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7.1.3 Oxidative induction time/temperature

Metals suffer from corrosion, and while plastics are immune to corrosion, they also are prone to degradation such as oxidation. Polymer producers normally add stabilizers to improve the resistance of susceptible polymers to oxidative degeneration. Polyethylene, for example, can suffer oxidation decomposition in the air at approximately 200 °C, whereas, in the absence of oxygen, in a nitrogen atmosphere, it undergoes thermal degradation at approximately 400 °C. Therefore, antioxidants are added to protect against oxidisation in applications.

Determination of oxidation induction time/temperature (OIT) is the primary means of finding out the resistance of polymeric products to oxidation. OIT is a standardized test performed using a DSC. The associated standard methods include:

ISO/TR 10837:1991 Determination of the thermal stability of polyethylene (PE) for use in gas pipes and fittings

ISO 11357-6:2008 Plastics - Differential scanning calorimetry (DSC) - Part 6: Determination of oxidation induction time (isothermal OIT) and oxidation induction temperature (dynamic OIT)

ASTM D3895 - 07 Standard test method for oxidative-induction time of polyolefins by differential scanning calorimetry

ASTM D5885 - 06 Standard test method for oxidative induction time of polyolefin geosynthetics by high-pressure differential scanning calorimetry

The test essentially subjects the specimen to an accelerated oxidation environment, while monitoring for the occurrence of exothermic and endothermic reactions. Thus, the higher the values for the OIT, the more oxidation resistant the sample is. The tests follow either a "dynamic" or "static" method: in dynamic method, the specimen is heated continuously under oxygen or air flow from the start, whereas, in static procedure, a semi-crystalline plastic, is heated continuously under nitrogen flow to above its melting peak and held at that temperature, then the atmosphere is changed from N₂ (inert) to O₂ or air and the heat is maintained (isothermal heating) until the exothermic degradation peak is reached.

The dynamic method enables the measurement of the oxidative induction temperature, T_oit (indicating the onset of oxidation), either as an extrapolated value or an exothermic offset value. The offset of heat flow from the base-line is used when the onset temperatures are difficult to reproduce by extrapolation, and consists of drawing a line parallel to the baseline at an offset distance of A = 0.05 W/g, as recommended by ISO 11357-6, and the intersection of this line with the exothermic peak is defined as the onset of oxidation, see Figure 7.3. The static method yields the oxidative induction time (the time period from the changeover to oxygen to onset of oxidation), see Figure 7.4. (ISO 11357-6:2008).

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Figure 7.3Illustration of a dynamic OIT scan for oxidation induction temperature, T_oi (source: ISO 11357-6:2008)

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exo

T

O)

о

го

CD

■N,

О

О

CD Q_

E

CD

time, min

Figure 7.4Illustration of a static OIT scan for oxidation induction time, t_ott

A useful application of the measurement is to find out the OIT of the unprocessed polymer and the OIT of the processed plastic. Any variation in measurements should indicate the extent of the impact of polymer processing on the reduction of oxidation resistance.

7.2 Thermogravimetric analysis

Thermogravimetric analysis (TGA) measures temperature and/or time-dependent mass changes in a sample of a material. The technique is popularly used to indicate the thermal stability of materials and to determine the composition of plastics, polymer blends and polymer-matrix composites. TGA is a convenient method of checking/verifying any modifications to material formulations.

