Introduction

Composites can bring about an improvement in the physical properties of polymer matrix by the inclusion of stiff and strong fillers [1]. The nanoscale fillers offer a prominent mechanism to enhance the composite system, and many studies have reported that nanoparticles at low percentage improve many properties of polymeric matrices, such as mechanical properties [1–3], thermal stability [4–6], viscoelastic properties [7–9], abrasion resistance [10], gas permeation [11, 12], electrochemical properties [13], anti-bacterial [14], and physical properties [15, 16] without any significant change in matrix properties.

There are plenty of inorganic materials which are used as fillers [17–19]; one of them is a non-porous type of silica nanoparticles. Silica particles are hydrophilic due to the presence of OH on their surfaces and do not show any inclination toward non-polar or weakly polar polymers. Thus, such particles tend to aggregate in polymeric matrix and do not disperse well. That is why in most cases, adding nanosilica makes no positive impact on the properties by weakening some of the matrix properties. Surface treatment of nanosilica with organosilane (through steric hindrance of grafted organic groups) is a useful way to prevent aggregation of particles. These materials form chemical bonds with silica surface, make nanoparticles more hydrophobic, and increase their compatibility with polymeric matrix [13, 20]. Thermoplastic polyurethanes (TPUs) are unique polymeric materials with a wide range of chemical and physical properties, and their nanocomposites with silica have been studied extensively. The unique characteristics of PUs make them advantageous for use as shape memory polymers, adhesives, foams, fiber, thermoplastic elastomers, membranes, and coatings [11, 21, 22]. Block copolymer of a TPU is comprised of soft and hard segments. Hard segments are formed through addition of a chain extender (such as butadiene diol) with isocyanate, and the soft segments consist of polyols (polyether or polyester). Since there are many differences between the soft and hard segments, phase separation occurs in TPUs. Phase separation occurs due to intrinsic incompatibility or thermodynamic immiscibility between the soft and hard segments and can affect final properties significantly [23–25]. The extent of the microphase separation is essential if a thermoplastic elastomer with good mechanical properties is to be made [21]. In polyurethane nanocomposites, nanosilica can change phase separation and microphase domain size [26]. Therefore, correlation of the molecular structure of a TPU polymer and its interactions with nanosilica in relation to the macroscopic properties of the system is very important in designing nanocomposites with desired properties. Thus, morphological study is absolutely necessary to understand the relationship between properties and structure of the TPUs in the presence of nanosilica. Morphology of TPU nanocomposites has been investigated by many researchers through FTIR [27–29], SEM or TEM [30, 31], and wide-angle X-ray scattering (WAXS) [32–34]. Zhou et al. have shown that the addition of nanosilica may improve thermal, rheological, mechanical, and adhesion properties of polyester-based PU due to the formation of hydrogen bonds between the silanol groups on the nanosilica surface and the ester carbonyl groups in soft segments [35]. Nunes et al. have demonstrated that the introduction of nanosilica up to 3 wt% could enhance both tensile and elongation-at-break of polymer films [36].

Since rheological properties of nanocomposite depend on the adhesion between the filler surface and the polymer matrix and also depend on the filler dispersion, thus, another useful way to examine the bulk of a polymeric nanocomposite is by rheological test which has attracted a great deal of attention in recent years [37]. Aurilia et al. have shown that the contribution of treated nanoclay can improve TPU microdomain morphology by increasing the interface between the hard and soft domains. Furthermore, silica plates form new interfaces with the soft domain at concentrations over 2 wt%. These two processes increase viscoelastic and thermal properties [26]. Barick et al. have investigated the effects of adding organically modified layered silica nanoclay on TPU dynamic rheology and observed that nanoclay particles increase phase separation, and by increasing the filler percentage, the viscoelastic properties improve at the same time. They argued that this increase is due to strong filler-polymer interaction and uniform dispersion of nanoclays [38]. To the best of our knowledge, in all these studies, the effect of fumed nanosilica, with different surface properties, on phase morphology, mechanical, thermal, and viscoelastic properties of TPU has been investigated methodically [2, 4, 38] and never directly correlated with each other. In this study, polyesterurethane filled with three different types of fumed silica nanoparticles, including non-treated silica and silica-treated with octylsilane and polydimethylsiloxane, was prepared by solution mixing. The dispersion of silica in the matrix and their influence on the phase morphology of TPU has been analyzed by means of different techniques (SEM, TEM, DSC, and FTIR), and the viscoelastic behavior of the silica nanocomposites has been probed through small amplitude oscillatory shear (SAOS) tests. Consequently, the phase morphology variations in the presence of unmodified silica and modified silica have been correlated with the viscoelastic behavior of the nanocomposites. As the relaxation time spectrum can show the effect of nanoparticles on the polymer chains dynamics, the results of small-amplitude oscillatory shear on PU nanocomposites, with different silica, were used to determine the parameters in a multimode Maxwell model.

