Transition temperature glass

Glass transition temperature is one of the most important parameters used to determine the application scope of a polymeric material. Properties of PVDF such as modulus, thermal expansion coefficient, dielectric constant and loss, heat capacity, refractive index, and hardness change drastically helow and above the glass transition temperature. A compatible polymer blend has properties intermediate between those of its constituents. The change of glass transition temperature has been a widely used method to study the compatibility of polymer blends. Normally, the glass transition temperatme of a compatible polymer blend can be predicted by the Gordon-Taylor relation  

The glass transition temperature (7 ) 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 7 differ considerably between different methods therefore, specification of 7 requires an indication of the method used. 

The glass transition temperature, T, is one of the most important parameters for characterization of the glassy state. The transition behavior has been usually explained in terms of the rather idealized concept of free volume, but the microscopic description of the 

We have measured a range of physical parameters for Ge-As-Se glasses, and these are listed in Table 4.2. Results on the correlation between Tg and the MCN in Ge-As-Se glasses are shown in Fig. 4.11. It can be found that the modified Gibbs-DiMarzio equation can be used to fit Tg of most glasses, except those heavily Se deficient with a high MCN. 

The glass transition temperature (Tg) of a polymer is a 2nd order transition, involving a change in the solid polymer, from a flexible state to a rigid state. 

There are a number of transitions, depending upon the complexity of the molecular structure, for example the temperature at which rotation stops for a styrene unit about its axis in a polystyrene polymer is a transition point. However the glass transition point or T, is the temperature at which all molecular movement including mobility about the bonds in the backbone of the polymer becomes frozen. 

Almost any intrinsic property of a polymer which is temperature dependent can be used to measure the Tg of the polymer. Properties which may be used include specific volume, specific heat and refractive index, etc. 

The measurement of Tg involves taking readings of the property, over a range of temperatures, either side of the Tg. 

A plot of temperature against the property value will produce a graph, the slope of which shows an inflexion at the Tg. 

1 Optical Properties of HoF3-BaF2-AlF3-Ge02 Glasses 

2 Optical Properties of CeF3-BaF2-AlF3-Si02 Glasses 

The glasses in this system were brown when they were produced, even in inert gas (Ar). 

The brown colour is attributable to the presence of both Ce and Ce ions that have different energy levels in the glass. The energy transition that takes place between Ce and Ce causes the brown colour. This mixed-valence state of cerium ion resulted from hydrolysis and oxidation at high temperature. It was first found as a result of this study that 

3 Optical Properties of the Glasses Co-doped with ThF3 and SmF3 

Since glasses do not have a specific melting temperature, temperature benchmarks used in the processing of glasses are defined in terms of viscosities as described in Table 14.1. 

Schematic illustration of the glass transition indicated by rate of volume change with temperature. 

The measurements of Young s modulus in dependence of the temperature (dynamic-mechanical measurements, see Sect. 2.3.6.2) and the differential thermal analysis (DTA or DSC) are the most frequently used methods for determination of 

When a gel is cooled, the solvent crystallizes and the gel networks freeze into a glassy state. Due to the fast crystallization rate of water in hydrogels, the majority of water crystallizes. However, a portion of water vitrifies along with the gel networks [225]. The vitrified water is thought to be directly or indirectly restricted by the polymer. 

When vitrified water is examined by heating using DSC, the water in the gel shows a glass transition temperature as a cooperative phenomenon 

The measured melting enthalpy is normalized (aH ) by the polymer weight and plotted against the water content (Wc = water weight/polymer weight) the slope is the standard melting enthalpy 

The peak at 0°C is due to the free water peaks below 0°C are all classified as due to restricted water from the total enthalpy of melting, the water that crystallizes can be obtained and subtracted from the total water content to obtain the quantity of nonfreezing water 

Differential scanning calorimetry (DSC) has been used to successfully characterize stracture and transitions (changes in structure) in plastics for more than 40 years. Plastics are becoming more complex in order to meet the demand for lower-cost materials and improved physical properties. Consequently, it is becoming increasingly more difficult to characterize the structure and resulting physical properties of 

Many other resists or their blends have been studied by TMDSC, including positive resists, which contain a protection group and no crosslinker. Typically, TMDSC experiments were conducted under a modulation amplitude of Ay = 0.8 K, a period of p = 60 s, and an average heating rate of = 2 K min . All samples analyzed had a mass of about 1-3 mg. 

