Morphological Changes Under Strain for Different Thermoplastic Polyurethanes Monitored by SAXS Related to Strain-At-Break

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Morphological changes under strain for different thermoplastic polyurethanes monitored by SAXS related to strain-at-break

Almut Stribeck1∗, Xuke Li1, Ahmad Zeinolebadi2, Elmar Pöselt3, Berend Eling3, Sérgio Funari4

1University of Hamburg, Department of Chemistry, Institute TMC, Bundesstr. 45, 20146 Hamburg, Germany 2Polymer Consult Buchner GmbH, Schwarzer Weg 34, 22309 Hamburg, Germany 3BASF Polyurethanes GmbH, Elastogranstr. 60, 49448 Lemförde, Germany 4HASYLAB at DESY, Notkestr. 85, 22603 Hamburg, Germany ∗E-mail: [email protected]

Abstract. In tensile tests of 6 different hand- that separates the weak discrete scattering from cast thermoplastic polyurethanes (TPU) with the height distribution of hard domains, whose a hard-segment content HSC=0.51 the vol- weight returns the variation of VH with the ume fraction of hard domains (VH) has been strain. All TPUs are based on 4,4’-methylene tracked. The materials exhibit a linear increase diphenyl diisocyanate (MDI). The other raw up to a strain of approx. 0.5 (strain-induced components are systematically varied. phase separation). Thereafter a linear decrease of VH is indicated. When stretched by 100% about 25% of the initially present hard domains are destroyed. The extrapolation to VH=0 is close to the elongation at break. Characteris- Two MDI units determine the height of the tic materials parameters are suggested by the average hard domain. The variation of VH found relation. with strain is described by a tensile augmenta- The tests (maximum strain: 3) are moni- tion (in analogy to the tensile strength) which tored by small-angle X-ray scattering (SAXS). is realized at an end-of-growth strain. The fol- The morphology is closer to particle scatter- lowing hard domain destruction is governed by ing than that of machine-processed material. a consumption factor. Deviations between ex- Therefore the longitudinal scattering appears trapolated and measured strain at break may be ﬁttable by a one-dimensional statistical model related to the TPU composition.

1 1 Introduction mer chains with different sequence statistics will have grown. The mixture is poured onto Thermoplastic polyurethanes (TPU) are pro- a cool plate for curing. During this step the duced in the reaction of a diisocyanate, a formation of convection cells is observed. Ma- short-chain diol and a polyol. The isocyanate terial taken from the center of the convection and short-chain diol form a rigid or hard seg- cells exhibits different composition as com- ment; these isocyanate-ended hard segments pared to material from the edges of the con- are linked through the polyol soft block to vection cells.4 So in the block sequences of form a statistical block copolymer of the (A- hand cast material a double variability is found, B)n type. When all the components of the where the primary one is the result of the sta- polyurethane are difunctional, a linear thermo- tistical nature of the polyaddition. This will plastic polymer is obtained. As the hard and probably affect even the morphology of hard soft chain segments are thermodynamically in- and soft domains, which should exhibit greater compatible, phase separation occurs resulting variability of domain sizes. Ultimately, hand- in the formation of domains that are either rich casting might even have an impact on the mate- in soft or hard segments. The exact nature rials properties. In studies that vary the mold- of the final morphology depends on both the ing conditions, effects on the materials perfor- molecular composition and the processing con- mance have been reported for PU5–7 or epoxy ditions. As far as the molecular composition resin.8 is concerned, it is commonly accepted that the In this study we carry out straining exper- extent to which phase separation in the elas- iments and simultaneously monitor the evo- tomer takes place depends on: i) the distribu- lution of its morphology by small-angle X- tion of hard and soft chain segments along the ray scattering (SAXS). To quantify the afore- chain, ii) the polarity difference or the compat- mentioned extra disorder in the already irreg- ibility between hard and soft chain segments ular topology of PU is difficult even if scat- and iii) the ability of the hard-segments to stack tering methods are employed. Here it may tightly and to establish strong intra-molecular help to project the scattering data back into interactions. Another generalization concern- real space using procedures similar to those ing phase separation may be that the larger the used in computed tomography. In a paral- difference between the glass transition temper- lel study9 of machine-processed thermoplastic atures of the soft and hard segment rich do- polyurethane (TPU) we have described mor- mains is, the higher is the extent of phase seg- phological peculiarities that have become vis- regation between the phases. This fact also re- ible after such a transformation. They have flects differences in polarity between the hard been related to excellent homogeneity of the and soft chain segments.1 mixing3 in the machine process and the ad- When TPUs are synthesized in a one-shot dressed primary variability of block sequence. method, the raw components are simply stirred Now we investigate corresponding hand-cast together. On a large scale, the process is car- material. ried out by machines (machine processing). Compared to machine-processed TPU the "Hand-casting" refers to a process in which morphology of hand-cast material resembles the components are poured into a bucket2 and an ensemble of particles which are almost un- stirred. In such a "bucket and paddle mix",3 the correlated. In this study we propose a proce- mixing quality may remain moderate. In other dure to strip the small effect of correlations words, at different places in the bucket copoly- from the scattering data by fitting, and thus to

