Thermoelasticity experiments

Values of the dipole moment ratio of PNS are obtained from dielectric measurements. From thermoelastic experiments, performed on polymer networks, the temperature coefficient of the unperturbed dimensions is determined. Analysis of these results using the RIS model is performed leading to the parameters given above. 

Values of the mean-square dipole moment, , of PDEI are determined as a function of temperature. The value of the dipole moment ratio is 0.697 at 303 K. Trifunctional model networks are prepared. From thermoelastic experiments performed on the networks over a temperature range 293 - 353 K, it is found that the value of the temperature coefficient of the unperturbed dimensions amounts to 1.05 0.17 K-1. The dipole moments and the temperature coefficients of both the dipole moments and the unperturbed dimensions are critically interpreted in terms of the RIS model, and are found to be in a reasonable agreement. 

Figure 5.7. Thermoelasticity experiments to estimate the entropic component of elastic force in pure water (curves B) and in the solvent mixture of 30% ethylene glycol 70% water (curves A). On increasing ethylene to 30%, the heat of the transition approaches zero, which means that the solvent entropy change approaches zero. The purpose of the experiment is to see if solvent entropy change contributes to the force developed on raising the temperature. Interestingly, the 90% entropic elastic force...

In experiments concerning the relationships between length, temperatnre, and force, usually the change in force with temperatnre at constant length is recorded (53,98-101). It is therefore necessary to extend the thermodynamic treatment of the elasticity. Moreover, the force is not purely entropic, and the energetic contribution carries useful information on the dependence on temperature of the average end-to-end distance of the network chains in the unstrained state (21,102). It is therefore important to know how to deduce these quantities from a thermoelastic experiment. 

The energetic and entropic components of the elastic force, fe and fs, respectively, are obtained from thermoelastic experiments using the following equations ... 

Fig. 1.3. Results of thermoelastic experiments carried out on a typical metal, rubber, and gas [3].

The simplest of the thermoelastic experiments described above were first carried out many years ago, by J. Gough, back in 1805 [1,2,9,10]. Gough was a clergyman. 

Thermoelasticity results are also used to test some of the assumptions used in the development of the molecular theories. The results [72] indicate that the ratio f /f is essentially independent of the degree of swelling of the network, and this supports the postulate made in Section 1.1.4 that intermolecular interactions do not contribute significantly to the elastic force. The assumption is further supported by results [72] showing that the values of the temperature coefficients of the unperturbed dimensions obtained from thermoelasticity experiments are in good agreement with those obtained from viscosity-temperature measurements on the isolated chains in dilute solution. 

With regard to differences in polymer behavior in solution versus the bulk state, several points must be made. Clearly, it is now well-established that the choice of theta solvent can affect chain dimensions to some extent [42-44, 46, 47]. Hence, only the chain in an amorphous melt of identical neighbors can be considered to be in the unperturbed state. Particularly striking are some of the differences noted in temperature coefficients measured by different techniques. Is it possible that the thermal expansion of a polymer molecule is fundamentally different in the bulk and in solution Can specific solvent effects exist and vary in a systematic way within a series of chemically similar theta solvents Does the different range of temperatures usually employed in bulk versus solution studies affect K Are chains in the bulk (during SANS and thermoelastic experiments) allowed adequate time to completely relax to equilibrium All of these issues need further attention. Other topics perhaps worthy of consideration include the study of the impact of deuterium labelling on chain conformation (H has lower vibrational energy than does H ) and the potential temperature dependence of the Flory hydrodynamic parameter . 

Figure 3 Results of thermoelastic experiments carried out on a typical metal, rubber and gas (reproduced by permission of the American Chemical Society from J. E. Mark, Audio Course Manual Physical Chemistry of Polymers , 1986)...

The SPATE technique is based on measurement of the thermoelastic effect. Within the elastic range, a body subjected to tensile or compressive stresses experiences a reversible conversion between mechanical and thermal energy. Provided adiabatic conditions are maintained, the relationship between the reversible temperature change and the corresponding change in the sum of the principal stresses is linear and indipendent of the load frequency. 

Lord Kelvin s close associate, the expert experimentalist J. P. Joule, set about to test the former s theoretical relationship and in 1859 published an extensive paper on the thermoelastic properties of various solids—metals, woods of different kinds, and, most prominent of all, natural rubber. In the half century between Gough and Joule not only was a suitable theoretical formula made available through establishment of the second law of thermodynamics, but as a result of the discovery of vulcanization (Goodyear, 1839) Joule had at his disposal a more perfectly elastic substance, vulcanized rubber, and most of his experiments were carried out on samples which had been vulcanized. He confirmed Gough s first two observations but contested the third. On stretching vulcanized rubber to twice its initial length. Joule ob-... 

