Structural studies of complex systems using small-angle scattering: a unified Guinier/power-law approach

Beaucage, Greg; Schaefer, Dale W.

doi:10.1016/0022-3093(94)90581-9

Cited by 279 publications

(266 citation statements)

References 8 publications

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“…The presence of some aggregates, still on the nanoscale size, seems to be probable in the material from the SAXS data since the number of power law decays is interrelated to the number of structural levels present in the materials. [30] However, the population of these aggregates could not be directly determined from the data and because of the minimum wave vector q min imposed by the beam stop, sufficient data points were not available for an accurate determination of mean size of the large structures (i.e., low q). The increase of TiO 2 content leads to the appearance of a correlation peak in the wave vector range 0.6 nm À1 < q < 1.2 nm À1 , which becomes clearly visible in the case of HBP(OH)-Si(OEt) 3 /20 wt.-%TiO 2 (see Figure 5).…”

Section: Methodsmentioning

confidence: 99%

“…This latter has been argued to be linked to the fractal nature of scattering objects in the literature. [28][29][30][31] The slope of I(q) profile is strongly influenced by the type of the particles (i.e., compact or ramified) and the nature of the interface separating the TiO 2 particles from the HBP. The increase of the TiO 2 content influences significantly the slope of the SAXS profile.…”

Section: Morphologymentioning

confidence: 99%

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Hyperbranched Polymer/TiO₂ Hybrid Nanoparticles Synthesized via an In Situ Sol‐Gel Process

Gianni

Trabelsi

Rizza

et al. 2007

Macro Chemistry & Physics

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Two different kinds of HBPs were used in the preparation of nanocomposite materials based on TiO 2 nanoparticles. One of the HBPs was characterized by the presence of free OH end groups in its structure, while the other one was obtained via a partial modification reaction which allowed to introduce some alkoxysilane functional groups. The TiO 2 particles were prepared in situ in the polymer solution by means of a sol-gel process starting from Ti(iOPr) 4 as precursor. The polymer/TiO 2 mixture, subsequently coated and cured in the presence of diisocyanate, gave rise to a hard coating. TiO 2 was found to be dispersed on nanometer scale inside the final coatings obtained from both the polymers, and the TiO 2 nanocomposite coatings were also characterized by improved thermal and hardness properties compared to TiO 2 free systems. Still the two different kinds of HBPs showed a different interaction with the TiO 2 particles, and it has been evidenced that the modification is required to achieve a better dispersion of the particles in the matrix and better properties for the final coating. Thus, by applying the modified HBP, TiO 2 could be dispersed and stabilized in the polymer matrix as individual nanoparticles of only 6 nm in diameter.

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Section: Methodsmentioning

confidence: 99%

Section: Morphologymentioning

confidence: 99%

Hyperbranched Polymer/TiO₂ Hybrid Nanoparticles Synthesized via an In Situ Sol‐Gel Process

Gianni

Trabelsi

Rizza

et al. 2007

Macro Chemistry & Physics

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“…To describe the scattering profiles of the rubberfiller systems over five decades, Beuacage proposed a unified Guinier/ power-law method. 34,35 According to this method, the hierarchical structure with an arbitrary number n of hierarchical levels can be described by:…”

Section: Scattering Theory For Rubber-filler Systemsmentioning

confidence: 99%

“…R SS and R gg correspond to the sizes of the aggregates and the agglomerates, respectively. The solid line is the best-fitted theoretical scattering profile expressed by Equation (35). Reproduced with permission from Macromolecules.…”

