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Structure Factors of Dispersible Units of Carbon Black Filler in Rubbers Tadanori Koga,*,†,§ Mikihito Takenaka,†,‡ Kazuya Aizawa,⊥ Masao Nakamura,†,∇ and Takeji Hashimoto*,†,‡ Hashimoto Polymer Phasing Project, ERATO, JST, Japan, Department of Polymer Chemistry, Graduate School of Engineering, Kyoto University, Katsura, Nishikyo-ku, Kyoto 661-8510, Japan, Department of Materials Science & Engineering, Stony Brook University, Stony Brook, New York 11794-2275, Neutron Science Research Center, Japan Atomic Energy Research Institute, Tokai, Ibaraki-ken 319-1195, Japan, and ZEON Corporation 1-2-1, Yako, Kawasaki, Kanagawa, 210-8507, Japan Received May 20, 2005. In Final Form: September 15, 2005 We report the structures of dispersible units, a most fundamental but minimal dispersible structural unit of a carbon black (CB) filler that is formed in two kinds of rubber (polyisoprene and styrene-butadiene random copolymer) matrices under a given processing condition. The results obtained from various smallangle scattering techniques showed that the CB aggregates, as observed after the sonification of a CB/ toluene solution, were a spherical shape composed of approximately nine primary CB particles fused together. In the rubber matrices, the aggregates clustered into higher order structures defined in this work as the dispersible units, which are the fundamental structural elements (or the “lower cutoff structures”) that build up a higher order mass-fractal structure. Furthermore, we found that the morphology of the dispersible units strongly depended on the rubber matrix, although the mass-fractal dimensions remained unchanged.
Introduction Reinforcing fillers, especially carbon black (CB) and silica (Si), are widely being used to improve the mechanical and barrier properties of rubber compounds. An important aspect of rubber reinforcement by active fillers is the dispersion of filler particles in rubber matrices during mixing procedures. It is well known that primary CB particles are mutually fused to form large particles called “aggregates”, which are not broken down further under conventional mechanical or sonic destruction. The aggregates further cluster into higher order structures called “agglomerates” when they are dispersed in rubber matrices. The agglomerates are weakly bonded structures comprised of the aggregates,1,2 and their size and shape depend on the mixing conditions and the matrix of the rubbers. So far, transmission electron microscopy (TEM) studies have provided us with the most reliable and significant information about these structures. A good example is the structural analysis of the aggregates.3-7 However, when the size of the structures of interest exceeds the thickness of the ultrathin sections (typically 50-100 nm thick), TEM gives only two-dimensional cross sectional images of the structures of interest or, at best, threedimensional (3D) images of the structures existing in the ultrathin sections. Thus, a characterization of 3D struc* To whom correspondence should be addressed. E-mail: tkoga@ notes.cc.sunysb.edu (T.K.);
[email protected] (T.H.). † Hashimoto Polymer Phasing Project, ERATO, JST. ‡ Kyoto University. § Stony Brook University. ⊥ Japan Atomic Energy Research Institute. ∇ ZEON Corporation. (1) Schaefer, D. W.; Rieker, T.; Agamalian, M.; Lin, J. S.; Fischer, D.; Sukunaran, S.; Chen, C.; Beaucage, G.; Herd, C.; Ivie, J. J. Appl. Crystallogr. 2000, 33, 587. (2) Schaefer, D. W.; Suryawanshi, C.; Pakdel, P.; Ilabsky, J.; Jemian, P. R. Physica A 2002, 314, 686.
