Influence of composition on the isothermal crystallisation of segmented thermoplastic polyurethanes

Borja Fernández-d'Arlas ab, Roelf P. Baumann c, Elmar Pöselt d and Alejandro J. Müller *ae
aPOLYMAT and Department of Polymer Science and Technology, Faculty of Chemistry, Basque Country University UPV/EHU, Paseo Manuel Lardizábal 3, 20018, Donostia-San Sebastián, Spain. E-mail:
bINAMAT (Institute for Advanced Materials) y Departamento de Física, Centro Jerónimo de Ayanz, Universidad Pública de Navarra (UPNA), Campus Arrosadía, Pamplona, Navarra, Spain. E-mail:
cBASF SE, RAA/OS, Carl-Bosch-Strasse 38, 67056 Ludwigshafen, Germany
dBASF-Polyurethanes GmbH, E-PME/NL, Elastogranstrasse 60, 49448 Lemförde, Germany
eIKERBASQUE, Basque Foundation for Science, Bilbao, Spain

Received 1st June 2017 , Accepted 5th July 2017

First published on 5th July 2017

The isothermal crystallisation of a series of segmented thermoplastic polyurethanes (TPUs) composed of 4,4′-methylene bisphenyl diisocyanate (MDI)-1,4-butanediol (BD) segments has been studied in detail. The influence of MDI-BD content within the TPUs on the nucleation, growth and resulting morphology has been analyzed by converging the results obtained from differential scanning calorimetry (DSC), polarised light optical microscopy (PLOM), synchrotron X-ray small angle scattering (SAXS), and atomic force microscopy (AFM). The materials crystallised from a single phase melt, as evidenced by SAXS. The increase of just 13 wt% in MDI-BD content leads to an increment of 4 orders of magnitude in the nucleation density and nucleation rate. In addition, the increase of MDI-BD content also enhances the spherulitic growth rate and overall crystallisation kinetics. The overall isothermal crystallisation kinetics determined by DSC can be described in an unusually large conversion range (i.e., beyond primary crystallisation) using the Avrami equation. The increase of the isothermal crystallisation temperature changes the superstructural morphology from spherulitic to axialitic, and therefore the Avrami index is reduced from approximately 3 to 2. Negative spherulites with the crystallographic c axis oriented tangentially to the spherulite were observed by PLOM and the spherulitic texture details were revealed by AFM and SAXS as a radial lamellar-like assembly of the MDI-BD segments. The energy barrier for nucleation and growth decreased exponentially with the increase in MDI-BD content. Finally, from all the evidence gathered here, a morphological schematic picture of the hierarchical structure of TPUs upon crystallisation is presented. The results presented in this report pave the way for a comprehensive guide to developing materials with the desired structure, based on the understanding of the intricate relationship between crystallinity, thermal history and composition of TPUs.


Polyurethanes are versatile materials that find application in many different fields. Optimization of their processing and final product performance requires full understanding of the impact of composition on their properties as well as the structure–property relationship, as defined by the thermal history.

Thermoplastic polyurethanes (TPUs) can be considered multiblock statistical copolymers with the structure –{[D–G]x–(D–M)y}n–, where D, G and M correspond to the structure of the diisocyanate, a short molecular weight glycol and a medium molecular weight macrodiol, respectively. The subscripts “n”, “x” and “y” represent the degree of polymerization of the multiblock copolymer, the urethane-rich segments, [D–G], and the macrodiol segments, (D–M), respectively. In order to endow TPUs with an elastomeric behavior, the macrodiol is usually chosen to be a flexible (TgTamb) medium molecular weight polyether or polyester. Usually, the urethane-rich segments, [D–G], form crystalline domains that provide rigidity and strength to the TPUs. Crystallisation of the [D–G] segments can occur from a single phase melt.1 The [D–G] crystals are highly cohesive since they are bound through inter-urethane (–O–CO–NH–) hydrogen bonding between the carbonyl groups (C[double bond, length as m-dash]O) and the amide proton (N–H).2,3 The extent of crystallisation of the [D–G] segments depends on the structure of the diisocyanate and glycol.

In the specific case of linear diblock copolymers, with only one crystallisable block, phase separation in the melt only occurs when the segregation strength, given by the product of χ (the Flory–Huggins interaction parameter) and N (the degree of polymerization), is high enough.4,5 When the value of χN is lower than 10, then the diblock copolymer forms a single phase in the melt. Crystallisation from a homogeneous melt generally leads to the development of lamellar crystals (and spherulites) regardless of the diblock copolymer composition, unless special confinement conditions exist (see ref. 6–9). Even when the copolymers in the melt are weakly segregated, crystallisation overcomes phase segregation (i.e., break-out) and the typical morphologies observed are based on lamellar superstructural aggregates. Only when the segregation strength is high (typically higher than 50) will crystallisation occur within the phase segregated microdomains previously formed in the melt state.4–9

Previous analysis of the self-assembly and crystallisation of similar TPUs to those employed in this work, using fast scanning calorimetry and SAXS, indicates that TPU hard blocks (i.e., usually MDI-BD rich blocks) crystallise from a homogeneous melt.1,10 As the TPUs crystallise from the melt, two phases could be identified: a crystalline phase (formed by MDI-blocks) and an amorphous phase where rigid and soft blocks co-exist. Therefore, in principle, the crystallisation phenomena of the segmented TPUs employed in this work can be regarded as very similar to that of melt mixed multiblock copolymers where only one of the constituents can crystallise. A review on the crystallisation and morphology of different types of segmented thermoplastic polyurethanes was published recently by Yilgör et al. (ref. 11 and references therein). The superstructural morphology of TPUs, including spherulites, are discussed in different types of polyurethanes. Although many works cited in this review have investigated the relationship between the chemical structure, morphology and ability to crystallise, very few have focused on isothermal crystallisation kinetics.