The associated standard methods include:

ISO 11358:1997 Plastics - Thermogravimetry (TG) of polymers - General principles

ISO 9924-1:2000 Rubber and rubber products - Determination of the composition ofvulcanizates and uncured compounds by thermogravimetry - Part 1: Butadiene, ethylene-propylene copolymer and terpolymer, isobutene-isoprene, isoprene and styrene-butadiene rubbers

ASTM D6370 - 99(2009) Standard test method for rubber-compositional analysis by thermogravimetry (TGA) ASTM El 131 - 08 Standard test method for compositional analysis by thermogravimetry

ASTM E1582 - 04 Standard practice for calibration of temperature scale for thermogravimetry DIN 51006 (2000) Thermal analysis (ТА) - Thermogravimetry (TG) - Principles

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TGA tests can be conducted either in temperature scanning mode or in isothermal mode. In temperature scanning mode,the sample is subjected to a controlled temperature programme in a controlled atmosphere (i.e., an inert gas (N₂ or argon) or oxygen or air purge at a certain flow rate) and its mass is monitored. Constant heating rates (or temperature scanning rates) are typically in the range of 5-20 °C/min, slower scans produce better resolution of transitions, but faster rates are useful for a quick initial assessment scan. Alternatively, tests can be conducted isothermallyand mass change is recorded against time (min). In this case the sample is rapidly heated (e.g., 100 °C/min) to the required temperature in order to avoid/minimize evaporation or reaction prior to reaching temperature. Isothermal runs are useful for studying processes such as moisture absorption or desorption, curing reactions that produce small chemicals (e.g., water or formaldehyde), and emission of HC1 as PVC degrades. In TGA, the specimen size and geometry should be controlled: since for evaporation, surface area is important, and for diffusion of volatiles from the body of the specimen to its surface, the area/volume ratio is a factor. In oxidative degradation, the diffusion of oxygen into the material would also be influenced by specimen size and shape.

The test results produce thermogravimetric curves (a plot of % mass change against temperature or time). From the TGA curves, data such as mass loss (sometimes mass gain as in oxidization) and associated temperature values can be extracted. The derivative of the TGA data (DTG) can also be plotted and produces a useful curve for a clearer identification of events, particularly if these events are either too close together or are not very distinct. The point of the greatest rate of change on the mass loss TGA curves, i.e., the inflection point, is indicated by a peak on a DTG curve, which makes identification of the events and the extraction of data from the curves easier, see Figure 7.5.

402 °C

778 °C

-2

To

To

ro

CD

-8 ■-§ ro

S

T3

-12

-14

100 200 300 400 500 600

temperature, °C

Figure 7.5(-)TGand (-) DTG traces for a blend of natural and SBR rubber (source: Netzsch GmbH (see Reference (Kaisersberger 1994))

TGA can quantify loss or gain of water, loss of solvent, loss of plasticizer, decarboxylation (release of CO₂), composition of polymer blends, curing-related emissions, pyrolysis and related emissions, oxidation, decomposition and filler/ash content. TGA is frequently used as a quality control tool, but is also used to reverse engineer a product and to distinguish between competing products. Figure 7.5 illustrates an application, showing the TGA and DTG traces for a blend of natural rubber (NR) with SBR, used as anti-vibration mountings in the automotive industry. The TGA scan was conducted on

Introduction to Polymer Science and Technology Thermal properties

13 mg cuttings from NR/SBR vulcanized sheet under 10 ml/min N₂ purge, heating at 20 °C/min up to 850 °C. The graph enables one to identify the composition of the blend and quantify the amounts of the component materials. The curve shows evolution of plasticiser, with a mass of 6.4%, at about 300 °C. The pyrolysis of NR, 40.6%, and SBR, 28.7%, follows at temperatures of approximately 400 and 467 °C. At 778 °C calcium carbonate filler (the chalk) decomposes into CO₂ (5.2 %) and CaO. This information enables the calculation of the filler content as shown in the text box below.

The chemical formula for decomposition of chalk: CaCO₃ -^CaO + CO₂t

Atomic masses of Ca = 40; С = 12; О = 16

.-. molecular masses for CaCO₃ = 100 and CO₂ = 44, yielding CaCO₃ / CO₂ = 100 /44 = 2.27.

.-. the amount of chalk is 2.27 times that of CO₂, i.e., 2.27 x 5.2 = 12 %.

Due to impurities in the chalk filler, a slightly higher factor, e.g. 2.5 gives a better estimate in practice. As filler, the pure form of chalk is normally used in thermoplastics, but not so in the rubber industry.

