11.8 Studying Biological Systems at the Nanoscale
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macromolecule differs from the medium and the mean-free path of the medium
particles is not much shorter than the distance between the macromolecules.
For random impulses coming from all directions, the impulses stopped by the first
molecule which would have hit the second will be in proportion to the area of that
first molecule over a sphere surrounding the second molecule. If the molecules are
separated by a distance r, that area will diminish as the square of r. Thus, for a fixed
impulse given by the media particles, the unbalanced force on the second molecule
must be in proportion to the inverse square of r. The force will drop even faster than
r −2 if the media particles have a mean-free path shorter than r. In addition, because
of fewer collisions in the shadow regions, the macromolecules may cool on their
shadow surfaces. This increases the net attraction due to the shadow force.
This shading effect has a long history. In 1748, Le Sage attempted to explain
gravity by postulating a background random flux of particles absorbed by masses.
Because the shading depends on the relative size of the area of one mass on a sphere
centered on the second mass, such a flux does produce a force inversely proportional
to the square of the separation between the masses. However, the requirement of
absorption creates far too much heating.
Shadow forces do come to play in the agglomeration of dust in hot plasma near
stars, and in the Casimir effect, i.e. the attraction of uncharged conducting plates in
a vacuum, which can be explained by the ‘quantum shading’ of the possible virtual
photons between the plates. The drifting together of two boats in rough waters has
a similar explanation: There are missing wave modes between the boats.
11.8 Studying Biological Systems at the Nanoscale
11.8.1 Spectral Identification of Biomolecular Structures
The structure of molecules can be investigated by studying how the molecule traps
and releases light. Photons, from microwaves to far ultraviolet, are absorbed and
emitted within molecules by electron transitions and by molecular vibrations, twists
and rotations. As these states are quantized, emitted and absorbed photon energies
hf are correspondingly quantized. Moreover, since the photon is a spin-1 particle,
the photon-induced transitions must change the angular momentum of the molecule
by one unit of Planck’s constant in the direction of the photon’s momentum.
As indicated in Sects. 7.17.1 and 7.22, the spectral absorption for molecular
rotations and vibrations are typically found in the infrared (IR), while valence
electron transitions produce spectra in the ultraviolet and visible. These observations
we understand by considering the energetics of molecular quantum excitations and
the corresponding photons energies.
In attempting to identify unknown organic substances, an IR spectra can serve as
a ‘fingerprint’ of each organic molecule present. In absorption spectra, the internal
vibrations of a set of identical molecules are stimulated by light which arrives
535
macromolecule differs from the medium and the mean-free path of the medium
particles is not much shorter than the distance between the macromolecules.
For random impulses coming from all directions, the impulses stopped by the first
molecule which would have hit the second will be in proportion to the area of that
first molecule over a sphere surrounding the second molecule. If the molecules are
separated by a distance r, that area will diminish as the square of r. Thus, for a fixed
impulse given by the media particles, the unbalanced force on the second molecule
must be in proportion to the inverse square of r. The force will drop even faster than
r −2 if the media particles have a mean-free path shorter than r. In addition, because
of fewer collisions in the shadow regions, the macromolecules may cool on their
shadow surfaces. This increases the net attraction due to the shadow force.
This shading effect has a long history. In 1748, Le Sage attempted to explain
gravity by postulating a background random flux of particles absorbed by masses.
Because the shading depends on the relative size of the area of one mass on a sphere
centered on the second mass, such a flux does produce a force inversely proportional
to the square of the separation between the masses. However, the requirement of
absorption creates far too much heating.
Shadow forces do come to play in the agglomeration of dust in hot plasma near
stars, and in the Casimir effect, i.e. the attraction of uncharged conducting plates in
a vacuum, which can be explained by the ‘quantum shading’ of the possible virtual
photons between the plates. The drifting together of two boats in rough waters has
a similar explanation: There are missing wave modes between the boats.
11.8 Studying Biological Systems at the Nanoscale
11.8.1 Spectral Identification of Biomolecular Structures
The structure of molecules can be investigated by studying how the molecule traps
and releases light. Photons, from microwaves to far ultraviolet, are absorbed and
emitted within molecules by electron transitions and by molecular vibrations, twists
and rotations. As these states are quantized, emitted and absorbed photon energies
hf are correspondingly quantized. Moreover, since the photon is a spin-1 particle,
the photon-induced transitions must change the angular momentum of the molecule
by one unit of Planck’s constant in the direction of the photon’s momentum.
As indicated in Sects. 7.17.1 and 7.22, the spectral absorption for molecular
rotations and vibrations are typically found in the infrared (IR), while valence
electron transitions produce spectra in the ultraviolet and visible. These observations
we understand by considering the energetics of molecular quantum excitations and
the corresponding photons energies.
In attempting to identify unknown organic substances, an IR spectra can serve as
a ‘fingerprint’ of each organic molecule present. In absorption spectra, the internal
vibrations of a set of identical molecules are stimulated by light which arrives