Effect of silica nanoparticles on morphology of segmented polyurethanes

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Polymer xx (0000) xxx–xxx www.elsevier.com/locate/polymer

Effect of silica nanoparticles on morphology of segmented polyurethanes Zoran S. Petrovic´a,*, Young Jin Choa, Ivan Javnia, Sergei Magonovb, Natalia Yerinab, Dale W. Schaeferc, Jan Ilavsky´d, Alan Waddone a

Kansas Polymer Research Center, Pittsburg State University, 1501 S. Joplin, Pittsburg, KS 66762, USA b Digital Instruments/Veeco Metrology Group, Santa Barbara, CA, USA c Department of Chemical and Materials Engineering, University of Cincinnati, Cincinnati, OH 45221-0012, USA d Purdue University, West Lafayette, IN 47907, USA e Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA 01003, USA Received 17 October 2003; received in revised form 25 March 2004; accepted 5 April 2004

Abstract Two series of segmented polyurethanes having soft segment concentration of 50 and 70 wt%, and different concentrations of nanometerdiameter silica were prepared and tested. Atomic force microscopy revealed a strong effect of nanoparticles on the large-scale spherulitic morphology of the hard domains. Addition of silica suppresses fibril formation in spherulites. Filler particles were evenly distributed in the hard and soft phase. Nano-silica affected the melting point of the hard phase only at loadings .30 wt% silica. A single melting peak was observed at higher filler loadings. There is no clear effect of the filler on the glass transition of soft segments. Wide-angle X-ray diffraction showed decreasing crystallinity of the hard domains with increasing filler concentration in samples with 70 wt% soft segment. Ultra smallangle X-ray scattering confirms the existence of nanometer phase-separated domains in the unfilled sample. These domains are disrupted in the presence of nano-silica. The picture that emerges is that nano-silica suppresses short-scale phase separation of the hard and soft segments. Undoubtedly, the formation of fibrils on larger scales is related to short-scale segment segregation, so when the latter is suppressed by the presence of silica, fibril growth is also impeded. q 2004 Published by Elsevier Ltd. Keywords: Segmented polyurethanes; Nanocomposites; Morphology

1. Introduction In spite of the breadth of research in the field of nanocomposites, only limited number of studies deal with colloidal fillers for polyurethanes. In this work, we study the effect of nearly monodisperse, unaggregated 12 nmdiameter spherical silica particles on the structure and properties of phase-separated segmented polyurethane (PU) elastomers. The motivation for this work is positive experience with silica reinforcement of analogous singlephase PUs [1]. In this case, the addition of nano-silica improved the strength by about three times and elongation at break by about 600%. Segmented polyurethane elastomers used in the present study are block copolymers with alternating soft and hard blocks that, due to structural differences, separate into two * Corresponding author. Tel.: þ 1-620-235-4928; fax: þ1-620-235-4919. E-mail address: [email protected] (Z.S. Petrovic´). 0032-3861/$ - see front matter q 2004 Published by Elsevier Ltd. doi:10.1016/j.polymer.2004.04.009

phases or domains. Hard domains play the role of physical cross-links and act as a high modulus filler, whereas the soft phase provides extensibility [2 –4]. The morphology of segmented PUs depends on the relative amount of the soft and hard phases. PUs with a 70 wt% soft segment concentration (SSC) typically have globular hard domains dispersed in the matrix of soft segments, while cocontinuous phases and even lamellar morphology have been postulated in the samples with 50 wt%-SSC. Polyurethanes with 70 wt%-SSC are soft thermoplastic rubbers whereas the ones with 50 wt%-SSC are hard rubbers, both being of significant industrial importance [5]. These systems are usually unfilled except for minor additives to improve aging properties. It is reasonable to expect that the effect of nanoscale fillers in segmented PUs would be quite subtle due to the intrinsic complexity of these systems. Since the hard domains in our case are semi-crystalline they may form large crystalline forms such as spherulites. It is of interest,

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therefore, to establish the effect of nano-silica on the twophase morphology. The filler may interact with the hard or soft segments or both. Since silica has OH groups on the surface, isocyanate may react with the particles thereby aiding dispersion of the particles in the polymer. Thus, the effect of the filler will be exerted through the adsorption of the soft and hard segments on the silica surface as well as through chemical bonding, potentially affecting the structure of both phases. With the advent of atomic force microscopy (AFM) the morphological changes in the polyurethane elastomers can be followed quite elegantly. AFM, complemented with X-ray analysis, is used to observe the changes in morphology over a wide range of length scales.