The glass transition temperature is also affected by pressure since an increase in pressure causes a decrease in the total volume, and an increase in is expected based on the prediction of decreased free volume. This result is important in engineering operations such as molding or extrusion, when operation too close to can result in a stiffening of the material. 

American Gas Association, Transmission measurement Committee, N8, American Petroleum Institute MPMS, Chapter 14.2, 2nd edn, November 1992. 

Simonet and E. Rauzy, Fluid Phase Equilibr, 1986, 21, 237. 

100-120 °C. It is important to know the glass transition temperature of polymer adhesive layers when high-temperature strain is to be expected. 

A common measure of compatibility is the glass transition temperature. In the case of miscibility, the glass transition temperature becomes somewhat a mixture of the glass transition temperature of the individual components. The Fox equation is suitable to predict the glass transition temperature of a miscible blend (4). 

In the limiting case of infinite molecular weight, the specific free volume is related to the temperature T above the glass transition temperature 

ar and Ug are the cubic thermal expansion coefficients in the rubbery and in the glassy state, respectively, and K is some additive constant. It was found that below the glass transition temperature basically the same relation holds. Thus it was concluded that the glass transition temperature is an iso-free-volume state. Therefore, for the glass transition temperature, r = T the relation 

In contrast, if the polymers are immiscible, the blend is composed of a superposition of the glass transition temperatures of the individual components. In the case of partial mixing, the situation becomes still more complex. 

A simple experimental method to measure the glass transition temperature consists in differential scanning calorimetry. 

How can Tg be determined In principle this can be achieved in various ways, however, two of the methods are of special importance and used in the majority of cases. These are temperature dependent measurements of the expansion coefficient or the heat capacity of a sample, carried out during heating or cooling runs. They need only small amounts of material, and standard equipment is commercially available. 

In view of the broadening of the step and the rate effects, it does not seem appropriate to introduce a sharply defined Tg. For the practical use as material parameter and for comparisons it is sufficient to conduct the measurements with a standard heating or cooling rate ( T = 10 — 1 Ks ) and to pick out some temperature near the center of the step, for example that associated with the maximum slope. The so-obtained values of Tg have a tolerance of some degrees but this must be accepted regarding the physical nature of the phenomenon. 

That a corresponding behavior is found for the enthalpy and the heat capacity is conceivable. As the free volume incorporates energy, changes in the volume and in the enthalpy are interrelated and this results in simultaneous steps in the expansion coefficient and the heat capacity. 

In an analysis, one has to consider the time dependence of relaxation processes under non-isothermal conditions as imposed during a cooling or heating run. Observations suggest that we represent the sample volume as a sum of two contributions 

The first part describes the volume of a hypothetical system without a-modes, being determined by the hard cores of the molecules, the anharmonic-ity of the vibrations and possible effects of local relaxation processes. The second term AVa accounts for the free volume produced by the a-modes. An analogous description is suggested for the enthalpy and we formulate correspondingly 

A plastic s thermal properties, particularly its Tg, influence its processability in many different ways. The selection of a plastic should take this behavior into account. The operating temperature of a TP is usually limited to below its Tg. A more expensive plastic could cost less to process because of its lower Tg that results in a shorter processing time, requiring less energy for a particular weight, etc. 

The glass transition generally occurs over a relatively narrow temperature span and 

Designers should know that above Tg, the mechanical properties of TPs are reduced. Most noticeable is a reduction in stiffness by a factor that may be as high as 1,000. 

