Differential Scanning Calorimetry; First and Second OrderTransitions in PETE Purpose: Determine the heat capacity, glass transition temperature, change in heat capacity for the glass transition, enthalpy of crystallization, enthalpy of melting (fusion), and percent crystallinity of a sample of polyethylene terephthalate, PETE. Introduction Differential scanning calorimetry (DSC) monitors heat effects associated with phase transitions and chemical reactions as a function of temperature. In a DSC the difference in heat flow to the sample and a reference at the same temperature, is recorded as a function of temperature. The sample is sealed in an aluminum pan. The reference is an inert material such as alumina, or just an empty aluminum pan. The temperature of both the sample and reference are increased at a constant rate. Since the DSC is at constant pressure, heat flow is equivalent to enthalpy changes: đqp dH dt = dt 1 Here dH/dt is the heat flow measured in mW or equivalently mJ s -1. The heat flow difference between the sample and the reference: dH dH dH ∆ = – 2 dt dt sample dt reference and can be either positive or negative. In an endothermic process, such as most phase transitions, heat is absorbed and, therefore, heat flow to the sample is higher than that to the reference. Hence ∆dH/dt is positive. Other endothermic processes include helix-coil transitions in DNA, protein denaturation, dehydrations, reduction reactions, and some decomposition reactions. In an exothermic process, such as crystallization, some cross-linking processes, oxidation reactions, and some decomposition reactions, the opposite is true and ∆dH/dt is negative. N2 Inlet Sample Temperature Reference Resistance Sensors Resistance Heater Heater Sample Reference Sample Reference Furnace Block Side View (without furnace block) Top View (cover off) Figure 1. Differential scanning calorimeter sample and reference holder. The calorimeter consists of a sample holder and a reference holder as shown in Figure 1. Both are constructed of platinum to allow high temperature operation. Under each holder is a resistance heater and a temperature sensor. Currents are applied to the two heaters to increase the DSC of PETE 2 temperature at the selected rate. The difference in the power to the two holders, necessary to maintain the holders at the same temperature, is used to calculate ∆dH/dt . A schematic diagram of a DSC is shown in Figure 2. A flow of nitrogen gas is maintained over the samples to create a reproducible and dry atmosphere. The nitrogen atmosphere also eliminates air oxidation of the samples at high temperatures. The sample is sealed into a small aluminum pan. The reference is usually an empty pan and cover. The pans hold up to about 10 mg of material. sample reference Linear Temperatu re Scan T T sample ref T dT ° -1 dt = 20 C min + – Scan Heater Heater ∆ Control T time endotherm sample reference power power monitor monitor ∆dq – dt -1 ∆ + mJ s tr Cp exotherm time or temperature Figure 2. Schematic of a DSC. You choose the linear temperature scan rate. The triangles are amplifiers that determine the difference in the two input signals. The sample heater power is adjusted to keep the sample and reference at the same temperature during the scan. en d o t he r mi c Me lt i ng pe ak gl as s en d i ng t ra ns i t i on t ra n s i en t he a t f l ux st ar ti ng (mW) t ra ns i e nt ∆Cp Cp Cr y s t al l iz at i on 0 pe a k st ar t 40 0 50 0 st op e xo t h e rm i c t im e a n d Te mp e ra tu r e (° C ) Figure 3. Typical DSC scan. The heat capacity of the sample is calculated from the shift in the baseline at the starting transient. Glass transitions cause a baseline shift. Crystallization is a typical exothermic process and melting a typical endothermic process, ∆tr H is calculated from the area under the peaks. Few samples show all the features shown in this thermogram. DSC of PETE 3 During the heating of a sample, from room temperature to its decomposition temperature, peaks with positive and negative ∆dH/dt may be recorded. Each peak corresponds to a heat effect associated with a specific process, such as crystallization or melting (Fig. 3). What kind of information is obtained from a DSC thermogram? The first and most direct information is the temperature at which a process occurs, for example, the melting point of a polymer. The temperature at which a reaction, such as decomposition, may start is another important parameter. For decompositions, the peak temperature is associated with the temperature at which maximum reaction rate occurs. The glass transition in polymers is an important type of phase transition. The glass transition temperature, T g, is the temperature at which amorphous (noncrystalline) polymers are converted from a brittle, glasslike form to a