performed in tapping mode with free oscillating amplitude, A0 in the 40 –60 nm range and set-point amplitude ø 0.4– 0.05 nm. Such conditions of enhanced tip-sample force interactions are most suitable for compositional imaging of heterogeneous polymer samples as micro-segregated polyurethanes are. Etched Si probes (spring constant ø 50 N/m) were applied for imaging. Imaging was conducted on flat surfaces prepared at 2100 8C with an ultramicrotome MS-01 (MicroStar Inc.) equipped with a diamond knife. Height and phase images were simultaneously recorded on polymer surfaces. Height images reflect surface morphology, whereas phase images provide a sharp contrast of fine structural features and emphasize differences in mechanical properties of different sample components.

2. Experimental

3. Results and discussion

2.1. Materials

In addition to nanometer-scale phase separation, segmented polyurethanes may also display coarser morphological features such as spherulites or spherulite-like forms. We have compared the morphology of four samples using AFM: the polyurethanes having 70 wt%-SSC without nanoparticles and 70 wt%-SSC with 20 wt% nano-silica, as well as the samples with 50 wt%-SSC without and with 20 wt% nano-silica. X-ray diffraction was carried out on samples with 0, 5, 10 and 20 wt% nano-silica in both series of PUs (with 50 and 70 wt%-SSC). USAXS was completed on the unfilled and filled samples with 50 wt% soft segment. Simple calculations show that for filler particles arranged on a cubic lattice, the inter-particle distance (surface to surface) is about one diameter at 10 vol%, i.e. about 12 nm in our case with 20 wt% (11.5 vol%) of nano-silica. Under such circumstances, the separation of filler particles is on the order of molecular dimensions and may also affect the morphology and matrix behavior. The above calculation illustrates the opportunities for modification of properties of polymeric matrices with nano fillers. Segmented polyurethanes are notoriously complicated systems due to structural heterogeneity arising from the distribution of the hard segment lengths and even the possible existence of hard-segment homopolymers formed at the given synthesis conditions. Also, isocyanates are somewhat soluble in the soft segment and thus potentially unavailable for the formation of the hard phase. The actual soft-segment concentration, therefore is somewhat higher than that calculated from stoichiometry. Finally, these systems are rarely in equilibrium; their morphology is dependent not only on the synthesis chemistry but also on their thermal history. Very large hard-segment rich structures have been observed by Raman spectroscopy [6]. Also, a number of morphological studies on similar polyurethane systems have been carried out using electron microscopy but due to the lack of contrast between phases the conclusions were often ambiguous. AFM, however, offers unprecedented

Polyurethanes were prepared from diphenylmethane diisocyanate (MDI), polypropylene oxide (PPO) glycol, and butane diol (BD). MDI was Isonate 125 M from Dow Chemical; it was distilled under vacuum at 170 8C. PPO diol used in this work was Acclaim 2020 from Lyondell; It had an OH number of 55 mg KOH/g, corresponding to the molecular weight of 2040. BD was purchased from Aldrich; it was distilled before use. Colloidal silica, having a particle diameter of about 12 nm, was obtained from Nissan Chemical Co. as a 30 wt% dispersion in methyl ethyl ketone (MEK). 2.2. Methods Polyurethane/filler composites were prepared by mixing the polyol with the filler solution, removing MEK by distillation, and mixing with diisocyanate to obtain the prepolymer, which was chain extended with BD. The mixture was then poured into the mold to obtain 1 mm thick sheets or thin films. Filler concentrations were 0; 5; 10; 20, and 30 wt% where possible. Higher concentrations were difficult to obtain because of the high viscosity of the polyol with nanoparticles. Thermal measurements were carried out using TA Instruments thermal analysis system consisting of a 3100 Controller, managing DSC 2910, TMA 2940 and DEA 2970 modules. The heating rate was 5 8C/min for all methods. WAXD was performed with a Siemens D500 diffractometer in transmission mode, using Ni filtered Cu Ka radiation from a sealed tube generator. Ultra small-angle X-ray scattering (USAXS) experiments were performed using the Bonse-Hart double crystal X-ray camera at the UNICAT beam line at Argonne National Laboratory. AFM was performed with a scanning probe microscope (MultiModee Nanoscope IIIa, Digital Instruments/Veeco Metrology Group, Santa Barbara, CA). Measurements were

