Thermoplastic Polyurethane Cross-Linked by Functionalized Silica

Article pubs.acs.org/Macromolecules

Thermoplastic Polyurethane Cross-Linked by Functionalized Silica. Nanostructure Evolution under Mechanical Load Norbert Stribeck,*,† Ahmad Zeinolebadi,‡ Frauke Harpen,† Gerrit Luinstra,† Berend Eling,§ and Stephan Botta∥ †

Department of Chemistry, University of Hamburg, Bundesstr. 45, D-20146 Hamburg, Germany Polymer Consult Ltd., Dorfgrund 6, D-22397 Hamburg, Germany § BASF Polyurethanes GmbH, Elastogranstr. 60, 49448 Lemförde, Germany ∥ HASYLAB at DESY, Notkestr. 85, D-22603 Hamburg, Germany ‡

ABSTRACT: Composites of TPU (Elastollan 685A by BASF) and 0−0.5 wt % 3-aminopropyltriethoxysilane functionalized silica spheres (diameter 14 nm) are strained and subjected to load cycling. Tests are monitored by SAXS which is analyzed by the chord distribution function (CDF) method. Extensibility of the soft phase is limited. Macroscopic strain is accomplished by failure of single soft domains. Broken entities comprise the overstretched soft domain, sandwiched between two hard domains. Macroscopic strain at failure determines the most probable thickness of the sandwich. Failure propagates from disordered regions into well-arranged ensembles (WAE) of domains. The higher the nanosphere content, the earlier the WAE are affected. Outbursts of local failure happen at strains of 100% and 200%. They relieve WAEs. Load cycling does not induce failure of pure TPU but of the nanocomposites. Here failure spreads in the material. The fraction of material that is not affected is a function of the nanosphere content. Extrapolation yields 1.25 wt % when all the material would be affected. Relaxed samples contain sandwiches.

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INTRODUCTION Thermoplastic polyurethanes (TPU) are produced in the reaction of a diisocyanate, a short chain diol, and a polyol. The isocyanate and the short chain diol form a rigid or hard segment. These isocyanate-ended hard segments are linked by polyol soft blocks (soft segments) to form a random block copolymer of the (A−B)n type. If all the components of the polyurethane are difunctional, a linear thermoplastic polymer is obtained. Because the hard and soft chain segments are thermodynamically incompatible, phase separation occurs. Thus, domains are formed that are either rich in soft or hard segments. The final morphology is uncertain because it depends on both the molecular composition and the processing conditions. Moreover, slow ripening of the phase separation is observed. Sizes and shapes of the domains vary considerably. Among the domains there is no lattice-like correlation. In addition, soft domains may contain hard chain segments, and soft chain segments may be trapped in the hard phases. The hard domains form physical cross-links and render the material behave rubber elastic. The structural integrity of the hard domains governs the mechanical properties, especially at high strain. Several papers describe a two-stage orientation− elongation mechanism. In the first stage the material deforms elastically, whereas higher strain leads to hard-domain disruption. Mechanically, these two processes are characterized by either low or high hysteresis. Kimura et al.1 describe these two stages qualitatively and call them deformation and disintegration, respectively. Authors from the group of Bonart2 © XXXX American Chemical Society

discuss that the disintegration mechanism already creeps in at low elongation. Moreland et al.3 associate the region below 50% strain with low hysteresis. Here the hard domains align more or less reversibly in the strain direction. At strains of more than 50% disruption of hard domains is said to become dominant. Wang et al.4 determine the respective boundary between 100% and 140% strain. It is obvious that the boundary is a function of chemical composition, processing, and ripening history of the TPU. Concerning a pure TPU under mechanical load, this strongly distorted nanostructure has been studied by some of us in a previous paper,5 and a peculiar nonaffine deformation mechanism of structural entities has been described. Each of these entities is made from only two hard domains and a soft domain in between (“sandwich”). Nanocomposites can be prepared from segmented polyurethane as from many other polymers. The reason to do so is in general the tailoring of materials properties. In the special case of TPU the large-scale disorder that is typical for all kinds of nanocomposites6 is already present in the pure material. The varieties of TPU nanocomposites and their importance are recently reviewed by Smart et al.7 In the focus of another review8 is the popular method to create nanocomposites by bonding a polymer with silica. Received: March 10, 2013 Revised: April 19, 2013

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dx.doi.org/10.1021/ma400512b | Macromolecules XXXX, XXX, XXX−XXX

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Figure 1. From segmented chains to TPU morphology. TPU is a multiblock copolymer. The blocks are soft segments and hard segments. Nanometer-size silica spheres (NSS) cross-link the material (novel chain topology). Phase segregation makes hard domains and soft domains. Poor statistics makes that a sandwich of three domains is the most complex scattering entity.

NSS) are reacted in situ into the TPU and become an integral part of the polymer. As the amino group density on the AFNSS is high, the NSS will act as a localized cross-linking moiety with a high functionality. Thus, a poly(urethane) is obtained that exhibits a mesophase morphology and a novel chain topology. Figure 1 shows a sketch. It is generally known that the extensibility of thermoplastic polymers is reduced when chemical cross-links are introduced. Moreover, in the case of a TPU, the introduction of cross-links can also impart the phase segregation as the cross-links reduce the chain mobility. Thus, incorporation of the AF-NSS into a TPU can have an effect on both the extensibility of the polymer and the extent to which phase separation occurs. Furthermore, upon deformation, the presence of the AF-NSS will impart the local deformation of the mesophase structure in the segmented polyurethane. The present study aims to the understanding of the deformation behavior of an AF-NSS modified TPU under strain (ε > 0.5) and cyclic deformation at intermediate levels of strain using real-time SAXS techniques. In this study small-angle X-ray scattering (SAXS) is applied in order to monitor the structure evolution of a material under mechanical load. This method has a long tradition in the field of segmented polyurethanes. In fact, Bonart18 has not only applied SAXS to polyurethane materials over a long time but also developed and collected fundamental concepts for the treatment of the SAXS data that are founded in scattering theory. In one of his early studies19 he has investigated TPU as a function of strain and after relaxation. Already there he states that the SAXS in the meridional section is not related to the sequence of hard and soft domains in meridional direction. A projection20 of the SAXS should be analyzed, instead. The CDF21 analysis that is applied in this paper is an advanced method that includes this principle. Later, Bonart has returned to the strain monitoring with a different TPU22 and has found structure evolution mechanisms that differ from those found in his early study. From TPU grade to grade the nanostructure and its evolution may vary. Even load cycling of TPU has already been monitored by Bonart,23 but only by birefringence