rubbery, flexible form. The glass transition involves a change in the local degrees of freedom. Above the glass transition temperature segmental motions of the polymer are comparatively unhindered by the interaction with neighboring chains. Below the glass transition temperature, such motions are hindered greatly, and the relaxation times associated with such hindered motions are usually long compared to the duration of the experiment. The motions are primarily torsional degrees of freedom around freely rotating bonds in the long chains of the polymer. The operative definition of glass transition temperature is that at this temperature, or within a few degrees, the specific heat, the coefficient of thermal expansion, the free volume, and the dielectric constant (in the case of a polar polymer) all change rapidly. Since the mechanical behavior of polymers changes markedly at the glass transition temperature, Tg is an important characteristic of every polymer. In the DSC experiment, Tg is manifested by a change in the base line, indicating a change in the heat capacity of the polymer (Fig.4). The baselines before and after the transition are extrapolated to the temperature where the change in heat capacity is 50% complete. The change in heat capacity is measured at the 50% point. Then Tg is often reported as the temperature at the intersection of the baseline and the line extrapolated from the linear portion during the phase transition. First order phase transitions have an enthalpy and a heat capacity change for the phase transition. Second order transitions are manifested by a change in heat capacity, but with no accompanying change in enthalpy. No enthalpy is associated with the glass transition, so the glass transition is second order. The effect on a DSC curve is slight and is observable only if the instrument is sufficiently sensitive. endothermic ∆ Heat flux Cp (mW) 0 Glass transition Tg 90 100 exothermic Time and temperature ( °C) Figure 4. The glass transition. If there are sloping baselines before and after the glass transition, the baseline before the transition is extrapolated forwards and the baseline after the transition is extrapolated backwards (as shown by dotted lines). The baseline shift is measured when the transition is about 50% complete (as shown by arrows). DSC of PETE 4 The second direct information obtainable from DSC thermograms is the enthalpy associated with first order processes. Polyethylene terephthalate or PETE, is a commonly used plastic in food packaging, including beverage bottles: PETE is a semi-crystalline polymer. After molding, the plastic has crystalline and amorphous regions. In semi-crystalline polymers the glass transition and crystallization transitions occur over a broad temperature range. Crystallization of the small amount of amorphous polymer begins with the glass phase transition. Rapid cooling of plastic melts produces an amorphous solid. The glass transition and crystallization transition are readily apparent and often occur at distinctly different temperatures in amorphous solids. The crystallization temperature is intermediate between the glass transition and the melting transition, at which temperature the polymer molecules gain sufficient translational and torsional energy to reorganize into the crystalline structure. If the crystallization exothermic peak can be discerned in the semi-crystalline state, the percent crystallinity of the original sample can be estimated by dividing the enthalpy change of the crystallization peak in the original sample by the enthalpy of crystallization for the amorphous sample, which is obtained after rapid quenching after the first DSC determination. Theory The integral under the DSC peak, above the baseline, gives the total enthalpy change for the process: ⌠ dH dt = ∆tr Hsample 3 ⌡ dt sample Assuming that the heat capacity of the reference is constant over the temperature range covered by the peak, ∆Hreference will cancel out because the integral above the baseline is taken. Therefore, Eq. 3 is also valid when the integral is taken from the DCS plot of ∆dH/dt. Heat capacities and changes in heat capacity can be determined from the shift in the baseline of the thermogram. The heat capacity is defined as: đqp dH Cp = = 4 dt dT p The temperature scan rate is: α dT = scan rate = dt 5 Using the chain rule: dH dH dt Cp = = 6 dT p dt dT DSC of PETE 5 where dH/dt is the shift from the baseline of the thermogram (Figure 3-4) and the last derivative is just the inverse of the scan rate. For differential measurements, we determine the difference in the heat capacity of the sample and the reference: ∆Cp = C p(sample) – Cp(reference) 7 dH dH dt ∆Cp = ∆ = ∆ 8 dT p dt dT The units of the heat flow are mJ s -1 and the temperature scan rate is usually expressed as °C min -1.