Transitions glass

Glass transition temperature or the fictive temperature may be investigated or diagrammed using different methods, resulting in different definitions. These 

Pa K and the unit of q is K/s. Clearly there is some arbitrariness in this definition, especially in the value of 10 Pa K, which does not correspond to any physically significant property. Hence, some authors have adjusted this parameter slightly to make the rheological definition to be the same as other definitions. 

The equivalence of these Tg definitions, or the equivalence of volume, enthalpy, viscosity, and reaction relaxation has been verified provided that the exact values such as Pa K can be varied by a small amount (e.g., Toplis 

3 Fictive temperature as a function of temperature and heating/cooling rate 

Glass Transition.—Many organic liquids can be supercooled to temperatures well below the melting temperature of the crystalline phase and at a certain temperature, the glass transformation temperature, there are marked changes in properties such as thermal expansivity, heat capacity, and viscosity. The glassy solid retains some of the disorder of the liquid state and the entropy does not approach zero as T 0. 

Seki and collaborators have devised apparatus for heat capacity measurements of the glass form of substances which cannot normally be prepared as glasses. They described a calorimeter in which a glass was formed in the sample measurement cell by carefully controlled condensation of the sample vapour. With this apparatus, measurements were made on amorphous samples of methanol and water, which exhibited glass transition phenomena. Methanol, which was deposited from methanol vapour in the measurement cell at 95 K, showed a glass transition phenomenon at 103 K, at which temperature the heat capacity rose by 26 J K  

Rapid crystallization started at 105 K accompanied by an exothermic eflfect amounting to 1.54 kJ mol.  

Several crystalline substances have been found to supercool and transform into glass-like forms which exhibit glass transition temperatures with sharp changes of heat capacity. Examples of organic substances in this class are cyclohexanol and 2-methylthiophen.  

The glass transition temperature (Tg) is defined as the temperature at which a material loses its glasslike, more rigid properties and becomes rubbery and more flexible in nature. Practical definitions of Tg differ considerably between different methods, therefore, specification of Tg requires an indication of the method used. 

For miscible systems, the glass transition temperature as a function of weight fraction can be predicted by various expressions starting with the simple linear form. 

Tgb = WiTgi + wiTgi or Tgb = (piTgi + iTg2 and the logarimetric form  

Couchman [4] applied thermodynamic principles to predict the Tg of miscible blends with derivation of the following equation  

A variation of the Couchman equation was proposed assuming Tgi ACpi = constant [5] 

There are cases with positive deviation from linearity of Tg versus composition and usually they involve strong specific interactions. Kwei [6] noted that the addition of an interaction term, qw- wi, could account for the positive deviation as a modification of Eq. 5.1. 

From the practical point of view, the glass transition is a key property since it corresponds to the short-term ceiling temperature above which there is a catastrophic softening of the material. For amorphous polymers in general, and thus for thermosets, one can consider that the glass transition temperature, Tg, is related to the conventional heat deflection temperature (FIDT) (usually, HDT is 10-15°C below Tg, depending on the applied stress and the criterion selected to define Tg). 

In the field of processing, the glass transition is rather a floor temperature because the polymerization (cure) exhibits a very slow or even negligible rate in the glassy state (see Chapter 5). Many important properties, such as the yield stress or the fracture toughness at a temperature T are sharply linked to (Tg —T). Some qualitative and important quantitative differences between the glassy and rubbery states are Hsted in Table 4.1. 

The glass transition is usually characterized as a second-order thermodynamic transition. It corresponds to a discontinuity on the first derivative of a thermodynamic function such as enthalpy (dH/dT) or volume (dV/dT) (A first-order thermodynamic transition, like melting, involves the discontinuity of a thermodynamic function such as H or V). However, Tg cannot be considered as a true thermodynamic transition, because the glassy state is out of equilibrium. It may be better regarded as a boundary surface in a tridimensional space defined by temperature, time, and stress, separating the glassy and rubbery (or liquid) domains. 

Most of the physical properties of the polymer (heat capacity, expansion coefficient, storage modulus, gas permeability, refractive index, etc.) undergo a discontinuous variation at the glass transition. The most frequently used methods to determine Tg are differential scanning calorimetry (DSC), thermomechanical analysis (TMA), and dynamic mechanical thermal analysis (DMTA). But several other techniques may be also employed, such as the measurement of the complex dielectric permittivity as a function of temperature. The shape of variation of corresponding properties is shown in Fig. 4.1. 

As indicated in Fig. 4.1, dynamic methods lead to a transition temperature T ( that depends on the frequency employed in the experimental test it is usually higher than Tg and the shift increases with frequency. For low frequencies, typically 10 Hz, the difference between both values is less than 20 K. As indicated in Fig. 4.1, there is a systematic shift between the maxima of E and tan 8. 