The blend formulation also contains carbon black, which can be quantified by cooling down the sample residue to 450 °C and changing the gas to O₂ (to burn C-black) and applying a second heating scan up to 800 °C (Kaisersberger 1994, p89). Instruments with modulated thermogravimetry (MTGA) (Blaine 1998) technique are also commercially available.

Introduction to Polymer Science and Technology Thermal properties

TGA can also be coupled with other analytical techniques to provide simultaneous information and enable more convenient and effective analysis in a shorter period of time, using less material. Simultaneous thermal analysis (STA)technique combines DSC (or DTA) with TGA. A mass spectrometer (MS) can also be attached to the STA instrument for evolved gas analysis and provides information about the cause of mass changes. Other combination techniques are used to analyze the gas products from a TGA experiment. This approach is called evolved gas analysis, EGA,include:

TGA-FTIRis a combination of TGA with a Fourier transform infrared spectrometer (FTIR).

A sample scanned on the TGA will release volatile materials or generate combustion components as it burns. These gases are then transferred to IB. cell, where the components can be identified. This technique is most useful when the evolved gases are small chemicals, such as water, carbon dioxide or common solvents which have characteristic IB. spectra.

TGA-MScombination allows detection of very low levels of impurities. By heating a sample on the TGA, the sample will emit volatile materials or generate combustion components as it burns. These gases are transferred to the MS where the components can be identified. Because of its ability to detect very low levels of material, the TGA-MS is a powerful tool for quality control, safety, and product development. This technique is most useful when the evolved gases or breakdown products are known in advance but are few in number.

TGA-GC/MScombination enables the released gases to be transferred to a gas chromatograph (GC) where the components can be collected and run on GC to separate the material and the peaks can be identified by the MS. Because of its ability to detect very low levels of material in a complex mixture, the TG-GC/MS is a powerful tool for quality control, safety, and product development.

7.3 Thermomechanical analysis

Temperature-dependent dimensional changes in materials, such as thermal expansion, can be determined using a dilatometer or a thermomechanical analyser. The expansion behavior changes significantly at relaxation transitions of viscoelastic materials, therefore, the technique can also be used to determine properties such as the T . This was covered in Section 5.3, together with a brief description of a dilatometer. In a dilatometer, the specimen is not subjected to any external loads other than the weight of the small amount of liquid surrounding it, whereas, in thermomechanical analysis (TMA), a constant level of small load is maintained on the specimen.

The associated standard methods include:

ISO 11359-1:1999 Plastics - Thermomechanical analysis (TMA) - Part 1: General principles

ISO 11359-2:1999 Plastics - Thermomechanical analysis (TMA) - Part 2: Determination of coefficient of linear thermal expansion and glass transition temperature

ASTM E831 - 06 Standard test method for linear thermal expansion of solid materials by thermomechanical analysis ASTM E1363 - 08 Standard test method for temperature calibration of thermomechanical analyzers

Introduction to Polymer Science and Technology Thermal properties

ASTM El 545 - 11 Standard test method for assignment of the glass transition temperature by thermomechanical analysis

ASTM El824 - 09el Standard test method for assignment of a glass transition temperature using thermomechanical analysis: tension method

DIN 5375 Testing of plastics; determination of the coefficient of linear thermal expansion

In a standard TMA experiment, the sample is positioned on a quartz stage and a moveable quartz glass probe is placed on the top of the sample. The furnace, surrounding the sample stage and probe, provides heating/cooling during the measurement. A thermocouple adjacent to the sample monitors sample temperature, and the dimensional changes occurring as a function of time, temperature or force are monitored by a linear variable differential transformer (LVDT) attached to the probe.