Isothermal crystallisation of linear aliphatic n-polyurethane homopolymers has been previously thoroughly analysed by Fernández et al.,12 determining their kinetic parameters and their ability to form spherulites. Other authors have shown the ability of MDI-BD segments in TPUs to form spherulites when cast from solution, after slow solvent removal,13 prolonged annealing at high temperatures,14,15 or after slow cooling (∼3 °C min−1) from the melt (250 °C).16 On the other hand, Begenir et al.17 studied the isothermal crystallisation of typical commercial TPUs formed from MDI-BD crystallisable segments combined with either polyether or polyether macrodiols, determining that generically, for a certain family of copolymers with a given macrodiol, the higher the MDI-BD weight fraction in the copolymer, the shorter the crystallisation half time, as determined by differential scanning calorimetry (DSC) for given crystallisation undercoolings. Their work and conclusions were based only on DSC data, and therefore the differences between nucleation and growth were not studied.

The aim of this work is to analyse the influence of MDI-BD block ratio and macrodiol nature (i.e., polyester versus polyether) on nucleation kinetics, morphology, spherulitic growth rate, and overall crystallisation kinetics of TPUs under isothermal conditions. A combination of polarised light optical microscopy (PLOM), differential scanning calorimetry (DSC), atomic force microscopy (AFM) and small angle X-ray scattering (SAXS) techniques has allowed us to show the relationship between the chemical structure and morphology upon TPU crystallisation, from the lamellar level to the superstructural semi-crystalline aggregates (i.e., axialites and spherulites).


The studied thermoplastic polyurethanes (TPUs)

The TPUs were prepared by a one-shot process by BASF Polyurethanes GmbH (Lemförde, Germany). They consist of 4,4′-methylenediphenyl diisocyanate (MDI) and 1,4-butanediol (BD) as components of the urethane-rich hard blocks (HB) and either a polytetrahydrofuran (polyether) or an adipic polyester macrodiol, both with Mn ∼1000 g mol−1 and a polydispersity index of ∼2, as the main component of the soft phase. Table 1 reports the composition and thermal properties of the studied TPUs.
Table 1 Composition and parameters related to crystallisation and melting of the studied TPUs
TPU HS, αb T c [°C] ΔHc [J g−1] T g (Tg-30) [°C] T m [°C] ϕ [°C min−1] T c,min [°C] T m,end [°C] ΔHm [J g−1] X c,PU [%] X c,HS [%]
a “eth” and “est” stand for polyether and polyester based macrodiols, respectively. b α corresponds to the MDI-BD weight fraction in the TPU. c The Tg values used to calculate Tg correspond to the MDI-BD segments in the amorphous phase. d The temperature indicated as Tm is defined as the temperature used to erase the thermal history prior to crystallisation. e Estimation of the degree of crystallinity of the TPU, employing ΔHom ∼ 155 J g−1, reported by Kajiyama and Macknight.19 f Estimation of the degree of crystallinity of the hard phase, considering the mass fraction of hard segments within the PU.
PUeth30 0.30 82 −9 28 220 100 108 200 10 6 20
PUest33 0.33 80 −11 30 220 100 108 198 10 6 18
PUeth43 0.43 106 −14 65 240 100 178 220 13 8 19
PUest64 0.64 120/142 −27 72 245 150 225 238 22 14 22
PU100 1.00 125/165 −51 80 245 150 236 241 54 35 35

Polarised light optical microscopy (PLOM)

The nucleation and growth kinetics were measured by PLOM using a Leica DFC320, a microscope coupled with a λ retardation plate in between the crossed polarizers at 45° to facilitate observation and determination of the sign of the birefringence. Visualization and image recording was performed with a Wild Leitz digital camera. The temperature was controlled with a Mettler Toledo FP82 hot stage. The samples for PLOM were first dissolved in a mixture of THF and DMF (THF/DMF 3[thin space (1/6-em)]:[thin space (1/6-em)]1), and then two drops of 1 wt% TPU solution were cast onto glass slides. The solvent was evaporated in a vacuum oven at 80 °C for 48 h. Film thicknesses fall within 10–20 μm. Before analysis of nucleation kinetics and growth at a particular temperature, the thermal history was erased by heating the samples for 1 min at 240 °C. Then the samples were cooled at 20 °C min−1 to the desired Tc, and the number of spherulites and their sizes were monitored as a function of time. One sample for each temperature was employed in order to minimize effects derived from degradation that may occur by holding the samples at high temperatures during prolonged times.

Differential scanning calorimetry (DSC)

A PerkinElmer 8500 DSC equipped with an Intracooler 3 accessory was employed. The tests were carried out under a N2 atmosphere and the equipment was calibrated using indium and tin. The protocol employed to analyse the isothermal crystallisation of the TPUs followed the recommendations of Müller et al. in ref. 18, including the determination of the minimum crystallisation temperature, Tc,min, for each of the TPUs.

Pieces of samples cut directly from the TPU sheets were weighed (5–10 mg) and encapsulated in aluminium pans. The thermal history was erased for 1 min (0.5 min for PUeth60 and PU100) at a temperature, Tm, above the end melting temperature, Tm,end, as described in Table 1 for each of the TPUs. Then the samples were cooled at 100–150 °C min−1 to the selected crystallisation temperature, above the minimum crystallisation temperature, Tc,min (i.e., that in which there is no crystallisation during cooling at the cooling rate employed, ϕ), and the heat flow was recorded until baseline stabilisation. The crystallisation temperature, Tc, and enthalpy, ΔHc, were recorded upon cooling scans at 20 °C min−1 from Tm. The melting enthalpy, ΔHm, was recorded during subsequent heating scans at 20 °C min−1.