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opportunities for revealing fine structure of the urethane morphology without the need for special treatment of the samples. AFM images of the PU sample with 50 wt%-SSC (Fig. 1) show spherulitic morphology. Height (Fig. 1(a)) and phase (Fig. 1(b) –(d)) images of 50 mm £ 50 mm surface reveal a number of large spherulites with diameters up to 20 mm. The spherulites are surrounded by amorphous material, which is the darker phase in both images. Bearing analysis shows that an area occupied by bright-contrast features is ø 52%, consistent with the ratio of the components with soft and hard segments. The fine structure of the spherulites is best resolved in phase images (Fig. 1(b) – (d)). It appears that the spherulites are formed of fibrils that are more densely packed in the center of spherulites. Phase image in Fig. 1(d) shows individual fibrils at spherulite edges where they are immersed in an amorphous background. The diameter of the fibrils is 50 – 120 nm range and their length is a few microns. At the moment, we can only speculate about the structural organization observed in the AFM images. Since the extended length of the hard and soft segments is only about 10 nm (both segments have molecular weight ø 2 K), soft and hard segments must coexist in the fibrils as

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well as in the amorphous regions. This picture is somewhat different from the established view that co-continuous sheet-like or lamellar phases exist at this concentration of soft segments. Morphology of PU with 50 wt%-SSC filled with 20 wt% nano-silica is characterized by more globular domains with amorphous materials between them (Fig. 2). The large-scale phase image in Fig. 2(b) shows 1– 10 mm domains with well-defined boundaries. Some of the domains are slightly elongated. Domains of the filled polymer are smaller than those of the un-filled material but they are characterized by a narrower size distribution. In the silica-loaded material, there is no well-defined spherulitic structure. Only some traces of tightly packed nano-fibrils with a width of 10– 40 nm can be found. Nano-fibrils are supposed to consist of almost pure hard segments. Due to interconnectivity of the hard and soft segments and the size of the hard segment, however, they may contain some soft segments. Indeed, USAXS studies confirm this picture. Silica nano-particles and their agglomerates in the filled material are best resolved in high-resolution phase images (Fig. 2(c) and (d)). The nano-particles are seen as bright spots, especially, when compared to the surrounding amorphous polymer. The particles are evenly distributed

Fig. 1. AFM images of the PU sample with 50 wt%-SSC. Image (a) is a height image. Images (b) –(d) are phase images.

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Fig. 2. AFM images of the PU sample with 50 wt%-SSC and 20 wt% nano-silica. Image (a) is a height image. Images (b) –(d) are phase images.

throughout the sample. The average particle size, which was estimated with the particle analysis software of the microscope manufacturer, is about 10 nm. This value is close to a particle size of 12 nm, which was determined from electron microscopy micrographs [7]. The morphology of the PU sample with 70 wt%-SSC is revealed in the height (Fig. 3(a)) and phase (Fig. 3(b) – (d)) images. In both cases, spherulites are seen as bright round-shape regions with dimensions varying from 0.8 to 7 mm. The phase image is the most informative regarding the morphology of this material. Spherulites, being more dense structures, appear bright. Bearing analysis of the phase image showed that dense areas occupy 28%, which is close to the content of hard segments, indicating that amorphous regions must contain both hard and soft segments. Darker regions are the amorphous phase that surrounds spherulites. These areas contain regions with different contrast (marked by arrows) that indicate inhomogeneity of the amorphous material. The nature of this inhomogeneity is not known. Spherulites of PU with 70 wt%-SSC (Fig. 3) are more compact than those of the polymer with 50 wt%-SSC (Fig. 1). Differences are also found in the structure and size of fibrils forming spherulites. In PU with 70 wt%SSC, there is a tendency toward radial growth of fibrils from a nucleating center. These fibrils are smaller