From a thermodynamic and mechanical point of view, the glass transition, Tg, is one of the most important parameters for characterizing a polymer system [1-3,24,29,32,33]. Consequently, the determination of the Tg is usually one of the first analyses performed on a polymer system. 

A polymer may be amorphous, crystalline, or a combination of both. Many polymers actually have both crystalline and amorphous regions, i.e., a semicrystalline polymer. The Tg is a transition related to the motion in the amorphous regions of the polymer [3,8,9], Below the Tg, an amorphous polymer can be said 

The glass transition temperature can be measured in a variety of ways (DSC, dynamic mechanical analysis, thermal mechanical analysis), not all of which yield the same value [3,8,9,24,29], This results from the kinetic, rather than thermodynamic, nature of the transition [40,41], Tg depends on the heating rate of the experiment and the thermal history of the specimen [3,8,9], Also, any molecular parameter affecting chain mobility effects the T% [3,8], Table 16.2 provides a summary of molecular parameters that influence the T. From the point of view of DSC measurements, an increase in heat capacity occurs at Tg due to the onset of these additional molecular motions, which shows up as an endothermic response with a shift in the baseline [9,24]. 

One criterion to distinguish the miscibility of blends is the glass transition temperature (Tg) that can be measured with different calorimetric methods [95]. Tg is the characteristic transition of the amorphous phase in polymers. Below Tg, polymer chains are fixed by intermolecular interactions, no diffusion is possible, and the polymer is rigid. At temperatures higher than Tg, kinetic forces are stronger than molecular interactions and polymer chain diffusion is likely. In binary or multi-component miscible one-phase systems, macromolecules are statistically distributed on a molecular level. Therefore, only one glass transition occurs, which normally lies between the glass transition temperatures of the pure components. 

In partly miscible systems, interactions cause a glass transition shift of the pure components toward each other. For immiscible blends, the components are completely separated in different phases and the glass transitions of the pure components remain at their original temperature. Here it is important to emphasize that the appearance of one glass transition is not a measure of complete misdbiUty rather than a correlation with domain sizes of less than 15 nm. Various examples were discussed elsewhere [95]. 

FIGURE 6.9 Storage modulus (a) and loss factor (b) against temperature for PLLA fully crystallized at different crystallization temperatures T, recorded at 1 Hz and during a heating scan at 3°C/ min. Reproduced from Ref. 49 with permission from Springer. 

FIGURE 6.10 Dielectric loss in the frequency domain of PLLA during crystallization process at 80°C (circles). The solid lines are the experimental fit to data obtained at different times with the sum of three Havriliak-Negami (HN) functions. Only the loss curves collected after every 10 min are shown for the first 3 h. The last three curves are collected at 4,5, and 6 h, respectively. The inset shows the experimental results at 2 h (points) and the fitting lines, with the corresponding three HN individual curves (solid lines). Reproduced from Ref. 50 with permission from Wiley Blackwell. 

In addition, Quan et al. [53] adopted TMDSC to investigate the glass transition behavior of PDLLA (a low optical activity PLA without crystallinity) and PLLA after physical aging at 273, 298, and 310K for up to 6 months. The results 

FIGURE 6.11 DSC curves on heating at 10°C/min in the glass transition region for (a) PLLA and (b) PDLLA samples annealed at 40° C for the time (in hours) indicated on each curve. Reproduced from Ref. 51 with permission from American Chemical Society. 

MTA has been nsed in surface and depth profiling studies on polypropylene (PP) [15, 16], multi-block copolymers [12], PTFE/silicone blends [13], polyethylene glycol (PEG) polylactic acid blends [17], PS-PVME blends [14] and PP [15]. 

Gorbunov and co-workers [5] have pointed out that local probing of surface thermal properties with a submicron resolution are possible by using scanning thermal microscopy. Two major designs, used to date, explore either a microthermocouple or a 

By using microthermic analysis it has been shown to be possible to conduct specific examination of changes in adhesive/metal joining parts on real systems [19]. Consequently, there is a method available that can use non-destructive means to characterise a glue joint by thermo-analysis. 

Glass transition studies have also been reported on thin polyethylene films [20], and PEG entrapped into poly lactic acid [17]. 

Slough, R. Blaine and J. Furry in Proceedings of the SPE Joint Regional Technical Conference on Thermal and Mechanical Analysis of Plastics in Industry and Research, Newark, DE, USA, 1999, p.8. 

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B. Widom, Interfacial Phenomena, in Liquids, Freezing and Glass Transition, Les Houches Session LI, 1989, Elsevier, 1991, pp. 507-546. 