Die Tg can be determined readily only by observing the temperature at which a significant change takes place in a specific electric, mechanical, or physical property. Moreover, the observed temperature can vary significantly, depending on the specific property chosen for observation and on details of the experimental technique (for example, the rate of heating, or frequency). Therefore, the observed Tg should be considered to be only an estimate. The most reliable estimates are normally obtained from the loss peak observed in dynamic mechanical tests or from dilatometric data (ASTM D-20). 

Polymer fibers typically are semicrystalline. The amorphous phase of polymer fibers exhibits glass transition, i.e., a reversible transition from a hard, glassy state 

Feed Roll Draw Roll Relaxation Roll 

At low temperature, an amorphous polymer is glassy, hard, and brittle, but as the temperature increases, it becomes rubbery, soft, and elastic. There is a smooth transition in the polymer s properties from the solid to the melt, as discussed above, so no melting temperature is defined. At the glass transition temperature, marking the onset of segmental mobility, properties like specific volume, enthalpy, shear modulus, and permeability show significant changes, as illustrated in Fig. 3.43. 

Consider a melted polymer that is cooling down. Assume that we monitor the value of the specific volume (v) as a function of temperature (T). Different curves of v versus T can be obtained depending on the rate of cooling and the capacity of the polymer to crystallize. 

First consider a polymer capable of crystallizing 100%, where the rate of cooling is slow enough to allow the chain polymers to form crystals. We can see that there is a drastic change in the specific volume once the melting temperature is passed (Fig. 3.44). The liquid melt state has a larger thermal expansion coefficient than the solid crystal state. 

Specific volume versus the temperature of crystalline and amorphous materials 

Whether the polymer is totally amorphous or partially crystalline, the material will be glassy (hrittle) or ruhher-like (soft) depending on its temperature with respect to Tg. If an amorphous polymer is at a temperature helow Tg, it will be brittle and will show properties of a glassy material for example, it will fracture more easily. As the temperature of the sample increases and approaches Tg, it adopts a leathery behavior and its elastic modulus decreases. When the sample has reached several degrees above Tg, it shows a clear rubbery behavior and is easily deformable. If the temperature is increased even more, the polymer reaches liquid flow behavior. If the polymer is semicrystalline, it exhibits similar behavior, but when it reaches the melting temperature the crystals will break up, and the polymer will then reach the melted liquid state. This behavior is illustrated in Fig. 3.45 where the elastic modulus is plotted versus temperature. 

When different elastomers are being described, a fundamental property which is often quoted is the glass transition temperature, Tg, which differs from one elastomer to another. For example, for natural rubber Tg is -70°C (-95°F). Broadly this means that above -70°C the material behaves as a rubber, but below -70°C the material behaves more like a glass. When glassy, natural rubber is about one thousand times as stiff as it is when rubbery. When glassy, a hammer blow on natural rubber will cause it to shatter like a glass when rubbery the hammer is likely just to bounce off. 

At normal temperatures, the rubber molecular chains are in a constant state of thermal motion, they are constantly changing their configuration, and their flexibility makes them reasonably easy to stretch. It is to be noted that as the temperature is lowered the chains become less flexible and the amount of thermal motion decreases. Eventually, a low temperature, the glass transition temperature, is reached, where all major motion of the chains ceases. The material no longer has the properties which make it a rubber, and it behaves as a glass. 

For all practical engineering uses of rubbers we require good flexibility, and, therefore, it is essential that we use them only at temperatures which are comfortably above the glass transition. 