Experimental

Materials

Thermoplastic polyurethane (LPR9025) was kindly provided by COIM S.p.A Co. The hard segment (HS) content in the TPU was about 35 wt% and composed of 4,4′-diphenylmethanediisocyanate (MDI) and 1,4-butanediol (BD), and its soft segment (SS) consisted of poly(butylene adipate) (PBA). Three different types of nanoparticles, including hydrophilic unmodified silica (PL-SiOF), hydrophobic silica modified by octylsilane (PL-SiOF-OS), and hydrophobic silica modified by polydimethylsiloxane (PL-SiOF-PDMS), were purchased from PlasmaChem Co., Germany. Their characterizations are shown in Table 1. Dimethylacetamide (DMAC, Merck, Co., Germany) was used as a solvent for preparation of TPU and PU/silica samples.

Table 1 Characteristics of silica nanoparticles
Full size table

Sample preparation

PU/silica nanocomposites, with different silica levels of 0, 5, 10, and 15 wt% for each type of nanosilica, were prepared. The films were named accordingly (Table 2). To this, TPU pellets were dried at 80 °C for 2-h prior to solution preparation to remove residual moisture in the pellets. To prepare neat TPU sample, its solution was made by dissolving 2 g of TPU pellets in 15 mL of DMAC under magnetic stirring at 75 °C for 2 h. The prepared solution was filtered and cast on Teflon-coated plate and heated at 80 °C for 24 h. Then, each resulting film was placed in a vacuum oven at 80 °C for complete degassing during 6 h. For preparation of nanocomposites, a predetermined amount of silica nanoparticles was dispersed in 5 mL of DMAC using a bath sonicator for 50 min before addition of the polymer. To improve polymer/silica interaction, the polymer granules were gradually dissolved in nanoparticles/solvent solution, stirred for 2 h at 75 °C and further sonicated for 10 min to ensure good dispersion of silica. The prepared solution was cast on Teflon-coated plate and dried in the same way as the neat TPU sample. The thickness range of the prepared samples was between 70 and 90 μm.

Table 2 Samples’ composition
Full size table

Characterization

The morphology of the samples and the distribution of silica nanoparticles in polymer were examined using scanning electron microscopy (SEM). The samples were fractured in liquid nitrogen, coated with gold, and tested by a Philips XL30 (Netherlands) scanning electron microscope. FTIR spectroscopy was used to monitor the incorporation of silica in the polyurethane matrix and to verify the final chemical structure of the polymer. Infrared spectra were collected in a Fourier transform infrared spectrophotometer (Bruker, model Equinox 55). Measurements were carried out using the attenuated total reflectance (ATR) technique. The scanning frequency range was 4000–600 cm−1. Thermal properties of the samples were measured by a Metller-Toledo differential scanning calorimetry (DSC DSC822e) at a heating rate of 5 °C/min and the temperature range of −120 to 250 °C. Thermogravimetric analysis was conducted with the temperature range of 30–650 °C using a Metller-Toledo TGA/DSC under a nitrogen atmosphere. A heating rate of 10 °C/min was used. Tensile test was conducted on a Santam universal testing machine (STM-20). The crosshead speed was 100 mm/min.

The viscoelastic properties of the nanocomposites were studied using an Anton Paar, rheometer (MCR300, USA) equipped with 25-mm parallel plate fixtures under nitrogen purge, with a gap of 1 mm.

To examine the rheological behavior, at first, a dynamic strain sweep was conducted at 185 °C and an angular frequency of 0.5 Hz. Then, dynamic frequency sweep was performed at 185 °C a tan angular frequency range between 0.05 and 600 Hz at constant strain which was in the linear area of dynamic strain sweep test.