Synchrotron small-angle-X-ray scattering (SAXS)

Isothermal crystallisation of PUeth30 was monitored by synchrotron radiation SAXS at ALBA Synchrotron (Cerdanyola del Vallés, Barcelona, Spain) using a Q315r SAXS detector from ADSC, with a sample to detector distance of 6428 mm. The radiation wavelength was 1 Å and the d spacing was calibrated using silver behenate as a standard. The isothermal crystallisation was carried out in a Linkam temperature control chamber, after erasing thermal history at 220 °C for 1 min. The temperature was lowered from the melt to the selected Tc (160 °C or 108 °C) at ∼60 °C min−1. Images were acquired at a rate of 10 images per min with an exposure time of 1 s and a latency of 5 s.

Results and discussion

Polyurethane characterization by DSC

The non-isothermal crystallisation and melting behaviour of all the TPUs employed here can be seen in the DSC cooling scans from the melt (after erasing thermal history) and subsequent heating scans presented in Fig. 1. Both crystallisation and melting temperatures are directly related to the MDI-BD content in the TPUs. In particular, both Tc and Tm increase as the MDI-BD content increases. In parallel, the crystallisation and melting enthalpies also increase with the MDI-BD content. The quantitative data have been gathered in Table 1.
image file: c7ce01028a-f1.tif
Fig. 1 Non-isothermal analysis by DSC. a) Cooling scans from the melt at 20 °C min−1. b) Subsequent heating scans at 20 °C min−1. The scale of the PU100 curve is displayed in the right hand side y-axis.

The increasing melting temperature with MDI-BD content is indicative of a higher degree of polymerisation of the MDI-BD segments within the multiblock copolymers. The melting enthalpy can be used to estimate the degree of crystallinity of the TPUs. This was done using the enthalpy data obtained by Kajiyama and Macknight for 100% crystalline MDI-BD TPUs by means of a combination of X-ray and DSC data, ΔH0m ∼ 155 J g−1.19 TPU crystallinity is estimated as Xc = 100 ΔHmH0m and gives the values of the total crystallinity present in the TPU. On the other hand, if such a value is normalised by the weight fraction of the crystallisable material or hard phase, then Xc,HS is obtained. Both quantities are reported in Table 1. It can be observed that for TPUs with the MDI-BD content in the range of 30–64 wt%, only about ∼20% of the MDI-BD segments are crystalline, accounting for a global material crystallinity in the range of 6–14%.

Nucleation kinetics studied by PLOM (primary nucleation)

A summary of the nucleation kinetics study by PLOM is presented in Fig. 2. Fig. 2a–c show plots of the nuclei density as a function of time of three TPUs crystallised at different temperatures. The insets show PLOM images of the morphology observed at 160 °C for the different TPUs at times indicated in the figure caption.
image file: c7ce01028a-f2.tif
Fig. 2 Nucleation kinetics studied by PLOM. Nuclei density as a function of time for different crystallisation temperatures: a) PUest33, b) PUeth30 and c) PUeth43. The insets correspond to PLOM images for TPUs crystallised at 160 °C, taken at 180 min (PUest33), 115 min (PUeth30) and 7 min (PUeth43). d) Nuclei density at 10 min for each of the TPUs as a function of Tc. e) Plot of log[thin space (1/6-em)]I versus 1/TT)2 and fitting to eqn (1).

PUeth30 and PUest33 exhibit similar nucleation kinetics, but PUeth43 presents a much higher nucleation density in the Tc range of 158–164 °C, as a result of a faster nucleation. This is also illustrated in the micrographs shown in Fig. 2. The saturation nucleation density of PUeth43 at 160 °C is very high, i.e., N = 108 nuclei per cm3 and the saturation occurs in a few seconds, while in the case of PUeth30 and PUest33 the nucleation densities are one order of magnitude lower and take much longer time (i.e., 150 min) to saturate. Similar trends are observed for a wide temperature range and they are presented in Fig. 2d, where nuclei densities, at a constant nucleation time of 10 min, are plotted as a function of Tc on a semi-log scale.

It can be seen that PUeth30 presents slightly higher values of nuclei density than PUest33, but the difference may be within the errors involved in the measurements. A much higher difference in nuclei density is observed when comparing these two TPUs with PUeth43, which has a larger number of crystallisable blocks (i.e., a higher content of hard segments). In the temperature range where the measurements overlap (i.e., 160 °C), the difference is over 4 orders of magnitude higher (∼1010 nuclei per cm3 for PUeth43, 106 nuclei per cm3 for PUeth30 and 104 nuclei per cm3 for PUest33). The comparison between PUeth30 and PUeth43, which are TPUs with around 13 wt% increment in the fraction of MDI-BD crystallisable blocks, leads to an increment of about 4 orders of magnitude in the nucleation density for a particular crystallisation time. This fact is related to a statistical phenomenon due to the presence of more MDI-BD segments and the higher probability of joining them together to form crystalline nuclei.

The nucleation rate, I = dN/dt, in polymer systems has been described by the Turnbull–Fisher model20,21 according to the equation:

image file: c7ce01028a-t1.tif(1)
where I0 is related to diffusion of polymeric segments from the melt to the nucleation site, ΔF* is a parameter proportional to the primary nucleation free energy, and σ and σe are the lateral and fold surface free energies, respectively. Tom is the equilibrium melting point, ΔHv is the volumetric melting enthalpy (J m−3) and ΔT is the supercooling defined as ΔT = TomTc. In this work, the values of Tom have been approximated to the values of the end melting temperature, Tm,end, which are listed in Table 1. To determine σ and σe from eqn (1), it is necessary to know the cross section of the macromolecule within the crystal (i.e., a0·b0) and the value of KGg (a parameter proportional to the energy barrier for crystal growth) determined by isothermal analysis of the spherulitic growth at different temperatures (the data of which will be shown below).