If nanocomposites of the latter kind shall be made, one of the methods is gentle cross-linking8 of TPU material by blending9 it with nanosize silica spheres (NSS) functionalized with 3aminopropyltriethoxysilane. In the present study the NSS are first dispersed in one of the reaction components of the TPU, viz., the short chain diol, and then reacted with 3-aminopropyltriethoxysilane and subsequently reacted with the other reaction components to form the final TPU.10 Such materials are investigated in this study in order to shed some light on the respective nanostructure evolution under mechanical load. Several papers compare TPU/silica blends and respective composites with pure TPU. Already in a simple blend the size of the filler silica has an effect on the mechanical properties. A nanometer-size silica filler is reported to increase strength and elongation at break beyond the level that can be reached by a micrometer-size filler.11,12 Functionalization of the silica is the general way to ensure in situ a good connectivity between the filler and the matrix, but Chen et al.13 report the generation of cross-links between the polymer and the fumed silica nanoparticles even after in-situ polymerization. A composite containing micrometer-size silica is reported to improve only hardness and abrasion, whereas nanometer-size spheres improve many mechanical properties.14 In an application to foams15 the nanofiller is clearly addressed as an additional cross-linker, and the composites are reported to show improved hardness, strength, and rebound resilience. Vega Baudrit et al.16 report that compounding with nanosilica increases the viscoelastic properties. Concerning the optimum amount of nanometer-size fumed silica in the composite, Lee et al.17 observe a dispersion limit at 3 wt % of silica, and the longest elongation at break is observed with the composite that contains 1 wt % silica. The present investigation deals with a TPU (Elastollan 685A, by BASF S.E.) produced from a polyester polyol, methandiphenyl diisocyanate (MDI), and butanediol. This TPU has been modified with different weight amounts of nanometer-size silica spheres (NSS) that are functionalized with aminopropylsilane groups. The amino functionalized NSS (AFB


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operated at cross-head speeds of 2 mm/min (plain straining experiments) and 2.9 mm/min (load cycling experiments). Using the fiducial marks, the local macroscopic strain ε = (S − S0 )/S0 is computed automatically37 from the average initial distance, S0 , of the fiducial marks and the respective actual distance, S . The true stress, σ = F/A, is computed from the force F measured by the load cell after subtracting the force exerted by the upper sample clamp, and A = A0/ (1 + ε), the estimated actual sample cross section. A0 is the initial cross section of the central zone of the test bar. The equation assumes conservation of the sample volume. The true local strain rates are ε̇ = 1.0 × 10−3 s−1 (plain straining experiments) and ε̇ = 1.5 × 10−3 s−1 (load cycling experiments). The frequency of load cycling is ν = 2.4 × 10−3 Hz. In the load-cycling experiments the samples are cycled between engineering strains of 5/42 = 0.12 and 15/42 = 0.36. The local macroscopic strain is higher because it is measured in the waist of the test bar. SAXS Setup. Small-angle X-ray scattering (SAXS) is carried out in the synchrotron beamline A2 at HASYLAB, Hamburg, Germany. The wavelength of radiation is λ = 0.15 nm, and the sample−detector distance is 2560 mm. Scattering patterns are collected by a 2D marccd 165 detector (mar research, Norderstedt, Germany) in binned 1024 × 1024 pixel mode (pixel size: 158.2 m × 158.2 m). Scattering patterns are recorded every 70 s with an exposure of 60 s. The patterns I(s) = I(s12,s3) cover the region −0.24 nm −1 ≤ s12, s3 ≤ 0.24 nm −1. s = (s12,s3) is the scattering vector with its modulus defined by |s| = s = (2/ λ) sin θ. 2θ is the scattering angle. It is not necessary to emphasize the small amount of extrapolated data at the beamstop because it covers an angular region in which the correlation among the hard domains has already dropped to zero. The scattering patterns are normalized and background corrected.38 This means intensity normalization for constant primary beam flux, zero absorption, and constant irradiated volume V0. Because the flat samples are wider than the primary beam, the correction has been carried out assuming V(t)/V0 = (1/(1 + ε(t)))0.5. The equation assumes constant sample volume. Radiation damage is observed after 12 h of irradiation in cycling experiments. Then a slight brown mark has developed at the surface of X-ray beam entrance. SAXS Data Evaluation. The patterns I(s) = I(s12,s3) are transformed into a representation of the nanostructure in real space. The only assumption is presence of a multiphase topology. This means that the local average density at each point in the sample can be picked from a short list of phase densities and that it is allowed to collapse transition zones into sharp edges. It is by no means required that the sample contains only a single structural morphology. The result of the transformation is a multidimensional chord distribution function (CDF), z(r).21 The method is exemplified in a textbook (ref 38, section 8.5.5) and in the original paper21 where figures show the change of the pattern from step to step. Here we only summarize the steps and introduce the important quantities. The CDF with fiber symmetry in real space, z(r12,r3), is computed from the fibersymmetrical SAXS pattern, I(s12,s3), of a multiphase material. In order to compute z(r12,r3), I(s12,s3) is projected on the representative fiber plane. Multiplication by s2 applies the real-space Laplacian. The density fluctuation background is determined by low-pass filtering. It is eliminated by subtraction. The resulting interference function, G(s12,s3), describes the ideal multiphase system. Its 2D Fourier transform is the sought CDF. In the historical context the CDF is an extension of Ruland’s interface distribution function (IDF)39 to the multidimensional case or, in a different view, the Laplacian of Vonk’s multidimensional correlation function.40 The CDF is an “edgeenhanced autocorrelation function”41−44the autocorrelation of the gradient field, ∇ρ(r). ρ(r) is the electron density inside the sample that is constant within a domain (crystalline, amorphous). Thus, as a function of ghost displacement r, the multidimensional CDF z(r) shows peaks wherever there are domain surface contacts between domains in ρ(r′) and in its displaced ghost ρ(r′ − r). Such peaks hi(r12,r3) are called39 distance distributions. Distance r = (r12,r3) is the ghost displacement. In this paper we are mainly studying the evolution of the strong meridional long-period peaks hL(r12,r3) in the CDF.