2 extract information on the ensemble of the un- tent is calculated according to correlated particles.10 As a function of strain nchainextender Mchainextender + Mdiisocyanate one expects that the hard domains appear rigid, HSC = m and that the gaps formed by the soft domains total expand with strain. As this feasibility test whilst neglecting the second terminal diiso- is passed we determine the variation of hard- cyanate. domain volume in the strain test and find a rela- Wide-angle X-ray scattering (WAXS) scans 5, 11 tion to one of the ultimate properties of the of the isotropic materials have been carried materials. To the best of our knowledge nei- out in a powder diffractometer X‘Pert Pro ther the variation of the hard domain content MPD manufactured by PANalytical in Bragg- during straining nor its relation to the strain at Brentano geometry with a wavelength λ = break has been quantified before. 0.1542 nm (Cu-kα ). The scans cover the angular range 2° ≤ 2θ ≤ 42°. 2θ is the scattering angle. 2 Experimental 2.2 Tensile testing 2.1 Materials Tests are run in a self-made20 machine. A grid of fiducial marks is printed21 on test bars We study thermoplastic polyurethanes (TPU) S3 (DIN 50125). The sample thickness is made from different components. The hard ts0 ≈ 2mm. The sample width is 2 mm. The segments of all materials are made from clamping length is 22.5 mm. Signals from 4,4’-methylene diphenyl diisocyanate (MDI). the transducer are recorded during the exper- The chain extenders are 1,4-butane diol (BD) iment. The sample is monitored by a TV- or hydroquinone bis(2-hydroxyethyl) ether camera. Video frames are grabbed every 12 s (HQEE), respectively. The soft segments and are stored together with the experimental are either made from polytetrahydrofuran data. The machine is operated at a cross-head (PTHF®, PTHF is a trade mark of BASF SE), speed of 1 mm/min. Using the fiducial marks, from polycaprolactone (PCL) or from adipic the local macroscopic strain ε = (ℓ − ℓ0)/ℓ0 ester (AE). The molar masses of all soft seg- at the position of X-radiation is computed au- ments are very close to Mn ≈1000 Da. tomatically from the initial distance, ℓ0, be- The raw materials have been produced by tween two fiducial marks and the respective BASF and all TPUs have been synthesized by actual distance, ℓ. Processing all the video BASF Polyurethanes Ltd in Lemförde, Ger- frames yields the curve ε (t) as a function of many by hand-casting in a one-shot process.12 the elapsed time. It is very well approximated After curing the materials have been milled and by a quadratic polynomial. The local strain rate ˙ −3 −1 injection molded to sheets of 2 mm thickness. is kept low ε ≈ 1.3×10 s in order to adapt Afterwards they have been matured13–19 by an- to the limitations of the synchrotron beamline. nealing at 100 °C for 20 h. The true stress, σ = F/A, is computed from the force F measured by the load cell after sub- Table 1 presents characterizations of the ma- tracting the force exerted by the upper sample terials. σmax and εb have been determined in separate tensile tests. The reported values for clamp, and from A = A0/(1 + ε), the estimated εb are the maximum values from several re- actual sample cross-section. A0 is the initial peated determinations. The hard segment con- cross section of the central zone of the test bar.

3 Table 1: Samples and their characterization. ρ: mass density, σmax: tensile strength, εb: elongation at break, Mw,TPU : weight-average molecular mass of the polymer, Xiso,TPU : isocyanate content of the polymer. All materials share the same hard-segment content HSC=51%. labeling mbt mqt mbl mql mba mqa hard segment MDI MDI MDI MDI MDI MDI chain extender BD HQEE BD HQEE BD HQEE soft segment PTHF PTHF PCL PCL AE AE ρ [g/cm] 1.172 1.185 1.215 1.23 1.239 1.255 Shore D 65 64 71 75 71 74 σmax [MPa] 54 40 42 33 42 34 εb 5.0 4.6 4.9 3.9 5.6 4.7 Mw,T PU [kDa] 88 55 103 54 80 66 Xiso,T PU [%] 0.06 0.10 0.04 0.04 0.04 0.08

The experiments are stopped at ε ≈ 3 when the Because the samples are narrower than the pri- observed SAXS intensity has become too low mary beam, the latter correction has been car- for a quantitative analysis. ried out by V (t)/V0 = 1/(1 + ε (t)). The equa- tion assumes constant sample volume and a sample that is fully immersed in the X-ray 2.3 SAXS monitoring beam. Absorption factors exp(−µts0) of the SAXS is carried out in the synchrotron beam- unstrained samples are determined by mea- line A2 at HASYLAB, Hamburg, Germany. suring the primary beam flux in front of the The wavelength of radiation is λ = 0.15 nm, detector with and without a sample, respec- and the sample-detector distance is 3022 mm. tively. From the result the linear absorption Scattering patterns are collected by a 2D mar- factor, µ, is computed using the known sam- ccd 165 detector (mar research, Norderstedt, ple thickness. Finally the actual absorption Germany) in binned 1024 × 1024 pixel mode factor exp(−µts (t)) that compensates the lat- (pixel size: 158.2 µm × 158.2 µm). Scat- eral thinning as well is assessed using ts (t)= tering patterns are recorded every 132 s with ts0/(1 + ε (t)). The absorption correction is an exposure of 120 s. The patterns I (s) = carried out by dividing the pattern intensity by −1 t (t) followed by the subtraction of the ma- I (s12,s3) cover the region −0.21nm ≤ s −1 chine background. The strain that is associ- s12,s3 ≤ 0.21nm . s = (s12,s3) is the scattering vector with its modulus defined by |s| = ated to each scattering pattern is related to the s = (2/λ)sinθ. It is not necessary to empha- time t + te/2 with t being the elapsed time at size the small amount of extrapolated data at the start of the exposure, and te the total ex- the beamstop, because it covers an angular re- posure of the pattern. After these steps the region in which the correlation among the hard sulting scattering patterns are still not in abso- domains has already dropped to zero. The scat- lute units, but their intensities can be compared tering patterns are normalized and background relatively to each other. This pre-evaluation is corrected.22 This means intensity normaliza- carried out automatically by procedures writ- 23 tion for constant primary beam flux, zero ab- ten in PV-WAVE. sorption, and constant irradiated volume V0.

