20
2 The Kinds of Ordinary Materials
molecule, giving collagen significant tensile strength compared to other organic
molecular tissue.
Vertebrates create and maintain bone as an endoskeletal structure. Bone is a
calcium phosphate in the chemical arrangement termed calcium hydroxyapatite,
Ca 10 (PO 4 ) 6 (OH) 2 , embedded in collagen.
2.2.2 Detecting Particle Size in Colloids
Dynamic Light Scattering
Consider a colloid of small round particles undergoing Brownian motion in a fluid.
By measuring the diffusion rate of the mixed particles, the effective diameter ‘d’ of
the particles can be found using the Stokes-Einstein Relation:
d =
k B T
3πηD
(2.1)
where D is the diffusion constant for the suspended particles. The viscosity of the
fluid, η, and its temperature, T , are assumed known.
The diffusion constant D can be measured by employing the technique of
‘dynamic light scattering’ from the particles in the fluid. If laser light, of wavelength
λ selected to be larger than the average interparticle distances, is passed through the
colloid, the light scattered from neighboring mixed particles will add coherently.
However, because the interparticle distances vary through Brownian motion, the
relative phase of the scattered light from individual particles in a neighboring
cluster will vary over time, typically fractions of a microsecond. This will cause
the scattered light intensity to show a variation when measured over time, as shown
in Fig. 2.2.
The variation of the scattered light intensity I (t) due to Brownian motion can be
characterized by the behavior of the normalized ‘auto-correlation’ function G(τ ),
defined by
G(τ ) ≡
I (t) · I (t + τ )
I (t) · I (t)
.
For short times (typically in the microseconds), there should be near perfect overlap
of intensity I (t) with itself, while for very long-time displacements τ (typically in
the hundreds of milliseconds), there will be a much smaller correlation between
various phases of light scattered from the particles as they are shifted by ‘random’
motion, so that G(τ ) drops down as τ increases. One can show that for particles of
uniform size,
G(τ ) = (1 + βe
−2τ ),
2 The Kinds of Ordinary Materials
molecule, giving collagen significant tensile strength compared to other organic
molecular tissue.
Vertebrates create and maintain bone as an endoskeletal structure. Bone is a
calcium phosphate in the chemical arrangement termed calcium hydroxyapatite,
Ca 10 (PO 4 ) 6 (OH) 2 , embedded in collagen.
2.2.2 Detecting Particle Size in Colloids
Dynamic Light Scattering
Consider a colloid of small round particles undergoing Brownian motion in a fluid.
By measuring the diffusion rate of the mixed particles, the effective diameter ‘d’ of
the particles can be found using the Stokes-Einstein Relation:
d =
k B T
3πηD
(2.1)
where D is the diffusion constant for the suspended particles. The viscosity of the
fluid, η, and its temperature, T , are assumed known.
The diffusion constant D can be measured by employing the technique of
‘dynamic light scattering’ from the particles in the fluid. If laser light, of wavelength
λ selected to be larger than the average interparticle distances, is passed through the
colloid, the light scattered from neighboring mixed particles will add coherently.
However, because the interparticle distances vary through Brownian motion, the
relative phase of the scattered light from individual particles in a neighboring
cluster will vary over time, typically fractions of a microsecond. This will cause
the scattered light intensity to show a variation when measured over time, as shown
in Fig. 2.2.
The variation of the scattered light intensity I (t) due to Brownian motion can be
characterized by the behavior of the normalized ‘auto-correlation’ function G(τ ),
defined by
G(τ ) ≡
I (t) · I (t + τ )
I (t) · I (t)
.
For short times (typically in the microseconds), there should be near perfect overlap
of intensity I (t) with itself, while for very long-time displacements τ (typically in
the hundreds of milliseconds), there will be a much smaller correlation between
various phases of light scattered from the particles as they are shifted by ‘random’
motion, so that G(τ ) drops down as τ increases. One can show that for particles of
uniform size,
G(τ ) = (1 + βe
−2τ ),