The cross sectional area of the macromolecule within the crystal can be approximated to the area of the cell parameters (a·b) when the unit cell comprises a single macromolecule. This was the case for the MDI-BD unit cell as proposed by Born et al.22 and recently confirmed by molecular simulations by Lempesis et al.23 Therefore, the values obtained by these authors, namely, a0a = 4.92 Å and b0b = 5.66 Å, were taken as fitting parameters. The MDI-BD zig-zag crystal structure24–26 along with a full morphology panorama will be discussed below (Fig. 10). The fitting of the nucleation rate data to eqn (1) allowed the calculation of Δσ, a parameter related to nucleation efficiency21 for each of the TPUs analysed, and the obtained values are reported in Table 2. This analysis required values for σ and σe parameters, which were obtained by applying the Lauritzen and Hoffman theory to spherulitic growth rate data, as will be discussed below.

Table 2 Nucleation and growth constants obtained from isothermal crystallisation kinetics of three representative TPUs as obtained by PLOM
Growth, eqn (2) Nucleation, eqn (1)
TPU G o [cm s−1] σ [erg cm−2] σ e [erg cm−2] K G g [K2] q [erg per fold] R 2 Δσ [erg cm−2] R 2
a R 2 is the correlation coefficient for the Lauritzen–Hoffman (eqn (2)) linear plots (i.e., ln[thin space (1/6-em)]G + U*/R(TcTα) vs. 1/fTcΔT). b R 2 is the correlation coefficient for the fitting to the nucleation kinetic model (eqn (1)), log[thin space (1/6-em)]I vs. 1/TT)2. ΔHom for PU100 ∼ 155 J g−1 according to Kajiyama and Macknight.19 MDI-BD chain cross section was considered to match the cell parameters by Born et al.22a0: 4.92 Å; b0: 5.66 Å. For the density of MDI-BD pure TPU the value reported in ref. 22 and 24 was used, which is ρ = 1.331 g cm−3. The volumetric enthalpy was estimated as: ΔHv = ΔHom·1.331 g cm−3 (155 J g−1)·(1.331 g cm−3).
PUeth30 4.50 × 102 10.9 136.5 2.80 × 105 7.60 × 10−13 0.987 0.94 0.983
PUest33 2.00 × 101 10.9 99.5 2.03 × 105 5.54 × 10−13 0.965 0.98 0.964
PUeth43 3.63 × 104 10.9 167.4 3.57 × 105 9.32 × 10−13 0.799 0.92 0.799

The TPUs' Δσ values are comparable to those of poly(ethylene)terephthalate (PET) (1.6 erg cm−2) but significantly lower than the values obtained for polyamide 6 (4.9 erg cm−2).21 Small values of Δσ are indicative of good efficiency of nucleation, since a lower amount of energy is required to form the crystal–substrate interface. Therefore the nucleation activity of the MDI-BD segments on TPU crystallisation might be considered very efficient. We were not able to find reported values of Δσ in the literature for TPUs.

Spherulitic and axialitic texture of crystalized TPUs

The morphology of the TPUs during isothermal crystallisation has been observed by PLOM. Fig. 3 shows micrographs of PUeth30, PUest33 and PUeth43 taken at two different crystallisation temperature ranges, i.e., at low and at high Tc values, where individual superstructures were observed. In the three cases, the morphology varies from approximately spherulitic (in the low Tc range) to approximately axialitic superstructures (in the high Tc range). This variation is observed along with a decrease in nucleation density and progressive fainting of the typical Maltese cross. In contrast, axialites obtained at crystallisation at higher Tc values exhibited open arm-like structures with side branches extending irregularly from each arm. These features are typical of two-dimensional lamellar aggregates (i.e., axialites). In qualitative correspondence with this trend, we will show below, when the overall crystallisation data are analyzed, that the Avrami index tends to decrease with Tc (even though nucleation is more sporadic at higher Tc values). Earlier reports on TPU superstructures by Wilkes et al. focused on PTMO-urethane copolymers where the hard segments were made up of piperazine and 1,4-butanediol, and these materials do not display the typical hydrogen bonding associations present in many types of polyurethanes, such as segmented polyurethanes with crystallisable soft segments28–30 and aliphatic polyurethanes.12,31 In addition, as has been mentioned in the introductory section, do not display the typical hydrogen bonding associations present in many TPUs, including those studied in the present work. Their morphological studies that included small angle light scattering, scanning electron microscopy and AFM have been recently reviewed (see ref. 11 and references there in). Based on AFM observations, they postulate that crystalline hard segments have their chains tangentially aligned inside the spherulite.11,27 They also speculate that no chain folding occurs during crystallisation.11 In more recent studies, different polyurethanes with MDI-BD segments have also been reported to exhibit a spherulitic texture under appropriate crystallisation conditions.13–16 Particularly, Furukawa et al.15 reported the formation of negative spherulites (i.e., macromolecular orientation perpendicular to the radii of spherulites) in MDI-BD based TPUs after prolonged annealing at high temperatures, as observed by PLOM.
image file: c7ce01028a-f3.tif
Fig. 3 Morphology after isothermal crystallisation. PUest33 crystallised at a) 155 °C and b) 162 °C. PUeth30 crystallised at c) 155 °C and d) 165 °C and PUeth43 crystallised at e) 164 °C and f) 171 °C. Scale bars: 40 μm.

The micrographs in Fig. 3(a–c) clearly show, by the use of a tint plate inserted at 45° in between the crossed polarisers, that the spherulites display a negative sign, as the first and third quadrant are yellow-red, while the second and fourth are mostly blue.32 Negative spherulites indicate that the crystallographic chain axis (“c” axis) is located tangentially in the spherulites. As we will show below, by AFM, the MDI-BD TPUs employed here exhibit a spherulitic texture with lamellar-like structures growing radially. The PLOM micrographs indicate that chains are crystallised perpendicularly in these lamellar structures, revealing similarities to the majority of polyesters, which also crystallise in negative spherulites.31

Kinetics of superstructural growth (secondary nucleation)

The growth of spherulites/axialites occurs by secondary nucleation and their growth rate is independent of primary nucleation or even of the nature of the nuclei.