4 22, 30 2.4 SAXS data analysis G1,i (s3), as is described elsewhere. Thus the interference function G (s ) is obtained. Analysis of projections. The best-known 1 3 Its one-dimensional Fourier transform is the projection in the field of scattering maps the longitudinal IDF g (r ). intensity I (s)/V that is normalized to the irra- 1 3 The IDF is fitted26 by a one-dimensional diated volume, V , onto the zero–dimensional model that describes the arrangement of alter- subspace. The resulting number Q is known as nating hard-domain heights and soft-domain “invariant” or “scattering power” heights along the straining direction. Visual inspection of the computed IDFs shows that {I} /V = Q = I (s)/V d3s. 0 ˆ the height distributions of hard domains can be modeled by Gaussian functions and that In a two-phase system Q = the range of correlation among the domains 2 26 vh (1 − vh)(ρh − ρs) is valid with vh the is short. Thus a short-range stacking model volume fraction of hard domains, ρh and ρs with few parameters is chosen, which is a vari- being the electron densities of the hard domain ant of the ideal stacking model.31 The parame- phase and the soft phase, respectively. ters of the model are a weight W that is related Bonart’s longitudinal scattering24 is ob- to the volume fraction of contributing chords tained by not integrating over the whole recip- (cf. Figure 1), average heights H¯h and H¯s of rocal space, but only over planes normal to the hard and soft domains, respectively, and the fiber axis yielding the curve relative standard deviations σh/H¯h and σs/H¯s ∞ of the domain height distributions. An addi- 32, 33 {I}1 (s3)/V = 2π s12 I (s12,s3)/V ds12, tional parameter that skews the Gaussians ˆ0 is present but not discussed here. which is a function of the straining direction s3. Fitted parameters and hard domain vol- {I}1 (s3) is a projection onto a 1D subspace as indicated by subscripting to the pair of braces. ume. By fitting the IDF, we determine the Projections are computed from normalized pat- height distributions Hh (r3) and Hs (r3) of hard terns. and soft domain chords, respectively. The From such projections interface distribution weight parameter of the IDF is defined 22, 25, 26 functions (IDF) g1 (r3) are computed W = H (r ) dr = H (r ) dr. (1) for further analysis. In this way it becomes ˆ h 3 ˆ s 3 possible to quantify several morphological parameters. Let us assume that the hard domains are the Technically, the first step involves subtrac- diluted phase, i.e. that the small-angle scattering counts all the chords which cross all the tion of a guessed constant density fluctuation 27–29 hard domains (in the matrix phase there may be background, IFl, from the measured curve chords which are so long that they will not be 2 2 and multiplication by 4π s3 to apply the sec- counted). Without loss of generality we con- ond derivative in reciprocal space. The result sider a single hard domain. Figure 1 shows a is an intermediate interference function sketch of this hard domain intersected by its chords. Obviously, the volume Vh of the hard 2 2 G1,i (s3) = ({I}1 (s3)/V − IFl) 4π s3. domain is V = dσ l (r ,r )dr dr = dσ r H (r )dr , The final background is constructed by appli- h ¨ 1 2 1 2 ˆ 3 h 3 3 cation of a narrow low-pass frequency filter to (2)

5 dσ polytetrahydrofuran PTHF® polyols and 1,4-

butanediol are most common. Polyethers like PTHF® are less compatible with the MDI based hard chain segments than polyesters and l( r 1, r 2 ) TPUs derived from them show a higher degree of phase separation. The hard domains straining direction r also tend to be larger and more complex than 3 those found in TPUs based on polyesters. r2 With regard to the short-chain diol, hy- r1 droquinone bis(2-hydroxyethylether) (HQEE) yields higher melting hard domains than those Figure 1: The (only) hard domain of a primi- produced from 1,4-butane diol.34 In this paper tive morphology intersected by chords of vary- we investigate MDI-based TPUs from PTHF®, ing length l, the lengths defined by the surface poly (alkylene adipate) and polycaprolactone of the hard domain. Every chord occupies an (PCL) polyols and 1,4-butane diol and HQEE infinitesimal cross section dσ. Only chords chain extenders. With the present series of which run in straining direction are considered, polyurethanes the TPU technology field is because the longitudinal scattering {I}1 (r3) is largely covered. The hard-segment content analyzed (HSC) has been kept constant for all TPUs and amounts to 51 wt.-%. In regard to their and the change of the integration variables mechanical properties (see Table 1) the TPUs from the first to the second integral is possible, based on PTHF® (mbt and mqt) are signifi- because Hh (r3) is just the function which gives cantly softer (5 – 10 shore-D units) than the the number of chords of length r3. Moreover, polyester based TPUs, which may originate the average hard-domain height is defined as from a higher degree of phase separation. In usual this respect the use of HQEE or BD has only a minor effect on the polymer hardness (1 – r3 Hh (r3)dr3 Vh/dσ Hh = = , (3) 4 shore-D units). Although being soft, the ´ H (r )dr W 3 3 highest tensile strength at break is measured ´ and it follows for mbt. Another observation made is that the HQEE based TPUs show significantly lower H W ∝ V . (4) h h values of both weight-average molecular mass Both Hh and W are fit parameters. Thus a Mw and tensile strength at break than those pro- quantity which is proportional to the total vol- duced from BD. The HQEE based hard chain ume of hard domains can be determined from segments have a higher tendency to phase- the fit. In the special case of rigid hard domains separate than those from BD, causing the phase the proportionality even simplifies to W ∝ Vh. separation to start already at a lower conver- sion. This earlier phase separation is believed to be the origin of the reduced Mw build- 3 Results up, and consequentially poorer ultimate tensile 3.1 Properties of the TPU materials properties. Early phase separation may also affect the polymer morphology and the nature of TPUs based on methylene diphenyl diiso- the hard domains. The combined effect of dif- cyanate (MDI), poly (alkylene adipate) and ferences in chain topology and polymer mor-