tures extending over a length scale larger than 100 nm would not be easily attained by TEM. Alternatively, small-angle scattering and ultra-smallangle scattering techniques have recently been utilized as powerful tools to investigate the hierarchical structures of fillers1,2,8-12 because they nondestructively probe statistically averaged structures over a length scale covering 1-104 nm under various sample environments. Recently, Schaefer et al. studied the morphology of Si particles subjected to sonic and mechanical destruction by using small-angle X-ray and light scattering techniques.1,2 They reported that (1) sonification did not significantly change the power-law scattering profile from the aggregates comprised of the fused primary particles, and (2) the size of the aggregates hardly changed upon being mixed with rubbers, whereas the agglomerates were destroyed under both of the destruction processes described above.2 However, the concentration of the Si powders in the water solution used must be low to conduct their light scattering experiments because of a turbidity-absorption problem, even though this was not mentioned explicitly in their reports. Furthermore, the morphology of the hierarchical structures of fillers that are highly loaded in rubbers is not fully clarified, albeit the manipulation of the mor(3) Medalia, A. I. J. Colloid Interface Sci. 1967, 24, 393. (4) Medalia, A. I.; Heckman, F. A. Carbon 1969, 7, 567. (5) Hess, W. M.; Ban, L. L.; McDonald, G. C. Rubber Chem. Technol. 1969, 42, 1209. (6) Hess, W. M.; McDonald, G. C.; Urban, E. M. Rubber Chem. Technol. 1972, 44, 204. (7) Herd, C. R.; McDonald, G. C.; Hess, W. M. Rubber Chem. Technol. 1992, 65, 107. (8) Suryawanshi, C. N.; Pakdel, P.; Schaefer, D. W. J. Appl. Crystallogr. 2003, 36, 573. (9) Rajan, G. S.; Sur, G. S.; Mark, J. E.; Schaefer, D. W.; Beaucage, G. J. Polym. Sci., Part B: Polym. Phys. 2003, 41, 1897. (10) Vu, B. T. N.; Mark, J. E.; Schaefer, D. W. Compos. Interfaces 2003, 10, 451. (11) Petrovic, Z. S.; Cho, Y. J.; Javni, I. Polymer 2004, 45, 4285. (12) Schaefer, D. W.; Agamalian, M. Curr. Opin. Solid State Mater. Sci. 2004, 8, 39.
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phology could be a key for controlling the macroscopic properties of rubber compounds. In this paper, we aim to quantitatively characterize the aggregates and agglomerates of CB particles loaded in rubbers by a typical amount employed for rubber compounds by using a combination of Bonse-Hart-type ultrasmall-angle neutron scattering (USANS) and BonseHart-type ultra-small-angle X-ray scattering (USAXS) as well as small-angle X-ray scattering (SAXS). A combined use of these scattering techniques permits us to study the hierarchical structures in length scales of 1 < q-1 < 3 × 103 nm, in which q is the magnitude of the scattering vector defined by q ) (4π/λ) sin(θ/2), with λ and θ being the wavelength of an incident beam and the scattering angle in the medium, respectively. We disperse CB powders in toluene under a sonic field or in rubbers under a mechanical field. The wide q-range of the scattering data allows us to separate the scattering from each structure level composed of the hierarchical structures. We find that the CB aggregates resulting from the sonification of the CB/toluene solution are spherical and are composed of approximately nine primary CB particles fused together and that the aggregates further cluster into a higher order structure in the rubbers, which is the agglomerate in the context of the common terminology. However, we shall hereafter refer to this agglomerate as a “dispersible unit” (or Agglomerate Level 1) because this agglomerate, rather than the aggregate itself, is the characteristic unit in the rubbers and further forms a higher order mass-fractal structure (Agglomerate Level 2). In this sense, the dispersible unit is identical to the lower cutoff object for the mass-fractal structure existing in our system. The CB hierarchical structures will be schematically shown later in Figure 3. We believe that the distinction between the two kinds of the agglomerates, Agglomerate Levels 1 and 2, is crucial for a better understanding of the hierarchical structures. Hereafter we refer to Agglomerate Level 2 as the “agglomerate” and to Agglomerate Level 1 as the “dispersible units” for simplicity, unless otherwise stated. Interestingly, the size and shape of the dispersible units strongly depend on the rubber matrix in a given mixing condition, as will be discussed below. We will be also discuss the fact that the mass-fractal dimensions of the agglomerates remain unchanged, even though the upper and lower cutoff lengths of the fractal structures depend on the matrix properties. Experimental Section CB particles (SHOBLOCK N339) obtained from Showa Cabot, Chiba, Japan were used in this study. The mean radius (RTEM) and specific surface area (SSA) of the CB primary particles were determined to be 13 nm and 88 m2/g by using TEM and a nitrogen adsorption method,13 respectively. The elastomers used in this study were polyisoprene (PI; Nipol IR-2200, ZEON Corporation, Tokyo, Japan) and styrene-butadiene random copolymer (SBR; Nipol 1502, ZEON Corporation; styrene content ) 23.5 wt %, (13) The corresponding average primary particle diameter (DB) is calculated under the assumption that the particles are spherical by DB ) 6/(FCB SSA), in which FCB is the density of the CB particles. With a FCB value of 1.85 g/cm3 and the SSA value of 88 m2/g, the DB value is 36.8 nm. As described in the text, by using TEM, we determined the size of the primary particles as DTEM ) 26 nm. The difference between DB and DTEM is possibly due to the turbostratic structures of the CB particles, resulting in an excess SSA. Consequently, it is reasonable to say that the DB value obtained corresponds to the average diameter of the CB primary particles in the powder. It seems that the N2 gas adsorption is controlled by the local structure (e.g., the surfaces and internal structures of the primary particles). Hence, the amount of adsorption is independent of the existence of aggregates or higher order structures such as the dispersible units defined in Figure 3.