(20 nm) and are densely packed as compared with the 50 wt%-SSC fibrils. The spherulite borders are well defined with few, if any, nano-fibrils entering amorphous phase. This picture is quite different from morphology of 50 wt%-SSC material. The height and phase images of the PU 70 wt%-SSC sample filled with silica nanoparticles (20 wt%) are shown in Fig. 4. The morphology of this sample is different from that of the non-filled material. The domain structure is bimodal with large domains (1.5 –2.5 mm) coexisting with small structures 300– 400 nm in size. This distribution is best seen in the phase images (Fig. 4(b) and (c)). Bearing analysis of both images shows that bright domains cover 30 wt% of the area. Therefore, as in previous samples, the ratio of spherulitic and amorphous materials is consistent with the SSC. Individual silica particles are distinguished as bright spots in the phase images (Fig. 4(d) and (e)). Silica particles are distributed rather homogenously. The particle analysis gives an average size of silica particles ø 13 nm. In summary, AFM images demonstrate that the morphology of PU samples depends on SSC and presence of silica particles. Differences include size and size distribution of spherulites, as well as the type and dimensions of nanoscale fibrillar structures forming the spherulites.

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Fig. 3. AFM images of the PU sample with 70 wt%-SSC. Image (a) is a height image. Images (b) –(d) are phase images.

3.1. Thermal behavior of the hard and soft segments in the presence of nano-silica Melting of segmented polyurethanes with MDI/BD hard segments was studied by differential scanning calorimetry (DSC). DSC does not reveal details of the sample morphology but it indicates the degree of organizational order of crystalline domains through the melting behavior of the crystalline phase, and the degree of interaction between particles and the soft or hard phase. Usually two and sometimes three peaks were observed in the DSC endotherms. This pattern was attributed to a distribution of crystallite sizes, smaller crystallites having lower melting points. Alternatively, some of the multiple melting peaks could be attributed to the release of the residual strain or packing disorder in the hard segments [8] or to the presence of different crystal forms [9,10]. DSC curves of the 50 wt%-SSC polymers with different silica content (Fig. 5) show two melting peaks at 201 and 221 8C and a shoulder at about 230 8C for samples with 0, 5 and 10 wt% silica, while the samples with 20 and 30 wt% filler display a single melting peak at 220 and 230 8C, respectively. The smaller peaks in the 10 wt% nanosilica sample were the result of the smaller sample size. The increase in size of the high temperature melting peak and disappearance of the low temperature peaks may be

attributed to different morphologies of highly filled samples as observed by AFM and SAXS (below). This result is opposite from what we observed previously in nano-silica filled polyethylene oxide [11], where both the degree of crystallinity and the melting point decreased with increasing nano-silica concentration. These PUs are more compatible with the filler not only because of higher polarity of the polymer but also as a result of possible chemical reaction of isocyanates with hydroxyl groups on the surface of silica. Lipatov’s theory of filler reinforcement of polymers predicts formation of a boundary layer of a matrix material on the surface of the filler [12,13]. The thickness of the layer depends on the strength of interaction, being greater for stronger interaction. The properties of a polymer in the boundary layer differ from those in the bulk of the matrix material primarily due to the decreased mobility of chains adsorbed on the filler surface, resulting in a higher glass transition and perhaps lower crystallinity. Hard segments may also be chemically bound to the surface of the nanosilica leading to reduced mobility. No obvious trends were observed in the glass transition temperature ðTg Þ of the soft segment as measured by DSC (Fig. 6), thermo-mechanical, dynamic mechanical (Fig. 7) and dielectric analysis. Tg of the PPO soft segment chains in the series with 50 wt%-SSC varied slightly with filler concentration (the value at 0 wt% filler may have been too

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Fig. 4. AFM images of the PU sample with 70 wt%-SSC and 20 wt% nano-silica. Image (a) is a height image. Images (b) –(d) are phase images.

low due to experimental difficulties). Generally, it is difficult to pinpoint the transition in these samples because of the lower concentration of soft segments and the effect of hard segments on their mobility. The glass transition with 70 wt%-SSC may even decrease with increasing silica content, but the variations were within few degrees as shown in Fig. 6. Thus, no increase of the soft segment Tg was observed unlike with the single-phase PUs with PPO

Fig. 5. DSC curves of the samples with 50 wt%-SSC showing the melting region. Note that the reduced size of the endotherms for the 10 wt% sample is due to small sample size.

chains. It appears that the hard/soft phase interaction is stronger than the silica/soft interaction. Also, nanoparticles may have introduced some extra free volume in the matrix, which was reflected in lower density of the composites than expected from individual densities of the matrix and filler.