Results and discussion

Morphology of silica-filled TPUs

The dispersion of nanosilica fillers in polyurethane matrix was analyzed using scanning electron microscopy (SEM). Figure 1 shows SEM micrographs for thin films of neat TPU and TPU filled with 5 and 15 wt% of various nanosilicas (Si-Un, Si-OS, and Si-PDMS). As it is shown, a uniform distribution is observed in all samples, except PU/Si-Un composite on which a large aggregation of silica nanoparticles is observed. It is known that fumed silica is inherently hydrophilic owing to its oxide nature as well as the presence of Si–OH groups on its surface [39]. Thus, when it is directly blended with an organic phase like TPU, it is often encountered by aggregated silica. Therefore, increasing the weight percent of unmodified silica in the nanocomposite can lead to very heterogeneous morphology (Fig. 1b, c). By the help of SEM analysis, it is shown that surface-treated silica nanoparticles can be dispersed much better in polyurethane matrix. This is consistent with the results reported for silica-filled polyurethanes by Dolatzadeh et al. [13]. The micrographs clearly illustrate that on the whole, two surface-treated silica nanoparticles are well dispersed in the polyurethane matrix giving particle sizes of less than 50 nm even at high silica loading. It is believed that the surface treatment of nanoparticles can increase the steric hindrance between the nanoparticles and can improve the wettability of the polymeric matrix [40]. According to Fig. 1d–g, we can see that the size of nanoparticles is increased with increase in silica content in the polymeric matrix. It is noted that in the treated silica-filled nanocomposites, particularly Si-PDMS-filled nanocomposites, some filler aggregates can be observed at 15 wt% silica loading. In addition, the effect of nanosilica with different surface modifications on the phase morphology of TPU was investigated by TEM. TEM micrographs of neat TPU and their nanocomposites with 10 wt% non-modified filler (Si-Un) and modified fillers (Si-OS and Si-PDMS) are shown in Fig. 2. As it is shown in Fig. 2, TPU exhibits phase separation, due to high degree of incompatibility between the hard and soft segments. The morphology of pure TPU can be described by globular hard segment microdomains (dark domains) within the soft segment phase (light domains) [41]. Figure 2b–d shows that three types of nanosilica used in this study show different impact behaviors on morphology. The results reveal that hard domain structures become more pronounced and visible in the sample morphology with addition of Si-Un. This change in morphology might be assigned to the nucleating ability of this filler [42] which is discussed later. TEM micrographs indicate the decrease in hard domain size which is disturbed with addition of surface-treated nanosilica. The observed effect can be ascribed to changes of surface free energy of fillers and, thus, its improved compatibility with soft segments. It is noted that silica nanoparticles modified with octylsilane (Si-OS) have a more prominent effect on disrupting the HDs than nanosilica modified with polydimethylsiloxane (Si-PDMS).

Fig. 1
figure 1

SEM micrographs of: a TPU, b, c PU/Si-Un5,15 d, e PU/Si-OS5,15, and f, g PU/Si-PDMS5,15

Full size image
Fig. 2
figure 2

TEM images of TPU (a), and TPU/silica nanocomposites: b PU/Si-Un10, c PU/Si-OS10, and d PU/Si-PDMS10

Full size image

Chemical characterization of PU/silica

The FTIR spectra of TPU and PU/silica nanocomposites containing 15 wt% silica are shown in Fig. 3. Silica particles produced characteristic bands associated with the stretching vibration of Si–O at 1073 cm−1 and asymmetric stretching vibration of free structural OH groups at 3700 cm−1 [13]. Based on a band evident at 3700 cm−1 (the position of free structural OH band) in Fig. 3b, it is presumed that maximum number of free Si–OH belongs to Si-Un15 nanoparticles. Both TPU and PU/silica nanocomposites show characteristic bands of hydrogen-bonded and free carbonyl groups (1690 and 1732 cm−1, respectively) confirming the formation of a phase separated morphology in TPU matrix [21, 41].