Fig. 4a–c show micrographs of PUeth30 spherulites at different times as they grow at 162 °C. The linear dependence of the spherulitic diameter as a function of time seen in Fig. 4d indicates that there are no limitations due to diffusion during growth. The growth rates can be determined from analogous linear plots of spherulite radius versus time. The growth rate analysis was performed with low MDI-BD content TPUs (i.e., <43 wt%), since PUest64 and PU100 are characterized by a large density of nuclei (i.e., with very small spherulites), and it was impossible to monitor spherulitic growth. These results are once more explained by the different MDI contents in the multi-block copolymers. They yield a similar trend to those corresponding to the nucleation rate, as both nucleation and growth are favored by higher contents of the crystallisable component in the TPUs.

image file: c7ce01028a-f4.tif
Fig. 4 Spherulitic growth studied by PLOM. a–c) PLOM images of PUeth30 crystallised at 162 °C taken at 31, 88 and 304 min, respectively. d) Spherulitic diameter as a function of time for the spherulites indicated in (b). e) Spherulitic growth rate, G, as a function of temperature for each of the indicated TPUs. The dotted lines correspond to fittings to eqn (2).

The G value as measured for different temperatures for PUeth30, PUest33 and PUeth43 are plotted in Fig. 4e. It can be seen that PUeth30 and PUest33 present similar growth rates in the temperature range studied, while PUeth43 exhibits much higher growth rate values when compared in the same temperature range.

In this work, we will fit the isothermal crystallisation kinetics data to the well-known nucleation and growth model of Lauritzen and Hoffman (LH). The LH theory has been under much criticism lately as it cannot explain morphological findings, especially at low undercoolings. Several alternative theories and models of polymer crystallisation, including computer simulation studies, have been published which in some cases can better explain recent morphological observations.33–35 However, the LH theory is still one of the few models that provide analytical solutions that can be used to fit experimental data. Careful handling of the different fitting parameters can also provide valuable information at least on a comparative basis for different polymer series.

The growth rate data can be fitted to the Lauritzen and Hoffman nucleation and growth model31,36–38 according to the following equation:

image file: c7ce01028a-t2.tif(2)
where G0 is a constant, U* is the activation energy for the transport of macromolecular chains to the crystallisation front (usually taken as 1500 cal mol−1 or 6280 J mol−1), and Tc is the crystallisation temperature; Tα is the temperature where the chain movement ceases (usually taken as Tg-30 °C); KGg is a parameter proportional to the energy barrier for secondary nucleation; Tom is the equilibrium melting temperature and f is a temperature correction factor defined as f = 2·Tc/(Tc + Tom). The solid lines of Fig. 4e correspond to fittings to eqn (2) using the parameters gathered in Table 1. The fitting to eqn (2) allows the calculation of G0, KGg, σ and σe, the values of which are reported in Table 2.

Fitting the data in Fig. 4e to the linearized version of eqn (2), i.e., ln[thin space (1/6-em)]G + U*/(R(TcTα)) vs. 1/(f·Tc·ΔT), allows the calculation of KGg, and knowing the cross-section of the MDI-BD macromolecules within the crystals (approximated to the a and b cell parameters obtained by Born et al.22 as a0a = 4.92 Å and b0b = 5.66 Å), it is possible to estimate the lateral surface free energy, σe, and the fold surface free energy, σ, which are characteristic parameters of lamellar crystals, by using the relations:35

image file: c7ce01028a-t3.tif(3)
image file: c7ce01028a-t4.tif(4)
where j = 2 for crystallisation in Regime II (secondary nucleation and spreading rate occurring at similar rates, i.e., the typical situation encountered when the crystallisation proceeds from the melt at relatively low supercoolings), k is the Boltzmann constant and ΔHom = 115 J g−1,19 the melting enthalpy of a perfect MDI-BD crystal.

The fittings to eqn (2) were performed using the Origin plug-in developed by Lorenzo et al.18 In Table 2, the σe and σ values along the energy required to form a fold, defined as q = 2·a0·b0·σe, are included for each of the three TPUs.

The orders of magnitude of the values obtained for KGg (a parameter proportional to the secondary nucleation or growth energy barrier) are of the same order of magnitude of other polymers.35 Unfortunately, the high dispersity obtained in the growth rate data (Fig. 4e), which is reflected in the low correlation coefficient values reported in Table 2, is probably responsible for the lack of a consistent trend in the values of KGg as a function of MDI content. However, in the next section it will be shown that when the overall crystallisation kinetics is studied by DSC, more reliable values of the energetic parameters related to TPU crystallisation were obtained, as the measured data were much smoother.

Overall isothermal crystallisation studied by DSC

The isothermal crystallisation kinetics determined by DSC yields a complete description of the polymer solidification phenomenon, as it encompasses both nucleation and growth. The inverse of the normalized half-crystallisation time is an experimental measure of the relative overall crystallisation kinetics.31,35,36Fig. 5a shows the experimental 1/τ50% data for each of the TPUs plotted against the crystallisation temperature. In this case, we were able to determine the overall isothermal crystallisation kinetics for all the samples prepared, encompassing a wide range of MDI contents from 30 to 100%.
image file: c7ce01028a-f5.tif
Fig. 5 a) Inverse of half crystallisation time as a function of crystallisation temperature for the studied TPUs. The solid lines correspond to LH model fits with the parameters in Table 3. b) Crystallisation temperature required to achieve an overall crystallisation rate of 0.1 min−1 as a function of TPU hard segment weight fraction, α.