6 10 mbt e.g. the sizes of hard and soft domains and their mqt arrangement in space. For distorted materials 8 mba mqa of low crystallinity like polyurethanes the mor- mbl mql phological relations between both views ap- 6 pear weak, as a previous study has shown35 ) [a.u.] θ and a WAXS study may be reported separately

(2 4 I from a SAXS study. 2 In a tensile test it is expected that the WAXS amorphous halo becomes oriented. It demon- 0 10 20 30 40 strates the orientation of the normal to the 2θ [°] chain direction. For the semicrystalline materials crystalline reflections may orient, grow or Figure 2: Thermoplastic polyurethane mate- decrease during the straining. rials hand-cast from different raw compo- From the shape of oriented peaks some in- nents. WAXS scans I (2θ) (wavelength λ = formation of the orientation distribution of the 0.1542 nm) of the virgin isotropic materials. crystals may be obtained. Similar to the analy- Some curves are shifted in vertical direction for sis of the orientation of the amorphous halo one clarity does not obtain absolute values, because there is no easy way to determine the background phology may be reflected in the morphologies that must be considered.35 Nevertheless, limits and their evolution under strain, notably for the and trends for an uniaxial orientation parame- polymer mqt. ter22, 36 can be determined. Similarly, the variation of the integral intensity of separated crys- 3.2 WAXS scans talline reflections as a function of strain yields indications of strain-induced crystallization or Figure 2 presents the WAXS scans of the stud- melting. Of course, the integration has to be ied materials. For mbt and mba only an amor- carried out in 3D reciprocal space and not only phous halo is observed. All materials with the in the detector plane. chain extender HQEE exhibit broad but clear crystalline reflections in addition, and mbl is 3.3 The tensile tests in between. This shows that the HQEE-based hard domains are more perfectly ordered than Figure 3 shows the stress-strain curves (true those from BD. stress vs. local strain) measured during the WAXS results monitor correlations on the straining experiments at the synchrotron. Bear scale of several Ångströms. The strongest scat- in mind that the tensile strength σmax from Ta- tering effect is related to the contrast between ble 1 is expressed in engineering stress, σeng ≈ chains and vacuum. Thus some information σ/(1 + ε). The local strain ε is computed on the orientation distribution of the normal- from the movement of two fiducial marks close direction to the chains may be obtained35 as to the point of X-irradiation. This is not the a function of strain. Beyond that, even short- engineering strain which is computed from the range correlations between different chemical movement of the machine cross-heads. Mate- groups along the chain may be detectable. On rials become stronger, when the chain exten- the other hand, the SAXS monitors the two- der BD (thin lines) is replaced by HQEE (bold phase morphology on the scale of nanometers, lines). Strengthening correlates with the de-

7 0.2 mbt mqt mba mqa mbl mql

0.1 [GPa] σ

0 0 1ε 2 3

Figure 3: Hand-cast thermoplastic polyurethane materials. True stress σ vs. local strain ε at the position of X-irradiation as measured in situ during the tensile tests tectability of crystallites (Figure 2). Related to the soft-segment component the softest material (dashed-dotted) contains PTHF®, the medium one (dashed) is based on adipic ester, and the hardest one (solid line) has soft segments from PCL. This shows that the tensile strength is determined by the chain ex- Figure 4: Selected SAXS data from continu- tender and the employed polyol. The differ- ous straining experiments of 6 hand-cast TPU ences in tensile strength could originate from materials. ε is the strain. Straining direction differences in phase separation and intramolec- is vertical (s3, r3 resp.). The top pattern in ular interactions between the polyol segments. each line is the scattering intensity (“SAXS”), −1 A comparison with the WAXS curves (Fig- shown as log(log (I (s12,s3))), −0.15nm ≤ −1 ure 2) further indicates a correlation with crys- s12,s3 ≤ 0.15nm . The bottom pattern tallinity of the hard domains: in the hardest in each line presents the long-period peaks material the crystallites are big enough to be in the chord distribution function (“-CDF”), clearly detected. −z(r12,r3), −50nm ≤ r12,r3 ≤50 nm on a log- arithmic pseudo-color intensity scale 3.4 SAXS data accumulated during the tests

Figure 4 presents recorded scattering patterns I (s12,s3) and CDFs z(r12,r3) computed from them. In fact, only central cutouts are displayed and only the long-period face −z(r12,r3) > 0 of the CDFs is shown. CDFs visualize the local structure in the neighbor- hood of a domain: Each peak shows, in which

