# Effect of Cobalt Fillers on Polyurethane Segmentations Investigated by Synchrotron Small Angle X-Ray Scattering

Authors: Krit Koyvanich; Chitnarong Sirisathitkul; Supagorn Rugmai
Journal: Advances in Materials Science and Engineering
 (2013)

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## Abstract

The segmentation between rigid and rubbery chains in polyurethanes (PUs) influences polymeric properties and implementations. Several models have successfully been proposed to visualize the configuration between the hard segment (HS) and soft segment (SS). For particulate PU composites, the arrangement of HS and SS is more complicated because the fillers tend to disrupt the chain formation and segmentation.  In this work, the effect of ferromagnetic cobalt (Co) powders (average diameter 2μm) on PU synthesized from a reaction between polyether polyol (soft segment) and diphenylmethane-4,4′-diisocyanate (hard segment) was studied with varying loadings (0, 20, 40, and 60 wt.%). The 300 μm thick PU/Co samples were tape-casted and then received heat treatment at 80°C for 180 min. From synchrotron small angle X-ray scattering (SAXS), the plot of the X-ray scattering intensity (I) against the scattering vector (q) exhibited a typical single peak of PU whose intensity was reduced by the increase in the Co loading. Characteristic SAXS peaks in the case of 0-20 wt.% Co agreed well with the scattering by globular hard segment domains according to Zernike-Prins and Percus-Yevick models. The higher Co loadings led to larger deviations from all theoretical models.


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## Body

## 1. Introduction

The versatility of segmented polyurethane (PU) is based on the combination of a rubbery soft segment (SS) and a semicrystalline hard segment (HS). Their properties are varied with the ratio of hard/soft segments and their segmentation. In addition to their conventional uses in forms of PU thermoplastics and foams, the incorporation of particulate fillers to obtain PU composites enhances the applications as smart materials. The magnetic fillers in polymeric matrix give rise to magnetic hysteresis, magnetoviscoelasticity, magnetorheology, and magnetoelectricity [1]. Cobalt (Co) is a soft ferromagnetic material with high magnetocrystalline anisotropy and saturation magnetization. It follows that Co is often found in functional magnetic compounds and composites. In our previous work [2], the incorporation of 20%–60 wt.% Co powders in PU gave rise to magnetic permeability useful for magnetic devices and components. Moreover, the change in the dielectric properties of PU by the inclusion of Co can be utilized in antistatic propose. However, the configuration of HS and SS in PU/Co composites which dictates the mechanical and chemical properties was not investigated. Only differential thermal calorimetry (DSC) spectra imply that PU chains were disrupted.Small-angle X-ray scattering (SAXS) is a nondestructive technique in morphological investigation of nanostructures [3]. The morphology changes can also be monitored in real time by the dynamic analysis without a need for special sample preparation process. The measured data are commonly presented as the plot between the intensity of scattered X-ray (I) and the scattering vector (q) which is given by [3]
(1)q=4πsinθλ,
where λ is the wavelength of the X-ray and θ is half the scattering angle with respect to the direction of the incident X-ray. These SAXS profiles are related to the contrast in the electron density (Δρ) of different microphases.In the case of PU and PU composites, SAXS profiles can be employed to complement DSC in the investigation of segmentation [4–10]. The arrangement of HS and SS can be deduced by fitting the characteristic SAXS peak with the equations from theoretical models [4]. With this knowledge, this work employed the synchrotron SAXS to study the effect of Co fillers of up to 60 wt.% on the segmentation between HS and SS of PU. The configuration can be concluded from the agreement between the experimental SAXS profiles and the theoretical model.


## 2. Models

The segmentation in PU can occur according to a variety of models, for example, lamellar model, Zernike-Prins model, Percus-Yevick model, and Teubner-Strey model [4]. The nanostructural arrangement can be concluded from the agreement between experimental results and the appropriate scattering model.


