Equilibrium melting temperature determination

The equilibrium melting temperature T was determined on ECSCs using Wunderlich s method [26]. The Tm of ECSCs was estimated from a tem-... 

Thus the initial crystal thickness can be determined if the equilibrium melting temperature (obtained from extrapolation of Tm versus 4 via eqn 5.5) is known. 

True thermodynamic equilibrium refers to the phase in their most stable state, and for the crystalline polymer phase the most stable conformation is the fully extended one. The equilibrium melting temperature, T , corresponds to the melting of perfect crystals of infinite size with fully extended chains. The value of for a polymer is unique. Since the crystalline samples of polymers are made up of crystals of finite size in which the chains are folded and not fully extended, the experimentally determined melting temperature, is always lower than There is a strong dependence of T on the thickness of the crystalline lamella, / always increases with /. 

Fig. 2. Determination of the equilibrium melting temperature, T/ °. (A) 26-80% blends of palm stearin in sesame oil, cooling rate 1°C/min, heating rate 5°C7min (adapted from Ref. 9) (B) 26 and 80% blends of palm stearin in sesame oil, cooling rates of 1, 10, and 30°C/min, heating rate 5°C/min. land Tm are defined in the text...

Physical properties of PHAs are determined by monomer units, which are predominantly responsible for the molecular interactions, the molecular weight, and the molecular weight distribution. In addition, different crystalline modifications and processing conditions have a considerable effect on the achievable property level of the samples. For this reason, only the basic material data are listed and compared the glass transition temperature (7 ), the equilibrium melting temperature of an infinite crystal (T ), the equilibrium heat of fusion (AH ), and the densities of the amorphous (yj and crystalline (yc) parts (Table 1). 

Non-equilibrium melting temperature of the preformed quadruplex, expressed in °C, in 0.11 M Na" and determined with a temperature gradient of 0.18°C min . 

The Tm(o)- and Hf(max)-values of PK copolymer Three extrapolation methods are, according to Cheng [5], available to determine the equilibrium melting temperature tTm(o)-value] of a polymer ... 

The values of the equilibrium melting temperature T, determined from Eq. (3), decrease in a continuous way with increasing PMMA content (Fig, 6). The depression observed for the equilibrium melting temperature of pure PEO, AT = T° - T j (where T° refers to pure PEO) has then been related to the volume fraction of the non-crystallizing polymer according to the equation derived by Nishi and Wang for compatible binary blends ... 

Assuming that the surface free energy of the fold surfaces is 93 mJ that the density of the crystallites p,. = 1-00 x 10 kg m and that the increase in enthalpy per unit mass, Ah, on melting is 2.55 x 10 J kg for an infinitely thick crystal, determine the equilibrium melting temperature. 

Note The equilibrium melting temperature (tJJ,) of copolymers depends on the molecular weight, sequence distribution and counit content. The T, value is determined by two commonly used techniques the Hoffman-Weeks plot and the Thompson-Gibbs plot. Tire application of the Hoffman-Weeks method to determine the tJ, of a copolymer is unreliable (see reference 43). The more reliable method is to use the Tliompson-Gibbs relationship of Tm as a function of lamellar thickness, provided a large range of lamella thickness can be obtained. Considerable disagreement exists between different authors on the exact value of transition that can be identified for fhe copolymers. Consequently, values tabulated in this table must be used cautiously. See references (39, 43, and 44) for detailed discussions. 

Examination of the directly determined melting temperatures makes abundantly clear that proposed equilibrium melting temperatures of 138.1°C and 138.9 C (24)(25) are incompatible with experiment. They obviously should be dismissed. The know experimental facts were apparently overlooked by the investigators. The remainder of the extrapolated Tm° s fall into two groups, one around 142°C and the other about 146°C. On more detailed analysis, the original Flory-Vrij conclusions are found to be strongly favored (32). 

We have seen that the experimental determination of the melting temperature of pol3nneric systems, suitable for use in thermodynamic analysis, possesses several inherent difficulties concerned with both concept and technique. Some of the main problems have been pointed out in this paper and the procedures by which they could be overcome has been indicated. Hence there are obvious difficulties in determining the equilibrium melting temperature from polymer data, even admitting the extrapolative procedure. A more detailed discussion of this aspect of the problem will be taken up in a subsequent publication (32). 