because a synchrotron radiation source has not been available in the early days. The predominant part of Bonart’s work on TPU is dedicated to the study of the isotropic SAXS of unoriented TPU material in order to assess the degree of phase segregation.24,25 This branch of studies is still very active. Concerning the SAXS monitoring of the nanostructure response of segmented polyurethanes to mechanical load, only few studies have been published over the years. Martin et al.26 demonstrate that microbeam SAXS on single struts of a TPU foam under load is possible. They perform one load cycle and discuss the evolution of the distance between the hard domains (long period) related to the macroscopic strain. Blundell et al.27 monitor the plain straining of two different TPU materials by SAXS. For the undeformed isotropic material a classical analysis has been carried out. The patterns recorded during deformation are integrated in reciprocal space to obtain the invariant. The movement of the maximum of the scattering peak is related to the macroscopic nominal strain. The authors find that the peaks move much slower than is expected and conclude that “the connectivity of the hard phase is resisting the affine separation of the hard domains”. A second paper28 of the same authors reports results on a load-cycling study on the same materials. A different group of authors proposes the application of a globular model29−31 to describe the small-angle scattering of deformed TPU. They fit meridional and equatorial sections to their model. The SAXS intensity indicates reversibility, but the mechanical properties do not. The authors speculate that the mechanical properties may have been dominated by few large microdomains that cannot be seen in the SAXS.31 The most recent papers published in this field32,33 refrain from a proper analysis of the anisotropic SAXS data. Disregarding the three-dimensional nature of the recorded SAXS fiber pattern, the data are isotropized by two-dimensional circular averaging. The resulting artificial curve is discussed.

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EXPERIMENTAL SECTION

Materials. The thermoplastic polyurethane (TPU) is an Elastollan 685A grade that has been prepared with precursors obtained from BASF SE. It is a clear grade elastomer with 85 Shore A durometer hardness and produced from 4,4′-methandiphenyl diisocyanate (MDI), an adipate based polyesterpolyol, and 1,4-butanediol as a chain extender. The silica nanospheres (NSS), having an average diameter of 14 nm, are dispersed in the butanediol and modified with 3- aminopropyltriethoxysilane (APTES)34 and used as such in the synthesis of the NSS-containing TPU. The grafting density of aminopropyl groups onto the NSS amounts to 12 groups/nm2. Samples with 0, 0.25 and 0.5 wt % of amino functionalized NSS have been prepared. Before the processing the TPU pellets are dried at 110 °C for 3 h. Test bars S2 according to DIN 53504 are injection molded in a MiniJet II (Thermo Scientific) from a melt of 215 °C: mold temperature, 35 °C; molding pressure, 700 bar; molding time, 15 s; holding pressure, 150 bar; holding time, 5 s. Slight parameter variations are necessary to obtain optimum results for the materials that contain NSS. After injection molding the test specimens are annealed at 100 °C for 20 h. The resulting test bars are slightly swollen, and the cross section of the central part is 4.3 mm × 2.2 mm. One week after the annealing the mechanical tests in the synchrotron beam have been performed. Tensile Testing. Testing is done in a self-made35 machine. A grid of fiducial marks is printed on the test bars.36 The clamping distance is 42 mm. A 1000 N load cell is used. Signals from load cell and transducer are recorded during the experiment. The sample is monitored by a TV camera. Video frames are grabbed every 10 s and are stored together with the experimental data. The machine is C


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Figure 2. Comparison of structure clarity in SAXS patterns and in CDFs (structure information transformed into real space). The transformation from I(s12,s3) to z(r12,r3) goes along with an enhancement of clarity concerning the visualized nanostructure data. This is demonstrated in Figure 2. The figure shows scattering patterns from three different uniaxially oriented polymer materials and their CDFs. From the interpretation of the scattering patterns only cursory information on the nanostructure can be gathered, as has been stated early by Debye and Menke.45 On the other hand, the CDF shows shape and arrangement of the domains in the multiphase topology directly.

branch points anchoring a relatively high number of linear TPU chains. Plain Straining. Fgure 3 presents the stress−strain curves recorded during the straining experiments. The experiments are

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RESULTS AND DISCUSSION Materials Chemistry and Properties. Poly(urethane) elastomers are synthesized in the simultaneous condensation copolymerization of three components: a polyol (a generic term for a hydroxyl-terminated poly(ether) or poly(ester) with a molecular weight between 100 and 4000 g/mol), a diisocyanate, and a chain extender. The present investigation deals with a TPU (Elastollan 685A, by BASF S.E.) produced from a polyester polyol, methandiphenyl diisocyanate (MDI), and butanediol. This TPU has been modified with different weight amounts of nanometer-size silica spheres (NSS) that are functionalized with aminopropylsilane groups. Amine groups react readily with isocyanate; they are about 100 times more reactive than hydroxyl groups. The amino functionalized NSS (AF-NSS) are reacted in situ into the TPU and become an integral part of the polymer. As such, the AF-NSS fulfill the role of a cross-linking moiety in an otherwise linear TPU. The grafting density of aminopropyl groups onto the NSS, calculated from the weight amounts of APTES and NSS and the surface area of the NSS, amounts to 12 groups per nm2. Theoretically, the amino-functionalized NSS (AF-NSS) could contain as much as 7000 amino groups per particle. At the present weight amounts of AF-NSS in the TPUs of 0.25 and 0.5 wt % there is no indication of the formation of a covalently cross-linked three-dimensional network as the material could be remelted and injection molded. This suggests that at the present amounts of AF-NSS in the TPU the NSS act as local