Fig. 3
figure 3

Comparative FTIR spectra of neat TPU, PU/Si-Un15, PU/Si-OS15 and PU/Si-PDMS15: a in the range of 3500–750 cm−1 wavenumber and b in the range of NH stretching wavenumber

Full size image

Analyzing the FTIR spectra in the region of carbonyl stretching band (1690–1732 cm−1) in Fig. 3a, it is shown that with adding treated silica, the relative proportion of non-bonded C=O increases. This is ascribed to weaker interactions or less ordered structures in hard domains, which may suggest that the SD/HD interactions become more important in polyurethane with treated silica [41, 42]. As can be seen in Fig. 3b, a broad band between 3400 and 3200 cm−1 in N–H stretching region is observed. The intensive band observed at 3330 cm−1 is assigned to the N–H stretching vibrations in hydrogen bond to carbonyl group (HS–SH interactions). Hydrogen bonding between N–H and urethane C–O–C groups (alkoxy oxygen) also displays a band near 3275 cm−1 [42]. When phase mixing is prevalent in TPU, a shoulder on the high-frequency side of the 3330 cm−1 peak, related to free N–H, will appear (3370 cm−1). In PUs, the extent of hydrogen bonding of N–H group in urethane can roughly show the degree of phase separation (DPS). DPS for a PU film is generally evaluated by the following relation:

$${\text{DPS}} = A_{\text{b}} /\left( {A_{\text{b}} + A_{\text{f}} } \right) = A_{{{\text{NH}},{\text{b}}}} /\left( {A_{\text{NH,b}} + A_{\text{NH,f}} } \right),$$
(1)

where A b and A f are the integrated bands of hydrogen bonded and free molecular group, respectively. A NH,b and A NH,f in Eq. 1 [42] are the areas under the hydrogen bonded and free N–H groups mentioned earlier. The N–H bands are deconvoluted using Gaussian shape, and the calculated values of DPS for PU/silica films are given in Table 3.

Table 3 Degree of phase separation (DPS), thermal transition (T g), temperature, and enthalpy of crystallization of PU/silica nanocomposites
Full size table

The results in Table 3 and Fig. 3b show that the partial phase mixing is enhanced in TPU after adding 15 wt% treated nanosilica (i.e., Si-PDMS and Si-OS) due to reduction of DPS (lowered relative ratios of peaks near 3330 and 3370 cm−1). While in the last nanocomposite, the incorporation of 15 wt% Si-Un does not significantly alter DPS. The obtained results may be attributed to the effect of modified silica on polyurethane microdomain morphology by increasing the interface between the hard and soft domains which have been reported in other studies on PU/clay nanocomposites [26].

Thermal characterization of PU/silica

The DSC thermograms of neat TPU and TPU nanocomposites filled with treated and un-treated silica particles are shown in Fig. 4. A summary of the results of DSC thermograms is shown in Table 3 [22]. At the temperature range of −30 to −50 °C in the heating scan of the nanocomposites, there is shown a glass transition temperature (T g) related to the soft domain (SD) of TPU. In addition, the heating scan of all samples shows multiple melting peaks in a temperature range of 130–170 °C; this is due to disruptions induced on crystalline hard domains with different sizes and various levels of packing order [41]. The high-temperature endotherm is attributed to melting of microcrystalline hard domains. Lower melting endotherms are assigned to dissociation of short-range and long-range order microdomains. The presence of these endotherms is an indication of phase separation morphology of hard and soft segments in TPU which is also observed in FTIR analysis. DSC results have also been used to evaluate non-isothermal crystallization behavior of HDs in PU/silica (Table 3). By comparing the exotherms in cooling runs and endotherms in heating runs for each sample, one can explain that the onset of HDs crystallization with different sizes and perfections, as discussed earlier, is nearly the same; hence, crystallization curves become narrower than melting curves. In PU/Si-Un nanocomposites, an increased crystallization temperature (T c) for HS was observed, and their T g remained approximately the same. This suggested that Si-Un particles were mainly present in HD and behaved as nucleation agent for HS crystallization. This phenomenon indicated an increased crystallization rate of HDs in the nanocomposites.

Fig. 4
figure 4

DSC thermograms of PU/silica nanocomposites consisting heating and cooling scans: a PU/Si-Un, b PU/Si-OS, and c PU/Si-PDMS [22]

Full size image

For PU/Si-OS nanocomposites, T g increased, while the crystallinity decreased with higher nanoparticle loading. As shown in Fig. 4, Si-OS incorporation of 15 wt% leads to a severe decline in the HS crystallization peak. These observations may be ascribed to the disordering and partial dissolution of HSs in the SD [26]. Apart from phase mixing, better dispersion (Fig. 1) and higher interface of Si-OS particles with the soft domain due to Si-OS particles stronger hydrophobicity compared with Si-Un may be another reason for the increase in T g of PU/Si-OS nanocomposites when compared with neat TPU and PU/Si-Un. It is also noteworthy that in PU/Si-OS15 nanocomposite, HDs nearly disappear, indicating that the interaction between HS and soft domain distorts HS chain conformation. According to these results, the Si-OS nanofiller seems to act as TPU compatibilizer (for hard and soft domains) which is consistent with the obtained results of TEM micrographs.

