Crystallization of Polymers Investigated by Temperature-Modulated DSC

Abstract

The aim of this review is to summarize studies conducted by temperature-modulated differential scanning calorimetry (TMDSC) on polymer crystallization. This technique can provide several advantages for the analysis of polymers with respect to conventional differential scanning calorimetry. Crystallizations conducted by TMDSC in different experimental conditions are analysed and discussed, in order to illustrate the type of information that can be deduced. Isothermal and non-isothermal crystallizations upon heating and cooling are examined separately, together with the relevant mathematical treatments that allow the evolution of the crystalline, mobile amorphous and rigid amorphous fractions to be determined. The phenomena of 'reversing' and 'reversible' melting are explicated through the analysis of the thermal response of various semi-crystalline polymers to temperature modulation.

Keywords: crystalline fraction; crystallization; differential scanning calorimetry; mobile amorphous fraction; polymer; reversible melting; reversing melting; rigid amorphous fraction; temperature-modulated differential scanning calorimetry.

Figure 1

Apparent specific heat capacity (c_p,app) by standard differential scanning calorimetry (DSC) and reversing-specific heat capacity (c_p,rev) of poly(3-hydroxybutyrate) (PHB) measured after cooling from the melt at 200 K min⁻¹ at modulation periods p = 60 s and 120 s (A_T = 1.0 K, q = 2 K min⁻¹). The thin solid lines are the solid- and liquid-specific heat capacities, as taken from [22]. The inset is an enlargement of the Figure in the cold crystallization region. (Reprinted (adapted) with permission from [35]. Copyright (2012) American Chemical Society).

Figure 2

Reversing-specific heat capacity (c_p,rev) of a melt-quenched amorphous poly(ethylene terephthalate) (PET) sample (filled circles) and a melt-crystallized PET sample (open circles) with crystallinity degree of 44%, measured by quasi-isothermal temperature-modulated differential scanning calorimetry (TMDSC) upon stepwise heating (p = 60 s and A_T = 1.0 K, oscillation time around each temperature: 20 min). The thin solid lines are the solid and liquid specific heat capacities, as taken from [40]. The broken line is the calculated specific heat capacity for a 40% crystalline PET. (Reprinted (adapted) with permission from [5]. Copyright (1997) American Chemical Society).

Figure 3

Time evolution of reversing specific heat capacity (c_p,rev) during quasi-isothermal crystallization of PHB at 23 °C (p = 100 s and A_T= 0.4 K), curve a. Curves b and c correspond to the solid and liquid specific heat capacities (c_p,solid and c_p,liquid), respectively, as taken from [22]. Curve d was estimated from a two-phase model, Equation (3), and curve e from a three-phase model, Equation (5). The squares represent measurements at modulation periods ranging from 240 to 1200 s. Curve f (thick dashed line) is the expected c_p,rev curve from model calculations, see text. At the bottom, HF is the average heat flow rate (Reprinted (adapted) with permission from [31]. Copyright (2003) Elsevier).

Figure 4

Crystallization time (t_c) evolution of the reversing specific heat capacities (c_p,rev) of poly(l-lactic acid) (PLLA) during quasi-isothermal crystallization from the melt at T_c = 90 °C, 130 °C, and 135 °C, respectively (p = 60 s: thick line, p = 120 s: thin line, A_T = 0.4 K). (Reprinted (adapted) with permission from [34]. Copyright (2011) Elsevier).

Figure 5

Crystallization time (t_c) evolution of the modulated heat flow rate (HF_mod: grey line) and average heat flow rate (HF: black line) during quasi-isothermal crystallization of PLLA (p = 60 s, A_T = 0.4 K) at T_c = 135 °C. (Reprinted (adapted) with permission from [34]. Copyright (2011) Elsevier).

Figure 6

Time evolution of crystalline (w_C), mobile amorphous (w_MA) and rigid amorphous (w_RA) weight fractions during quasi-isothermal crystallization from the melt of PLLA at T_c = 90 °C, 130 °C, and 135 °C (p = 60 s: thick line, p = 120 s: thin line, A_T = 0.4 K). Estimated errors: ±0.02 for w_C and w_MA, ±0.04 for w_RA. (Reprinted (adapted) with permission from [34]. Copyright (2011) Elsevier).

Figure 7

Apparent specific heat capacity (c_p,app) of an amorphous PLLA sample (thickest solid line) and after complete isothermal crystallization at T_c = 85 °C (dotted line) and T_c = 145 °C (solid line) (heating rate 10 K min⁻¹). The thin solid lines are the solid and liquid thermodynamic specific heat capacities, as taken from the literature [45]. The inset is an enlargement of the T_g region. (Reprinted (adapted) with permission from [46]. Copyright (2015) Elsevier).

Figure 8

Reversing-specific heat capacity (c_p,rev) during crystallization of PCL at 55 °C as a function of crystallization time (A_T = 0.5 K). c_{p,base,2phase} was calculated according to Equation (3). (Reprinted (adapted) with permission from [7]. Copyright (2000) Springer).

Figure 9

Excess specific heat capacity of PCL (c_p,exc) after 2000 min of crystallization at 55 °C as a function of the modulation frequency. (Reprinted (adapted) with permission from [7]. Copyright (2000) Springer).