Figure 3. TPU with varying amount of nanometer-size silica spheres (NSS) (0%, 0.25%, and 0.5%) in plain straining experiments. Curves end when the material slips from the clamps.

stopped when the samples slip from the clamps of the tensile tester. Obviously the extensibility is increasing with increasing NSS content. Moreover, the material with the highest NSS content is harder than the other materials. An averaged distance between neighboring hard domains is the long period L. It can be determined both directly from I(s) and from the CDF. Table 1 presents the long periods of the virgin samples. At ε = 0 only the bottom long period, Lbott, exists. The table shows that the determined values are close to each other. Figure 4 displays the central part of characteristic SAXS patterns that have been recorded during the straining experiments. The initial orientation of the test bars is a consequence of the preparation by injection molding at only 215 °C. All images are presented in the same way using the D


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Comparison shows little difference. Only the shape of the long period peak appears deformed from a straight layer line to a bent “banana” shape. If we would interpret the peaks in the SAXS patterns directly, we would come to the same conclusion as others,31 namely, that the nanostructure monitored by the SAXS is more or less reversible. It is important to note that at zero strain the samples with and without AF-NSS show the same scattering pattern, indicating that the AF-NSS in the present concentration range do not, or if so, only marginally affect the development of the mesophase structure. Under deformation the SAXS patterns show differences, indicating that the presence of AF-NSS does affect the deformation of the mesophase structure; however, after relaxation all the samples turn back to their original state. Moreover, inspection shows that the nanospheres themselves contribute only to the diffuse SAXS background which is eliminated anyway in the evaluation. The fraction of nanospheres is too low to yield discernible form-factor scattering above the noise level. Deeper insight into the nanostructure evolution is gained by the chord distribution functions (CDFs) computed from the SAXS patterns. Figure 5 displays the central regions of the functions in the presentation |z(r12,r3)|. This presentation visualizes both the domain peaks (that stick out in positive direction from the base plane) and the long-period peaks (that protrude in negative direction).21,39,46 In the presented pseudocolor images some large dark areas show up. In these areas the value of the CDF function is, indeed, negligibly low. They are not generated artificially by setting all positive values to a value of zero. White arrows point at the main long-period peak (L-peak). These rather narrow peaks in the CDF originate from well-arranged ensembles (WAE) of hard domains. Poorly arranged regions (PAR) in the material contain hard domains that are placed randomly in the soft matrix. Thus, their scattering is diffuse. In the CDF it only contributes to the single-domain peaks next to the center. Figure 6 sketches a PAR. For low ε the L-peaks are arc-shaped, indicating some orientation distribution. Nevertheless, their intensity maximum is in the longitudinal direction of the test bar. There is little lateral arrangement, so the WAEs can be addressed as microfibrils (i.e., ensembles of hard domains that are preferentially correlated in one direction). At ε ≈ 0.7 one observes six long-period reflections in an elongated hexagonal arrangement. Thus, moderate strain induces some lateral correlation among the hard domains from neighboring microfibrils. At ε ≈ 1, the strong meridional long period (white arrow) relaxes and a new, increasing long period (green arrow) starts growing outward. This is a dissociation of the previously unimodal ensemble of microfibrils. Many microfibrils relax, but some are rapidly strained further. Thus, the answer of the WAEs to considerable strain is selective breaking of connectivity between hard domains. A common explanation for such failure is pull-out of taut tie molecules33,47 from the hard domains. Where the connection fails, the two partner hard domains rapidly move apart. They form a new ensemble of scattering entities that we call demerged sandwich entities (DSE). Green arrows point at the DSE peaks. The DSE peaks rapidly grow asymmetric during the experiment. Thus, on a nanoscopic level the corresponding straining mechanism is highly nonaffine. It resembles the process observed previously with a different TPU.5 In practice, the nonaffine behavior

Table 1. TPU Material with Varying Content of NanometerSize Silica Spheres (NSS)a NSS [%]

Lbott,I(ε = 0) [nm]

Lbott,CDF(ε = 0) [nm]

0 0.25 0.50

12.7 13.3 13.5

12.9 13.1 13.3

a

Long periods Lbott(ε = 0) of the unstrained samples as determined from the positions of the peak maxima in the scattering intensity I(s) and in the CDFs z(r).

Figure 4. TPU with varying amount of NSS (0%, 0.25%, and 0.5%) in a plain straining experiment. Observed SAXS patterns I(s12,s3) as a function of the local macroscopic strain ε at the point of irradiation. The top row shows patterns taken 5 min after the sample slipped from the clamps. Arrows indicate the maximum long period L. All patterns are on the same logarithmic pseudocolor scale. The graphs show the region −0.15 nm−1 ≤ s12, s3 ≤ 0.15 nm−1. Straining direction s3 is vertical.

identical logarithmic pseudocolor scale. The patterns show only few details. The extended layer lines indicate the scattering of an ensemble of rather narrow hard domains that are arranged along the straining direction. Thus, the hard domain is not a lamella but rather a grain. The high extension of the peaks in vertical (straining) direction shows that the arrangement of the hard domains is strongly distorted. Peculiarly, the peak moves inward only up to a strain ε = 0.7. There it stops until ε = 1 and, finally, starts moving outward, again. Thus, the average long period is decreasing with increasing macroscopic strain for ε > 1. The top row of Figure 4 shows scattering patterns taken after the samples slipped from the clamps. In the row underneath the data of the virgin material is presented. E