The blends prepared by mixing iPP and PB-1 with HOCP were investigated by DSC to obtain information about their glass transition temperature, Tg. Before scans, the 

The amorphous blends showed a single Tg with numerical value dependent on composition. The dependence of Tg on the weight fraction of HOCP (referred to the overall amorphous content in the blends) is shown in Table 6.1. The Tg values of the blends were also calculated by using the theoretical relation of Fox (34)  

A good agreement was observed between the experimental values obtained for the iPP/HOCP blends and the ones calculated by Fox equation. The appearance of a single glass transition temperature should suggest that the blend presents a single homogeneous amorphous phase, that is, the two components are miscible in the amorphous phase. For the PB-l/HOCP blends, the experimental values of Tg always below the theoretical values. This behavior could be an indication of specific interactions between the two components in the amorphous phase and/or an indication of incomplete compatibility between the components (15). 

One of the major drawbacks associated with starchy materials is their brittleness. This is related to a relatively high glass transition temperature (Tg). This temperature marks the transition from a highly flexible state to a glassy one. Tg is considered the most important parameter for determining the mechanical properties of amorphous polymers and for control of their crystallization processes [40, 41]. 

The effect of starch plastification with water has been repeatedly studied, and various techniques for glass transition temperature have been compared. Differential scaiming calorimetry (DSC) is used most commonly, but the glass transition temperatures found by DSC can be 10-30 °C higher than the Tg values obtained by NMR (nuclear magnetic resonance) or DMTA (dynamic mechanical thermal 

However, the results of measurements published by various authors are inconsistent to a high degree, due to complex changes that occur in starch as a result of high temperatures and different measurement conditions. 

Estimates found the Tg values of dry amylose and amylopectin to be 227 °C, whereas Bizot et al. [42] determined that the glass transition temperature of dry starch is 332 °C. An increase in water content in extruded TPS caused a drop in Tg irrespective of the starch type used. To decrease the Tg of potato TPS close to room temperature, about 0.21 g water is needed for Ig starch [44—46]. 

Zeleznak and Hoseney [47] found that the glass transition temperature of wheat starch with 13-18.7% moisture varies between 30 and 90 C and that Tg is likely to be lower than room temperature if the starch humidity increases above 20%. Van Soest et al. [48] determined a Tg value of 5 C for extruded potato starch with 14% moisture content, whereas at higher moisture content the Tg could not be determined. Shogren showed that the glass transition temperature for starch with 7-18% moisture content ranged from 140 to 150 C [49, 50]. 

The physical properties of a polymer are different in the amorphous and crystalline regions and are therefore covered separately. The glass transition temperature discussed in this section is only relevant for the amorphous regions. 

It should be noted that orthotropic FRP composite materials show distinct differences of T-modulus and strength in longitudinal and transverse direction, while the difference of glass-transition temperature in both directions are small, as demonstrated in Table 2.3. 

In addition, Tg determined through DMA measurements is obtained at a prescribed heating rate and dynamic loading frequency (see Table 2.2). It is found that the Tg values may change with the heating rate [3] or frequency [13], therefore it is necessary to specify the heating rate and frequency for the T value measured. 

Similar behavior was also reported for the dielectric permittivity for polymer the temperature corresponding to the maximum of permittivity T ) also shifts 

Heating Rate Dependence of Class-Transition Temperature 

Several effects may lead to this result of heating rate-dependent decrease of modulus (i) a nonuniform through-thickness temperature gradient, or (ii) a thermal lag between the specimen and the DMA temperature measurement, or (iii) a general time dependence, in addition to the temperature dependence of the polymer properties. 

Many different methods can be used to measure the degree of crosslinking within an epoxy specimen. These methods include chemical analysis and infrared and near infrared spectroscopy. They measure the extent to which the epoxy groups are consumed. Other methods are based on the measurements of properties that are directly or indirectly related to the extent and nature of crosslinks. These properties are the heat distortion temperature, glass transition temperature, hardness, electrical resistivity, degree of solvent swelling and dynamic mechanical properties, and thermal expansion rate. The methods of measurement are described in Chap. 20. 

Perhaps the most significant property that is controlled by the degree of crosslinking is the glass transition temperature Tg. The importance of Tf in epoxy adhesive formulations is discussed next. 

