Thermal expansion, thermomechanical

Network properties and microscopic structures of various epoxy resins cross-linked by phenolic novolacs were investigated by Suzuki et al.97 Positron annihilation spectroscopy (PAS) was utilized to characterize intermolecular spacing of networks and the results were compared to bulk polymer properties. The lifetimes (t3) and intensities (/3) of the active species (positronium ions) correspond to volume and number of holes which constitute the free volume in the network. Networks cured with flexible epoxies had more holes throughout the temperature range, and the space increased with temperature increases. Glass transition temperatures and thermal expansion coefficients (a) were calculated from plots of t3 versus temperature. The Tgs and thermal expansion coefficients obtained from PAS were lower titan those obtained from thermomechanical analysis. These differences were attributed to micro-Brownian motions determined by PAS versus macroscopic polymer properties determined by thermomechanical analysis. 

Thermal expansion and contraction are reversible effects of temperature which may be very important in some applications. Usually expansion is measured using thermomechanical analysis (TMA) (see ISO 11359-2 [4]). 

ISO 11359-2, Plastics - Thermomechanical analysis (TMA) - Part 2 Determination of coefficient of linear thermal expansion and glass transition, 1999. 

To measure the thermal expansion coefficients, a 0.125 in. thick sample was taken from the cured plates. The Increase in length with temperatures was measured by use of a Dupont 941 Thermomechanical Analyzer (TMA), with a heating rate of 5°C/min. The instrument was calibrated with an aluminum standard. Three runs were made for each sample and standard deviations calculated. 

We see from Eq. (21) that the internal energy inversion occurs at compression of the system with a positive thermal expansivity and at extension with the negative one. Occurrence of the thermomechanical internal energy inversion in Hookean solids is a result of a different dependence of the work and heat on strain (Fig. 1). 

The interchain effects in polymer networks are reflected in the thermomechanical inversion at low strains, which arises from a competition of intra- and interchain changes. Calorimetric studies of unidirectional deformation demonstrates this fact very obviously (Fig. 4). The point of elastic inversion of heat (Table 3) is dependent on the energy contribution and the thermal expansion coefficient in an excellent agreement with the prediction of Eq. (45). The value of (AU/W)VjT for the only one point of deformation, i.e. the inversion point, coincides with data obtained by a more general method (Fig. 3). 

A surprising disappearance of the thermomechanical inversion of heat at elevated temperatures has been observed by Kilian 9,88). At 90 °C, the thermomechanical inversion in SBR and NR is found to disappeare in spite of the constant value of the thermal expansion coefficient. This means that the temperature dependence of elastic force should be negative from the initial deformations, which is in contradiction with experiment. This very unusual phenomenon was supposed to be closely related to rotational freedom which will continuously be activated above some characteristic temperature 9,88). 

Kilian 103) has used the van der Waals approach for treating the thermoelastic results on bimodal networks. He came to a conclusion that thermoelasticity of bimodal networks could satisfactorily be described adopting the thermomechanical autonomy of the rubbery matrix and the rigid short segments. The decrease of fu/f was supposed to be related to the dependence of the total thermal expansion coefficient on extension of the rigid short segment component. He has also emphasized that calorimetric energy balance measurements are necessary for a direct proof of the proposed hypothesis. 

The linear thermal expansion coefficient p calculated from these measurements are in excellent agreement with literature data obtained by the conventional method. For example, the values of P calculated from the thermal effects Q during stretching of PS and PET films agree well with conventional dilatometric results, i.e. for PS PQ = 6.8xKT5 -1, PdU = 7.0x 10-5 K 1 for PET PQ = 5.4x 10 5 K-1, Pdu = 5 0 x 10"5 K 1. The characteristic heat to work ratio q depends hyper-bolically on strain which is also in an excellent agreement with prediction following from the thermomechanical analysis (see Fig. 1). 

The thermomechanical behaviour of undrawn semicrystalline polymers above Tg is shown in Fig. 14. The values of the coefficients of thermal expansion calculated from the heat effects agree well with dilatometric results. For PE, the influence of degree of crystallinity on the value of thermal effects and thermal expansion coefficients was also studied 64). 

Because Pn may be negative, there may exist such directions in oriented crystalline polymers along which the thermal expansivity is zero. Thermomechanical studies of oriented LDPE, PA and PET have shown that a reversible extension of the films at an angle of 30° to the orientation axis is not accompanied by thermal effects 64), i.e. p30. 0. The dependence of P, on the angle for LDPE is shown in Fig. 22. 

ASTM E831, 2003. Standard test method for linear thermal expansion of solid materials by thermomechanical analysis. 

Thermomechanical analysis (TMA). In this technique, information on changes in the size of a sample is obtained, e.g. thermal expansion and coefficient of thermal expansion, cure shrinkage, glass transition, thermal relaxations, any phase transformation involving volume change in the material. We describe the measurement of the coefficient of thermal expansion in detail later in this section. 

Other types of damage may be produced through thermomechanical effects. For example, when being annealed at 450°C a CVD aluminum film on a Si substrate is subjected to compressive thermoelastic stresses owing to the considerable difference between the thermal expansion coefficients of aluminum (a = 23 x 10 °C 0 and the silicon substrate (a. = 3.5 x 10 °C 0-When cooling, the film may therefore contract by as much as 1%. Due to the combined action... 

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