### 2.1. Lamellar Model

For the lamellar model illustrated in Figure1(a), HS and SS are separated as parallel layers called lamellae. If the edge effect is neglected, the scattering intensity perpendicular to a stack containing a considerable number of infinite lamellae, Iinf(q), can be given by
(2)Iinf(q)=(Δρ)2q2×Re[{1-exp(-q2σH2)exp(-iqdH)}×{1-exp(-q2σS2)exp(-iqdS)}×(1-exp(-q2(σH+σS)2)exp(-iq(dH+dS)))-1]=(Δρ)2q2Re[{1-ϕHexp(-iψ)}{1-ϕSexp(-iχ)}1-ϕHϕSexp(-i(ψ+χ))],
where the subscripts H and S denote the parameters associated with HS and SS, respectively. ϕ, d, and σ are the volume fraction, thickness, and standard deviation of each segment. Assuming that the lamellar thickness follows the Gaussian distribution with ψ=qdH, the term 1-exp(-q2σH/2)exp(-iqdH)=ϕHexp(-iψ) is a Fourier transform of the lamellar thickness distribution for HS. Likewise, the expression for SS can be derived using χ=qdS. Equation (2) can be reduced to
(3)Iinf(q)=2(Δρ)2q2×{1-ϕH2ϕS2-ϕH(1-ϕS2)cosψ-ϕS(1-ϕH2)cosχ1+ϕH2ϕS2-2ϕHϕScos(ψ+χ)}.
In the case of isotropic assembly of lamellar stacks, the scattering intensity becomes
(4)I(q)=Iinf(q)4πq2=I0q4×{1-ϕH2ϕS2-ϕH(1-ϕS2)cosψ-ϕS(1-ϕH2)cosχ1+ϕH2ϕS2-2ϕHϕScos(ψ+χ)},
where I0 is a scaling factor which depends on several parameters in the measurement including the scattering contrast, surface area per unit volume, and intensity of incident X-ray.The schematic diagram of PU segmentations according to (a) lamellar, (b) Zernike-Prins, (c) Percus-Yevick, and (d) Teubner-Strey models.
(a)
(b)
(c)
(d)


### 2.2. Zernike-Prins Model

Originally proposed for a liquid, the Zernike-Prins model has been applied to segmented copolymers. To explain the scattering from dense disorder systems, the crystal imperfection and separated minor phase are treated like the scattering bodies in arbitrary direction for one-dimensional random statistical lattice as illustrated by Figure1(b). The observed scattering intensity from globular domains of HS on a distorted lattice in SS matrix is composed of the form factor, P(q), and the structure factor, S(q)(5)I(q)=I0P(q)S(q).
By omitting the interference effect, the term P(q) representing the scattering from spherical bodies with radius, R, and volume, V, can be written as
(6)P(q)=9(Δρ)2V2{sin(qR)-qRcos(qR)(qR)3}2.
On the other hand, S(q) corresponds to the interference by the scattering from neighboring bodies aligning in one dimension which is given by
(7)S(q)=1-ϕH21-2ϕH2cos(qd)+ϕH2,
where d is the mean distance between the center of randomly distributed neighboring bodies. The parameter ϕ=exp(-q2σ/2) is the volume fraction of each segment. By substituting (6) and (7) into (5), the scattering model can be expressed as
(8)I(q)=I09(Δρ)2V2{sin(qR)-qRcos(qR)(qR)3}2×{1-ϕH21-2ϕH2cos(qd)+ϕH2}.


### 2.3. Percus-Yevick Model

The scattering equation from globular domains in a liquid-like dispersion is based on statistical-mechanical treatments by Percus and Yevick. In Figure1(c), the structure factor of matrix containing spheres of radius, R, with the thickness of the boundary layer th is
(9)S(q)=[1+24ϕx6×{αx3(sinx-xcosx)+βx2(2xsinx-(x2-2)cosx-2)+γ((4x3-24x)sinx-(x4-12x2+24)cosx+24)}24ϕx6]-1.
The parameter x=2qRH where RH=R+th. Three other parameters (α,β,γ) in (9) are defined in terms of the volume fraction occupied by the spheres, ϕ:
(10)α=(1+2ϕ)2(1-ϕ)4,β=-6ϕ(1+0.5ϕ)2(1-ϕ)4,γ=(ϕ2)(1+2ϕ)2(1-ϕ)4=ϕ2α.
By substituting the form factor from (6) and the structure factor from (9), the scattering intensity in (5) becomes
(11)I(q)=I09(Δρ)2V2×{sin(qR)-qRcos(qR)(qR)3}2×[1+24ϕx6×{αx3(sinx-xcosx)+βx2(2xsinx-(x2-2)cosx-2)+γ((4x3-24x)sinx-(x4-12x2+24)cosx+24)}24ϕx6]-1.