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Figure 1. (a) Combined USANS, USAXS, and SAXS profiles for CB/PI having φCB ) 0.2. The dotted line corresponds to the calculated form factor for the primary CB particles having a spherical shape with RTEM ) 13 nm and σR ) 4 nm. The X-ray scattering data are on an absolute scale (e2/nm3), and the neutron data is shifted to make them match in the overlap q-regimes. (b) TEM image for CB/PI having φCB ) 0.2. vinyl content ) 15 wt %). The CB fillers were compounded into the rubbers by using a Banbury mixer heated to T ) 80 °C, and the mixtures were then molded at T ) 155 °C for typically 5 min. USANS measurements were performed with a PNO spectrometer at the beamline of a JRR-3M research reactor at JAERI, Tokai, Japan.14 SAXS profiles were taken with an apparatus that consisted of an 18-kW rotating-anode X-ray generator with a copper target (M18XHF-SRA, MAC Science Co., Ltd. Yokohama, Japan), a graphite monochromator, and a camera with a distance from the sample to the one-dimensional position-sensitive proportional counter (PSPC) of 2 m. The exposure time for each SAXS measurement was set to 30 min. USAXS profiles were taken with the same X-ray generator and target described above and a Bonse-Hart-type camera described in detail elsewhere.15 With the USAXS configuration,15 a q-range of 0.002-0.45 nm-1, which is partially overlapped by those of the USANS and SAXS configurations, was covered. Thus, a combined use of USAXS with USANS and SAXS overcomes the demerits caused by the high-intensity background in the large-q tail of the USANS rocking curve and the low-q resolution limit of the SAXS rocking curve. All of the samples were measured at room temperature under atmospheric pressure. The USAXS and SAXS profiles were corrected for air scattering, absorption, thermal diffuse scattering, and slit-width and slit-height smearing. The USANS profiles were corrected for background scattering and slit-height smearing. The X-ray scattering data were measured on an absolute scale (e2/nm3) using the nickel-foil method,16 and the neutron data were then shifted to make them match in the overlap q-regimes. Therefore, we do not indicate a units for the scattering intensities shown in Figures 1a and 4a.
Results and Discussion Figure 1a shows the combined USANS, USAXS, and SAXS scattering profiles for CB/PI with a volume fraction for the CB filler (φCB) of 20%. The most important feature (14) Aizawa, K.; Tomimitsu, H. Physica B 1995, 213, 884. (15) Koga, T.; Hart, M.; Hashimoto, T. J. Appl. Crystallogr. 1996, 29, 318. (16) Hendricks, R. W. J. Appl. Crystallogr. 1972, 5, 315.