There are several available probes (expansion, penetration, macro-expansion, hemispherical) which can be used to vary probe contact area and stress on the sample in order to obtain a desired mode of deformation. Normally, expansion is observed with large contact areas and low forces, and penetration with small contact areas and high forces. The larger surface area of the macro-expansion probe enables a larger contact area and therefore facilitates analysis of soft or irregular samples, powders, and films. Depending upon the probe / sample contact area and the load applied, the T can be detected by either an upward (expansion) or downward (penetration) movement of the probe.

Penetration measurements use an extended tip probe to focus the drive force on a small area of the sample surface for measurements of T , softening temperature, and melting behaviour. It is valuable for characterizing coatings without their removal from a substrate. The probe operates like the expansion probe, but provides a larger applied stress. The hemispherical probe is an alternate penetration probe for softening point measurements in solids.

TMA can also measure viscoelastic properties of creep or stress relaxation. However, the main property measurement, in expansion mode, is the coefficient of thermal expansion (CTE) for solid samples. The linear (a) and the volume ф) CTEs are defined as

a = (AL / AT) / (L_o) [\im I m °C] or simply "С¹; p = (AV / AT) / (V) [°C^l]

where , L_o and V_o are the initial length and volume, AL and AV are the changes in length and volume, and AT is the change in temperature from the initial temperature associated with L_o and V_o. For an isotropic and homogeneous material, the CETs are related by p = 3a.

Expansion and contraction of materials with temperature variation generates thermal stresses, which can cause undesirable consequences. Unstrained isotropic materials will be free of thermal stresses; however, in most practical applications the material is under restrain and therefore suffers thermal stresses. The situation becomes worse when the stress is uneven/ unbalanced. The magnitude of stress resulting from a temperature change AT is

a = EaAT.

Introduction to Polymer Science and Technology Thermal properties

The thermal stressesthat are frozen in the material as residual stresses,depending on the magnitude, can cause fracture or permanent deformation. It is of concern particularly in materials with low heat conductivities such as polymers when the rate of heating or cooling is too fast, and therefore, temperature gradients form between the surface and the bulk of the material causing differential expansion or contraction: upon heating, the surface expansion is restricted by the cooler inner mass and therefore experiences compressive stresses, which are balanced by the tensile stresses induced inside; the nature of stresses are reversed upon quenching. The situation becomes more intense in composite materials, where the material is a mixture of components with different CETs, and unless the structure of the material in the product is symmetrical/balanced, then residual stresses can ensue from heat inputs involved in processing and subsequently in service.

In glass-fibre-reinforced polyester resin, for instance, the fibre and the matrix undergo a differential thermal contraction, with linear coefficients of expansion of 4.7 x 10~⁶/°C for GF and as high as 1.5 x 10⁴/°C for polyester resin, cooling to 20 °C from 120 °C curing temperature produces a differential strain of approximately 1.5 % which is approximately 75 % of the elongation to failure of the resin. The carbon and Kevlar 49 fibres have -ve linear coefficients of expansion parallel to their lengths; therefore, they exert even greater thermal stresses than glass fibres on the resin along their lengths. In contrast, the expansion coefficients for carbon and Kevlar fibres in perpendicular direction to the fibre axis are +ve and this also results in differences in micro-stresses.

Figure 7.6 shows the CET values for some thermoplastics. The tests were conducted at a heating rate of 3 °C/min, using 6x6 mm specimens under a macro-probe and 0.5 g load (Ehrenstein 2004, pl75). The significant variations in CET are dictated by T in the case of amorphous thermoplastics, and by the softening temperature, which is close to melting point, in the case of semicrystalline thermoplastics.

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50 100 150

Temperature, °C

Figure 7.6CET (a) vs. temperature for PS, PE, PC, PP and PI (source: Ehrenstein 2004, pi 73)

Modulated thermo mechanical analysis (MTMA) was reported by Price inl998, and is a useful tool for determining/ identifying thermo dynamic and kinetic, reversing and non-reversing, changes that take place simultaneously. In MTMA, a sinusoidally varying temperature program is added to an underlying linearly changing or static temperature program. Fourier transformation of the oscillatory temperature "forcing function" produces reversing and non-reversing components for the dependent variable. The reversing signal is associated with properties dependent upon the temperature rate of change and, therefore, enhances CET and T measurements. The non-reversing signal contains events that relate to kinetic processes, which are both temperature and time dependent (e.g., stress relaxation, softening and heat shrinking). This ability to separate thermodynamic from kinetic events aids in the interpretation of the thermal curve, measures expansion and contraction taking place at the same time and provides a more accurate estimation of the glass transition temperature than the softening temperature.