D. W. Oxtoby, Liquids, Freezing and the Glass Transition, in Les Houches Session 51, J. P. Hansen, D. Levesque, and J. Zinn-Justin, eds., Elsevier, New York, 1990. 

Samples can be concentrated beyond tire glass transition. If tliis is done quickly enough to prevent crystallization, tliis ultimately leads to a random close-packed stmcture, witli a volume fraction (j) 0.64. Close-packed stmctures, such as fee, have a maximum packing density of (]) p = 0.74. The crystallization kinetics are strongly concentration dependent. The nucleation rate is fastest near tire melting concentration. On increasing concentration, tire nucleation process is arrested. This has been found to occur at tire glass transition [82]. 

Pusey P N 1991 Colloidal suspensions Liquids, Freezing and Glass Transition ed J P Flansen, D Levesque and J Zinn-Justin... 

Material properties can be further classified into fundamental properties and derived properties. Fundamental properties are a direct consequence of the molecular structure, such as van der Waals volume, cohesive energy, and heat capacity. Derived properties are not readily identified with a certain aspect of molecular structure. Glass transition temperature, density, solubility, and bulk modulus would be considered derived properties. The way in which fundamental properties are obtained from a simulation is often readily apparent. The way in which derived properties are computed is often an empirically determined combination of fundamental properties. Such empirical methods can give more erratic results, reliable for one class of compounds but not for another. 

Polymers will be elastic at temperatures that are above the glass-transition temperature and below the liquiflcation temperature. Elasticity is generally improved by the light cross linking of chains. This increases the liquiflcation temperature. It also keeps the material from being permanently deformed when stretched, which is due to chains sliding past one another. Computational techniques can be used to predict the glass-transition and liquiflcation temperatures as described below. 

Many polymers expand with increasing temperature. This can be predicted with simple analytic equations relating the volume at a given temperature V T) to the van der Waals volume F and the glass transition temperature, such as... 

Irregularities such as branch points, comonomer units, and cross-links lead to amorphous polymers. They do not have true melting points but instead have glass transition temperatures at which the rigid and glasslike material becomes a viscous liquid as the temperature is raised. 

Homogeneous alloys have a single glass transition temperature which is determined by the ratio of the components. The physical properties of these alloys are averages based on the composition of the alloy. 

The polymers compared in Table 2.3 were not all studied at the same temperature instead, each was measured at a temperature 100°C above its respective glass transition temperature Tg. We shall discuss the latter in considerable detail... 

Table 2.3 Segmental Friction Factors Ranked in Order of Decreasing Values for Polymers Compared 100°C Above Their Respective Glass Transition Temperatures...

Figure 4.3b is a schematic representation of the behavior of S and V in the vicinity of T . Although both the crystal and liquid phases have the same value of G at T , this is not the case for S and V (or for the enthalpy H). Since these latter variables can be written as first derivatives of G and show discontinuities at the transition point, the fusion process is called a first-order transition. Vaporization and other familiar phase transitions are also first-order transitions. The behavior of V at Tg in Fig. 4.1 shows that the glass transition is not a first-order transition. One of the objectives of this chapter is to gain a better understanding of what else it might be. We shall return to this in Sec. 4.8. 

The kinetic nature of the glass transition should be clear from the last chapter, where we first identified this transition by a change in the mechanical properties of a sample in very rapid deformations. In that chapter we concluded that molecular motion could simply not keep up with these high-frequency deformations. The complementarity between time and temperature enters the picture in this way. At lower temperatures the motion of molecules becomes more sluggish and equivalent effects on mechanical properties are produced by cooling as by frequency variations. We shall return to an examination of this time-temperature equivalency in Sec. 4.10. First, however, it will be profitable to consider the possibility of a thermodynamic description of the transition which occurs at Tg. 

In this section we resume our examination of the equivalency of time and temperature in the determination of the mechanical properties of polymers. In the last chapter we had several occasions to mention this equivalency, but never developed it in detail. In examining this, we shall not only acquire some practical knowledge for the collection and representation of experimental data, but also shall gain additional insight into the free-volume aspect of the glass transition. 

Note that subtracting an amount log a from the coordinate values along the abscissa is equivalent to dividing each of the t s by the appropriate a-p value. This means that times are represented by the reduced variable t/a in which t is expressed as a multiple or fraction of a-p which is called the shift factor. The temperature at which the master curve is constructed is an arbitrary choice, although the glass transition temperature is widely used. When some value other than Tg is used as a reference temperature, we shall designate it by the symbol To. 

In addition to thermodynamic appUcations, 62 values have also been related to the glass transition temperature of a polymer, and the difference 62-61 to the viscosity of polymer solutions. The best values of 6 have been analyzed into group contributions, the sum of which can be used to estimate 62 for polymers which have not been characterized experimentally. 

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