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When the DSE peak is evolving, it develops a peculiar asymmetric shape. Its border looks like an isosceles triangle. From its shape and evolution the failure mechanism can be reconstructed in more detail. Figure 7 presents an explanatory sketch. Let us start the discussion on the left. A taut tie molecule (red line) is defining the distance between two hard domains from a WAE. Their distance can be read from the position of the red WAE-peak in the CDF. Then the tie molecule is pulled out, the distance between the hard domains increases, and the subensemble is turned into a DSE. The signature of the DSEs are in the triangular DSE-peak. Most of the DSEs reside at the base of the triangle, where the peak intensity is highest. A corresponding DSE is shown directly left to the CDF. Half the width of the triangular peak gives the lateral extension of the hard domains. Anticipating the analysis shown in Figure 12, it is not changed with respect to the lateral extensions of the WAEs. Thus, this DSE has been generated by chain pull-out without further damage of the domains. Moving up in the triangle, the DSEs become thicker but narrower. Respective sandwiches are sketched to the right of the CDF. The chain pull-out has broken the hard domains of thicker sandwiches. Extrapolating along the legs of triangle toward the meridian one estimates a maximum sandwich thickness. Thicker sandwiches do not exist because the corresponding hard domains have no lateral width anymore. This is a harddomain destruction limit. As the DSEs are formed, the long period shrinks that is directly observed in the SAXS. Thus, the remnant WAEs relax. Obviously, as one spring from a sequence breaks, the rest of the springs contract. In the material with the high NSS content a second dissociation process sets in at ε = 2, before the material starts to slip from the clamps. Addressing a sequence of springs here is by no means a contradiction to the finding that the scattering entities are only sandwiches. A scattering entity ends after a distance beyond which no prediction on the placement of the next (hard) domain can be made. This concept of correlation loss is essential for scattering in general and thus for the drawing and understanding of the sketches presented in this study. The top row in Figure 5 presents CDFs determined on the relaxed materials after the end of the straining experiment. The row beneath shows the nanostructure of the virgin material. Compared to the virgin material, the relaxed material clearly shows the asymmetric signature of the DSEs that had been generated by dissociation of the WAE. Thus, the macroscopic straining experiment has caused a fundamental and at least short-time persistent change of the hard-domain arrangement inside the material. Some of the scattering entities have been strained much more than the majority. In order to retrieve this information, an analysis like the CDF method is required that takes into account the complete scattering pattern.45 So some of the postulated “few, larger microdomainsa that were too large to be observed by SAXS”31 are, in fact, contained in the SAXS data and waiting for an adequate analysis. Figure 8 sketches the fundamental mechanisms of the observed nanostructure evolution. The initial nanostructure is characterized by two kinds of well-arranged ensembles (WAEs) of microfibrillar structure. Isolated microfibrils (Figure 8a′) have space to develop some misorientation. Microfibrils in bundles (Figure 8a″) exhibit lateral correlation. With increasing strain (Figure 8b) the majority of the microfibrils begin to feel each other. They orient and develop lateral correlation. Figure 8c sketches the situation at ε ≈ 1. Now dissociation is

Figure 5. TPU with varying amount of NSS (0%, 0.25%, and 0.5%) in a plain straining experiment. CDF patterns |z(r12,r3)| computed from I(s12,s3) as a function of the local macroscopic strain ε at the point of irradiation. The top row shows the nanostructure information recorded 5 min after the sample slipped from the clamps. All patterns are on the same logarithmic pseudocolor scale. The graphs show the region −50 nm ≤ r12, r3 ≤ 50 nm. Straining direction r3 is vertical. White arrows: peak of strong but low long period Lbott. Green arrows: dissociation of a weaker but higher long-period Ltop. The red U-shape indicates the place of the sections displayed in Figure 9.

Figure 6. Sketch of a region (poorly arranged region (PAR)) in the TPU material in which the hard domains are placed at random.

means that the distance by which the partners move varies. Many partners move only a short distance until they are stopped by activated backup chains; few move a long way apart. As a result, the corresponding peak in the SAXS pattern is very broad and shallow. The DSEs are only seen in the CDF. F


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Figure 7. Triangular DSE peak in the CDF (here overexposed for clarity) and the peculiar sandwich nanostructure related to it. The height of the CDF clipping is 50 nm.

Figure 8. Sketch of the fundamental nanostructure evolution stages during straining in the studied TPU materials. Hatched ellipses represent hard domains. Two models (a′ and a″) describe the initial structure of well-arranged ensembles (WAEs) at low strain. (b) At ε ≈ 0.7 misorientation is negligible and the microfibrils are laterally correlated. (c) At ε ≈ 1 dissociation is considerable: demerged sandwich ensembles (DSEs) arise from connectivity break. They show a high Ltop with asymmetric distribution. Leftover WAEs relax (Lbott decreases) and lateral correlation is lost. Figure 9. TPU with varying amount of NSS (0%, 0.25%, and 0.5%). CDFs −z(r12,r3) as a function of macroscopic strain ε. The choice of the presented clippings is indicated in Figure 5 by a red U-shape. Solid lines connect long period peaks. Long-period dissociation with relaxation of the lower long-period takes place. All patterns are on the same logarithmic pseudocolor scale. They show the region |r12| < 16 nm, 0 nm ≤ r3 ≤ 80 nm.

