How Nano Are Nanocomposites?

Small-angle scattering (SAS) intensities observed experimentally are often characterized by the presence of successive power-law regimes with various scattering exponents whose values vary from -4 to -1. This usually indicates multiple fractal structures of the sample characterized by different size scales. The existing models explaining the crossover positions (that is, the points where the power-law scattering exponent changes) involve only one contrast parameter, which depends solely on the ratio of the fractal sizes. Here, a model that describes SAS from a multi-phase system with a few contrast parameters is described, and it is shown that the crossover position depends on the scattering length density of each phase. The Stuhrmann contrast variation method is generalized and applied to experimental curves in the vicinity of the crossover point beyond the Guinier region. The contrast variation is applied not to the intensity itself but to the model parameters, which can be found by fitting the experimental data with the suggested interpolation formula. The model supplements the existing two-phase models and gives the simple condition of their inapplicability: if the crossover point depends on the contrast then a two-phase model is not relevant. The developed analysis allows one to answer the qualitative question of whether one fractal 'absorbs' another one or they are both immersed in a surrounding homogeneous medium like a solvent or solid matrix. The models can be applied to experimental SAS data where the absolute value of the scattering exponent of the first power-law regime is higher than that of the subsequent second power-law regime, that is, the scattering curve is 'convex' near the crossover point. As is shown, the crossover position can be very sensitive to contrast variation, which influences significantly the length of the fractal range.

show abstract

“…(11) and (13) [and correspondingly Eqs. (12) and (14) in the fractal ranges]. As a consequence, it governs the form of the scattering intensity.…”

Section: The Interpolating Formula and The Generalized Methods Ofmentioning

confidence: 99%

“…SAS data (X-ray or neutron) often show a succession of power-law regimes whose scattering exponents are taking arbitrarily values from −4 to −1 [11][12][13][14][15][16][17]. On a double logarithmic scale, the scattering intensity looks like connected straight-line segments.…”

Section: Introductionmentioning

confidence: 99%

Small-angle scattering from multiphase fractals

et al. 2014

View full text Add to dashboard Cite

show abstract

“…The number of macromolecules n, penetrating into these regions, is given by the following relationship [6]: (12) where D f is the fractal dimension of polymer melt macromolecular coil, determined as follows [1]:…”

Section: Resultsmentioning

confidence: 99%

Dependence of Melt Viscosity of Polymer Nanocomposites on Type of Carbon Nanotubes Fractal Structures

Mikitaev¹,

Козлов²,

Микитаев³

et al. 2015

Vestn. Volgogr. gos. univ., Ser. 10. Innov. deiat.

View full text Add to dashboard Cite

“…[72][73][74][75][76][77] Silica rubber systems also form hierarchical structures consisting of agglomerates, aggregates and particles and the size of each structure can be estimated from the scattering function. Moreover, we can estimate the size distribution of silica particles.…”

Section: Applicationsmentioning

confidence: 99%

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

Takenaka

2012

Polym J

View full text Add to dashboard Cite

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

show abstract

How Nano Are Nanocomposites?

Cited by 726 publications

References 64 publications

Small-angle scattering from multiphase fractals

Small-angle scattering from multiphase fractals

Dependence of Melt Viscosity of Polymer Nanocomposites on Type of Carbon Nanotubes Fractal Structures

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

Contact Info

Product

Resources

About