### 2.4. Teubner-Strey Model

The Teubner-Strey model illustrated in Figure1(d) is commonly used for explaining the scattering from microemulsion systems. This random two-phase model assumes the spatial dependence of a pair correlation function, γ(r), of the form
(12)γ(r)=d2πrexp(-rξ)sin(2πrd).
The sine term indicates the periodicity in the correlation function with the domain sizecharacterized by d. The exponential term expresses the loss of long range order with the correlation length, ξ. The scattering intensity is written as
(13)I(q)=8πϕ(1-ϕ)(Δρ)2×{(ξ-2+4π2d2)2+2q2(ξ-2-4π2d2)+q4}-1.


## 2.1. Lamellar Model

For the lamellar model illustrated in Figure1(a), HS and SS are separated as parallel layers called lamellae. If the edge effect is neglected, the scattering intensity perpendicular to a stack containing a considerable number of infinite lamellae, Iinf(q), can be given by
(2)Iinf(q)=(Δρ)2q2×Re[{1-exp(-q2σH2)exp(-iqdH)}×{1-exp(-q2σS2)exp(-iqdS)}×(1-exp(-q2(σH+σS)2)exp(-iq(dH+dS)))-1]=(Δρ)2q2Re[{1-ϕHexp(-iψ)}{1-ϕSexp(-iχ)}1-ϕHϕSexp(-i(ψ+χ))],
where the subscripts H and S denote the parameters associated with HS and SS, respectively. ϕ, d, and σ are the volume fraction, thickness, and standard deviation of each segment. Assuming that the lamellar thickness follows the Gaussian distribution with ψ=qdH, the term 1-exp(-q2σH/2)exp(-iqdH)=ϕHexp(-iψ) is a Fourier transform of the lamellar thickness distribution for HS. Likewise, the expression for SS can be derived using χ=qdS. Equation (2) can be reduced to
(3)Iinf(q)=2(Δρ)2q2×{1-ϕH2ϕS2-ϕH(1-ϕS2)cosψ-ϕS(1-ϕH2)cosχ1+ϕH2ϕS2-2ϕHϕScos(ψ+χ)}.
In the case of isotropic assembly of lamellar stacks, the scattering intensity becomes
(4)I(q)=Iinf(q)4πq2=I0q4×{1-ϕH2ϕS2-ϕH(1-ϕS2)cosψ-ϕS(1-ϕH2)cosχ1+ϕH2ϕS2-2ϕHϕScos(ψ+χ)},
where I0 is a scaling factor which depends on several parameters in the measurement including the scattering contrast, surface area per unit volume, and intensity of incident X-ray.The schematic diagram of PU segmentations according to (a) lamellar, (b) Zernike-Prins, (c) Percus-Yevick, and (d) Teubner-Strey models.
(a)
(b)
(c)
(d)


## 2.2. Zernike-Prins Model

Originally proposed for a liquid, the Zernike-Prins model has been applied to segmented copolymers. To explain the scattering from dense disorder systems, the crystal imperfection and separated minor phase are treated like the scattering bodies in arbitrary direction for one-dimensional random statistical lattice as illustrated by Figure1(b). The observed scattering intensity from globular domains of HS on a distorted lattice in SS matrix is composed of the form factor, P(q), and the structure factor, S(q)(5)I(q)=I0P(q)S(q).
By omitting the interference effect, the term P(q) representing the scattering from spherical bodies with radius, R, and volume, V, can be written as
(6)P(q)=9(Δρ)2V2{sin(qR)-qRcos(qR)(qR)3}2.
On the other hand, S(q) corresponds to the interference by the scattering from neighboring bodies aligning in one dimension which is given by
(7)S(q)=1-ϕH21-2ϕH2cos(qd)+ϕH2,
where d is the mean distance between the center of randomly distributed neighboring bodies. The parameter ϕ=exp(-q2σ/2) is the volume fraction of each segment. By substituting (6) and (7) into (5), the scattering model can be expressed as
(8)I(q)=I09(Δρ)2V2{sin(qR)-qRcos(qR)(qR)3}2×{1-ϕH21-2ϕH2cos(qd)+ϕH2}.