considerable. The breaking of connectivity between some hard domains has demerged sandwich ensembles (DSEs) from the WAEs. They consist of only two hard-domains with a high long period Ltop. Nevertheless, the distribution of long periods among the DSEs is wide and asymmetric. The left over WAEs feel the relief and relax. In this process the lateral correlation among these microfibrils is lost. In order to demonstrate the nanostructure evolution in smaller steps, Figure 9 presents clippings from the CDFs close to the meridian. The broken blue lines indicate the second order of the virgin long period that can only be identified before the dissociation becomes dominant. Black lines connect the most-probable long-periods Lbott of the WAEs. The relaxations of the WAEs during the dissociation are clearly demonstrated. The brightest red line in each graph connects the most-probable long periods Ltop of the DSEs. A quantitative analysis of the most-probable L values as a function of the macroscopic local strain ε is presented in Figure 10. Here the long periods have been normalized with respect to the initial

long-period Lbott(ε = 0), yielding εnano,Lbott(ε) = (Lbott(ε)/Lbott(ε = 0)) − 1 and εnano,Ltop(ε) = (Ltop(ε)/Lbott(ε = 0)) − 1. In order to carry out the automated analysis, the PV-WAVE48 program for peak analysis has been rewritten. sf_anapeakrev.pro49 starts from the peak in the last pattern of the experiment and propagates backward until the peak merges with Lbott. During the propagation it automatically tracks a user-defined circular region of interest so that it is always centered on the position of the last peak analyzed. Then the peak is fitted by a bivariate polynomial37,50 of second order. From the returned coefficients peak position, peak width, and peak height are computed. G


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Figure 10. TPU with varying amount of NSS (0%, 0.25%, and 0.5%). Nanoscopic strain εnano(ε) computed from the evolution of the bottom long-period Lbott and from the (dissociated) top long-period Ltop (height of brightest red lines in Figure 9). Lbott is the height of the black lines in Figure 9.

Figure 11. TPU with varying amount of NSS (0%, 0.25%, and 0.5%). Standard deviations of the long-period peaks in meridional direction, σmer(ε) computed for the evolution of the bottom long-period Lbott and from the (dissociated) top long-period Ltop. σmer is a measure of the variability of the long periods.

result, the additional cross-links introduced by the NSS increase the coupling between the macroscopic load and the WAEs and probably reduce their critical load. Consequently, their dissociation already sets in at low strain. This behavior can be explained by the novel polymer chain topology that is created upon the addition of AF-NSS. Several high molecular weight TPU chains are grafted onto the NSS and as such the NSS functions as a multifunctional cross-link. Through entanglement of the free and the grafted TPU chains there will be less mobility on a molecular level which results in locally higher strain levels upon submitting the samples to a macro strain. Figure 12 presents the result of the peak-width analysis in the direction perpendicular to the strain (equatorial direction). The

Figure 10 shows that already at the beginning of the straining experiments εnano < ε is valid. Thus, already at low mechanical load the WAEs are less extensible than the PARs. This has as well been found by Blundell et al.27 Clear dissociation processes are initiated at ε ≈ 1 and ε ≈ 2. DSEs separate from the old ensemble. Their strain escalates and reaches the actual macroscopic strain. Thus, it is most probable that directly after the tie molecule pull-out the two hard domains are intercepted in a distance that complies with the actual macroscopic strain. This finding might become important for the modeling of the mechanical response of TPU materials. However, after this extension jump the position of the peak maximum continues to increase only very slowly. Thus, most of the DSEs are not damaged by the pull-out and are hardly further extended after having been intercepted. Consequently, there is probably a new taut tie-molecule at the interception distance. As shown in Figure 7, this is different for the fewer DSEs whose hard domains are damaged by the chain pull-out. The observed decrease of εnano for ε > 2.3 may either be an artifact resulting from beginning sample slippage, or it is related to the indicated further dissociation step (cf. Figure 9, bottom row right: discrete peak above the one that is crossed by the upper red line) that cannot be analyzed quantitatively anymore because of its weakness. Figure 11 shows the evolution of the peak width parameter in meridional direction, σmer(ε). It is a measure of the variability of the long periods of those nanostructural entities that generate the corresponding peak. The values from the Ltop analyses related to the DSE are considerably higher than the values of the Lbott analyses that are related to the WAE. Here this difference predominantly reflects the nonaffine character of the DSE deformation that has already been demonstrated in Figure 9. For the Lbott analyses σmer(ε) decreases considerably between ε ≈ 0.5 and ε ≈ 1. This means that the nanostructure within the WAE becomes more uniform in this deformation interval before assertion of the dissociation process. The graph shows that the elongation of maximum unification is a function of the NSS content. The higher the NSS content, the earlier is the maximum unification accomplished. For the pure TPU the unification is finished at ε = 1.2, for the material with 0.25% NSS at ε = 1, and for the material with 0.5% NSS already at ε = 0.8. In the section Load Cycling we will illuminate this effect from a different point of view in more detail. Anticipating the

Figure 12. TPU with varying amount of NSS (0%, 0.25%, and 0.5%). Standard deviations of the long-period peaks in equatorial direction, σeq(ε) computed for the evolution of the bottom long-period Lbott and from the (dissociated) top long-period Ltop. σeq is a measure of the lateral size of the hard domains.

computed standard deviation is some measure of the lateral extension of the hard domains. Disregarding the strain region around the first dissociation, σeq(ε) decreases continuously from 8 to 3 nm. Thus, the hard domains become continuously narrower with increasing strain. There is no influence of the NSS content, and there is little difference between the harddomain extensions in the WAEs (Lbott) and in the DSEs (Ltop). The erratic course of the parameter in the intermediate region demonstrates the difficulty to separate the two long-period peaks in the CDF. H


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= c(∞)/c(0). It is the time-independent fraction of εnano/ε. Table 2 presents the coupling parameters determined for the three samples that have been studied in the dynamic experiment.