Fig. 5a clearly shows the strong dependence of the crystallisation rate and the temperature range where measurements were possible on the MDI-BD content. As expected on the basis of the nucleation and growth rate kinetics determined above (Fig. 2 and 4), PUeth30 and PUest33 exhibited very similar overall crystallisation kinetics, indicating that the dominant factor is not the type of flexible segment (ether or ester) but the almost identical content of crystallisable hard segments. As the MDI-BD content increases, the samples can crystallise at higher temperatures and therefore faster when compared at identical temperatures.

With the purpose of visualizing the influence of hard segment content, a plot of the temperature required to achieve a relative half-crystallisation time of 10 min (i.e., 1/τ50% = 0.1 min−1) versus the MDI-BD weight fraction in the TPU, α, is presented in Fig. 6b. It can be seen that the difference between PUeth30 and PU100 (i.e., 100 wt% MDI-BD) in terms of the temperature required to achieve the same specified half crystallisation value is approximately 80 °C. The increase of just 13 wt% in hard segment content (i.e., from 30 to 43 wt%) increases this temperature by around ∼40 °C, from ∼120 °C to ∼160 °C. In other words, we need to apply increasingly larger supercoolings to the TPUs as the number and length of crystallisable blocks decrease in the chains.

image file: c7ce01028a-f6.tif
Fig. 6 Isothermal crystallisation studied by DSC. a) Avrami plot of the data obtained during crystallisation of PUeth30 at 110 °C. b) Raw heat flow data of PUeth30 during crystallisation at 110 °C, compared to the data predicted by the Avrami model (see Fig. S1 for heat flow data for all the TPUs analyzed).

Comparing PUeth30, PUest33 and PUeth43, the relative crystallisation rates follow the same trend as observed in the experiments performed by PLOM (where only secondary nucleation or spherulitic growth was measured) and are presented in Fig. 4e (i.e., PUeth30 ≈ PUest33 < PUeth43). The difference with PUeth43 is even enhanced in the case of the overall kinetics, determined by DSC, since the nucleation factor further accelerates the kinetics. In Fig. 4e, it is seen that in order to have identical growth rates as in PUeth43 at 168 °C (∼1 mm min−1), the Tc values for PUeth30 and PUest33 should be ca. 20 °C lower (i.e., ∼145 °C), while in the case of the DSC experiments shown in Fig. 5a and b, in order to attain a rate of 0.1 min−1, the Tc of PUeth30 and PUest33 should be ∼40 °C lower than that of PUeth43. The higher nucleation rate of PUeth43 has been discussed above in the nucleation experiments carried out by PLOM.

Fitting of DSC isothermal data to the Avrami model. The Avrami equation31,35,36 can usually describe the primary crystallisation process in many polymers (i.e., the nucleation and free growth of spherulites until the early stages of impingement). The equation can be written in the following form, as postulated by Lorenzo et al.,18 in order to take into account the induction time (the time elapsed before crystals are detected by means of their released exothermic heat during isothermal DSC measurements):
1 − ϕc(tt0) = exp[−K(tt0)n](5)
where ϕc(t) is the relative volumetric crystalline fraction at a time t; K the overall crystallisation rate constant; t, the crystallisation time; t0 is the induction time and n is the Avrami exponent. Several reviews on the Avrami equation and its correct application to fit overall polymer crystallisation data have been published recently.18,39,40Fig. 6 shows a representative fitting to the Avrami model for the crystallisation of PUeth30 at 110 °C performed with the complimentary Origin plug-in software developed by Lorenzo et al.18

Fig. 6a shows the so-called Avrami plot or double logarithmic representation that linearizes eqn (5) in the conversion range of 3–20% corresponding to the primary crystallisation. In the inset, the obtained Avrami index, n, the K constant and the regression coefficient for the fitting, R, are included. Using these values in eqn (5) and by differentiating the equation, the experimental heat flow data can be modelled by the Avrami equation, and it is shown in Fig. 6b.

As previously mentioned, the Avrami equation normally works well during the primary crystallisation range. However, in the case of the TPUs employed here, the fittings are remarkable (see Fig. 6b), since they almost perfectly fit the DSC data until 50% conversion (i.e., up to the point where spherulites normally impinge on each other). In the inset of Fig. 6b, the experimental half crystallisation time is compared to that obtained by the fitting to eqn (5), as the agreement is excellent with a difference between predicted and experimental values of only 2%. In fact, the Avrami equation can describe in this case with a relatively good fit the entire isothermal crystallisation process of the TPUs employed here. This is not common but has also been reported for the crystallisation of polyesters.18,41,42 The analysis of the results in terms of the Avrami equation will be presented below, together with results from the LH model.

Overall isothermal crystallisation data analysed by the Lauritzen–Hoffman and the Avrami models. To fit isothermal DSC data to the Lauritzen–Hoffman model, eqn (2) was modified, substituting the spherulitic growth rate (G) with the half crystallisation time, τ50%, as follows:37
image file: c7ce01028a-t5.tif(6)
where Kτg is a constant proportional to the energy barrier that the polymer chains have to surmount in order to undergo both nucleation (primary nucleation) and growth (secondary nucleation or superstructural growth).

As in the case of PLOM data, the fitting to eqn (6) was performed using the end melting temperature as an approximation of Tom. The parameters used for the data fitting to eqn (6) are gathered in Tables 2 and 3. Similarly to eqn (2), the Lauritzen and Hoffman plots, where ln(1/τ50%) + U*/R(TcT) versus 1/(Tc·ΔT·f) are presented, yielded straight lines (see the ESI, Fig. S2) which allow calculating Kτg, σ, σe and q (according to eqn (3) and (4)). The resulting values are gathered in Table 3.