Section: Applicationsmentioning

confidence: 99%

Analysis of structures of rubber-filler systems with combined scattering methods

Takenaka

2012

Polym J

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This review presents an analysis of the hierarchical structures formed in rubber-filler systems by using combined scattering methods. The combined scattering methods utilize various scattering methods and are powerful tools for the quantitative characterization of hierarchical structures over a wide range of length scales, ranging from nanometers to micrometers. Scattering theories for the analysis of the experimental scattering functions and their applications are described. Polymer Journal (2013) 45, 10-19; doi:10.1038/pj.2012.187; published online 21 November 2012Keywords: combined scattering methods; hierarchical structure; rubber-filler systems INTRODUCTION Rubber-filler systems have been widely used in industrial applications, such as for tires and belts so on. 1-6 The use of fillers in rubber compounds reinforces the rubber material and improves the barrier properties. There are several important factors for controlling the efficiency of rubber reinforcement by fillers. The dispersion of filler particles in the rubber matrix is one of the most important factors in this process. Typically, following the use of conventional compounding processes, the fillers are not dispersed homogeneously and form hierarchical structures within the rubber matrices. For example, in rubber-carbon black (CB) systems, the CB primary particles are not distributed independently but coalesce into aggregates, which are indestructible units of CB, during conventional compounding processes. 2 The aggregates of CB, which are called aggregates or agglomerates, can also lead to the formation of hierarchical structures, which consist of higher levels of ordered structure. 2 It is believed that the hierarchical structures affect the efficiency of filler reinforcement. Other rubber-filler systems also form hierarchical structures; furthermore, the characteristic lengths and morphologies of each level of ordered structure, such as agglomerates, vary with the specific combination of rubber and filler used in the system in addition to the compounding processes. To analyze the hierarchical structure, scattering techniques are one of useful techniques. In scattering experiments, we investigated the angular dependence of the scattered intensities induced by the incident beam hitting samples. Although the interpretation of the scattering intensities is complicated, nonetheless, scattering techniques are suitable for obtaining the statistical features of rubber-filler systems. However, the length scales of the hierarchical structures can extend from nanometers to micrometers, which prevents the characterization

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“…More complicated equations requiring numerical calculations are involved for inhomogeneous rods (Radulescu et al, 2004) or for rods with elliptical cross-section (Bergström & Pedersen, 1999). The combination of scattering data with fractal geometry concepts recently commenced to become a general path of investigating the complex morphologies displaying multiple structural levels on wide length scales (Beaucage & Schaefer, 1994). Fractal approaches describe power-law regimes often observed in measured scattering profiles with the exponents depending on the geometric structure of the scattering objects, d/d(Q)≈Q -p .…”

Section: Sans Cross-section Of Simple Structuresmentioning

confidence: 99%

Tailored Polymer Additives for Wax (Paraffin) Crystal Control

Rădulescu¹,

Fetters²,

Richter³

2012

Crude Oil Emulsions- Composition Stability and Characterization

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Structural studies of complex systems using small-angle scattering: a unified Guinier/power-law approach

Cited by 279 publications

References 8 publications

Hyperbranched Polymer/TiO₂ Hybrid Nanoparticles Synthesized via an In Situ Sol‐Gel Process

Hyperbranched Polymer/TiO₂ Hybrid Nanoparticles Synthesized via an In Situ Sol‐Gel Process

Analysis of structures of rubber-filler systems with combined scattering methods

Tailored Polymer Additives for Wax (Paraffin) Crystal Control

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Structural studies of complex systems using small-angle scattering: a unified Guinier/power-law approach

Cited by 279 publications

References 8 publications

Hyperbranched Polymer/TiO2 Hybrid Nanoparticles Synthesized via an In Situ Sol‐Gel Process

Hyperbranched Polymer/TiO2 Hybrid Nanoparticles Synthesized via an In Situ Sol‐Gel Process

Analysis of structures of rubber-filler systems with combined scattering methods

Tailored Polymer Additives for Wax (Paraffin) Crystal Control

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Product

Resources

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Hyperbranched Polymer/TiO₂ Hybrid Nanoparticles Synthesized via an In Situ Sol‐Gel Process

Hyperbranched Polymer/TiO₂ Hybrid Nanoparticles Synthesized via an In Situ Sol‐Gel Process