Fig. 6. Effect of nano-silica concentration on soft segment Tg as measured by DSC in series with 50 and 70 wt%-SSC.

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Fig. 7. Effect of nano-silica concentration on soft segment Tg in series with 50 and 70 wt%-SSC as measured by DMA.

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Fig. 9. Wide angle X-ray diffractograms of polyurethanes with 70 wt%SCC and different concentrations of nano-silica.

3.2. X-ray diffraction 3.3. Ultra small angle X-ray scattering WAXD shows significant change with loading for both the 50 and 70 wt%-SCC materials (Figs. 8 and 9). There is a ˚ ) in the un-filled crystalline peak at 19.4 degrees (4.6 A sample. This peak persists throughout the 50 wt%-SCC series (5, 10, 20 wt% silica). By contrast, in the 70 wt% series, there is a clear effect of the nano-spheres on the crystalline component (Fig. 9). At zero loading, the crystalline peak at 19.4 degrees is clear. This feature progressively weakens and broadens with loading until by 20 wt% the trace appears to be wholly amorphous. This result is consistent with the AFM images that indicate a decrease in the hard domain size at 20 wt% loading in the 70 wt%-SSC-the size of the hard domains becomes too small to give discrete WAXD peaks. Irrespective of the details of interpretation, however, it is clear that the nanospheres are affecting the crystallization of the hard segment when above ø 20 wt% loading levels in the 70 wt%-SSC, while no such interference was observed for the 50 wt%SSC.

Fig. 8. Wide angle X-ray diffractograms of polyurethanes with with 50 wt%-SCC and different concentrations of nano-silica. Reheating the sample without filler improves crystallinity.

Ultra small angle X-ray scattering was used to assess the effect of the filler particles on the morphology of the matrix and to determine the degree of aggregation of the filler particles. Three samples were studied, all with 50 wt%-SCC and silica loadings of 0, 10 and 20 wt%. The data were measured on samples of known thickness and density to give the scattering cross section, dS; per unit sample volume, V; per unit solid angle, dV;

IðqÞ ;

dS VdV

ð1Þ

The data are shown in Fig. 10, where IðqÞ is plotted versus

Fig. 10. USAXS profile for filled and unfilled polyurethanes with 50 wt%SCC. Solid lines are unified fits the data.

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the scattering vector, q; which is related to the scattering angle, u; as q ¼ ð4p=lÞsinðu=2Þ: l is the incident wavelength. The profiles for the unfilled and filled samples are quite different in the region q . 0:01 A21 : For q , 0:001 A21 ; however, the profiles are similar, showing power-law dependence with a power law exponent of about 2 4.0. The limiting slope of 2 4.0 is consistent with Porod’s law for scattering from an interface that is smooth on a lengthscale of 1=q: This scattering could to be due to asperities on the sample surface, rather than the spherulitic features seen by AFM, since the stringy structures would not be expected to follow Porod’s law. This issue needs to be investigated with an instrument capable of reaching smaller q-values. At any rate, the scattering in small-q region is indicative of morphological features in excess of 6 mm in radius.  21 ; scattering arises from In the region around q ¼ 0:01 A ˚ . Consider first morphological features of the order of 100 A of all the unfilled sample where a broad maximum is  21 indicative of a Bragg spacing observed at qmax ¼ 0:035 A 21   of 2p=0:035 A ¼ 180 A: This feature is attributed to segmental phase separation, but the data are not rich enough to distinguish detailed morphology such as the difference between lamellar and globular domains. At this point, we cannot say whether the phase-separated domains exist within one or both of the large-scale domains observed by AFM. Very likely this short-scale domain structure observed in USAXS exists within both of the large-scale domains observed by AFM. To further quantify the short-scale domain morphology of the unfilled sample, the USAX data were fit to a simple damped spherical-domain model [14]. If I1 ðq; RG Þ is the scattered intensity for uncorrelated domains of radius RG ; then the intensity for the correlated model is IðqÞ ¼

