Volume temperature curves

No crystalline order is visible for the bead-spring model upon cooling to the frozen-in phase at T = 0.3. The break in the volume-temperature curve (described in the section on thermodynamic information) occurring between T = 0.4 and T = 0.45 leads us to expect that the two-step decay described by MCT should be observable at simulation temperatures above (and close to) this region. This expectation is borne out in Figure 10, which shows the... 

In Fig. 3 c the schematic volume-temperature curve of a non crystallizing polymer is shown. The bend in the V(T) curve at the glass transition indicates, that the extensive thermodynamic functions, like volume V, enthalpy H and entropy S show (in an idealized representation) a break. Consequently the first derivatives of these functions, i.e. the isobaric specific volume expansion coefficient a, the isothermal specific compressibility X, and the specific heat at constant pressure c, have a jump at this point, if the curves are drawn in an idealized form. This observation of breaks for the thermodynamic functions V, H and S in past led to the conclusion that there must be an internal phase transition, which could be a true thermodynamic transformation of the second or higher order. In contrast to this statement, most authors... 

In Fig. 4 the experimental isobaric volume temperature curve of the 1-l.c. 4-hexyloxybenzoic acid 4 -hexyloxyphenylester is shown, which possesses a nematic phase 37,38). Two phase transformations are indicated by the jumps of the V—T curve the isotropic to nematic and, at lower temperatures, the nematic to crystalline transformation. As well known, both transformations are of first order and obey the Clausius-Clapeyron equation. 

Fig. 4. Specific volume-temperature curves at different pressures of the 1-l.c. (isobaric measurements) 37 38)...

As there exists a phase equilibrium both phases must have reached in the internal thermodynamic equilibrium with respect to the arrangement and distribution of the molecules the measuring time. Therefore, no time effects or path dependencies of the thermodynamic properties in the liquid crystalline phase should be expected. To check this point for the l.c. polymer, a cut through the measured V(P) curves at 2000 bar has been made (Fig. 6) and the volume values are inserted at different temperatures in Fig. 7, which represents the measured isobaric volume-temperature curve at 2000 bar 38). It can be seen from Fig. 7 that all specific volumes obtained by the cut through the isotherms in Fig. 6 he on the directly measured isobar. No path dependence can be detected in the l.c. phase. From these observations we can conclude that the volume as well as other properties of the polymers depend only on temperature and pressure. The liquid crystalline phase of the polymer is a homogeneous phase, which is in its internal thermodynamic equilibrium within the normal measuring time. 

The shape of the enthalpy-temperature curve is similar to the volume temperature curve through the order-disorder temperature range in the case of polytetrafluoro-ethylene, Fig. 14. The difference in temperature between the two curves at the inflection point may be due to a difference in heating rate or to a difference in the samples studied, probably the former. 

J.C. Mauro, A.K. Varshneya Ab initio modeling of volume-temperature curves for glassforming systems. J. Non-Crystalline Solids 353, 1226-1231 (2007)... 

Dilatometry (volume-temperature curves) and dielectric constant. The latter method appears to be as accurate as the other techniques, and. by virtue of use of an extensive property, it is nol influenced by the amount of material used. These methods will not be discussed here. 

The specific volume v also shows an anomalous temperature dependence near 7. The behavior of v is universal among all systems having a finite 7. When measured at a constant cooling rate q, tJ follows the behavior of the enthalpy, shown in Fig. 3, as it decreases linearly with T and changes shape at a temperature dependent on q but close to the 7 observed for Cp. Below this breakaway temperature, the system is not in equilibrium. If the system is annealed, not far below 7, the behavior shown in Fig. 5 is observed. Volume v decays toward a lower asymptotic value Jq, which can lie either on the extrapolated volume-temperature curve for the liquid or above it, if the annealing temperature is low enough. The latter observation suggests the existence for metastable equilibrium of a Oq versus T curve that breaks away from the extrapolated liquid curve, but no information is yet available on where or how it breaks away. There is also... 

Figure 4.3 Specific volume-temperature curves for a semicrystalline polymer. (A) Liquid region (B) viscous liquid with some elastic response (C) rubbery region (D) glassy region (E) crystallites in a rubbery matrix (F) crystallites in a glassy matrix. 

Solids absorb heat on melting and, with the notable exception of ice, expand. They evolve heat when they undergo polymorphic transformation to a more stable polymorphic and contract. Consequently, dilatometric (specific volume-temperature) curves bear a close resemblance to calorimetric (enthalpy-temperature) curves. The melting dilation corresponds to the heat of fusion, and the coefficient of cubical expansion, a, corresponds to the specific heat capacity, c. The ratio cja is virtually a constant independent of temperature. 

