Dispersion

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Dispersion

General information

The term dispersion is used in the natural sciences to refer to a variety of meanings in accordance with its Latin origin (Latin: dispergere – to distribute, spread and scatter).

The Wiki-lexicon ‘Polymer Testing & Diagnostics’ contains the terms

• elastomer dispersion filler and
• layered silicate-reinforced polymers,

where dispersion is used to describe the type of distribution of filler particles in a rubber matrix [1] or in a polymer nanocomposite [2]. The term dispersion is also very often used in connection with the propagation of light

• ABBE refractometer
• Refraction index
• Refraction light]]

and the propagation of sound waves

• Reflection sound waves
• Refraction sound waves
• Sound emission analysis
• Sound emission testing,

where it specifically refers to frequency dispersion.

The dispersion of light

Light dispersion refers to the dependence of a material's refraction index on the frequency f of the light or the wavelength λ. Dispersion is referred to as normal dispersion if the refraction index or refractive index increases with increasing frequency or decreases with increasing wavelength. In the opposite case, i.e. when the refraction index increases with increasing wavelength, dispersion is referred to as abnormal.

In anisotropic materials, the refraction index n and all related optical characteristics (e.g. birefringence or optical axis angle) depend on the wavelength λ of the incident light. In plastics and inorganic glasses, the refraction index decreases with increasing wavelength and thus decreasing frequency of the light. When white light passes through a dispersion prism, it is reflected and split into the individual wavelengths or colours of the spectrum (Fig. 1). The different media differ in the size of the deflection angle for the individual colours.

Fig. 1:

Dispersion of white light through a prism: (a) frequency dispersion and (b) wavelengths of the colour spectrum

For characterisation, the ground dispersion GD is determined according to Eq. (1) for the middle part of the spectrum, whereby the refraction indices nF and nC are measured.

$GD=n_{F}-n_{C}\!$

(1)

The selected wavelengths of the Fraunhofer lines F (λ_F = 486 nm), C (λ_C = 656 nm) and D (λ_D = 589 nm) are most easily adjusted using metal interference filters of the corresponding wavelengths or optical monochromators. This makes it easy to determine the ABBE number ν in the microscope according to Eq. (2).

$\nu ={\frac {n_{D}-1}{n_{F}-n_{C}}}$

(2)

The dispersion can be determined using an ABBE refractometer. A large ABBE number means low wavelength dependence of the refractive index at normal dispersion and vice versa [3].

The dispersion of ultrasound

The spatial and temporal propagation of mechanical waves in elastic media in a frequency range from 1.6·10⁴ Hz to approx. 10¹² Hz is referred to as ultrasound. Mechanical or electromechanical sound sources are used to generate ultrasound, of which piezoelectric oscillators are the most widely used.

The phenomena of ultrasonic propagation, reflection, refraction and birefringence are comparable to those of light propagation and are subject to the physical laws of geometric optics.

See also

• Particle-filled thermoplastics
• Elastomers
• Macrodispersion degree elastomers
• Sound emission analysis
• Sound velocity

References

[1]	Reincke, K.: Elastomere Werkstoffe – Zusammenhang zwischen Mischungsrezeptur, Struktur und mechanischen Eigenschaften sowie dem Deformations- und Bruchverhalten. Habilitation, Martin-Luther-Universität Halle-Wittenberg, Shaker Publishing, Herzogenrath (2016), (ISBN 978-3-8440-4637-3; see AMK-Library under B 2-2)
[2]	Monami, A.: Struktur, Exfolierungszustand und Eigenschaften von PA/OMMT-Verbundwerkstoffen. Dissertation, Martin-Luther-Universität Halle-Wittenberg, Mensch & Buch Publishing, Berlin (2014), (ISBN 978-3-86387-402-5; see AMK-Library under B 1-26)
[3]	Trempler, J.: Optical Properties. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3rd Edition, pp. 305/306 (ISBN 978-1-56990-806-8; E-Book: ISBN 978-1-56690-807-5; see AMK-Library under A 22)