When chain segments can move relatively freely in cured polymers, it is most likely due to low crosslink density or the mobility of the molecular chain structure. The glass transition temperature is a measure of the mobility of the molecular chains in the polymer network as a function of temperature. The glass transition is the reversible change in a polymer from (or to) a rubbery condition to (or from) a hard and relatively glassy state condition (Fig. 3.14). This transition occurs at a temperature called the glass transition temperature or Tg. It is 

FIGURE 3.14 Relationship between elastic modulus and temperature showing the glass transition region.22 

As shown in Fig. 3.14, the glass transition temperature is usually a narrow temperature range rather than a sharp point, as is the freezing or boiling point. Molecular motion at this point does not involve entire molecules, but in this region deformation begins to become nonrecoverable as permanent set takes place. 

In contrast to small organic molecules, long hain polymers are characterized not only by the center of mass diffusion, but also by small-scale diffusion of a few monomer units. It is generally observed that even monomolecular reactions could happen only if these motions are unfrozen. In the wider sense, the dependence of reaction efficiency on polymer morphological structures can be described in terms of the free volume concept, and of diffusion constants [6]. These molecular characteristics are themselves dependent on the thermal transitions in polymers, the most important of which being ffie glass transition temperature. 

The glass transition corresponds to the onset of large-scale motions of long seg- 

Chain mobility has important implications for bimolecular reaction efficiency. Bimolecular reactions depend on (i) the frequency of encounter and (ii) the concentrations of the reactive species. Upon bond cleavage, macroradicals are formed in pairs and can initiate degradative reactions only if they are sufficiently flexible to move apart. If the macroradicals are held rigid, as in thermosets or below the Tg, they may recombine by the cage effect without any detectable molecular change. 

Mass transfer limitations are a function of the diffusion coefficient for each species. Two situations can be encountered [6]  

The rate constant for this radical relay transfer reaction has the same activation energy as that of the j8-relaxation in the corresponding polymer. This result again suggests that the kinetics of macroradical reactions in solid polymers is sensitive to small-scale molecular dynamics characterized by the secondary 

The Tg of the resulting polymers can be steered in this way to any desired value between the Tg of the two homopolymers involved by adjusting the level of co-mono-mer employed. The Tg of homo(polynorbornene) is around 370-390 °C. The measured Tg of 5-decylnorbornene homopolymer is around 150-160 °C. Longer alkyl substituents (e.g. hexadecylnorbornene) have a more pronounced impact on Tg. 

An alternative interpretation of the entanglement phenomenon is to consider that a large MW polymer flows by a series of snake-like motions called reptation (De Gennes 1971). The concept of entanglements will be adopted in this text because it has been commonly used in polymer science and may be more intuitively understood by cereal chemists who are new to the area. 

How do we interpret dough mixing characteristics such as those displayed by mixograms or farinograms Several observations give us clues and we 

In order to develop a dough that has properties suitable for bread-making, two requirements need to be met (Kilborn and Tipples 1972). First, a critical amount of work must be imparted to the dough. Second, optimum 

Tg is dependent on degree of cross-linking area and molecular weight. The value of Tg increases as molecular weight of a polymer increases or as the branching or cross-linking increases. Thus, for PS 3, Table 11.4, Tg = 100°C which is much higher than for PE 5, Tg = 125°C. Similarly, the 

The Tg of a polymer can be reduced by the addition of a plasticizer to the solid plastic. This reduces the van der Waals interactimi between the polymer chains and allows the molecules to move. The plasticizer may be considered as an internal lubricant. The plasticizer can also be cmisidered to increase the free volume of the polymer by allowing increased motion of the chain ends, the side chains, or even the main chain. Another possible mechanism by which the plasticizer lowers the is in terms of the solvent/ solute system that forms when the plasticizer can be considered to solubilize the polymer. The plasticizer is usually a low volatile, low molecular weight organic compound which is compatible with the polymer. 

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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...

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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