Within the context of thermal expansion, the unusual behaviour of rubbers should also be mentioned: under normal, unstressed, conditions rubber expands like other materials as it is heated, however, when under tension it behaves differently, contracting in the loading direction, rather than expanding, as it is heated. The explanation of this behaviour lies in the contribution of entropy to the elasticity of rubber: the deformation of ordinary elastic solids are controlled by changes in internal energy (storage and release of strain energy as material is stressed and released), resulting in the increase of the inter-atomic bond lengths with rising temperature; whereas rubber elasticity is controlled by changes in entropy.

Randomly coiled/entangled rubber molecules in their equilibrium state uncoil on being stressed, and in this stressed state the input of energy in the form heating causes the rubber to contract and enable individual chain segments to recoil back to their equilibrium state, thus raising the entropy and reducing the free energy. In other words, as it is stretched, the rubber chain moves from a more probable (higher entropy) to a less probable (lower entropy) state. It is this lowering of entropy of the conformation that generates the retractive force, so rubber is described as an 'entropy spring'.

The fact that rubbers deform elastically by the uncoiling of long, disordered molecule segments in between sparsely spaced crosslinks and/or entanglements, rather than by the stretching of individual inter-atomic bonds, is also the reason why the stiffness of rubber is so much lower than other materials. It is thus possible to predict the stiffness of a rubber solely from knowledge of its crosslink density (which dictates the chain segment length). There are approximately 500 to 1000 monomers in between cross-links in rubber. Increasing the degree of crosslinking would change the behaviour: e.g., when

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the rubber band is left out for a long time, the excess UV light provides the polymer molecules with the activation energy to form more cross-links, resulting in less stretch-ability in the rubber band, the chains are prevented from uncoiling or sliding past each other, due to the higher number of cross-links. Stretching, therefore, is effectively pulling on the C-C backbone bonds of the polymer, which are very stiff and will not stretch much. Instead the rubber band snaps with very little extension.

Some oils and other chemicals have a similar effect on rubbers. However, if the initial density of cross-links is very low as in butyl rubbers, then it becomes less likely that some further cross-linking would bring it to a level sufficient for degradation, accordingly, butyl rubbers are resistant to degradation from U.V. light and from oils, and become suitable in making products such as bungee jumping cord.

7.4 Dynamic mechanical thermal analysis

Dynamic mechanical thermal analysis (DMTA) or just dynamic mechanical analysis (DMA) (although this second description may be confused with fatigue testing), places the specimen, often a small rectangular bar, under vibration, normally sinusoidally varying stress/strain, and measures mechanical properties in terms of various modulus parameters and damping as a function of temperature, time and frequency. DMTA is a powerful technique and provides information on material rigidity, mechanical damping, relaxation behaviour and material composition and structure for polymers. It must be the best technique for determining relaxation temperatures of T and various other secondary glass transition temperatures (and for this reason the subject matter was covered extensively in Section 5.2.3). The tests are standardized: the general principles are covered in ISO 6721-1 and ASTM 4092. The tests can also be conducted in different loading modes (the loading modes are depicted in Figure 7.7). The standards describing the test procedures under different loading modes are listed below.