Table 3 Parameters obtained from fitting the DSC data presented in Fig. 5a to the Lauritzen–Hoffman model (eqn (6))
TPU 1/τo [cm s−1] K τ g [K2] σ [erg cm−2] σ e [erg cm−2] q [erg] R 2
a R 2 is the correlation coefficient for the Lauritzen–Hoffman (eqn (6)) linear plots (i.e., ln(1/τ50%) + U*/R(TcTα) vs. 1/f·Tc·ΔT). The fitting parameters (ΔHv, a0, b0) are similar to those gathered in Table 2 with TomTm,end.
PUeth30 5.73 × 1016 1.05 × 106 10.9 512 2.85 × 10−12 0.995
PUest33 8.90 × 1014 9.07 × 105 10.9 445 2.48 × 10−12 0.988
PUeth43 3.98 × 108 4.55 × 105 10.9 213 1.19 × 10−12 0.992
PUest64 5.63 × 106 3.90 × 105 10.9 174 9.70 × 10−13 0.980
PU100 5.69 × 106 3.37 × 105 10.9 150 8.36 × 10−13 0.988

Fig. 7 shows the plots of several crystallisation kinetic parameters as a function of crystallisation temperature. First of all, the inverse of the half-crystallisation time experimental data are plotted on a semi-log scale with the LH fittings and are shown as continuous lines in Fig. 7a. The overall crystallisation rate constant calculated by the Avrami fit to the data has units of timen, and since n values are not constant, a direct comparison cannot be made. This is the reason why the values of K have been normalized by elevating them to the 1/n power. As a result, K1/n (with units of min−1) has been plotted on a semi-log scale in Fig. 7b. The values of K1/n also represent an overall crystallisation rate, and therefore they can also be fitted with the Lauritzen and Hoffman theory, as represented by the continuous lines in Fig. 7b. This is an excellent way to compare the experimental data points (experimental values of 1/τ50% in Fig. 7a) with the fittings of the Avrami theory (calculated K1/n values, represented as data points in Fig. 7b) and at the same time check how the Lauritzen and Hoffman model can also make a reasonable prediction of the overall crystallisation kinetics at 50% conversion to the crystalline state.

image file: c7ce01028a-f7.tif
Fig. 7 a) Half crystallisation times for the TPUs as a function of Tc presented on a logarithmic scale. b) Normalized crystallisation constant of the Avrami model as a function of Tc. c) Avrami index for each of the TPUs as a function of Tc. Solid lines in (a) and (b) correspond to fittings to the Lauritzen–Hoffman model.

Fig. 7c shows the Avrami index values as a function of Tc for each of the TPUs. As the crystallisation temperature increases, the Avrami indexes tend to decrease, for example, from n ∼ 2.7 (which can be approximated to 3) at Tc = 110 °C to n ∼ 2.0 at Tc = 120 °C for PUest33. Taking into account the observations made using PLOM in Fig. 3, it is clear that a correlation can be found, as spherulites were preferentially observed at relatively low Tc values and axialites at high Tc values.

Normally, as Tc increases, the nucleation becomes more sporadic; therefore, the Avrami index could increase as it depends on the nucleation rate. However, if there is a change in growth dimensionality as the temperature increases, as has often been observed in other polymers (see ref. 36), then the Avrami index should decrease. PLOM observations are in line with the results obtained by the Avrami fittings, as long as the nucleation is considered always instantaneous. Therefore, according to Fig. 7c, a change in growth dimensionality occurs from 3D spherulites (corresponding to n = 3), formed at low Tc values, to 2D axialites (corresponding to n = 2), formed at high Tc values.

The increment of the overall crystallisation rate with the hard segment content is also reflected on the overall crystallisation constant, Kτg, which decreases as the MDI-BD weight fraction, α, increases. The values of this kinetic constant are gathered in Table 3, but they have also been presented as a function of α in Fig. 8, where it can be seen that the relationship of Kτg with α is of the double logarithmic type (i.e., linear when a representation of log[thin space (1/6-em)]Kτgvs. log[thin space (1/6-em)]α is performed). The double logarithmic relation between Kτg and α corresponds to an equation of the type:

Kτg = Kτ0g·αβ(7)
where Kτ0g is proportional to the crystallisation energy barrier related to a 100 wt% MDI-BD homopolymer TPU, and β is a constant. The pair of values obtained from the data fitting to eqn (7) are {Kτ0g, β} = {∼105.4 K2, −0.94}. Eqn (7) fulfils the condition that when the crystallisable segments' content approaches zero, the crystallisation constant increases to infinity, since the statistical probability of the different MDI-BD segments to become close to each other and crystallise diminishes exponentially:
image file: c7ce01028a-t6.tif(8)

image file: c7ce01028a-f8.tif
Fig. 8 Secondary nucleation constant, Kτg, as a function of the hard segment weight fraction, α. The line corresponds to the fitting to an exponential curve, such as the one shown in the inset. The above scheme depicts qualitatively the impact of α on the crystallisation morphology for a given volume (not in scale).

In contrast, when the weight fraction of the MDI-BD segment increases, the energy barrier values become closer to that of PU100. This concept of behaviour is also depicted in Fig. 8 where different TPU copolymer compositions represent the conditions for extreme α and Kτg values.

Crystallisation kinetics monitored by synchrotron SAXS

In order to determine the differences in morphology at the temperatures selected for PLOM and DSC experiments (compare Fig. 4e and 6a and Fig. S3), in situ isothermal crystallisation experiments with PUeth30 at two representative temperatures (108 and 160 °C) were carried out using synchrotron radiation for small angle X-ray scattering (SAXS) and wide angle X-ray scattering (WAXS, see Fig. S4) analysis.

Fig. 9a shows the SAXS intensity (a.u) profiles obtained as a function of crystallisation time at 160 °C. At initial times, no scattering is revealed due to the slow nucleation process at this temperature. The SAXS pattern at initial times is similar to that at 220 °C, when the material is fully melted (Fig. 9b). The absence of any signal in the melt is consistent with our previous works1,10 and reflects the absence of phase segregation in the melt. The crystallisable sequences will start their crystallisation from a single phase melt.

image file: c7ce01028a-f9.tif
Fig. 9 Isothermal crystallisation monitored by synchrotron SAXS. a) Evolution of the SAXS pattern during isothermal crystallisation of PUeth30 at 160 °C during the first 22 min. b) SAXS profiles of PUeth30 at (a) 220 °C (i.e. melt); (b) 160 °C after 10 min; (c) 160 °C after 22 min and (d) 108 °C after 10 min. (c′) Corresponds to the subtraction of the curve at 220 °C (melt) from curve (c).