I1 ðq; RG Þ 1 þ 8wuðq; jÞ

u¼

3ðsin 2qj 2 2 cos 2qjÞ ð2Þ ð2qjÞ3

where 2j is the mean correlation distance between domains and (w is the volume fraction of the minority phase. I1 ðq; RG Þ is assumed to follow a simple Guinier form [14]. 2q2 R2G I1 ðq; RG Þ ¼ G exp 3

! ð3Þ

For q ! 1=RG ; I1 ðq; RG Þ follows Guinier’s law, so the curvature at small q provides a measure of the size of the domains. Guinier radius, RG ; is the radius-of-gyration of the domains, which for spherical domains of radius, R; is RG ¼ ð3=5Þ0:5 R: The pre-factor, G; is a measure of the degree of phase separation. Although a detailed model is required to interpret this parameter, for spherical domains, G can be estimated as G ¼ wvðSLD1 2 SLD2 Þ2

ð4Þ

where w is the volume fraction of the minority phase, v is the

domain volume ½v ø ð3=4ÞpR3  and SLD1 and SLD2 are the scattering-length densities of the two phases. The result of fitting the data for the unfilled samples in the region of the maximum is shown in Table 1 and the curve is plotted as a solid line in Fig. 10. The fitting  G ¼ 16 cm21 ; j ¼ 153 A  and parameters are RG ¼ 31 A; f ¼ 0:14: Although, this analysis is approximate at best, it does show that the relevant length-scales are substantially larger than the segment length and w is substantially less than the domain volume fraction calculated from the composition ðw ¼ 0:43Þ: In addition, G can be compared to that expected for a fully phase separated system. Plugging w ¼ 0:43; SLD hard ¼ 11.6 £ 1011 cm 22 and SLD soft ¼ 9.3 £ 1011 cm 22 into Eq. (4) gives G ¼ 61 cm21, which is to be compared to the measured value of 16 cm21. The diminished G shows that the segments are not fully segregated. These observations all imply substantial intermixing hard and soft segments in the short-scale domains. The addition of the silica filler particles leads to substantial modification of the scattering profile as seen in Fig. 10. The resulting profile shows no hint of the domain structure seen in the unfilled samples even though the scattered intensity is comparable to the unfilled case for q . qmax : The absence of the correlation peak implies that segment domain structure is disrupted by the silica particles. The scattering for q . 0:008 is consistent with scattering ˚ in from unaggregated silica particles of the order of 100 A diameter in a matrix of uniform SLD. To quantify the nature of these particles, the data were fit to a simple Guinier-pluspowerlaw profile [15] using code developed by Beaucage [16] and implemented by UNICAT: " #4 ! 2q2 R2G ðerfðqRG ÞÞ3 I1 ðq; RG Þ ¼ G exp þB þFB; ð5Þ 3 q where erf is the error function and FB is an uninteresting flat background. The results of the fitting are captured in Table 1, where, in addition to the parameters discussed above, the Porod constant, B; is included. The functional form of Eq. (5) follows Guinier’s law at small q and Porod’s law at large ˚ are found q: The measured hard radii of R ¼ 87 and 101 A to be substantially larger than that expected for nominal ˚ diameter particles. The difference is due to the fact 120 A that the R ¼ ð5=3Þ0:5 £ RG is weighted by the square of the particle volume, so large-radius particles dominate the average when the distribution of particle sizes is polydisperse. Insight into the particle size distribution comes from Porod analysis. The Porod constant, B; is proportional to the surface area per unit volume, Sv : That is, B ¼ 2pðSLD2 2 SLD1 Þ2 Sv

ð6Þ

The contrast in this case is between the matrix (SLD 1 ¼ 1.01 £ 1011 cm22) and the silica particles (SLD2 ¼ 1.69 £ 1011 cm22). The SLDs are calculated

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Table 1 Parameters from a unified fit to the filled and unfilled samples Loading (wt%)

SCC wt%

r (g/cm3)

r1 (g/cm3)

G (cm21)