The standard test methods for tension modeinclude:

ISO 6721-4:2008 Plastics - Determination of dynamic mechanical properties - Part 4: Tensile vibration -- Non-resonance method

ISO 6721-9:1997 Plastics - Determination of dynamic mechanical properties - Part 9: Tensile vibration -- Sonic-pulse propagation method

ASTM D5026 - 06 Standard test method for plastics: Dynamic mechanical properties: in tension

The test methods for torsion mode:

ISO 6721-2:2008 Plastics - Determination of dynamic mechanical properties - Part 2: Torsion-pendulum method

ISO 6721-7:1996 Plastics - Determination of dynamic mechanical properties - Part 7: Torsional vibration -- Non-resonance method

ASTM D5279 - 08 Standard test method for plastics: Dynamic mechanical properties: in torsion

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The test methods for flexure mode:

ISO 6721-3:1994 Plastics -- Determination of dynamic mechanical properties - Part 3: Flexural vibration - Resonance-curve method

ISO 6721-5:1996 Plastics - Determination of dynamic mechanical properties - Part 5: Flexural vibration - Non-resonance method

ASTM D5023 - 07 Standard test method for plastics: Dynamic mechanical properties: in flexure (three-point ending) ASTM D5418 - 07 Standard test method for plastics: Dynamic mechanical Properties: in flexure (dual cantilever beam) The test methods for shear mode:

ISO 6721-6:1996 Plastics - Determination of dynamic mechanical properties - Part 6: Shear vibration - Non-resonance method

ISO 6721-8:1997 Plastics - Determination of dynamic mechanical properties - Part 8: Longitudinal and shear vibration - Wave-propagation method

ISO 6721-10:1999 Plastics - Determination of dynamic mechanical properties - Part 10: Complex shear viscosity using a parallel-plate oscillatory rheometer

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The test methods for compression mode:

ASTM D5024 - 07 Standard test method for plastics: dynamic mechanical properties: in compression The test methods for melt rheology and resin cure include:

ASTM D4440 - 08 Standard test method for plastics: Dynamic mechanical properties: Melt rheology ASTM D4473 - 08 Standard test method for plastics: Dynamic mechanical properties: Cure behaviour

An aerospace-specific standard is given in DIN 65583:1999-04 Aerospace -Fibre reinforced materials - Determination of glass transition of fibre composites under dynamic load.

tension

compression

shear

3-point bending

single-cantilever bending

dua^cantilever bending

Figure 7.7Different deformation modes (source: Mettler-Toledo AG, Analytical)

Tension mode is suitable for specimens of low cross-sectional area, compression for low elastic modulus specimens, shear for soft/flexible specimens, 3-point bending for high elastic modulus specimens, single-cantilever bending for medium modulus and high CET specimens, and dual-cantilever bending for low-to-medium modulus specimens.

Instrumental considerations, besides the modes of deformation, include many more parameters: including frequency range, temperature range, heating rate, range of amplitudes of vibration and force range. Commercially available equipment quote values of 10~³ to 10³ Hz frequency range (many fixed values can be selected within this range, -170 to 600 °C temperature range, 0-20 °C/min heating rate, 0-40 °C/min cooling rate, amplitude of vibrations of + 0.5 u,m-10 mm, and 1 mN to 40 N force range. Normally the temperature range is dictated by the type of polymer being tested and the property being measured (e.g., T ), frequency of 1 Hz (note that the frequency can only be set on non-resonant forced vibration machines), and amplitude of vibration 50 u,m are selected. The maximum frequencies differ for modes of deformation, for example a manufacturer indicates 1000 Hz for shear, 300 Hz for bending, 300 Hz for tension, and 300 Hz for compression. At very high frequencies, one should be aware of machine resonance!