8 direction and distance neighbor domains are rial are fortified by the chain extender HQEE. found. It appears worth to mention that scat- Up to ε ≈ 1 several long-period peaks are ob- tering cannot detect the presence of a co- served. This is similar to the morphology continuous morphology. This is a consequence found in machine-cast materials,9 but here no of the mathematical relation (notably: an au- static long-period bands are observed. Thus tocorrelation) between structure and scattering the series of peaks only indicates morphologi- pattern. Thus in the SAXS data, domains that cal disintegration37, 38 of hard domains, but the bend away from the normal plane to the strain- extensibility of these morphological entities is ing direction appear as if they were cut-off in not limited as is the case with the mentioned the direction transverse to the straining (cf. the machine-cast materials. discussion of the breadth of the long-period Straining divides the hard domains into dif- peaks below). ferent classes. The brightest spot (most fre- For each material a row of images is pre- quent class) has the shortest long period. Af- sented. The leftmost row shows the softest mater an initial upward movement at low strain, terial, the hardest one is found on the right. the spot moves down as the strain increases In each row the strain ε increases from top further. This means relaxation after initial in- to bottom. Compared to respective machine- crease. Simultaneously a long tail emerges cast materials9 the SAXS patterns look simi- which points upward. This means that the dis- lar, but the CDFs are fundamentally different. tribution of long periods becomes extremely With the hand-cast materials the long-period broad and asymmetric. The other classes of peaks are broad (in vertical direction). They hard domains have disappeared. It seems that are neither narrow nor found in static discrete they have been weaker than the domains from bands like with the machine-prepared TPUs. the most frequent class. Instead, the CDFs look very similar to those The discussed tail formation is found with from a previous TPU study of some of us.37 all materials. It has earlier been observed with Also those samples were prepared by the hand other hand-cast polyurethanes.37 Both a long- casting process. period relaxation and a formation of a long tail have been explained by a “sacrifice-and-relief” 37 3.5 Nanostructure from CDF mechanism that requires the destruction of a analysis considerable amount of hard domains. To capture the nanostructure change quanti- The 6 materials exhibit morphological differ- tatively by means of the long period peak, we ences. Compared to the given overview they track its position and shape during the tensile are more clearly presented in meridional cuts tests. In previous work on polyurethanes we of the CDFs (Figure 5). In one of the subfig- have done this as well.9, 37, 39 Figure 6 presents ures straight lines are drawn as guides to the the evolution of the nanoscopic strain εn (ε) eye. They connect the first-order peaks (solid) computed from the most-frequent long period. and the second-order peaks (dashed). In each Only the material mqt exhibits the relaxation strip the brightest spot on the central line indi- behavior known from machine-cast materials9 cates the most-frequent long period. that has already been discussed qualitatively. Only mqt shows peculiarities that have pre- With the other hand-cast materials the known9 viously been found with machine-cast mate- slow increase of the nanoscopic strain εn (ε) ≈ rials.9 It is the softest-but-one material (Fig- 0.6ε continues up to the end of the experiment. ure 3). The hard domains of the softest mate- We explain the low slope (0.6 < 1) by the rigid-

9 Figure 5: Meridional long-period regions cut from the CDFs. −z(r12,r3) 0 ≤ r3 ≤ 50nm, |r12|≤8 nm is presented on a varying log(log (−z)) intensity scale In subﬁgure mba: Lines indicate ﬁrst-order (solid) and second-order (broken) long period peaks

10 3 15 mbt mqt mba mqa 2 mbl mql 10 ) ) [nm] ε ε ( ( n eq ε

σ mbt 1 3 5 mqt mba mqa mbl mql

0 0 0 1ε 2 3 0 1ε 2 3 Figure 7: σ (ε) computed for the evolution of Figure 6: Nanoscopic strain ε (ε) = eq n the first-order long period peak is a measure r (ε)/ε computed from the position 3,Lmax of the transverse straight extension of the hard r (ε) of the first-order long period max- 3,Lmax domains imum in the the CDF as a function of the macroscopic local strain ε dedicated experiments. We speculate that the origin of the observed phenomena could lie in ity of the hard domain (average height: Hh) the preparation of the sample and its premature that is part of the long period L = Hh + Hs. The breadth of the long-period peak yields a phase separation. measure of some average straight hard-domain extension transverse to the straining direction. 3.6 Bonart’s longitudinal scattering By “straight extension” we indicate that the anisotropic SAXS cannot determine, if the Direct analysis. The longitudinal scatter- loss of correlation is a consequence of either ing {I}1 (s3) exhibits morphological differ- narrow hard-domains or of laterally extended ences, as well. Figure 8 displays the re- hard-domains which bend away from the trans- sults. A first inspection of the data shows verse plane after a short distance. Sufficient that the PTHF® based TPUs show a more in- anisotropy of the CDF is required for its deter- tense scattering profile than those based on the mination. Figure 7 displays the results. The polyesters. This is readily explained by differ- hard domain extensions decrease with increas- ent polarity. Because PTHF® is less polar than ing strain. This indicates disruption. Most of the two polyesters, a stronger phase separation the materials show a very similar behavior with should have occurred, resulting in a more in- an almost constant value reached for ε > 1.5. tense scattering.34 There the disruption appears to have stopped. In the PTHF® based materials (Figure 8 up- Again, an exception is the material mqt. It per subfigures) substitution of the chain exten- appears logical that a material with different der BD by HQEE has several effects. The in- classes of hard domains shows a more complex tensity is doubled, the peak position is affected, decay curve than the other materials, but we and its response to strain is changed. With the have no explanation for the observation that in peculiar material mqt the long-period peak is the interval 1 < ε < 2 the stable hard domains much less pronounced than with the material are much narrower than with the other mate- mbt. This is readily explained by the observed rials. This feature can only be elucidated by superposition of several hard domain classes.