In PU/Si-PDMS samples, T g of TPU slightly decreases in the presence of silica. Moreover, crystallization enthalpy of hard segments almost shows no change in comparison with neat TPU. It appears that Si-PDMS nanoparticles mostly prefer to distribute in the soft segment of polyurethane. It seems that in the presence of this type of silica, hydrogen bonding between hard and soft segments of polymer is not completely replaced by hydrogen bonding between treated silica particles and polyol chains, and the total chain mobility of polyol is increased. Therefore, T g of such nanocomposites is slightly dropped after the arrival of Si-PDMS. Since TPU crystallization occurs during the cooling cycle, slightly lower crystallization temperature for HSs in PU/Si-PDMS nanocomposites suggests higher crystallization barrier energy with respect to neat TPU. This may indicate a relatively good interaction between hard and soft segments in the presence of Si-PDMS that hinders the crystallization of hard segments [43].

Thermal stability of PU nanocomposites

TGA curves for neat TPU, PU/Si-Un5, PU/Si-OS5, and PU/Si-PDMS5 are shown in Fig. 5. All composites show the same degradation profile, which reveals that nanoparticles do not play any significant role in changes in polymeric matrix degradation mechanism [44]. T 95 is related to the temperature at which 95 % of the weight of the sample has remained, and it is a good indication of thermal stability and degradation temperature which are shown in Table 4. As can be seen in Table 4 and Fig. 5, T 95 is increased by adding nanoparticles to TPU matrix. Moreover, the weight of the residue of PU/silica nanocomposites at 600 °C was increased ranging from 14 to 17 % with silica concentration of 5 wt%, when compared with pure TPU (7 %). This enhancement of the char formation is ascribed to the high heat resistance exerted by the silica. In general, nanoparticles can improve thermal stability in organic matrix due to their high heat capacity and act as a barrier that delays the escape of volatile degraded products from the nanocomposite [44–46].

Fig. 5
figure 5

TGA curves of neat TPU, PU/Si-Un5, PU/Si-OS5, and PU/Si-PDMS5

Full size image
Table 4 Thermogravimetric analyses of neat TPU, PU/Si-Un5, PU/Si-OS5, and PU/Si-PDMS5
Full size table

Tensile properties

Figure 6 shows the results of mechanical properties for three types of TPU/silica nanocomposites. The shape of the stress–strain curve of the neat TPU is typical for elastomeric materials with hard domains dispersed in the matrix of soft segments. The results show that mechanical properties of TPU change in the presence of nanosilica which is to be discussed here.

Fig. 6
figure 6

Stress–strain curves of: a PU/Si-Un, b PU/Si-OS, and c PU/Si-PDMS nanocomposites

Full size image

By adding unmodified silica into the TPU matrix up to 10 %, as shown in Fig. 6a, the modulus and tensile strength are decreased, while the elongation-at-break is increased. This change in properties may be attributed to the formation of an interfacial polymer layer (shell) attached to the particle core. Thus, the polymer chain mobility due to repulsive forces between the particle and the interfacial layer yields further to plasticizing effect. This process could lead to lowering of modulus and maximum tensile strength of the composites accompanied with decreased modulus [47]. However, PU/Si-Un15 shows a high modulus and low elongation, a behavior which is different from that of other percentages. At low stresses, because of restricted motion of TPU chains in the presence of filler networks, PU/Si-Un15 can show high modulus and resistance, but as the stress is increased, the weak points become larger and lead to uneven distribution of stress, so the sample becomes highly brittle and the strain-at-break decreases [48].