Load Cycling. Compared to previous work,5 only a part of the analysis yields significant results, and this part is presented here. The reason is deficient shielding of some coaxial cables that led to extra noise and beat superimposed to the cyclic mechanical data. Figures 13 and 14 present macroscopic and nanoscopic data collected for the pure TPU and for the nanocomposite with

Table 2. Coupling of the Well-Arranged Ensembles (WAE) of Hard Domains in TPU Nanocomposites to the Macroscopic Dynamic Strain in a Simple Relaxation Modela NSS [wt %]

c(0) = cc + ct

τ [h]

R = c(∞)/c(0)

0 0.25 0.50

0.63 0.74 0.69

0 2.6 2.5

1 0.78 0.59

c(0) is the starting value of the coupling, τ is the lifetime of relaxation, and R is the remnant fraction of coupling after long time.

a

c(0) characterizes the initial extensibility of the WAEs compared to the macroscopic extensibility of the material. A value of 1 would mean that the WAEs are as extensible as the sample as a whole. However, the actual value is only about 70%. (The differences among the materials may be caused from variations in the sample preparation process.) The effect has previously been found by Blundell et al.27 and explained “the connectivity of the hard phase is resisting the affine separation of the hard domains”. Apart from the sketchy phrasing (“hard phase” is a WAE) this statement appears somewhat misleading but appropriate: a nonaffine disruption of WAEs is not excluded. τ quantifies the decay of the coupling between the macroscopic strain and the nanoscale strain determined from Lbott. Both nanocomposites exhibit a decay with the same time constant τ. After 2.5 h the relaxing fraction of its WAEs has decayed to 1/e of its initial value. Beyond that, even in c(t) of the nanocomposites a remnant, time-independent component R is present. As the nanosphere content in our series is stepwise increased by 0.25%, R is decreased from step to step by 20% each. Extrapolating the observed effect linearly, a nanocomposite with about 1.25% NSS should stop showing a breathing SAXS pattern after having been exposed to a slow dynamic load for several hours. After having been subjected to dynamic load, the WAEs appear increasingly decoupled from the dynamic mechanical load, and the decoupling increases with the amount of NSS. This effect may be explained by a combination of the chemistry of the composite and the peculiar failure mechanism of the WAEs. Let us start with the chemistry. As the amount of AF-NSS is increased, the number of grafted TPU chains increases at the expense of free TPU chains. Above a critical concentration of AF-NSS all the TPU must be grafted and in essence a fully cross-linked elastomer is obtained. The extrapolated value of 1.25 wt % of NSS suggests that a complete cross-linking has occurred around this concentration range. This finding is supported by swelling measurements of the TPUs in dimethylformamide: at low concentrations of AF-NSS the polymer dissolves, but typically at concentrations above 1 wt % of AF-NSS the material just swells, occupying volumes several times its original volume while no sol is present. Thus, it is not surprising that with increasing AF-NSS content the WAEs appear to become increasingly decoupled from the uptake of mechanical load as part of the load is taken over by the entanglement network of free and grafted chains eventually even by largely a covalent network. The present type of cross-

Figure 13. Pure TPU in a dynamic fatigue experiment. Macroscopic and nanoscopic strain, ε and εnano, plus the ratio of both. At t ≈ 40 min the X-ray has been interrupted. ε/εnano shows no fatigue.

Figure 14. TPU nanocomposite with 0.25% NSS in a dynamic fatigue experiment. Macroscopic and nanoscopic strain, ε and εnano, plus the ratio of both. At t ≈ 280 min the X-ray has been interrupted. ε/εnano exhibits fatigue.

0.25% NSS, respectively. Bold solid lines show the signal ε(t), the bold broken lines present a nanoscopic response of the material, εnano(t) = L(t)/L(0) − 1 with L(t) the most-probable long period as determined from the position of the peak maximum in the CDF. L(t) = Lbott(t) because of the low strains applied in the cycling experiments. Comparison shows that the signal ε(t) is always in phase with the response εnano(t). Consequently, the elastomers appear purely elastic under the applied low-frequency load. The thin solid lines present coupling curves c(t) = εnano(t)/ ε(t). They exhibit clear differences. For the pure TPU c(t) stays constant. However, for the nanocomposites c(t) decreases from cycle to cycle. This shows that only for the nanocomposites the coupling between the WAEs that are detected by SAXS and the poorly arranged regions (PAR) is gradually decaying. The curve shapes suggest a simple relaxation model c(t ) = cc + ct exp( −t /τ )

with cc defining a constant background and ct defining the strength of a time-dependent decay. Corresponding fits have been carried out. For the discussion let us define a remanence R I


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linking with AF-NSS is heterogeneous in nature as we deal with a particle cross-linker. This is different from a cross-linking on a molecular level, e.g., as obtained by incorporation of some low molecular weight cross-linkers like glycerol. Thus, hard domains in close proximity of an AF-NSS consist of chains of which a significant fraction is grafted to the NSS. Therefore, they appear to be hardened as they are protected from the macroscopic strain whereas hard domains further away from the AF-NSS appear to be weaker. Hence, in the two nanocomposites the dissociation of part of the WAEs already starts at the low elongations (0.2 ≤ ε ≤ 0.45) applied in the dynamic experiment and the remaining WAEs appear to be less extensible. The WAEs that fail and turn into DSEs5 act like fuses that blow and disconnect the neighboring WAEs from the power. Figure 15 shows the CDFs of the first and the last cycle for the pure TPU. The intensity scale is logarithmic for the

Figure 16. TPU nanocomposite with 0.25% NSS in a dynamic fatigue experiment. CDFs log|z(r12,r3)| on a logarithmic scale for visualization of low intensity peaks. White arrows point at the regions where dissociation of the long period is already visible. Numbers indicate the local strain ε in percent.