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in the scattering profiles is represented by the Guinier region17 (shown by the arrow) and the power-law (I(q) ≈ q-R; R ) 2.3) region at q < 0.01 nm-1. We interpret that the power law represents a mass-fractal structure with a fractal dimension Dm ()R) of 2.3. Moreover, we can observe another power law (I(q) ≈ q-R; R ) 3.4) at q > 0.1 nm-1, which seems to reflect the surface-fractal structure of the primary CB particles with a fractal dimension of Ds ) 2d - R ) 2.6, with d being the space dimensionality (d ) 3 in our case). It should be noted that similar surfacefractal-like power-law regimes have been reported in various polymer-CB composites.18-20 In particular, here we focus on the scattering profile around q ) 0.05 nm-1 in the rubber matrix. To evaluate the size of the structure that corresponds to the lower cutoff of the mass-fractal structure, we first explored a part of the scattering profile at q g 0.05 nm-1, assuming a spherical model for the primary CB particles, F(q), that is,
F(q) ∝ R6Φ2(u)
(1)
in which
Φ(u) )
3 (sin u - u cos u) u3
(2)
and u ) qR. Here we considered the polydispersity of the radius (R) of the structure as a Gaussian function:
P(R) ≈ exp[(R - R h )2/2σR2],
(3)
in which R h and σR are the average R and corresponding standard deviation, respectively. The averaged scattering intensity, I(q), is given by
I(q) ≈ F(q) )
∫0∞ P(R)R6Φ2(u;R)dR/∫0∞ P(R)dR
(4)
The dotted line in Figure 1a shows the calculated form factor of the primary CB particles F(q) with RTEM ) 13 nm and σR ) 4 nm. From the figure we can see that the Guinier region for the calculated form factor exists at a higher q-region relative to the observed one, indicating that the CB primary particles themselves do not correspond to the lower cutoff objects for the mass-fractal structure. This may be inferred from TEM experiments. As shown in Figure 1b, apparently no isolated primary particles were found in the rubber matrix. Rather, the CB primary particles appear to be either mutually fused to form aggregates or connected to form their higher order structures (dispersible units or agglomerates). To further explore the size and shape of the lower cutoff objects for the mass-fractal structure, we tried to extract their form factor from the whole scattering profiles according to the treatment proposed by Sinha et al. for the cutoff problem of power-law scattering curves:21 the pair-correlation function G(r) between the particles that build up the mass-fractal objects is zero at small r, satisfying 0 < r e 2Rd, with Rd being the radius of the lower cutoff objects, so that the scattering intensity at q (17) Guinier, A.; Fournet, G. Small-Angle Scattering of X-rays; Wiley: London, 1955. (18) Hjelm, R.; Wampler, W.; Seeger, P.; Gerspacher, M. J. Mater. Res. 1994, 9, 3210. (19) Beaucage, G.; Rane, S.; Schaefer, D. W.; Long, G.; Fischer, D. J. Polym. Sci., Part B: Polym. Phys. 1999, 37, 1105. (20) Rieker, T. P.; Hindermann-Bischoff, M.; Ehrburger-Dolle, F. Langumuir 2000, 16, 5588. (21) Freltoft, T.; Kjems, J.; Sinha, S. K. Phys. Rev. B 1986, 33, 269.
> Rd-1 is dominated by the particle scattering that is defined by F′(q). We therefore approximated the scattering profiles around q ) 0.05 nm-1 as the sum of the two components, that is, the mass-fractal power-law scattering (the first term on the right-hand side of eq 5 below) and the form factor F′(q) for the lower cutoff objects:
I(q) = A exp(-Rg2q2/3)q-Dm + BF′(q)
(5)
in which A and B are numerical constants, and Rg is the radius of gyration for the lower cutoff objects. Note that the mass-fractal scattering, q-Dm, is assumed to damp, according to the Guinier function (-Rg2q2/3), when q increases across the upper cutoff wavenumber, and that data analysis was performed at q < 0.1 nm-1 to avoid the dominance of the surface-fractal scattering at q > 0.1 nm-1, as is obvious from Figures 1a and 4a. It should be noted that eq 5 can be also derived from the recently reported unified approach proposed by Beaucage and coworkers.19,22-26 The details of the derivation and analysis using the global scattering functions to obtain the fundamental features of each structure level at larger length scales in the hierarchical structures will be described elsewhere. First, we fit the data, assuming that the lower cutoff objects were sphere with a radius of Rd, and hence the form factor F′(q) is given by F(q). However, as shown in Figure 2a, which shows the expanded view of the USAXS scattering profile around q ) 0.05 nm-1, we found that the best-fitted spherical model with R h d ) 30.3 ( 0.5 nm and σR > 9 nm (dotted line) using eq 5 could only satisfy q values up to 0.05 nm-1. Taking this deviation from the spherical model fit at 0.05 < q < 0.1 nm-1 into account, we adopted an ellipsoidal model as the shape of the lower cutoff objects in the PI matrix. The scattering intensity from the ellipsoid of revolution having radii of Rd, Rd, and wRd with the random orientation F′(q) in eq 5 is then expressed as17