In Fig. 6b, stress–strain curves for PU/Si-OS nanocomposites are presented. As it is evident in this figure, the increase in tensile strength and elongation-at-break is achieved with addition of Si-OS up to 10 %, while maximum tensile strength is reached at 5 %. The enhancement in tensile strength and elongation-at-break for low percentage of Si-OS in the nanocomposites is a result of uniform distribution of Si-OS within the TPU matrix and the changed microphase separation toward phase mixing. According to DSC results, the phase mixing in TPU observed for PU/Si-OS nanocomposites is increased at higher percentage. The good tensile property of PU/Si-OS suggests a strong and specific interaction of Si-OS nano-filler with both hard and soft domains, which ensures an efficient loading transfer between the TPU matrix and the nanoparticles. This results in higher tensile strength and elongation-at-break with respect to neat TPU and its nanocomposite with unmodified silica. It is noted that further increase in Si-OS content to 15 % leads to lower strength and strain-at-break, due to emerging aggregations. When the filler forms aggregate, the wetting at the interface between matrix and filler is poor. Therefore, in such points, the force distributes unevenly and the nanocomposite strength falls. Figure 6c shows stress–strain curves for PU/Si-PDMS at different percentages. By adding a low content of Si-PDMS nano-filler into TPU, the stiffness and strength are increased, and the elongation-at-break is decreased; this is due to good dispersion of nanoparticles and formation of additional interface by these particles (hard and soft domains) [34]. At low strains, PU/Si-PDMS15 modulus is slightly higher than those of other samples with Si-PDMS nanosilica which shows the restricted motion of polyurethane chains. Nanoparticles act as a physical crosslink, restrict the motion of TPU chain, and cause an increase in modulus and tensile strength. However, as the strain increases, the modulus of PU/Si-PDMS15 becomes lower than those of other compositions. Because at high percentages of nanoparticles, as the strain increases, the weak points and cracks are formed, and the strain force is unevenly distributed in the nanocomposite which leads to lower modulus and tensile strength [34, 49]. The strain-at-break for PU/Si-PDMS nanocomposites, as shown in Fig. 6c, is lower than that of TPU. This may be due to more hydrophobicity of Si-PDMS and their preferential interaction with the soft domain which leads to restricted motion of the SD in this nanocomposite.

Dynamic rheological properties

Strain sweep

To specify the viscoelastic linear limit and the effect of strain on rheological properties, a dynamic strain sweep test was conducted. The test was carried out for neat TPU and different percentages of PU/Si-PDMS. Since nanocomposites embodied smaller linear limits at high percentages of filler, the test was also conducted for PU/Si-OS15 and PU/Si-Un15 (Fig. 7). Because of more aggregations and strong filler network in PU/Si-Un nanocomposite (in section “Morphology of silica filled TPUs”), PU/S-Un15 became highly brittle, and it was not melted in RMS system; therefore, no data have been recorded for this sample. As shown in Fig. 7a, at low strains, the storage modulus of all samples indicated a linear region which was independent of strain, and it is a linear viscoelastic region. By adding Si-PDMS and increasing its percentage, the linear region has become smaller which is justified by the Payne effect [50]. This smaller linear limit was due to greater rigidity and brittleness of the sample. It was also observed in the tensile test that yield point had shifted to lower strains. The transfer from the linear to non-linear region was considered dependent upon the type and quality of dispersion and filler percentage. In non-linear region, as the strain increased, the storage modulus decreased, which was due to disentanglement of polymer macromolecules and the breakdown in filler-polymer network [8, 37, 51]. Moreover, the results show the rising in modulus of the nanocomposites with higher percentage of Si-PDMS. Because the mobility of entrapped chains within the filler network is prevented and as the percentage of nanosilica increases, the filler network becomes stronger and larger which leads to higher modulus in these samples. Therefore, dynamic frequency sweep was performed in viscoelastic linear region of all nanocomposites at 2 % of strain which is to be discussed later.

Fig. 7
figure 7

Dynamic strain sweep of: a Gʹ and b tan δ for pure TPU, PU/Si-OS15, and PU/Si-PDMS5, 10, 15 nanocomposites at frequency of 0.5 Hz (T = 185 °C)

Full size image

The obtained results from dynamic strain sweep test (Fig. 7b) display that at high strains, the loss tangent is increased which shows the irreversible deformation which is due to the breaking of the filler network [38]. The amount of tanδ for neat TPU is more than 1 which shows that the rheological response is determined by viscous behavior in this sample, but in all other nanocomposites, the amount of tanδ is less than 1 which shows the dominance of the elastic behavior and the samples display solid-like behavior [46, 52]. As the filler percentage has increased in PU/Si-PDMS system, the elasticity has further increased, and consequently, the tanδ has decreased.