11 1.5 3 ε = 0.0 ε = 0.0 0.2 ε = 0.3 ε = 0.3 ε = 0.6 ε = 0.6 mqt mbtε = 0.9 mqt ε = 0.9 ε = 1.2 ε = 1.2 ε = 1.5 ε = 1.5 mbt 1 ε = 1.8 2 ε = 1.8 ε = 2.1 ε = 2.1 mqa ε = 2.4 ε = 2.4 ) [a.u.] ) [a.u.] ε = 2.7 ε = 2.7 3 3 s s ε = 3.0 mba ( ( 1 1 ε = 3.2 0.15 } } I I mql

{ 0.5 { 1 mbl

0 0 0 0.05 0.1 0.15 0 0.05 0.1 0.15 -1 -1 0.1 s3 [nm ] s3 [nm ] ) [a.u.] ε

0.5 0.5 ( ε = 0.0 ε = 0.0

ε = 0.3 ε = 0.3 Q ε = 0.6 ε = 0.6 0.4 mbaε = 0.9 0.4 mqa ε = 0.9 ε = 1.2 ε = 1.2 ε = 1.5 ε = 1.5 ε = 1.8 ε = 1.8 0.3 ε = 2.1 0.3 ε = 2.1 0.05 ε = 2.4 ε = 2.4

) [a.u.] ε = 2.7 ) [a.u.] ε = 2.7 3 3

s ε = 3.0 s ε = 3.0 ( ( 1 0.2 1 0.2 } } I I { {

0.1 0.1 0 0 1 2 3 0 0 0 0.05 0.1 0.15 0 0.05 0.1 0.15 ε -1 -1 s3 [nm ] s3 [nm ] 1 1 ε = 0.0 ε = 0.0 ε = 0.3 ε = 0.3 ε = 0.6 ε = 0.6 Figure 9: Variation of the scattering power Q 0.8 ε = 0.9 0.8 ε = 0.9 ε = 1.2 ε = 1.2 mblε = 1.5 mql ε = 1.5 ε = 1.8 ε = 1.8 0.6 ε = 2.1 0.6 ε = 2.1 in the tensile tests ε = 2.4 ε = 2.4

) [a.u.] ε = 2.7 ) [a.u.] ε = 2.7 3 3

s ε = 3.0 s ε = 3.0 ( ( 1 0.4 ε = 3.2 1 0.4 ε = 3.2 } } I I { {

0.2 0.2

0 0 0 0.05 0.1 0.15 0 0.05 0.1 0.15 IDF analysis. From Bonart’s longitudinal -1 -1 s3 [nm ] s3 [nm ] scattering {I}1 (s3) and interface distribution Figure 8: Evolution of Bonart’s longitudinal function g1 (r3) can always be computed. It scattering as a function of strain. Intensities are describes the statistics and arrangement of do- normalized for constant X-ray flux and con- main heights in straining direction r3. Nev- stant irradiated volume ertheless, an analysis that may yield deeper insight is only possible, if the IDF can be fitted by a suitable model. In the case of machine-processed materials9 a peculiar band Such strong effects are not found with the structure has been found. This complex topol- middle and the bottom subfigures, but minor ogy requires either the construction of an in- differences with respect to both the varying volved morphological model based on quasi- long-period and changing intensity can still periodicity or the development of appropriate be read from the curves. In Figure 8 the approximations. The inspection of Figure 4 in- area under the curves is the scattering power dicates that here an IDF analysis by a simple Q. Curves Q(ε) are reported in Figure 9. model appears promising. Obviously, the chain extender BD yields lower In a first step the IDFs are computed and vi- Q than HQEE. The relative variations of Q as sually inspected. Their features and the trend a function of ε are similar for all materials. as a function of ε is similar for all materials. If the initial volume fraction of hard domains Figure 10 shows 3 IDFs of the material mql at vh (ε = 0) < 0.3, a decrease of Q is approxi- different strains. There is a very strong positive mately proportional to a reduction of vh. For peak which contains the thickness distributions all materials an initial increase is followed by of hard and soft domains, Hh (r3) and Hs (r3), a decrease. This qualitative result concerning respectively. The first negative peak is the long vh can be quantified for the studied samples period distribution L(r3). It is extremely broad with moderate effort, because the morphology and shallow. This means that one of the pos- of the hand-cast materials is blurred consider- itive distributions (Hh (r3) or Hs (r3)) must as ably. For this purpose the corresponding inter- well be broad and shallow. We assume that face distribution functions are analyzed. this is the distribution of soft domains, Hs (r3).

12 5 can be ﬁtted by Gaussian distributions. The ε = 0.3 ε = 1.5 blurred morphology of the hand-cast material 4 ε = 3.0 is demonstrated by the fact that the oscillations 3 Hh ( r 3 ) , Hs ( r 3 ) in g1 (r3) have already died out for r3 > 25nm. ) 3

r A short-range model appears to be applicable, ( 1 2 g and we must be careful to choose a simple L ( r ) 1 3 model with few parameters because the few broad peaks overlap considerably. 0 The strong positive domain peak dominates