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Figure 7.8 shows the property vs. temperature curves for the main DMTA properties. It is also indicated that in the glassy state the elastic behaviour is energy dominated and in the rubbery state, it is entropy dominated, particularly with cross-linked polymers. Further increases in temperature beyond the rubbery state will cause flow in thermoplastics and therefore, the storage modulus (E') and the complex modulus (E*) will drop off significantly from the rubbery plateau, leading to liquid phase, whereas, thermosetting polymers will maintain their rubbery state.

energy-elastic state

glass transition

_entropy-elastic_ state

E"

tanS

Л

temperature

Figure7.8.lllustration of DMTA curves for an amorphous polymer (source: Ehrenstein 2004, p239)

7.4.1 Applications

Applications of DMTA are covered widely, for example, Turi (1997), Nielsen (1974, p 139), Gearing (1999, p501), Ehrenstein (2004, p236) and support notes from various well known manufacturers such as Netzsch, PerkinElmer, ТА Instruments, Mettler-Toledo AG, etc. for various polymer types and polymeric products, such as coatings, adhesives and composites as well as some non-polymeric materials.

A few examples of material characterisations using DMTA are briefly described in the following sub-sections.

7.4.1.1 Molecular-relaxation transitions

Molecular-relaxation transition temperatures are summed up in Figure 7.9 for amorphous and crystalline thermoplastics and thermosetting plastics. The extent of rubbery plateau is dictated by the molecular weight (M), which dictates the degree of chain entanglement, in amorphous thermoplastics; by the degree of crosslinking in thermosetting polymers; and by the degree of crystallinity in crystalline TPs. Chain entanglements have similar effects to that of cross-links, and, therefore, with greater chain entanglement (high M) a longer rubbery region is observed, prior to the onset of flow region, where solid changes to viscous liquid and molecular chain slippage occurs readily. In the rubbery region, depending on the factors such as the degree of crosslinking and crystallinity, molecular weight and therefore the level of molecular entanglement that a slight rise in elastic modulus with increasing temperature may be observed due to entropy effects described briefly in Section 7.3.

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temperature, °C

Figure 7.9A sketch of real modulus (E') vs. temperature, showing various transitions in polymers

Not all the transitions shown on the graph would be exhibited by all the polymer types. The terms a, p and у transitions are often used in association with both amorphous and semicrystaUine polymers. In amorphous thermoplastics and in thermosets, a-transition is the glass transition, but with some semicrystaUine thermoplastics the a-transition indicates a transition that may occur between T and T , and B-transition becomes the glass transition. A clearer nomenclature, however, includes sub-scripts "a" for amorphous and "c" for crystalline so that the transitions are indicated as y_a, P_a and oc_a, and the higher temperature a-transition observed between T and T_m is distinguished as oc_c,

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Suggested mechanisms for the high temperature a_c-transition in semicrystalline polymers include the shearing of the amorphous tie-molecules between crystalline lamellae and/or the rotation of polymer chain segments about their axis in the crystalline regions. In amorphous polymers P-transition is normally referred to as a secondary-glass transition, occurrence of which contributes to improvement in material toughness. Rigid polymers with high impact strength exhibit prominent secondary transitions, such as PCs, PAs, polyethersulphones, PVC, PET and epoxy resins.

The molecular relaxations that occur in the glassy amorphous regions are in the form of local motions, e.g., at the Y-transition as bending and stretching of bonds, at the P-transition as the movement of side groups, and at glass/a-transition gradually segments of the main backbone chain is set in motion.

Energy requirement for these transitions to happen can be calculated using the Arrhenius relationship.A large number of processes in materials science and engineering, e.g., the diffusivity of elements in metals, creep deformation in structural materials, stress relaxation in polymers and molecular-relaxation transitions obey the Arrhenius equation, which indicates that the process rate rises exponentially with temperature.

The process rate = Ae~^{Ea/ (RT)}

where, E_a is the activation energy, R is the gas constant (R = 8.3145 J/mol.K), T is the absolute temperature, and A is a pre-exponential constant.

The process rate, in this case, is the frequency of specimen oscillations. The frequency is essentially a rate expression (I/time, s~'), therefore expressing the equation in terms of frequency, F, and expressing it as a logarithmic equation gives

ln(F) = ln(A) - E_a/(RT).