Frequency sweep

To investigate the effects of type and percentage of nanoparticle on rheological properties of TPU, a dynamic frequency sweep test was conducted for all samples in the viscoelastic linear region. The rheological profiles for neat TPU, PU/Si-PDMS, and PU/Si-Un nanocomposites are shown in Fig. 8. It is apparent that the behavior of PU/Si-OS nanocomposites is different from the others; thus, To provide a more accurate figure and make a better comparison, the PU/Si-OS nanocomposite curves are separately shown in Fig. 9.

Fig. 8
figure 8

Dynamic frequency sweep of: a Gʹ and b G″ for pure TPU, PU/Si-Un, and PU/Si-PDMS nanocomposites containing various weight percentages of fumed silica at strain of 2 % (T = 185 °C)

Full size image
Fig. 9
figure 9

Dynamic frequency sweep of: a Gʹ and b G″ for pure TPU and PU/Si-OS nanocomposites containing various weight percentages of fumed silica at strain of 2 % (T = 185 °C)

Full size image

Figures 8, 9 show that the storage modulus (G′) and loss modulus (G″) are raised as the frequency is increased (the samples become more solid-like), and the time-dependent mechanisms are less able to follow the rapidly reversing stress. However, at low frequencies, there is enough time for entanglement unraveling and a large relaxation occurs; as a result, the values of G′ and G″ are low.

By adding nanosilica to the matrix and increasing its percentage, both G′ and G″ are raised, but the primary slope of nanocomposites is lower than that of neat TPU which shows the strength that is imparted by silica nanoparticles in the matrix. This enhancement can be explained on the basis of resistance to deformation of the molten polymer chains imposed by silica nanoparticles favoring the formation of a structural network even at low nanosilica content [53].

At the same percentage, G′ and G″ of PU/Si-PDMS nanocomposites are higher than those of PU/Si-Un; this is ascribed to the stronger interaction of modified nanosilica with TPU caused by better dispersion of nanoparticles and greater interfacial interaction of filler matrix [37].

G′ and G″ of PU/Si-OS5, as shown in Fig. 9a, b, are higher than those of PU/Si-OS10. In DSC analysis for PU/Si-OS, phase mixing of TPU is increased as the filler percentage is raised. Therefore, lower modulus for PU/Si-OS10 may be due to higher phase mixing in this sample with respect to PU/Si-OS5 which might have led to weaker rheological properties. According to DSC results, in PU/Si-OS15, phase mixing is the highest among PU/Si-OS nanocomposites. However, the stronger filler network in this sample may help to overcome phase mixing and increase its viscoelastic properties. As shown in Fig. 9, G′ and G″ of PU/Si-OS15 versus ω have gentler slope compared with other nanocomposites; this shows the strength provided by the filler network.

Cole–Cole plots (imaginary versus real part of dynamic viscosity) are also helpful in explaining viscoelastic characteristics of the polymers with a relaxation time distribution [54]. Figure 10 shows Cole–Cole plot of neat TPU and PU/silica composites. As can be observed in this figure, nanocomposites graphs are similar to each other and have a greater relaxation time in comparison with neat TPU. This observation results from the delay in the movement of long polymer chains in the presence of silica nanoparticles which has led to a longer relaxation time and shows the dominance of solid-like behavior of the composites.

Fig. 10
figure 10

Cole–Cole plot of η″ vs η′ for neat TPU and PU/silica nanocomposites

Full size image

Modeling

The Maxwell model, consisting of a Hookean spring and a Newtonian dashpot in series, is suitable for understanding stress relaxation data, but it fails in that, the relaxations observed are broader than the predictions (i.e., polyurethanes with divided microphase morphology). The failure of the Maxwell model is easily rectified by assuming that the mechanism is a set of relaxation processes with a band of relaxation times which are closely spaced (i.e., generalized Maxwell model). It seems that the obtained dynamic data can be modeled by this method. According to the following equations, the dynamic parameters G′(ω) and G″(ω) are fitted by generalized Maxwell model [55]:

$$G^{\prime}(\omega ) = \sum\limits_{i = 0}^{n} {\frac{{G_{i} (\omega \lambda_{i} )^{2} }}{{[1 + (\omega \,\lambda_{i} )^{2} ]}}} ,$$
(2)
$$G^{\prime\prime}(\omega ) = \sum\limits_{i = 0}^{n} {\frac{{G_{i} (\omega \,\lambda_{i} )}}{{[1 + (\omega \lambda_{i} )^{2} ]}}} ,$$
(3)

where G i, λ i, ω, and i show the elastic constant, relaxation time, angular frequency, and the number of needed Maxwell elements for fitting the dynamic moduli, respectively. The experimental data shown in Figs. 8, 9 can be described by Eqs. 2 and 3 by means of some Maxwell elements which are connected in series G i and λ i are parameters which are determined for each sample by experimental data. To calculate G i and λ i, a genetic algorithm optimization was used. Description of data was obtained by six parallel Maxwell elements.