0 10 20 30 the IDF. Even if second-order features are not r [nm] 3 correctly considered by a simple model, it may be able to separate the hard-domain peak Figure 10: Material mql. Interface distribu- H (r ) from the contribution of the discrete tion functions (IDF) g (r ) computed from h 3 1 3 scattering. A failure of the separation can be {I} (s ) for selected ε. The data of the 1 3 assessed by discussing the plausibility of the other materials look similar. Bold lines: mea- extracted morphological parameters as a func- sured data. Thin lines: fits by the stacking tion of ε. model. The main peak is made from H (r ) h 3 Thin lines in Figure 10 show the best fits us- and H (r ), the height distributions of hard and s 3 ing the one-dimensional stacking model.26, 31 soft domains in straining direction r . Long pe- 3 The strong peak appears to be fitted well, but riod distributions L(r ) are peaking in negative 3 the long-period peak L(r ) is poorly fitted for direction 3 low and medium strain. This shortcoming may be related to remnant features of quasi-periodic sequences of hard and soft segments that have So the very strong positive peak is a good ap- been found with machine-cast TPUs.9 proximation of H (r ), and the rest of the IDF h 3 Results of the fits by nonlinear regression30 describes the poor correlations among the do- of g (r ) are presented in the following fig- mains. In other words, the predominant infor- 1 3 ures. They present morphological parameters mation content of the IDF is particle scattering. as a function of strain. In this notion the integral W of the IDF is pro- Figure 11 displays the variation of the av- portional to the volume of the particles with the erage hard-domain height H (ε) for all mate- narrow height distribution, i.e. to the volume of h rials. H (ε) varies only slightly with ε and hard domains. Then in Figure 10 the decrease h has a value of about 8 nm. 8 nm is also of the integral with increasing strain describes the height of hard domains that has been ex- the loss of hard-domains during the tensile test. tracted from the data of machine-cast materi- It appears worth to mention that even the un- als9, 40 containing MDI hard segments, as well. correlated particles (from the diffuse particle Hh has been identified from a peculiar quasi- scattering) contribute to the first peak in the periodic signature of the CDF peaks and re- IDF, but only to this peak. The higher peaks lated to a sequence of 2 MDI segments along beginning with the long-period peak require the chain of the copolymer. This is in excellent order among particles. With respect to our ten- agreement with crystallographic data41–43 from sile experiments we have named such ordered model urethanes made from alternating MDI entities “strain probes”. and BD. The papers find unit cell heights of The shape of the curves indicates that they 3.8 nm. Thus a hard block that contains 2 MDI

13 14 mbt 8 mqt 12 mba mqa 6 10 mbl mql 8 [nm] [nm] s h

4 H H mbt 6 mqt mba 4 2 mqa mbl 2 mql 0 0 0 1 2 3 0 1ε 2 3 ε

Figure 11: Variation of the average hard do- Figure 12: Average soft domain height, Hs (ε) main height, Hh (ε) as determined from fits of of the studied materials as determined from fits g1 (r3) of g1 (r3) segments should have a height of 2 × 3.8 nm = Hs (ε) iterates towards zero. There the distri- 7.6 nm. butions Hs (r3) are extremely wide. The sim- Also the relative breadths σh/Hh of Hh (ε) ple model is unable to fit the different mor- vary only slightly between 0.4 and 0.6. Thus, phological classes (see above). The observed the hard domain ensemble has an almost con- monotonous increase of the average soft do- stant average height and distribution width. In- main height is a second indication for a suc- elastic behavior is what one expects. This find- cessful separation of the distributions Hh (r3). ing indicates that Hh (ε) has probably been sep- The parameters of Hs (r3) must not be dis- arated from the scattering data successfully. cussed in detail. In particular its width com- There are slight changes that may be re- pensates the systematic deviations of the mor- lated to growth and destruction of hard do- phology from the simple stacking model. A mains. Thickness growth at low strain is only straight solution would be to use a two- observed for the material mqt. There the other component model. Then an additional com- materials exhibit constant thickness followed ponent would describe the uncorrelated hard by increasing average thickness for 0.5 < ε < domains only. Nevertheless, in this case 1.5. We will show that this is already the re- cross-correlation among the parameters of the gion in which hard domains are destroyed. So two models returns morphological parame- the finding shows that for most of the materials ters of low significance. The reason is the thin hard domains fail more easily than thick poorly structured scattering pattern of the ones. polyurethanes. Figure 12 presents Hs (ε), the variation of Figure 13 shows the result of the weight the average soft-domain height between two analysis (cf. derivation of Eq. (4)). For all ma- hard-domains. To keep the effort manageable terials a strain-induced formation of hard do- only some of the measured data have been pro- mains is observed up to ε ≈ 0.5. cessed. The strong and monotonous increase Moreland and Wilkes44 have identified a of Hs (ε) describes the expected contribution two-step orientation–elongation mechanism. of the soft phase to the nanoscopic elongation The region ε < 0.5 has been associated with of the materials. Only for the material mqt low hysteresis. Here the hard domains aligned

14 Aε is the corresponding end-of-growth strain, i.e. 1.2 model mba mqa Aε = vrh (εg). The slope of the subsequent de- 1 mbl struction decay, c = dv /dε = 0.25 is identi- mql rε rh 0.8 mbt cal for all materials. It deﬁnes the relative ten-

) mqt ε ( sile hard-domain consumption. A reason for rh

v 0.6 experiment extrapolated the identical value may be that all materials 0.4 share the same HSC. Comparing the variety

