Tg and

The term transition refers to a change of state induced by changing the temperatures or pressure. Two major thermal transitions are the glass transition and the melting, the respective temperatures beiiig called Tg and Tm- 

The different types of thermal response in the transition of a thermoplastic polymer from the rigid solid to an eventually liquid state can be illustrated in several ways. One of the simplest and most satisfactory is to trace the change in specific volume, as shown scherriatically in Fig. 2.19. 

In a perfectly crystalline polymer, all the chains would be contained in regions of three dimensional order, called crystallites, and no glass transition would be observed. Such a polymer would follow the curve G-F-A, melting at T to become a viscous liquid.,  

Perfectly crystalline polymers are, however, rarely seen in practice and real polymers may instead contain varying proportions of ordered and disordered regions in the sample. These semicrystalline polymers usually exhibit both Tg and T i (not r, ) corresponding to the disordered and ordered regions, respectively, and follow curves similar to E-H-D-A. Tm is lower than and more often represents a melting range, because the semicrystalline polymer contains crystallites of various sizes with many defects which act to depress the melting temperature. 

Both Tg and Tm are important parameters that serve to characterize a given polymer. While Tg sets an upper temperature limit for the use of amorphous thermoplastics like poly(methyl methacrylate) or polystyrene and a lower temperature limit for rubbery behavior of an elastomer-like SBR rubber or 1,4-cw-polybutadiene, Tm or the onset of the melting range determines the upper service temperature for semicrystalline thermoplastics. Between T,n and Tg, these polymers tend to behave as a tough and leathery material. They are generally used at temperatures between Tg and a practical softening temperature that lies above Tg and below Tm- 

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Here, consider that the initial time is tg and the potential is V eht, where the positive... 

The left-hand side of the equation relates the times required for a specific displacement to occur at Tg and at a distance T- Tg above Tg. 

The time-temperature superpositioning principle was applied f to the maximum in dielectric loss factors measured on poly(vinyl acetate). Data collected at different temperatures were shifted to match at Tg = 28 C. The shift factors for the frequency (in hertz) at the maximum were found to obey the WLF equation in the following form log co + 6.9 = [ 19.6(T -28)]/[42 (T - 28)]. Estimate the fractional free volume at Tg and a. for the free volume from these data. Recalling from Chap. 3 that the loss factor for the mechanical properties occurs at cor = 1, estimate the relaxation time for poly(vinyl acetate) at 40 and 28.5 C. 

Under 0 conditions occurring near room temperature, [r ] = 0.83 dl g for a polystyrene sample of molecular weight 10. f Use this information to evaluate tg and for polystyrene under these conditions. For polystyrene in ethylcyclohexane, 0 = 70°C and the corresponding calculation shows that (tQ /M) = 0.071 nm. Based on these two calculated results, criticize or defend the following proposition The discrepancy in calculated (rQ /M) values must arise from the uncertainty in T>, since this ratio should be a constant for polystyrene, independent of the nature of the solvent. 

Equation (6.8), to (d /dx)g. Figure 6.1 shows how the magnitude /r of the dipole moment varies with intemuclear distance in a typical heteronuclear diatomic molecule. Obviously, /r 0 when r 0 and the nuclei coalesce. For neutral diatomics, /r 0 when r qg because the molecule dissociates into neutral atoms. Therefore, between r = 0 and r = oo there must be a maximum value of /r. Figure 6.1 has been drawn with this maximum at r < Tg, giving a negative slope d/r/dr at r. If the maximum were at r > Tg there would be a positive slope at r. It is possible that the maximum is at r, in which case d/r/dr = 0 at Tg and the Av = transitions, although allowed, would have zero intensity. 

The gas absorptivity may also be obtained from the constants for emissivities. The product CiaTi absorptivity for black surface radiation), x (surface temperature), is gTi evaluated at T instead of Tg and at pL-Ti/Tc instead of pL, then multiplied by (Tg/Ti), or... 

Though this is a quartic equation, it is capable of explicit solution because of the absence of second and third degree terms. Trial-and-error enters, however, because (GSi)r and are mild functions of Tg and related Te, respectively, and aprehminary guess of Tg is necessaiy. An ambiguity can exist in interpretation of terms. If part of the enclosure surface consists of screen tubes over the chamber-gas exit to a convection section, radiative transfer to those tubes is included in the chamber energy balance, but convection is not, because it has no effect on chamber gas temperature. 

The first term on the right side of Eq. (5-179) is so nearly dominant for most furnaces that consideration of the main features of chamber performance is clarified by ignoring the loss terms and Lr or by assuming that they and have a constant mean value. The relation of a modified chamber efficiency T g(1 o) lo modified firing density D/(l — and to the normahzed sink temperature T = T-[/Tp is shown in Fig. 5-23, which is based on Eq. (5-178), with the radiative and convective transfer terms (GSi)/ja(TG — T ) -i- hiAijTc Ti) replaced by a combined radiation/conduction term (GS,) ,a(T - T ). where (GS])/ = (GS])/ + /jiA]/4oTgi Tg is adequately approximated by the arithmetic mean of Tg and T. ... 

FIG. 23-7 Imp ulse and step inputs and responses. Typical, PFR and CSTR. (a) Experiment with impulse input of tracer, (h) Typical behavior area between ordinates at tg and ty equals the fraction of the tracer with residence time in that range, (c) Plug flow behavior all molecules have the same residence time, (d) Completely mixed vessel residence times range between zero and infinity, e) Experiment with step input of tracer initial concentration zero. (/) Typical behavior fraction with ages between and ty equals the difference between the ordinates, h — a. (g) Plug flow behavior zero response until t =t has elapsed, then constant concentration Cy. (h) Completely mixed behavior response begins at once, and ultimately reaches feed concentration. 