## 2.3. Percus-Yevick Model

The scattering equation from globular domains in a liquid-like dispersion is based on statistical-mechanical treatments by Percus and Yevick. In Figure1(c), the structure factor of matrix containing spheres of radius, R, with the thickness of the boundary layer th is
(9)S(q)=[1+24ϕx6×{αx3(sinx-xcosx)+βx2(2xsinx-(x2-2)cosx-2)+γ((4x3-24x)sinx-(x4-12x2+24)cosx+24)}24ϕx6]-1.
The parameter x=2qRH where RH=R+th. Three other parameters (α,β,γ) in (9) are defined in terms of the volume fraction occupied by the spheres, ϕ:
(10)α=(1+2ϕ)2(1-ϕ)4,β=-6ϕ(1+0.5ϕ)2(1-ϕ)4,γ=(ϕ2)(1+2ϕ)2(1-ϕ)4=ϕ2α.
By substituting the form factor from (6) and the structure factor from (9), the scattering intensity in (5) becomes
(11)I(q)=I09(Δρ)2V2×{sin(qR)-qRcos(qR)(qR)3}2×[1+24ϕx6×{αx3(sinx-xcosx)+βx2(2xsinx-(x2-2)cosx-2)+γ((4x3-24x)sinx-(x4-12x2+24)cosx+24)}24ϕx6]-1.


## 2.4. Teubner-Strey Model

The Teubner-Strey model illustrated in Figure1(d) is commonly used for explaining the scattering from microemulsion systems. This random two-phase model assumes the spatial dependence of a pair correlation function, γ(r), of the form
(12)γ(r)=d2πrexp(-rξ)sin(2πrd).
The sine term indicates the periodicity in the correlation function with the domain sizecharacterized by d. The exponential term expresses the loss of long range order with the correlation length, ξ. The scattering intensity is written as
(13)I(q)=8πϕ(1-ϕ)(Δρ)2×{(ξ-2+4π2d2)2+2q2(ξ-2-4π2d2)+q4}-1.


## 3. Experimental

PU composites incorporating 0, 20, 40, and 60 wt.% Co powders (99.98%,ϕ≈2 μm) are, respectively, referred to as PU, PU20, PU40, and PU60. Polyether polyol (SS) and diphenylmethane-4,4′-diisocyanate (HS) were used as starting materials in the conventional prepolymer method. Firstly, polyol (20 g) was mixed with Co dispersed in silicone oil, and the mixture was heated to 75°C. Under constant stirring without creating air bubble, diisocyanate (2.1 g) was then added. After the homogeneous mixture became viscous by the addition of the catalyst, PU/Co composites were tape-casted to obtain approximately 300 μm thick samples. They were dried and received thermal treatment at 80°C for 180 min.The characterizations of PU/Co composites by microscopy, DSC, vibrating sample magnetometry, complex permittivity, and permeability spectroscopy were presented elsewhere [2]. The SAXS experiment was carried out at BL 2.2, Siam Photon Laboratory, Synchrotron Light Research Institute, Nakhon Ratchasima, Thailand [11]. The X-ray energy used was 8 keV. A CCD (Mar SX165) was used to record the 2D SAXS patterns. The sample-detector distance was calibrated using scattering of silver behenate powder. The patterns were then circularly averaged to obtain 1D SAXS profiles. The peak of SAXS profiles was curve-fitted according to the lamellar (see (4)), Zernike-Prins (see (8)), Percus-Yevick (see (12)), and Teubner-Strey (see (16)) models using the least square method in MatLab.