A plot of [In (frequency)] vs. [l/(transition-temperature)] is the Arrhenius plot, and should yield a straight line; the slope of this line is equal to - E_a/R, from which the activation energy can be calculated. Examples of these calculations are given by PerkinElmer in their application notes. One of these is for a and p transitions in PMMA: a specimen of 7.3 mm length, 7.4 mm width and 2 mm thickness is DMA tested in single-cantilever bending mode at a heating rate of 2 °C/min at fixed frequencies of 0.1; 0.3; 1; 3 and 10 Hz. Tan 5 vs. temperature curves obtained at various frequencies are shown for the p transition (Figure 7.10), and the associated Arrhenius plot with a line of best fit and the equation of that line is presented in Figure 7.11. The slope of each line is equal to the negative of the activation energy divided by the gas constant. Therefore, the activation energy for the (3 relaxation is calculated to be approximately 65 kj/mol and for the glass (a) transition 368 kj/mol.

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0.02

-20 0 20 40 60 80

___________________ temperature, °C________

Figure 7.10Tan 5 vs. temperature at various frequencies over the p-transition of PMMA (source: PerkinElmer-1)

Figure 7.11Arrhenius plots for (■) p and (■) a transitions of PMMA (source: PerkinElmer-1)

Figures 7.10 and 7.12 also demonstrate how the relaxation-transition temperatures are dependent on the strain rate (i.e., frequency). Measurements which take place over a large timescale will result in a lower glass transition temperature, and hence exhibit rubbery behaviour at lower temperatures. Measurements which take place on a short timescale will result in a higher value of T and hence exhibit glassy behaviour at higher temperatures. This can be seen by experimenting with silly putty at room temperature: flowing like a viscous liquid over a long timescale and breaking like glass over a short timescale.

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7.4.1.2 Time-temperature superposition

It is known that there is a time and temperature equivalence for viscoelastic materials. For example, a polymer that exhibits rubber-like characteristics under a given set of testing conditions can be induced to show rigid behaviour by either reducing the temperature or increasing the rate of strain or the frequency of testing. The concept of shift factor', a_r has been used to construct master curves from a limited number of tests in order to predict the viscoelastic properties of polymers over a wide range of time (or frequency) outside the range easily accessible by experiment.

Williams, Landel and Ferry (WLF) defined 'a_T' in an equation that has become known as the WLF equation (Ferry, 1980). The equation is empirical in origin and has the form

log a_T = -СДТ - T) / [C₂ + (T - T)]

where, T_o is the reference temperature, T is the measurement temperature (the temperatures are in K), and C_l and C₂ are constants. For many amorphous polymers, C_t = 17.44 and C₂ = 51.6 when T_o is taken as the static T . The WLF expression was subsequently given theoretical basis from the free-volume theory of T , which is that the fractional free volume in the material increases linearly with temperature above T .

.

An application of the WLF concept is demonstrated for polycarbonate in their application brief by ТА Instruments. Frequency multiplexing data (see Figure 7.12) was obtained in the glass transition region (i.e., 130 to 160 °C) at frequencies of 0.01; 0.02; 0.05; 0.1; 0.2; 0.5; and 1.0 Hz, and at amplitude of deformation (p-p) of 0.5 mm. It is recommended that a minimum of four frequencies over two decades be used when generating a master curve.

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Figure 7.12E'and E"vs. temperature at various frequencies for PC (source:ТА lnstruments-1)

The loss modulus (E") data is used to generate a master curve. Figure 7.13 is a plot of the entire individual E" data points as a function of log frequency.

Figure 7.13Loss modulus (E") vs. frequency at all the test temperatures for PC (source: ТА lnstruments-1)

In the construction of an isothermal master curve, a reference set of data needs to be chosen. In this case, the data at 145 °C was selected and they form the initial framework of the master curve, the remaining sets of data obtained at other temperatures are shifted horizontally either to higher or lower frequencies to fall upon the chosen reference data and establish a smooth curve. The data points below the reference set of points (the data at!45 °C) will be shifted to the left

Date: 2015-12-11; view: 981