In 2004, our group calculated the solubility parameters for two polymers (PHB and PEO). The solubility parameters of the two polymers are similar and are consistent with the literature values. This means that PHB may be compatible with PEO. Then the volume-temperature curve of PHB/PEO blend system (12 blends in terms of repeated units) is simulated. From the curve, we got only one Tg for the blend system. The calculated Tg is consistent well with the experimental results. Based on the above two points, we concluded that PHB/PEO is a miscible blend. To confirm this conclusion further, the MD simulation was also carried out for an immiscible PHB/PE blend. Two Tg are observed for the immiscible blend. This is qualitatively in agreement with the experiment and supports our conclusion. 

One of the most important conclusions associated with the Takayanagi model is that the distribution function of the free volume fraction Fj f) is evaluated by the following equation based on the specific volume-temperature curve ... 

It was established by the earlier authors that the specific volume of polymers diminishes linearly with the temperature until the Tg. Below this temperature the diminution continues but at a small rate, as shown in Figure 5.4 obtained by Fox and Floiy for fractions of polystyrene of different molecular weights. Moreover, it was observed " that all the volume-temperature curves of the liquid state above the transition temperature, if they are extrapolated, intersect each other practically at the same point, at absolute zero temperature (V(o)iiq = 0.7674 cm /g). This volume was considered as the remaining space between atoms and molecules when no movement is allowed. Kanig ° proposed that the difference between the volume observed at absolute zero temperature and the volume measured at the transition temperature was constant for all polymers and equal to 0.0646 cm /g. This volmne difference was considered the space which, in the amorphous solid, is available for oscillations. 

Figure 5.4. Specific volume-temperature curves for polystyrene fractions [Adapted, by permission, from Fox TQ Flory P J, J. Appl Phys., 21, 581, 1950].

TgA and TgB to TgA and TgB , respectively), the volume-temperature curves (Fig. 8) of the components in the blends follow the dotted lines instead of the solid lines. Thus, the volume of each component becomes smaller than that of the pure component, which results in higher density at room temperature. Note that the dens-ification of the IPN s is due to interpenetration, which produced the Tg shift and that the effect was the greatest with full IPN s, in agreement with glass transition behavior and electron microscopy. Thus, it may be possible to predict the glass transition behavior of the pol3niier blends by measuring the densities at several temperatures. 

Using dilatometer and thermal mechanical analysis (TMA), one can measure the volume of polymers as a function of temperature, as illustrated in Fig. 6.14. The step change in the slopes of the volume-temperature curve, i.e., the coefficients of thermal expansion, determines the glass transition temperature of the polymer. 

A more proper theoretical consideration to interpret glass transition starts from the dynamic point of view. Fox and Flory supposed that the motion of polymer chains is realized via chain monomers entering the void sites of free volume, and the free volume contains a relatively large thermal expansion coefficient above the glass transition temperature and thus they explained phenomenologically the slope change of the volume-temperature curve at Tg (Flory and Fox 1951). The free volume is... 

F. 6.17 Illustration of the separation of polymer volume-temperature curve into the van der Waals volume and the free volume... 

One can see that, as illustrated in Fig. 10.1a, the practical Tc is always lower than The volume-temperature curves for crystallization/melting are roughly the same results. Such a hysteresis loop is an important feature of first-order phase transitions. If we make a reference to the melting point of infinitely large crystals, we can define the... 

FIGURE 12.12. Specific volume - temperature curves for four epoxy resins with increasing crosslink density from 1007/DPS to 828/DPS. Measurements were made during cooling at 57min under a pressure of 5 MPa. 

Fig.3. -1 Schematic volume-temperature curves for glass formation along path 1-2-3 and crystallization along path 1-4. Ts, melting temperature Tg, transformation temperature. 1, liquid 2, supercooled liquid 3, glass 4, crystal...

Under some favorable circumstances, some polymers can align their molecules in a regular lattice shape. Such materials are said to be crystallizable. Often, if the cooling starts from the melt phase, the crystallization is only partial, and hence the materials possess both crystalline and amorphous structure and so are called semicrystalline. There is a jump of specific volume at a transition zone in the specific volume/temperature curve below the melting temperature (T ), and then there is a region of tough solid. The mechanism of the crystallization is still the object of intense discussions (Tanner and Qi 2005 Pantani et al. 2005). 

A review article (59) on the prediction of Tg by extending volume-temperature curves generated by molecular dynamics simulations to low temperatures. 

All polymers do, however, undergo second-order transitions, which occur when the volume-temperature curve at a given pressure undergoes a discontinuity but not a volume change at constant temperature. The most important of these transitions is the glass transition temperature Tg. Figure 2-9 shows the occurrence of such a point for atactic polypropylene. Table 2-2 [21] lists Tg... 

---