## 4. Results and Discussion

The SAXS profiles of PU and PU/Co composites shown in Figure2 exhibit the single peak around q = 0.8–0.9 nm−1. Such peak is commonly observed in PU. The intensity of the peak is decreased with the increase in the Co loading. This implies that HS and SS are increasingly mixed with the reduction in clear scattering boundaries [6, 7]. In addition to the reduction in intensity, the peak position corresponding to HS distance calculated by using Bragg’s law is slightly shifted by the inclusion of Co fillers. It can be inferred that the length of the HS has been reduced by the inclusion of Co. The densely packed Co aggregates may also shield some X-ray but should not affect the scattering because their sizes are much larger than the characteristic size measurable by the measurement setup.Figure 2
SAXS profiles of PU composites loaded with 0–60 wt.% Co showing the normalized scattering intensity as a function of the scattering vector.The curve fitting with four different models is shown in Figures3, 4, 5, and 6, and the obtained parameters are listed in Table 1. The best fit of the unfilled PU peak is obtained in the case of Zernike-Prins model. The Percus-Yevick model also agrees well with experimental SAXS profiles in a narrower q range around the peak. These results indicate that the PU segmentation resembles the configurations of globular domains of HS in Figures 4 and 5. However, the values of R obtained from these two models are greatly different. Instead, the d from the Zernike-Prins model is comparable to the length scale in the lamellar and Teubner-Strey models.Table 1
Parameters obtained from the fitting of SAXS peaks of PU composites with four theoretical models.
Co loading (wt.%)
Lamellar
Zernike-Prins
Percus-Yavick
Teubner-Strey
d
H (nm)
R(nm)
d(nm)
R (nm)
th (nm)
ξ (nm)
d (nm)
0
7.156 ± 0.022
2.029 ± 0.007
7.365 ± 0.006
3.100 ± 0.0120
0.620 ± 0.0136
5.8074 ± 0.0664
7.475 ± 0.019
20
6.479 ± 0.014
3.175 ± 0.009
7.278 ± 0.013
3.047 ± 0.0290
0.675 ± 0.0186
3.8435 ± 0.1750
7.700 ± 0.035
40
6.193 ± 0.014
2.962 ± 0.008
6.654 ± 0.017
2.925 ± 0.0450
0.25 ± 0.0530
2.0970 ± 6.87e − 19
7.550 ± 0.026
60
6.166 ± 0.028
3.582 ± 0.007
6.893 ± 0.012
2.970 ± 0.0640
0.450 ± 0.0324
2.2108 ± 0.128
7.774 ± 0.037Curve fitting according to the lamellar model for PU composites loaded with (a) 0, (b) 20, (c) 40, and (d) 60 wt.% Co.
(a)
(b)
(c)
(d)Curve fitting according to the Zernike-Prins model for PU composites loaded with (a) 0, (b) 20, (c) 40 and (d) 60 wt.% Co.
(a)
(b)
(c)
(d)Curve fitting according to the Percus-Yavick model for PU composites loaded with (a) 0, (b) 20, (c) 40, and (d) 60 wt.% Co.
(a)
(b)
(c)
(d)Curve fitting according to the Teubner-Strey model for PU composites loaded with (a) 0, (b) 20, (c) 40, and (d) 60 wt.% Co.
(a)
(b)
(c)
(d)The effect of Co fillers on PU segmentations is evident from the comparison of SAXS profiles. The profile in the case of 20 wt.% Co is still consistent with the Zernike-Prins model but the shape of the peak is better described by the Percus-Yevick model. The higher loadings of 40–60 wt.% Co lead to larger discrepancy between experimental results and theoretical models. It is inferred that each segment is increasingly disrupted and both segments become mixture. Only the Percus-Yevick model still fits well with the SAXS profiles around the peak. From this model, theR in PU/Co composites is slightly less than that of unfilled PU, and the minimum R with the thinnest shell occurs in the case of 40 wt.% Co. Interestingly, the lengthscale is monotonically decreased with the increase in Co loading when the lamellar model is applied. The fluctuation in the R from both Zernike-Prins and Percus-Yevick models with the loading is likely to originate from the large size distribution of the scattering bodies.


## 5. Conclusions

The peaks of SAXS profiles analyzed by fitting with the theoretical models led to the conclusion about arrangements of HS and SS in PU filled with 0–60 wt.% Co. The experimental result in unfilled PU had a better agreement with the scattering models from globular HS domains (i.e., Zernike-Prins and Percus-Yevick models) than the lamellar and Teubner-Strey models. The introduction of 20 wt.% Co fillers into PU gave rise to the configuration best described by globular HS domains in a liquid-like dispersion according to Percus and Yevick. The high loading levels of 40–60 wt.% severely affected the segmentation of PU. The SS was increasingly mixed with the HS in these highly loaded PU composites, and only Percus-Yevick model can adequately fit the experimental results. The peak position corresponding to the length of hard segment was slightly shifted by the increase in Co fillers.



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*Source: 493867-2013-01-29.xml*