F′(q) )
∫0π (4πwRd3/3)2Φ2(U) sin βdβ
(6)
in which
U ) qRd[sin2 β + w2 cos2 β]1/2
(7)
and β is the polar angle between the axis of revolution and the reference axis. As shown in Figure 2a, the ellipsoidal model (solid line) with Rd ) 27.4 ( 0.5 nm and w ) 4.0 ( 0.2 shows a good fit to the data (open circles) up to q ) 0.09 nm-1. It should be noted that considering the polydispersity of the radii of the ellipsoidal shape further improves the small deviation between the observed and calculated profiles in the vicinity of q ) 0.1 nm-1. The Rg value for the ellipsoid, Rg ) Rd[(2 + w2)/5]0.5, was calculated to be 51 nm, which agreed with the fitting result (Rg ) 48 ( 1 nm) obtained using eq 5. A comparison of the average volume of the lower cutoff objects to that of the primary CB particles predicts that approximately 37 ()w(Rd/RTEM)3) primary CB particles cluster into the ellipsoidal lower cutoff objects in the PI rubber. It is important to add that the size of the dispersible units (22) Beaucage, G. J. Appl. Crystallogr. 1995, 28, 717. (23) Beaucage, G.; Schaefer, D. W. J. Non-Cryst. Solids 1994, 172174, 797. (24) Beaucage, G. J. Appl. Crysallogr. 1996, 29, 134. (25) Beaucage, G.; Kammler, H. K.; Pratsinis, S. E. J. Appl. Crystallogr. 2004, 37, 523. (26) Kammler, H. K.; Beaucage, G.; Mueller, R.; Pratsinis, S. E. Langmuir 2004, 20, 1915.
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Figure 2. (a) Expanded view of the USAXS scattering profile shown in Figure 1a in the q-range of 0.005 nm-1 < q 9nm, respectively, using eq 5. (b) Expanded view of the USAXS scattering profiles for CB/toluene. The solid line corresponds to the best-fitted spherical model to the data using eq 5 with R h ) 27.1 ( 0.5 nm and σR > 10 nm.
remained unchanged, even in the compounds prepared with the much longer mixing time (∼60 min). The crucial question is whether the lower cutoff objects represent the aggregates themselves (a number of primary particles fused together) or not. To explore this, we measured the USAXS and SAXS scattering intensity of a CB/toluene system in which CB particles with φCB ) 20% were placed into a glass capillary tube (diameter ) 1 mm) filled with toluene. We used an ultrasonic cleaner for 60 min to disperse the CB particles well and then let them precipitate completely. An incident X-ray beam was irradiated on the precipitates. The USAXS data for CB/ toluene (circles) around q ) 0.05 nm-1 is highlighted in Figure 2b. A comparison of panels a and b of Figure 2
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showed that the Guinier region for CB/toluene existed at the higher q-region relative to that for CB/PI, indicating that either the size of the lower cutoff objects formed in the rubber is larger than that of those formed in CB/toluene after sonification or the lower cutoff objects in the rubber can be further broken down into a smaller unit known as the aggregate. The best fit to the data using eq 5 (solid line) elucidated that the spherical structures with R h ) 27.1 ( 0.5 nm and σR > 10 nm were possible structures for the lower cutoff objects of CB/toluene after sonification. This reveals that the spherical structures resulting from sonification are composed of approximately nine ()(R h/ RTEM)3) fused CB primary particles and hence correspond to the aggregates, and that the form factor for CB/PI represents the ellipsoidal dispersible units (lower cutoff objects), which are composed of approximately four aggregates, on average, on the basis of the volume consideration described above. Hence, the scattering results clearly demonstrate that the dispersible units are the most fundamental, yet the minimum structural units that build up the agglomerate, as characterized by the mass-fractal structure in the rubber under a given mixing condition. Figure 3 shows a schematic model of the CB hierarchical