0.2 of chemical compositions, the identical hard- domain consumption per strain-step show that 0 0ε 1 2 3 4 5 this is a principle which appears to govern the g ε straining of several important classes of TPU. Figure 13: Variation of the relative volume This should be different for, e.g., chemically fraction of hard domains, vrh (ε) for 0 ≤ ε ≤ 3 crosslinked materials. as determined from Hh W (ε) in fits of g1 (r3). In summary, for the studied materials a first- Characteristic parameters Aε and εg are indi- approximation model for the relative volume cated with the model curve (dotted). Linear change of hard domains is extrapolations hit the ε-axis at a model strain- at-break, ε . Circular arrows point at ε val- 1 + (Aε − 1)ε/εg for ε ≤ εg bm b vrh (ε) ≈ . ues from Table 1, if significant differences are (Aε − crε (ε − εg) for ε > εg observed (5) Does the material break, if almost all hard domains are consumed? This would mean more or less reversibly in the strain direc- vrh (εb)= 0, and if the linear relation of Eq. (5) tion. For ε > 0.5 hard domains are disrupted holds up to the materials failure, then the ap- by pulling away individual segments from the proximation hard domains. Our investigation supports and further refines this mechanism. In analogy εb ≈ Aε /crε + εg (6) to the accepted mechanism of strain-induced should be valid. Comparison with Table 1 and crystallization, we imagine that the chain ori- the extrapolations sketched in Figure 13 indi- entation induced by a low tensile force induces cates that Eq. (6) is not too bad, in particu- an additional separation of the phases. lar considering the wide variation in chemical The gain is different for the different mate- composition of the TPUs. The differences may rials. It is lowest for mqt and highest for mbl. be related to secondary mechanisms like frac- For 0.5 < ε < 3 all materials show a linear de- ture, strain-induced crystallization of the soft crease of the hard-phase volume. In several phase and subtle differences in chain topology previous studies we have found by different and polymer morphology. analysis methods that hard domains must be For the materials with HQEE but not ® sacrificed. Our trial plot indicates that a sim- PTHF , εb is somewhat shorter than predicted, ple quantitative relation appears to hold for all for the inverse composition (BD and PTHF®) the investigated materials. εb is longer. This indicates that secondary As sketched in Figure 13 we define two mechanisms which cause deviations from the material constants. Aε is a tensile augmenta- typical cohesion of a TPU may probably be tai- tion (in analogy to the definition of the ten- lored by choice of its components and process- sile strength in a stress-strain curve), and εg ing conditions.

15 4 Conclusions have varied the TPU composition, but have kept constant the hard-segment content. There- The studied hand-cast TPU materials exhibit a fore we have been able to show that the found morphology in which particles (hard domains) empirical relation is valid for a broad range are almost placed at random, and the present of compositions, but we have not been able to faint correlations do not reach far. There- determine, if the tensile domain consumption fore, one can describe the topology of their do- crε is a function of HSC. Finally, we hope that mains by a simple standard two-phase model, Eq. (5) and Eq. (6) may become useful in the fit the data with low error and thus quantita- modeling of material properties of thermoplas- tively track the evolution of the morphology in tic polyurethanes. the strain test. As has been derived in the data evaluation section, the product of two fit pa- Acknowledgements. The authors thank rameters is proportional to the volume of the the Hamburg Synchrotron Radiation Labora- dilute phase. For the studied materials the di- tory (HASYLAB) for beam time granted in the lute phase is formed by the hard domains, as frame of project I-2011-0087. Almut Barck is has been verified by comparing the height dis- acknowledged for the WAXS scans and Ben- tributions of soft and hard domains. jamin Nörnberg for tensile tests. For all materials similar curves describe the variation of the hard-domain volume as a function of strain. For ε > 0.5 the volume de- References creases linearly and the material breaks, when all domains are destroyed. This correlation [1] Petrovic,´ Z. S.; Ferguson, J., Progr. with the macroscopic mechanical parameter εb Polym. Sci. 1991, 16, 695–836. indicates how fundamental the destruction of [2] Axelrood, S. L.; Hamilton, C. W.; Frisch, physical crosslinks (the hard domains) appears K. C., Ind. Eng. Chem. 1961, 53, 889– to be with the non-crosslinked polyurethanes. 894. As an explanation for the poorly modulated [3] Clemitson, I. R., Polyurethane Casting discrete scattering of hand-molded materials, Primer, CRC Press, Boca Raton, FL, we have adopted a double-sequence variability 2012. of the hard and soft blocks along the chains. [4] Harpen, F.; Luinstra, G. A.; Eling, B., in The second variability can be generated by Moritz, H.-U., ed., 11th Int. Workshop on factors that are related in the broad sense to Polymer Reaction Engineering. Book of the processing and intrinsic properties of these Abstracts, Dechema e.V., Frankfurt, 2013 materials. We have referred in detail to the p. 135, p. 135, poster P68. incomplete mixing, but there are also other [5] Rausch Jr, K. W.; Sayigh, A. A. R., factors that are governed by the kinetics and Ind. Eng. Chem. Prod. Res. Development, thermodynamics of the phase separation pro- 1965, 4, 92–98. cess. Despite the wide choice in raw materials [6] Yen, M.-S.; Kuo, S.-C., J. Appl. Polym. and the basic preparation technique that have Sci. 1996, 61, 1639–1647. been used to produce the TPUs, they all have [7] Fan, L. H.; Hu, C. P.; Ying, S. K., Polym. shown a common behavior which is captured Eng. Sci. 1997, 37, 338–345. in Eq. (5) and Eq. (6). [8] Bell, J. P., J. Appl. Polym. Sci. 1982, 27, In order to be able manage the experimen- 3503–3511. tal and evaluation effort of a SAXS study we [9] Stribeck, A.; Jokari Sheshdeh, F.; Pöselt,

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