To decrease computation and increase accuracy of fitting, Subramanian et al. chose a group of λ i with decade intervals. To obtain λ is, they applied the following limitations [56]:

$$\lambda_{\hbox{max} } \omega_{\hbox{min} } > 1,$$
(4)
$$\lambda_{\hbox{min} } \omega_{\hbox{max} } < 1,$$
(5)

where λ max is the longest relaxation time, λ min is the shortest relaxation time, ω max is the highest frequency for which data were available, and ω min is the lowest frequency for which data were available.

In the dynamic frequency sweep test, angular frequency ranged from 0.05 to 625 Hz. By considering the above limitations, the integer power λ i was considered as ranging from 10−3 to 102. Now, using optimizing methods, G i was obtained far more easily. The calculated G is for all samples are included in Table 5. As one would expect, the obtained G is strongly depends on the sample structure. Since G 6 has the strongest effect in comparison with other elastic constants, it can be a good measure to compare samples’ elasticity. It is obvious that TPU nanocomposites with the modified silica show higher elasticity in comparison with PU/Si-Un nanocomposites. In other words, the remarkable improvement in elastic constants, related to the strong interaction between the matrix (TPU) and nanosilica, is clearly observed in PU/Si-PDMS and PU/Si-OS nanocomposites. This behavior was similarly observed for ABS/silica nanocomposites [57]. For better comparison, the experimental modulus and the modulus based on modeling are shown in Fig. 11. The errors of data obtained by the model are calculated and presented according to Eq. 6 in Table 5.

Table 5 The elastic constants and errors obtained from generalized Maxwell model for TPU and their nanocomposites
Full size table
Fig. 11
figure 11

Comparison of experimental curves of moduli (E) with curves obtained from the model (M) for TPU (a), and PU/silica nanocomposites: b, c PU/Si-Un5 and 10, d–f PU/Si-PDMS5, 10 and 15 and g–i PU/Si-OS5, 10 and 15

Full size image
$${\text{Error}} = [(\log \,G^{\prime}_{\text{m}} - \log \,G^{\prime}_{\text{e}} )/\log \,G^{\prime}_{\text{e}} ]^{2} + [(\log \,G^{\prime\prime}_{\text{m}} - \log \,G^{\prime\prime}_{\text{e}} \,)/\log G^{\prime\prime}_{\text{e}} ]^{2} .$$
(6)

As can be inferred from the data given in Table 5, the generalized Maxwell model with six elements excellently fits the experimental data.

Conclusion

The aim of this study was to explore how addition and surface modification of nanosilica filler affected the structure and properties of polyesterurethane. Three different types of nanosilica, including unmodified silica and two different organically modified silicas by means of octylsilane and polydimethylsiloxane, were used. PU nanocomposites were made by solution casting. SEM images showed that all types of nanoparticles display good distribution in polyurethane, but some aggregation of nanoparticles is observed in PU/Si-Un. The results of DSC and FTIR showed phase separation morphology for all samples. In addition, DSC analysis showed that in PU/Si-OS nanocomposites, phase mixing and T g increased by adding nanoparticle and increasing its percentage; but in PU/Si-PDMS nanocomposites, T g and phase mixing were decreased. The results of TGA showed that nanocomposites containing treated nanoparticles have higher thermal stability. In general, there were two reasons which led to improvements in nanocomposites properties: better dispersion of nanoparticles in the matrix and higher phase separation of TPU. Si-OS nanoparticles showed a better dispersion in TPU in comparison with Si-PDMS. Therefore, a larger interface was formed between the matrix and the filler, and as a result, viscoelastic and mechanical properties of PU/Si-OS5 increased in comparison with PU/Si-PDMS5. However, as the percentage increased, PU/Si-PDMS with higher value of DPS showed better properties in comparison with PU/Si-OS. PU/Si-Un nanocomposites showed weaker properties in comparison with nanocomposites containing treated nanoparticles due to weaker dispersion of unmodified silica in TPU.