In addition to the ambiguities inherent to the physical concept, the determination of thermodynamic quantities such as the latent heat and the volume change at the transition is often hampered by the fact that the crystalline state of chain molecules is quite complex. The polymer crystals are usually polycrystalline and coexist with the disordered amorphous domain. An accurate estimation of the equilibrium melting temperature defined for a perfectly aligned crystal requires great effort [5,18,19]. At the melting temperature, equilibrium usually exists between the liquid and somewhat imperfect crystalline phases. 

The equilibrium melting temperature may also be determined by extrapolation of lamellar thickness / (Keller, 1968 Strobl, 2000 Al-Hussein and Strobl, 2002). In contrast to extended-chain crystals, lamellae grow at large undercoolings. 

Determination of the equilibrium melting temperature of polymer crystals linear and nonlinear Hofiman-Weeks extrapolations. Macromolecules, 31, 8219-8229. 

The kinetic restraints that are placed on the crystallization of polymers make it difficult, if not impossible to directly determine their equilibrium melting temperatures. The directly observed melting temperatures are primarily a reflection of the structure and morphology of the actual crystalline systems. The primary factors involved are the crystallite thickness, the interfacial free energy, and the influence, if any, of the noncrystalline region. There are, however, indirect methods by which to estimate the value of T. One of these is a theoretical method. The others are based on extrapolative procedures. To properly use the T values that are tabulated, and to understand their limitations, the basic assumption involved and the problems in execution need to be recognized. 

The other thermodynamic method that can be used to determine A// involves the variation of the equilibrium melting temperature with applied hydrostatic pressure, p. The ClapeyrOTi equatimi... 

In Fig. 3.25 Hoffman-Weeks plot for PCL/PBT blends is compared to pure PBT sample. A nonlinear extrapolation procedure was applied for the determination of the equilibrium melting temperature of the crystallizing phase. The linear extrapolation as proposed initially by Hoffman-Weeks neglects the contribution of the increment of the lamellar thickness. Note that the PCL is miscible with PBT only when the PCL molecular weight is equal or lower than MW = 1,250. The blend samples having a PCL molecular weight of 10,000 or 50,000 form immiscible mixture for which the crystallization behavior of pure PBT is recovered. The T ° of... 

When a crystallizable polymer is cooled below its equilibrium melting temperature, the hierarchical structure formed can be probed by in situ scattering. Crystallization mechanisms can be determined by comparing the time evolution of the degi ee of crystallinity (wc) determined from WAXS and the total integrated scattering intensity or invariant during crystallization [27,38] from SAXS. 

The equilibrium melting temperature can be determined in a number of dilferent ways. The melting point of samples with a well-defined crystal thickness can be measured and the data extrapolated to =0 using the Thompson-Gibbs equation ... 

The melt temperature will rise initially and then level off as the viscous dissipation reduces with increasing melt temperature. When a steady state is achieved, the melt temperature no longer changes along the length of the extruder. This is called the fully developed melt temperature or equilibrium melt temperature. This temperature Te can be determined from a simple energy balance equating the viscous dissipation to the conductive heat loss ... 

Kressler et al. [106] also determined the melting behaviour of the spherulites. They determined the variation in T with T<- and found very large melting point depressions extrapolation of T s of samples crystallised at different T -S to T = T(. led to an equilibrium melting temperature of about 85 °C which is far greater than the usually accepted value of 71.5 °C observed melting points were nonlinear with Tj. and varied with time of crystallisation, indicating some complexity in the system. 

Estimates of equilibrium melting temperatures of PCL crystallites were made, for various binary and ternary systems, with the aid of Hoffman-Weeks plots. The observed melting points of PCL were between 55 ° C and 65 ° C and varied by about 3 °C with changes in from 38 °C to 48 °C. From the melting-point depressions, as a function of composition and pressure-volume temperature data, Kim and Paul estimated equation-of-state parameters. During the course of this study Kim and Paul determined specific volume data for PCL at a series of hydrostatic pressures (Fig.51) [87]. 

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