˚) R (A

˚ 24) B (cm21 A

P

0 10 20

50 50 50

1.13 1.19 1.24

1.13 1.13

16 291 328

40 101 87

6.10 £ 1025 7.51 £ 1025

4 4

˚) j (A

f

153

0.14

f is the volume fraction of the minority phase, r is the sample density, r1 is the matrix density (unfilled PU), G is the Gunier pre-factor, B is the Porod constant, R is the effective domain hard radius, and j is the correlation range.

assuming a skeletal density of 2.0 g/cm3 for silica and 1.13 g/cm3 for the matrix whose chemical formula is assumed to be C36.4O9.8H36.8N2. Table 2 shows the results of the calculation of S and S0 where S is the surface area per unit sample mass and S0 is the surface area per unit mass of silica. The two differ by the silica volume fraction, f; which is calculated from the densities as f ¼ ðr 2 r1 Þ=ðr2 2 r1 Þ; where r is the sample density, r1 is the matrix density and r2 is the silica density. In a generic sense [17], the surface area can be related to the mean chord, d2 ; of the filler (particle) phase as d2 ¼

4f Sv

ð7Þ

where f is the volume fraction filler and Sv ¼ rS is the surface area per unit sample volume. The mean chord of a spherical particle of radius R is 4R=3 from pure geometry, so R¼

3f Sv

ð8Þ

This value is also tabulated along with the matrix chord, d1 ; which is also calculated from Sv and the volume fraction filler: 4ð12fÞ d1 ¼

ð9Þ

Sv

This calculation gives an average hard radius for the two ˚ , somewhat less than that expected based on samples of 47 A the nominal size of the particles. Here, the discrepancy is attributed to the fact that the surface area is related to the first reciprocal moment of the size distribution, which is dominated by the small particles. In addition, errors are introduced through the assumed density of the silica particles. Since the data are on an absolute scale, it is possible to Table 2 Porod analysis assuming a silica skeletal density of 2.0 g/cm3 Loading (wt%)

r2 (g/cm3)

S (m2/g)

S0 (m2/g)

d2 ˚) (A

d1 ˚) (A

R ˚) (A

f

10 20

2.0 2.0

38 69.5

358 284

87 102

1001 505

42 52.7

0.126 0.065

f is the volume fraction silica. S is the surface area per gram sample, S0 is the surface area per gram silica. d1 and d2 are the matrix and particle chords. r2 is the assumed silica skeletal density. R is the particle hard radius.

use the Porod invariant, Qp ; to calculate the contrast, lSDL2 2 SLD1l: ð1 dqq2 IðqÞ ð10aÞ Qp ; 0

Qp ¼ 2p2 ðSLD2 2 SLD1 Þ2 fð1 2 fÞ:

ð10bÞ

So, Sv ¼ pfð1 2 fÞB=Qp :

ð11Þ

In this method, the densities of the phases need not be known. Since the sample and matrix density are known, the skeletal density, r2 ; of the silica particles can be calculated. The details of how r2 ; and surface area are extracted selfconsistently from the measured QP and B are given by Schaefer et al. [18,19]. To summarize, self-consistency is impressed on Eqs. (6) and (11). First, QP is determined by integrating the measured SAXS data [Eq. (10(a))] in the qregion where the particles scatter. Assuming some value for r2 (say 2 g/cm3), one then calculates w from r2 ; the measured matrix density ðr1 Þ and the measured sample density ðrÞ: The matrix density is taken to be that of the corresponding unfilled PU. One then calculates an interim contrast, lSLD2 2 SLD1l, using Eq. (10(b)). A new approximation to SLD2 (and therefore r2 ; since the composition of silica is known) is then obtained from this interim contrast and the SLD1 calculated from the known density and composition of the matrix. The cycle is repeated until convergence is obtained on values of SLD2 and f: Typically about 5– 50 iterations are needed to achieve convergence. The surface area per unit volume, Sv ; follows from either Eq. (6) or (11) using the measured value of B: The outcome of this exercise is tabulated in Table 3. The resulting r2 ¼ 1:6 g=cm3 ; substantially smaller than that assumed for Table 2. The resulting particle radius, however, ˚ ), but is only 10 wt% larger than Table 2, (average ¼ 53 A still less than the nominal radius. The distribution of particle sizes can be extracted from Table 3 Porod analysis using the Porod invariant to calculate the skeletal density, r2 ; of silica Loading (wt%)

S (m2/g)