Figure 10

(A) Reversing specific heat capacity (c_p,rev) of a linear polyethylene (PE) during quasi-isothermal crystallization at 126 °C (solid line). A sinusoidal temperature modulation was applied with A_T = 1.0 K and p = 60 s. The linear solid line is the liquid thermodynamic specific heat capacity of PE at 126 °C [63]. The c_p,base curve (dotted line) was calculated according to Equation (3), on the basis of the variation of the crystalline weight fraction (w_C) with time. At the bottom, HF (dashed line) is the average heat flow rate. (B) Time evolution of the crystalline weight fraction (w_C), calculated as the ratio between the integrated average heat flow rate (HF) and the literature value for the heat of fusion of 100% crystalline polyethylene [63]. (Reprinted (adapted) with permission from [8]. Copyright (2001) American Chemical Society).

Figure 11

The effect of the modulation amplitude on the quasi-isothermal crystallization of linear PE at 128.5 °C: top: reversing-specific heat capacities (c_p,rev) curves, bottom: average heat flow rate (HF) curves. (Reprinted (adapted) with permission from [26]. Copyright (1999) Elsevier).

Figure 12

Evolution of the excess specific heat capacity (c_p,exc) with time during quasi-isothermal crystallization of a linear PE at the indicated temperatures (A_T = 0.8 K and p = 48 s). (Reprinted (adapted) with permission from [60]. Copyright (2004) American Chemical Society).

Figure 13

Correspondence between the three stages of the melting temperature (T_m) evolution, plotted as the difference between the melting temperature and the crystallization temperature (T_c), and the decay of the excess heat capacity at the indicated crystallization temperature. (Reprinted (adapted) with permission from [60]. Copyright (2004) American Chemical Society).

Figure 14

Time dependence of the reversing specific heat capacity (c_p,rev) of PBT isothermally crystallized at 200 °C for 30 min, during quasi-isothermal measurements over long time periods in the melting region at T_o = 216.5 °C (□) and 225.2 °C (○) (p = 120 s, A_T = 0.2 K). The dashed lines with squares and circles are the c_{p,base,2phase} values calculated by Equation (3) from the crystallinity degrees measured at the end of the quasi-isothermal annealing at T_o = 216.5 °C and 225.2 °C, respectively, by using the solid and liquid specific heat capacities of PBT as taken from [40]. (Reprinted (adapted) with permission from [73]. Copyright (2004) American Chemical Society).

Figure 15

(A) Apparent specific heat capacity (c_p,app, dashed line) and reversing specific heat capacity (c_p,rev, solid line) of PBT isothermally crystallized at 200 °C for 30 min as a function of temperature during heating (heating rate: 0.5 K min⁻¹, modulation period: 120 s, temperature modulation amplitude: 0.2 K); (B) time dependence of the reversing specific heat capacity (c_p,rev) of PBT during quasi-isothermal measurements of 6 h at the indicted T_os. The data are from separate measurements and are collected in a single graph in order to compare the c_p,rev trend at different temperatures. The dashed lines are the c_{p,base,2phase} values calculated by Equation (3) from the values of the crystallinity degrees measured at the end of the quasi-isothermal annealing, by using the solid and liquid specific heat capacities of PBT as taken from [40]. (Reprinted (adapted) with permission from [73]. Copyright (2004) American Chemical Society).

Figure 16

Apparent specific heat capacity (c_p,app) by standard DSC and reversing specific heat capacity (c_p,rev) of PET at modulation period of 60 s and 120 s, measured upon cooling from the melt at 2 K min⁻¹ (A_T = 1.0 K). The black solid line with circles is the approximate linear baseline, whereas the solid grey line is the two-phase baseline (c_{p,base,2phase}). The black thin solid lines are the solid and liquid specific heat capacities of PET, as taken from [40]. The inset shows the entire c_p,app curve. (Reprinted (adapted) with permission from [37]. Copyright (2014) Elsevier).

Figure 17

Temperature evolution of the crystalline weight fraction (w_C) of PET during non-isothermal crystallization at 2 K min⁻¹. (Reprinted (adapted) with permission from [37]. Copyright (2014) Elsevier).

Figure 18

Reversing-specific heat capacity (c_p,rev) of PET (filled circles) during stepwise quasi-isothermal TMDSC cooling from the melt (p = 60 s and A_T = 1.0 K, oscillation time around each temperature: 20 min). The thin solid lines are the solid and liquid specific heat capacities, as taken from [40]. The broken line is the calculated specific heat capacity for a 49% crystalline PET. The open circles describe the c_p,rev curve of a melt-crystallized PET sample (crystallinity degree: 44%). (Reprinted (adapted) with permission from [5]. Copyright (1997) American Chemical Society).

Figure 19

Apparent specific heat capacity (c_p,app: solid lines) of PLLA and reversing specific heat capacity (c_p,rev) on cooling at 2 K min⁻¹ as a function of temperature (p = 60 s: dashed line; p = 120 s: dashed dotted line). The thin solid lines are the thermodynamic solid and liquid specific heat capacities of PLLA as taken from the literature [45]. (Reprinted (adapted) with permission from [79]. Copyright (2017) Springer).

Figure 20

Temperature evolution of the mobile amorphous (w_MA: dashed line), crystalline (w_C: solid line), and rigid amorphous (w_RA: dotted line) weight fractions during non-isothermal crystallization of PLLA at 2 K min⁻¹. Estimated errors: ±0.02 for w_C and w_MA, ±0.04 for w_RA. (Reprinted (adapted) with permission from [79]. Copyright (2017) Springer).