In Fig. 9a, it can be appreciated how a small shoulder at q ≈ 0.025 Å−1 arises when the crystallisation time reaches around 20 min. This corresponds to an inter-domain distance of d ∼ 28.5 nm, which matches values obtained previously for the same material after self-nucleation and non-isothermal (slow cooling) crystallisation.10

The crystallisation at lower temperatures developed smaller inter-domain distances in a much shorter period of time (Fig. 9b). The kinetics of both nucleation and growth is accelerated and the higher supercooling applied typically leads to the formation of thinner lamellar crystals. The obtained inter-lamellar distances are of d ∼ 18.5 nm, which are significantly smaller values than those obtained at 160 °C. This value lies between the 28 and 11 nm obtained after slow and fast cooling, respectively, after a self-nucleation process,10 which suggests that the morphology is that of a more super-cooled material (i.e., more nuclei and smaller lamellae) in comparison with the material crystallised at 160 °C.

Overview of the TPU morphology

Fig. 10 presents an overview of the typical morphologies encountered for the TPUs examined in this work. Fig. 10a shows a polarized light optical micrograph, which shows on a large scale the typical superstructures of PUeth43 during isothermal crystallisation at 172 °C. A sample of this copolymer was left to crystallise at the same temperature until saturation, so that all the superstructures impinged on one another, and then quenched to room temperature. Fig. 10b shows an AFM micrograph where individual superstructures (spherulites or axialites) can be recognized via the inter-spherulitic regions that separate one spherulite from the next (they are all impinged on one another).
image file: c7ce01028a-f10.tif
Fig. 10 Morphological overview of PUeth43 after isothermal crystallisation. a) PLOM image obtained after crystallisation at 172 °C. b) 20 × 20 μm2 AFM modulus image of a PUeth43 sample crystallised at 172 °C, with a sketch of a spherulite. c) A 2 × 2 μm2 close-up of (b). d) Sketch of the TPU nanostructure indicating lamellar sizes and average interlamellar distances, and e) schematic illustration of the 3D lamellar morphology of the MDI-BD crystals indicating the unit cell parameters according to Born et al.22

By closer inspection of the superstructural features performed using AFM yielded images like that shown in Fig. 10c, individual lamellae can be clearly observed growing from a relative centre or nucleus. The analysis by AFM of all the crystallised TPU samples showed that both spherulites and axialites are made up of similar lamellar-like structures growing radially from the nucleus.

Fig. 10c can be inspected with the AFM software and the thickness of the lamellae can be measured. The lamellar thickness of the sample shown in Fig. 10c has an average value of ∼20 nm. As shown in Fig. 10d, the average long period or average distance between the centres of one lamella to the centre of the neighbouring lamella was also determined and found to be also close to 20 nm. These values fit well to the long period obtained for this sample by small angle X-ray scattering.

Fig. 10 also includes a sketch qualitatively describing the full morphological panorama of TPU crystals, which are made up of MDI-BD lamellae, constructed by taking into consideration all the evidence gathered by DSC, PLOM, AFM and SAXS. The macrodiols are also schematically represented outside of the MDI-BD blocks. In addition, a representation of the MDI-BD crystal zig-zag structure and unit cell according to Born et al.,22 Terban et al.26 and Blackwell et al.24,25 has also been included. Notice the tangential orientation of the c axis of the chains within the crystals, which is consistent with the negative sign of the spherulites determined by the red tint plate in the PLOM observations.


We have shown that various segmented thermoplastic polyurethanes with crystallisable MDI-BD units and different macrodiols nucleate and crystallise in a similar way to melt mixed multi-block copolymers. The TPUs studied crystallise from a single phase melt, as evidenced by SAXS measurements.

The nucleation rate, the spherulitic growth rate and therefore the overall crystallisation rate are strong functions of the content of the crystallisable phase. The increase of just 13 wt% in MDI-BD content leads to an increment of 4 orders of magnitude in the nucleation density and nucleating rate, and the energy barrier for nucleation and growth decreased exponentially with the increase in MDI-BD content. By applying classical theories of nucleation and crystallisation, the nucleation kinetics and the overall crystallisation kinetics were well described and the corresponding parameters quantitatively determined and reported for the first time for MDI-BD TPUs.

The overall crystallisation kinetics can be modelled by the Avrami equation up to an unusually high conversion degree encompassing both primary and secondary nucleation. As shown by the Avrami coefficient and the PLOM observations, the morphology of the crystallites changes from 3D-spherulites at low undercoolings to 2D-axialites at higher undercoolings.

From a detailed morphological study comprising PLOM and AFM observations together with SAXS experiments, a complete overview of the morphological hierarchy of the TPUs employed is presented.

Conflict of interest

There are no conflicts of interest to declare.


The authors would like to acknowledge funding by BASF and by the ALBA project 2015091420 (2016). We would also like to acknowledge the staff from the BL11 beamline at the ALBA synchrotron, as well as the travel funding by “Ministerio de Economía y Competitividad” and “Generalidad de Cataluña” (Proposal Number: 2015091420). The authors gratefully acknowledge fruitful discussions with Prof. A. Stribeck and also with Dipl.-Ing. Raphael Dabbous from BASF. BFD also wants to acknowledge “Fundación Caja Navarra” and “Obra Social La Caixa” in the framework of UPNA's program “Captación de Talento” for the funding during the writing of this manuscript.

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Electronic supplementary information (ESI) available. See DOI: 10.1039/c7ce01028a

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