structures in PI, as summarized from the scattering results. From the figure we can see two kinds of agglomerates: the dispersible units and the mass-fractal structure built up by the former. The upper cutoff length of the mass-fractal objects for CB/PI is estimated to be larger than 2π/(3 × 10-4) nm = 20 µm, as the power law extends to q < 3 × 10-4 nm-1, that is, the resolution limit of the USANS. Detailed characterizations of their morphology will be described elsewhere. Next, we shall discuss how a polymer matrix affects the size and shape of the dispersible units. Figure 4a shows the combined scattering profiles for CB/SBR with φCB ) 20%. From the figure we can see that both the mass-fractal dimension of Dm ) 2.3 and surface-fractal dimension of Ds ) 2.6 are identical to those of the CB/PI system and that the calculated form factor of the primary CB particles (dotted line) could not predict the observed form factor, suggesting the existence of CB dispersible units in the SBR matrix as well. To further characterize it, we fit the data up to q = qc ) 0.1 nm-1, in which the surface roughness of the CB particles does not make a significant contribution to I(q), by using eq 5. It should be pointed out that the low-q cutoff of the surface-fractal qc is inherent in the CB primary particles, regardless of the choice of rubbers. As shown in Figure 4b (solid line), we found that using eq 5 with the assumed ellipsoidal lower cutoff objects with Rd ) 27.0 ( 0.5 nm and w ) 1.8 ( 0.2 could successfully express the scattering data up to q ) 0.09 nm-1 for CB/ SBR. Hence, it is clear that the lower cutoff objects
Figure 3. Schematic model for the hierarchical structures of the CB fillers in the rubbers.
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aggregate size is identical, because the same CB was used. The changes in the size and shape of the dispersible units under the same mixing conditions could be due to the differences in the interaction parameters between CB and the polymer and/or the difference in the viscosity of the two matrices during the mixing process. In fact, the Mooney viscosity of the SBR and PI rubbers was determined to be 54 and 72 (ML1 + 4(100 °C)), respectively, suggesting that a polymer matrix with higher viscosity causes a larger CB dispersible unit size. In addition, the small aspect ratio and Rg value of the dispersible units seem to make the upper cutoff length (lu) of the massfractal structure (see Figure 3) in CB/SBR smaller (lu ) 2π/ql = 9 µm) on the basis of the lower wavenumber cutoff of ql = 7 × 10-4 nm-1 from Figure 4a, compared to that in CB/PI. This should be further studied in future works.
Figure 4. (a) Combined scattering profiles for CB/SBR having φCB ) 0.2. The dotted line corresponds to the calculated form factor for the CB primary particles. (b) Expanded view of the USAXS scattering profiles for CB/SBR shown in Figure 4a in the q-range of 0.005 nm-1 < q < 0.1 nm-1. The solid line corresponds to the best fit to the data using eq 5 with Rd ) 27.2 ( 0.5 nm and w ) 1.8 ( 0.2.
identified as the dispersible units in the SBR matrix are less elongated than those in the PI matrix, although the
Conclusion In summary, by utilizing a combination of USANS, USAXS, and SAXS techniques, we have clarified the hierarchical structures of the CB filler highly loaded in the rubber matrices over a wide range of the reciprocal space. We found that the aggregates of the CB filler used in this study had a spherical shape and were composed of approximately nine primary CB particles fused together. In the rubber matrices, the aggregates clustered into the higher order structure defined as the dispersible units, that is, the fundamental structural elements (or the lower cutoff objects) that build up the higher order mass-fractal structures. For CB/PI, the dispersible units were well approximated as an ellipsoidal shape composed of approximately four aggregates on average, whereas they were composed of approximately 2 aggregates on average and have a less elongated ellipsoidal shape in the SBR rubber. The difference in the size of the dispersible units is reflective of that of the upper cutoff lengths of the massfractal structures, >20 µm for PI and ∼9 µm for SBR, although the mass-fractal dimensions themselves remained unchanged. Acknowledgment. We thank Y. Ishikawa and N. Amino, The Yokohama-Rubber Co. Ltd., for providing all of the samples used in this study. LA051352S