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CONCLUSIONS In the small-angle X-ray scattering experiment predominantly the well-arranged ensembles (WAEs) of hard domains are visible. In the case of such irregular polymers like the studied segmented polyurethanes the WAEs appear to be little representative for the nanoscopic response to mechanical load. The materials are heterogeneous on the nanometer scale. Already before the straining experiments there exist WAEs and poorly arranged regions (PARs) in the materials. At the begin of a mechanical loading, the predominant straining appears to happen in the structureless PARs. Even when the WAEs start to carry the load, they do not respond by a simple deformation. Instead, a dissociation process sets in that allows the majority of the elastically active hard domains to relieve the local stresses to which they are exposed at the expense of those domains that fail and form demerged sandwich ensembles. Consequently, the material becomes even more heterogeneous. Such dissociation processes appear to be typical for the studied TPU. With respect to this dissociation the studied materials differ from a TPU that has been studied earlier.5 However, there is as well a similarity. In the TPU from our earlier study all the discrete SAXS had been generated by such sandwich ensembles. They carried the same characteristics as our present “failing springs”. These characteristics are a highly asymmetric distribution of distances (after the failure) and a nonaffine straining mechanism. This leads us now to the hypothesis that even in the older study the elongation of the material on the nanometer scale is driven by local failure: The straining of the soft domains between every two hard domains in the material is suppressed by taut tie molecules until suddenly the blocking is surmounted and the hard domains spring apart. In our earlier study the failure process could not be detected because there were no SAXS-visible probes like the WAEs that would have allowed us to monitor the strain response of the intact material to the applied load. Similar to the material from our earlier study,5 the wide-angle X-ray scattering (WAXS) is too diffuse to test the validity of the presented model. The modification of the TPU/685A material by incorporation of relatively small amounts of 3-aminopropyltriethoxysilane functionalized silica nanospheres (AF-NSS) leads to heterogeneous local cross-linking of the TPU chains. Thus, the tension develops in zones that are in between shell regions

Figure 15. Pure TPU in a dynamic fatigue experiment. CDFs log| z(r12,r3)| on a logarithmic scale for visualization of low-intensity peaks. The white arrow indicates the region where no dissociation of the long period is visible. Numbers present the local strain ε in percent. Data show the nanostructure evolution during the first and the last cycle (after 8 h).

visualization of low background peaks. In each cycle the local strain ε varies between approximately 0.2 and 0.45. Little difference is observed between the two cycles. No dissociation in the WAEs is indicated. Figure 16 presents the respective diagram for the TPU with 0.25% NSS. White arrows point at the regions in the CDF in which dissociation has been observed in the plain-strain experiments. On the chosen sensitive scale the onset of dissociation is already visible in the first cycle. The last cycle shows that the dissociation has increased considerably with respect to the first cycle. Thus, the initiated dissociation of the nanostructure is as well advancing under cyclic load, not only under increasing strain. The corresponding diagram for the nanocomposite with 0.5% NSS is very similar to Figure 16. Thus, the apparent decoupling of the WAEs from the external load is, in fact, only concerning leftover WAEs which are relieved at the expense of few WAEs that fail and form DSEs. Under cyclic strain several WAEs fail and form DSEs while the stress has been taken over by the entanglement network composed of free and grafted TPU chains. Under certain conditions of cyclic strain the DSEs will deform, break apart, and reform. This time-dependent process is believed to be the origin of the increased relaxation times for the TPUs containing AF-NSS. J


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around the local cross-links. There the local fuses are blown (WAEs transforming into DSEs). After that, the WAEs inside the shell are partly detached from the macroscopic mechanical load. This detachment is demonstrated by the response of the nanostructure to the load. The SAXS patterns of the relaxed materials look very similar to the SAXS patterns of the virgin materials. This is no evidence of complete reversibility because the almost diffuse scattering effect of the disrupted sandwiches cannot be detected by the eye directly in the pattern. In order to visualize these entities, the complete45 scattering pattern must be consulted by an analysis like, e.g., the CDF method. Our CDF analysis considers the complete shape of the SAXS diagram. It shows thatfrom the point of view of the SAXS the minimum heterogeneous model that describes the studied nanocomposite has three components. These are the PARs that do not contribute to the discrete SAXS, the WAEs that exist from the beginning and make discrete SAXS, and the DSEs the demerged sandwich ensembles that are generated by failure inside the WAEs. In the studied materials the discrete SAXS of the DSEs is hidden under the outstanding peaks of the WAEs. Considering these components and assuming that the functionalized silica spheres are generating a heterogeneous distribution of additional cross-links on the nanometer scale, the observed response of the nanostructure on mechanical load is readily explained. We believe that for a practical application two of the found components can be lumped together because it is merely an intrinsic feature of the SAXS method itself that leads to the discrimination between them. The well-arranged ensembles inside the poorly arranged regions will automatically be generated in a process that generates some weak short-range ordered structure (WSS) when it distributes the hard domains in space. Of course, a placing procedure must pass two tests. First, the local strain in the material must be correlated with local disorder. Second, under strain the WAE microfibrils must develop lateral correlation to their neighbors in the same way as they do in the real TPU structure. Nowadays the modeling51−53 of polymer composites has become an issue aiming at an relocation of the tailoring of the material from the laboratory to the computer. In general, the present computer models are based on simple assumptions on the materials structure. Moreover, profound transformation mechanisms that happen under load are rarely considered. Nevertheless, a useful model must both map at least the essential components of the structure (here: WSS = PAR + WAE and DSE) and must reproduce the conversion processes among them that happen under the mechanical load. In order to retrieve such parameters, SAXS monitoring of polymer materials under service may become useful. Such monitoring studies return not only information on the basic processes but also quantitative results that can help with the modeling. These include, e.g., the variation of the hard-domain sizes in the components as a function of strain, the most probable distance of the strain-jump of a released soft domain (“it jumps to the length that represents the actual macroscopic strain”), and the asymmetric distribution of the resulting DSEs. We have demonstrated that the polymer physics can determine these parameters already now. With advancing simulation technology it may become possible in the future to save laboratory work by computer-assisted tailoring of a polymer composite.

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (N.S.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the Hamburg Synchrotron Radiation Laboratory (HASYLAB) for beam time granted in the frame of project I-2011-0087. Xuke Li is acknowledged for his assistance during the beamtime.

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ADDITIONAL NOTE Instead of microdomains more clearly: extended scattering entities, i.e., regions with a considerable distance between adjacent hard domains. a

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Thermoplastic Polyurethane Cross-Linked by Functionalized Silica

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