciferri, Hoeve and Flory (66")], according to which such a value of A is in excellent agreement with the observed temperature coefficient, as deduced from intrinsic viscosities and from stress-temperature coefficients for cross-linked polyethylene networks. 

From the above equations and equation (6-11), find an expression for the stress-temperature coefficient of an ideal elastomer at constant pressure and length, that is (df / dT)PL. 

Equation (6-11) defines the stress-temperature coefficient in terms of pertinent quantities. 

The second approach is indirect and involves the measurement of the stress-temperature coefficient of a solid polymer. For the measurement, the polymer must be in the rubbery state. Crosslinking a thermoplastic polymer at room temperature and then heating it above its melting point accomplishes this. Chapter 3 describes the mathematics involved in calculating stress-temperature coefficients. Other approaches use the birefringence dependence on temperature or the Kerr Effect to measure the stress-temperature coefficient. 

Ciferri, A., Hoeve, C.A.J. and Flory, PJ. (1961) Stress-temperature coefficients of polymer networks and conformational energy of polymer chains. J. Am. Chem. Soc., 83, 1015. 

We have demonstrated in previous publications that the stress-temperature coefficient at constant pressure can be recast as s ... 

The alternative procedure is to keep the applied stress constant, and then determine the variations of the sample lengths as a function of temperature. The latter simply corresponds to the condition that the stress-temperature coefficient at constant pressure (but not constant length) vanishes. Differentiation of eq. 3 iinder these conditions yields ... 

Rory (pages 5-9 of ref. 22) reported three types of experiments from which he deduced no evidence for structure (1) stress-temperature coefficients, (2) vapor pressure of a PIB-diluent system, and (3) ring-chain equilibrium constants between cyclic and linear siloxanes. In each case the systems were evaluated far above their respective T/ s. Such results are not pertinent to our present inquiry. We have searched sporadically but without success for physical measurements which span a temperature region across Tu in elastomers. Finally, we note that because elastomers tend to be flexible hydrocarbons, Tu should be weak and may not have a great influence on physical properties. The marked exception to this generalization is PIB with its stiff, stereoregular backbone. Tu in PIB has been discussed recently in great detail, with Tu 250 K, Tip 290 K. 

D) Method yielding the temperature dependence of ro. ST stress - temperature coefficient of undiluted or swollen samples. 

More recently, test products were created of a blend of PMMA with a phenyl-substituted methacrylate these products have a glass-transition temperature of around 125°C, a significantly reduced water absorption compared to pure PMMA of about 0.32%, but also a higher birefringence (a stress-optic coefficient of 5.2 X 10 , compared with 0.3 X 10 for PMMA and 6.8 x 10 for BPA-PC). 

Fig. 101.—Experimental and theoretical (dashed line) stress-strain curves for tetra-linked polyamide with y/V) X10 = 1.34 at low elongations. Temperatures (in °C) were 229° 241° O 253° 281° 3. The range is too small to show a definite temperature coefficient beyond the experimental error. (Schaefgen and Flory. )...

Figure 7. Stress optical coefficient X temperature as a function of temperature (3). PBD is poly butadiene. Key O, p-xylene A. toluene , benzene CClt all of swollen trans-/,4 PBD.

Finally, we turn from solutions to the bulk state of amorphous polymers, specifically the thermoelastic properties of the rubbery state. The contrasting behavior of rubber, as compared with other solids, such as the temperature decrease upon adiabatic extension, the contraction upon heating under load, and the positive temperature coefficient of stress under constant elongation, had been observed in the nineteenth century by Gough and Joule. The latter was able to interpret these experiments in terms of the second law of thermodynamics, which revealed the connection between the different phenomena observed. One could conclude the primary effect to be a reduction of entropy... 

Moderate coefficient of friction and low wear rate. Medium performance bearing material. Wear accelerated by water. Relatively low temperature limit Performance similar to nylon. Durable in rolling contacts High operating temperature limit. Resistant to most chemical reagents. Suitable for high contact stress. High coefficient of friction in pure form... 

The stress-optical coefficient of PE networks is calculated, and results are compared with experimental data. Observed temperature coefficients of AT and the optical anisotropy for unswollen samples are much larger than those calculated using acceptable values of E(g), the energy of the gauche conformation, relative to that of Vans. It is concluded that observed temperature coefficients should Include some contributions other than those implied in the theory, i.e., those arising from the conformational change with temperature. 

The stress-optical behaviour of an unswollan elastomeric network of PMTHF is measured for different elongation ratios at several temperatures. Values of 4a range from 2.4 to 2.8 in units of 10 A cm3, in the temperature range studied. Theoretical calculations carried out with the RIS model give values of 4a noticeably smaller than the experimental results however, a small increase in the backbone valence angles improves the theoretical results. Theoretical and experimental values of the temperature coefficient of 4a are in clear disagreement a qualitative explanation for this discrepancy is discussed. 

Hydroxyl-terminated POET chains are end-linked into noncrystallizable trifunctional networks using an aromatic triisocyanate. The networks thus obtained are studied with regard to their stress-strain isotherms. The analysis of the temperature coefficient of PDET in terms of the RIS model confirms the results obtained from NMR studies, according to which the gauche states... 

Fig. 42. Temperature dependence of the product of stress optical coefficient and temperature CT for natural rubber (NR), poly(ethylene) (PE) and the l.c. elastomer No. 2a from Table 10...

Here n is the average refractive index, k is Boltzman s constant, and T is absolute temperature (13). If a polyblend were to form a homogeneous network, the stress would be distributed equally between network chains of different composition. Assuming that the size of the statistical segments of the component polymers remains unaffected by the mixing process, the stress-optical coefficient would simply be additive by composition. Since the stress-optical coefficient of butadiene-styrene copolymers, at constant vinyl content, is a linear function of composition (Figure 9), a homogeneous blend of such polymers would be expected to exhibit the same stress-optical coefficient as a copolymer of the same styrene content. Actually, all blends examined show an elevation of Ka which increases with the breadth of the composition distribution (Table III). Such an elevation can be justified if the blends have a two- or multiphase domain structure in which the phases differ in modulus. If we consider the domains to be coupled either in series or in parallel (the true situation will be intermediate), then it is easily shown that... 

Figure 2.31 Reduced first normal stress difference coefficient for a low density polyethylene melt at a reference temperature of 150°C.

The material functions, k i and k2, are called the primary and secondary normal stress coefficients, and are also functions of the magnitude of the strain rate tensor and temperature. The first and second normal stress differences do not change in sign when the direction of the strain rate changes. This is reflected in eqns. (2.51) and (2.52). Figure 2.31 [41] presents the first normal stress difference coefficient for the low density polyethylene melt of Fig. 2.30 at a reference temperature of 150°C. 

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