S0 (m2/g)

d2 ˚) (A

d1 ˚) (A

R ˚) (A

r2 (g/cm3)

f

10 20

70.5 95.1

409 313

59.7 81.4

508 258

44.8 60.8

1.64 1.58

0.11 0.24

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the scattering data if a form is assumed for the distribution functions. We used standard least-squares fitting procedures and assumed a Gaussian distribution of the particle volumes. The scattering cross section is modeled as ð1 IðqÞ ¼ ðSLD2 2 SLD1 Þ2 N lFðq; rÞl2 v2 ðrÞ PðrÞdr ð12Þ

Table 4 Results of least squares analysis of the USAX profile assuming a Gaussian distribution of particle volumes

where Fðq; rÞ is the form factor of a sphere of radius r; N is the total number of particles, v is the particle volume, and PðrÞ is the probability of observing a particle of size r: The fitting code is implemented as part of the Irena software provided by UNICAT [20]. A Gaussian form of width s is assumed for the volume distribution function $ %  1=2 1 ð2r 2 2r0 Þ2 vðrÞPðrÞ ¼ ð13Þ exp 2 s2 2ps2

The quotient 3=Sv 0 is the particle hard radius assuming spherical particles. Sv 0 is the surface to volume ratio of the silica particles. Sv 0 is calculated from the particle size distribution in Fig. 11.

The resulting distribution, using the skeletal densities from Table 3, is shown in Fig. 11 for the 20 wt% silica sample. Comparison of the two data sets indicates a number-average ˚ for both, quite close to the mean radius of about 65 A nominal size of the silica used. The distribution is 25% broader, however, for the 20 wt% sample, which indicates a small degree of aggregation at higher loading. (Table 4). Overall, the USAXS data confirm the presence of phaseseparated domains in the unfilled samples. The presence of even 10 wt% silica, however, disrupts the short-scale segment domains. The silica is highly dispersed at both ˚ . A Gaussian loadings with a mean radius of 65 A distribution of particle sizes with a full-width-at-half-height comparable to the mean fits the data. The broad distribution

4. Conclusion

0

Loading (wt%)

r (g/cm3)

˚ sA

˚) r0 (A

S0 (m2/g)

˚) 3=Sv 0 (A

f

10 20

1.6 1.6

33.9 25.7

65.5 66.0

442 358

41 53

0.11 0.21

of particle sizes accounts for the fact that the mean radius calculated from Guinier analysis is considerably larger than that calculated from Porod analysis.

It has been shown that addition of nanoparticles radically alters the morphology of the hard phase both at 50 and 70 wt% SSC by suppressing the formation of fibrils within spherulites and decreasing hard domain size. A single melting peak in DSC suggests that either the distribution of crystallite sizes is narrower or that a single type of crystalline structure is formed at higher filler loadings. There was no clear effect of the filler on the glass transition of soft segments. Wide-angle X-ray diffraction showed decreasing crystallinity of the hard domains with increasing filler concentration in samples with 70 wt%-SSC. USAXS provides a link between the presence of the silica and the alteration of the large-scale fibrillar morphology. Even a small amount of silica disrupts the shortscale phase-separated morphology attributed to segment phase separation in unfilled PU. Apparently, the large-scale morphology results from the short-scale domain growth in the same way that lamellar crystals result from short-scale segregation of crystalline and amorphous regions in semicrystalline polymers. When the short-scale domain structure is disrupted, fibrillar growth is impeded.

Acknowledgements

Fig. 11. Particle volume distribution obtained by fitting the USAX data to a Gaussian distribution of particle volumes. Parameters are collected in Table 4.

The UNICAT facility at the Advanced Photon Source (APS) is supported by the US DOE under Award No. DEFG02-91ER45439, through the Frederick Seitz Materials Research Laboratory at the University of Illinois at Urbana-Champaign, the Oak Ridge National Laboratory (US DOE contract DE-AC05-00OR22725 with UT-Battelle LLC), the National Institute of Standards and Technology (US Department of Commerce) and UOP LLC. The APS is supported by the US DOE, Basic Energy Sciences, Office of Science under contract No. W-31-109-ENG-38.

ARTICLE IN PRESS Z.S. Petrovic´ et al. / Polymer xx (0000) xxx–xxx

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