Fig. 24.1. (a) A copolymer of vinyl chloride and vinyl acetate the "alloy" pocks less regularly, has a lower Tg, and is less brittle than simple polyvinylchloride (PVC). (b) A block copolymer the two different molecules in the alloy ore clustered into blocks along the chain. 

The glass transition temperature of a random copolymer usually falls between those of the corresponding homopolymers since the copolymers will tend to have intermediate chain stiffness and interchain attraction. Where these are the only important factors to be considered a linear relationship between Tg and copolymer composition is both reasonable to postulate and experimentally verifiable. One form of this relationship is given by the equation... 

The average polymer melt relaxation times between the processing temperature Tp and the solidifying temperature (the Tg in amorphous polymers and somewhere between Tg and with polycrystalline polymers). 

After-shrinkage is an additional problem with crystalline polymers and depends on the position of the ambient temperature relative to Tg and T. This was discussed in Chapter 3. 

In the case of crystalline polymers such as types E and F the situation is somewhat more complicated. There is some change in modulus around the which decreases with increasing crystallinity and a catastrophic change around the. Furthermore there are many polymers that soften progressively between the Tg and the due to the wide melting range of the crystalline structures, and the value determined for the softening point can depend very considerably on the test method used. 

By plasticisation. This in effect reduces the Tg and in the case of nylon which has absorbed small quantities of water the toughening effect can be quite substantial. It should, however, be noted that in the case of PVC small amounts of plasticiser actually reduce the impact strength. 

Equation (9.7) implies that if we know the viscosity at some temperature T we can estimate the viscosity at the Tg and hence in turn estimate the viscosity at another temperature Tj, i.e. the WLF equation gives the effect of temperature on viscosity. 

Because the polymer is polar it does not have electrical insulation properties comparable with polyethylene. Since the polar groups are found in a side chain these are not frozen in at the Tg and so the polymer has a rather high dielectric constant and power factor at temperatures well below the Tg (see also Chapter 6). This side chain, however, appears to become relatively immobile at about 20°C, giving a secondary transition point below which electrical insulation properties are significantly improved. The increase in ductility above 40°C has also been associated with this transition, often referred to as the 3-transition. 

As might be expected from a consideration of the factors discussed in Section 4.2, the imidisation process will stiffen the polymer chain and hence enhance Tg and thus softening points. Hence Vicat softening points (by Procedure B) may be as high as 175°C. The modulus of elasticity is also about 50% greater than that of PMMa at 4300 MPa, whilst with carbon fibre reinforcement this rises to 25 000 MPa. The polymer is clear (90% transparent) and colourless. 

Whilst increasing the length of alkyl side chain can, to some extent, depress Tg and improve low-temperature properties this is at the expense of oil resistance. On the other hand lengthening of the side chain by incorporation of an —O— or an —S— linkage could often depress Tg and reduce swelling in hydrocarbon oils. This led to the commercial development of copolymers of either ethyl or butyl acrylate with an alkoxy acrylate comprising some 20-50% of the total composition. Typical of such alkoxy compounds are methoxyethyl acrylate (1) and ethoxyethyl acrylate (11) ... 

The high intermolecular attraction leads to polymers of high melting point. However, above the melting point the melt viscosity is low because of the polymer flexibility at such high temperatures, which are usually more than 200°C above the Tg, and the relatively low molecular weight. 

As with the aliphatic polyamides, the heat deflection temperature (under 1.82 MPa load) of about 96°C is similar to the figure for the Tg. As a result there is little demand for unfilled polymer, and commercial polymers are normally filled. The inclusion of 30-50% glass fibre brings the heat deflection temperature under load into the range 217-231°C, which is very close to the crystalline melting point. This is in accord with the common observation that with many crystalline polymers the deflection temperature (1.82 MPa load) of unfilled material is close to the Tg and that of glass-filled material is close to the T. ... 

When polymerised the polymer is crystalline but has a surprisingly low reported melting point (T ) of 257°C. The ratio T /T of 0.91 (in terms of K) is uniquely high. Because of the small difference in Tg and there is little time for crystallisation to occur on cooling from the melt and processed polymer is usually amorphous. However, if molecular movements are facilitated by raising the temperature or by the presence of solvents, crystallisation can occur. 

Structurally the difference between PEN and PET is in the double (naphthenic) ring of the former compared to the single (benzene) ring of the latter. This leads to a stiffer chain so that both and are higher for PEN than for PET (Tg is 124°C for PEN, 75°C for PET is 270-273°C for PEN and 256-265°C for PET). Although PEN crystallises at a slower rate than PET, crystallization is (as with PET) enhanced by biaxial orientation and the barrier properties are much superior to PET with up to a fivefold enhancement in some cases. (As with many crystalline polymers the maximum rate of crystallisation occurs at temperatures about midway between Tg and in the case of both PEN and PET). At the present time PEN is significantly more expensive than PET partly due to the economies of scale and partly due to the fact that the transesterification route used with PEN is inherently more expensive than the direct acid routes now used with PET. This has led to the availability of copolymers and of blends which have intermediate properties. 

With these criteria, Chu [10] has suggested that the first step in designing a PSA is to formulate the adhesive to a predetermined target Tg and modulus window. This is discussed further in Section 7.1.5. 

While there are a large number of elastomers that can be formulated into pressure sensitive adhesives, the following list is intended to focus on commercially significant materials. Two subsets are differentiated in Table 1 those polymers that can be inherently tacky, and those that require modification with tackifiers to meet the Tg and modulus criteria to become pressure sensitive. 

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