Low temperature behaviour

Low-temperature behaviour. In the Debye model, when T < 0q, the upper limit, can be approximately... 

Low-temperature behaviour. In the Debye model, when T upper limit, can be approximately replaced by co, die integral over v then has a value 7t /15 and the total phonon energy reduces to... 

This model, the Einstein model for heat capacity, predicts that the heat capacity is reduced on cooling and that the heat capacity becomes zero at 0 K. At high temperatures the constant-volume heat capacity approaches the classical value 3R. The Einstein model represented a substantial improvement compared with the classical models. The experimental heat capacity of copper at constant pressure is compared in Figure 8.3 to Cy m calculated using the Einstein model with 0g = 244 K. The insert to the figure shows the Einstein frequency of Cu. All 3L vibrational modes have the same frequency, v = 32 THz. However, whereas Cy m is observed experimentally to vary proportionally with T3 at low temperatures, the Einstein heat capacity decreases more rapidly it is proportional to exp(0E IT) at low temperatures. In order to reproduce the observed low temperature behaviour qualitatively, one more essential factor must be taken into account the lattice vibrations of each individual atom are not independent of each other - collective lattice vibrations must be considered. 

The experimental constant-pressure heat capacity of copper is given together with the Einstein and Debye constant volume heat capacities in Figure 8.12 (recall that the difference between the heat capacity at constant pressure and constant volume is small at low temperatures). The Einstein and Debye temperatures that give the best representation of the experimental heat capacity are e = 244 K and D = 315 K and schematic representations of the resulting density of vibrational modes in the Einstein and Debye approximations are given in the insert to Figure 8.12. The Debye model clearly represents the low-temperature behaviour better than the Einstein model. 

The effect of degradation agents on low temperature behaviour must be relevant in many applications but is virtually never specifically measured. There are low temperature tests for flexible materials (ISO 458 [36] and ISO 974 [37]), but generally DMTA or impact methods might be more appropriate. 

Better low-temperature behaviour regulations tend towards an increase in low-temperature impact resistances and a more ductile behaviour. 

There are many methods to test low-temperature behaviour and the possibility to use a thermoplastic at low temperature depends on the service conditions. Some grades can be used at -200°C or less if there are no impacts. Some other thermoplastics can be brittle at ambient temperature like the polystyrene used for yoghurt packaging. 

General drawbacks are the innate relative sensitivity to heat and creep, low rigidity, significant shrinkage and poorer low-temperature behaviour than polyethylene. 

Rubber-modified SAN are appreciated for their better impact strength and low-temperature behaviour. 

All the PAs are engineering polymers with good mechanical performances, fair heat and fatigue resistances, interesting low-temperature behaviour, and resistance to oils, greases, hydrocarbons and numerous common solvents, but each subfamily has its features ... 

PPEs are used in technical parts because of the good price/performance ratios for mechanical and electrical properties creep behaviour, low moisture uptake, heat and low-temperature behaviour, resistance to moisture and hot water good dimensional stability. 

PCTFE is appreciated for good chemical resistance exceptional low-temperature behaviour down to -240/250°C gas barrier properties excellent resistance to light, UV and... 

PP/IIR-V is appreciated for its low gas permeability combined with compliance with the pharmacopoeia, fair compression sets, the rubber-like hardness range, low density, low-temperature behaviour, fair ageing resistance, sterilization resistance, damping properties, ease of waste recycling... 

Figure 4.139. TPE/PVC compression set (%) after 22 h at 70°C versus Shore A hardness Low-temperature behaviour...

Flexible PVC characteristics depend broadly on the formulations flexibility improved low-temperature behaviour fire-retardant grades low cost possible food contact and transparency easy to weld and stick. 

ABS better impact and low-temperature behaviours, better chemical resistance similar to SAN. 

Measuring Tg by mechanical methods is usually done with the dynamic methods, as discussed in Chapter 9, but estimates could be made from the standardised low temperature tests discussed in the next section. Indeed, these tests have been the most widely used to study the low temperature behaviour of rubbers although the transition temperature is not specifically derived. Occasionally, electrical methods have also been used. 

A particular form of recovery test developed as a measure of low temperature behaviour is the so-called temperature-retraction test (TR test) which is standardised internationally as ISO 292113. The test consists of stretching a dumb-bell test piece, placing it in the stretched condition in a... 

Perhaps the most simple approach to measuring the low temperature behaviour of rubbers is to find the temperature at which it has become so stiff as to be glassy and brittle. The main disadvantage of this approach is that only one facet of low temperature behaviour is measured and that is at a point where, for many purposes, the rubber has long since become inadequate for its job. Nevertheless, brittleness temperature has been found to be a useful measure and innumerable ad hoc brittleness tests have been devised. These tests usually take the form of quickly bending a cooled strip of rubber and are almost inevitably very operator dependent and do not define the strain rate or the degree of strain precisely. Hence, they show poor between-laboratory variability. 

As the previous sections have shown, there are a large number of low temperature tests in existence. Even when ad hoc bending tests are disregarded, together with the use of the normal range of physical tests, such as tensile modulus and resilience, and the automation of a mechanical test by thermal analysis, there remain several types of specially developed low temperature tests. The various tests do not all have equal relevance to a given product. A test, or tests, should wherever possible, be chosen to provide the information most relevant to the particular application, but for many quality control purposes a test is used simply as a general indication of low temperature behaviour. Whatever the relative merits of the different methods in any situation, the question of correlation between the methods is frequently asked. 

Differences in results can occur between tests in a liquid and a gaseous medium. This is often because different times are required to reach equilibrium temperature, and if crystallisation is occurring, for example, the stiffness will be dependent on time of conditioning. It is also essential that if a liquid medium is used the liquid does not affect the rubber by swelling it or removing extractables, as either process can have a considerable effect on low temperature behaviour. Ethanol is most widely used but acetone, methanol, butanol, silicone fluid and n-hexane are all suggested in ISO 2921. Not all of these will be suitable for all rubbers and the suitability of any proposed liquid must be checked by preliminary swelling tests. 

Concerning the l.STyli copolyamides (Fig. 92b), the main difference to the lTyli.y copolyamide results deals with the low temperature behaviour. Indeed, instead of the plateau of nSSA occurring for the latter series, there is an increase from - 100 °C. Such an increase of nSSA corresponds, in the proposed mechanism, to a gradual increase in the softening of the material. Indeed, in the l.STyli copolyamides there is an additional y transition, with a maximum around - 90 °C at 1 Hz, due to COaiiPh 2 amide group mo-... 

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