The thermoelastic behavior of these materials has also been reported [188]. Such experiments resolve the nematic to isotropic transition into entropic and enthalpic contributions as already described, and provides values of the corresponding energetic and entropic parts of the force, fe and fs [175] (see Section 7). 

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... 

The calibration constant K strongly depends on the instrumental specifications, geometry of the calorimeter (Kd), and the solvent thermoelastic properties (x ) It can be determined through a comparative assay made under the same conditions as the main experiment but using a photoacoustic calibrant instead of the sample compound. The calibrants are substances that have known values of (pm from independent measurements, or more conveniently, substances that dissipate all of the absorbed energy as heat (e/>nr = 1), like ferrocene [286] or ort/w-hydroxybcnzophenone [287]. Note that the computation of K is not really needed, because a direct comparison of the signals obtained with sample and calibration compounds allows it to be eliminated from the calculations. 

What are the main error sources in PAC experiments One of them may result from the calibration procedure. As happens with any comparative technique, the conditions of the calibration and experiment must be exactly the same or, more realistically, as similar as possible. As mentioned before, the calibration constant depends on the design of the calorimeter (its geometry and the operational parameters of its instruments) and on the thermoelastic properties of the solution, as shown by equation 13.5. The design of the calorimeter will normally remain constant between experiments. Regarding the adiabatic expansion coefficient (/), in most cases the solutions used are very dilute, so the thermoelastic properties of the solution will barely be affected by the small amount of solute present in both the calibration and experiment. The relevant thermoelastic properties will thus be those of the solvent. There are, however, a number of important applications where higher concentrations of one or more solutes have to be used. This happens, for instance, in studies of substituted phenol compounds, where one solute is a photoreactive radical precursor and the other is the phenolic substrate [297]. To meet the time constraint imposed by the transducer, the phenolic... 

It is important to stress that the experiment must be preceded by a calibration made with the calibrant dissolved in the same phenol solution used in the experiment, to ensure that the thermoelastic properties of the fluid will be as close as possible in the two runs. 

The results presented demonstrate that auditory systems of animals and humans respond to pulsed microwaves. However, there is little likelihood of the microwave acoustic effect arising from direct interaction of microwave pulses with the cochlear nerve or neurons at higher structures along the auditory pathway. The pulsed microwave energy, instead, initiates a thermoelastic wave of pressure in the head that travels to the cochlea and activates the hair cells in the inner ear. This theory covers many experimental observations, but it may be incomplete and thus require further extension to account for certain additional experimental findings. Tyazhelov, et al. (1 1) found in their beat frequency experiment that matching of microwave pulses (10 ps, 8000 pps) to a phase-shifted 8 kHz sinusoidal sound input... 

Results of force-temperature experiments for a PAA solution on rubber are shown in Figure 2. For the first cycle, the initial load is that of the rubber since the coating is still in the liquid state and cannot support a load. At this load the rubber is just below its thermoelastic inversion point and its contribution to the force change is negligible. 

As far as the thermoelasticity performance of a polymer network k concerned, it is generally true that the hi er the concentration of crosslinks or the lower the dimensions of loopholes in the network, the more significant are the changes in the polymer I operties. The elasticity of a polymer is also enhanced by i iyskally entangled chains, whose number increases with the number of crosslinks, the character of the crosslinks being interrdated with the character of the physical aitan ements [27]. This may be illustrated by experiments with two crosslinked samples prepared from low density polyethylene. The first sample was crosslinked via the silane pathway, the second by... 

With respect to localized corrosion, various experiments with focused laser light were carried out. They show that the passive film may be destroyed by a laser pulse. The mechanism of destruction depends on the band gap of the oxide and the photon energy. In case of hv < g, photons generate a thermoelastic effect at the... 

FIGURE 14.3 Thermoelastic behavior of a rubber sample. Stress-temperature (O-T) curves for a series of extension values. The percentage strain is shown against each curve. (Adapted from Beevers, R.B., Experiments in Fibre Physics, Butterworths, 1970.)... 

Hot secondary forming Used for amorphous thermoplastics in the thermoelastic (entropy elastic) range above Tg or in semicrystalline thermoplastics 30 °C below (see cup experiment below). 

Experiments performed at lo i/er elongations (or compressions) belovi/ the so-called thermoelastic inversion point lead to decreasing o-values i/ith increasing temperature because the thermal expansion of the samples predominates the effect of the retractive force. 

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