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The measurement of molecular orientation in polymeric solids

  • G. L. Wilkes
Conference paper
Part of the Advances in Polymer Science book series (POLYMER, volume 8)

Keywords

Orientation Function Polymeric Solid Molecular Orientation Electric Vector Reference Axis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Principal Symbols Used

a, b, c

The three crystalline axes of a unit cell.

[h, k, l]

The notation used for the Miller indices in X-ray diffraction.

2θ

The Bragg angle when discussed with respect to X-ray diffraction.

fi

In general refers to the orientation function of the i th component or i th crystalline axis such as f c for the c axis.

χ

The angle the stretching direction makes with the reference axis in X-ray diffraction — see Fig. 3.

ω

The angle the film normal makes with a second reference axis in X-ray diffraction — see Fig. 3.

Δf*, Δf′, Δf

The complex, real part (in phase) and imaginary part (out of phase) of the orientation function respectively.

Z

Generally referred to as the stretching direction or machine direction.

Δij

Birefringence with respect to the i th and j th axes. The subscripts are not generally present for conventional notation.

ni

Refractive index along the i th axis.

ν

Frequency of light.

λ0

Wavelength of light in vacuo or air.

λi

Wavelength of light in a medium. The subscript refers to the direction in which the wavelength is oscillating normal to its propagation direction.

C0

Velocity of light in vacuo.

Ci

Velocity of light in the medium when polarized along the i th axis.

Rij

The optical retardation associated with Δ ij .

d

Thickness.

It

Intensity transmitted during a birefringence measurement.

I0

Incident intensity of light on the sample during a birefringence measurement.

δs

Phase difference giving retardation R ij .

\(\bar n\)

Average refractive index of the medium.

Δf

Form birefringence.

\(\mathop \Delta \limits^ \circ _i\)

Intrinsic birefringence of the i th component.

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{\mu }\)

The transition moment associated with absorption of radiation.

A

The absorption that occurs with radiation polarized parallel to the stretching direction.

A

The absorption that occurs with radiation polarized perpendicular to the stretching direction.

D

The dichroism which is the ratio of A /A .

Cu

The velocity of sound in a randomly oriented material.

Ct

The velocity of sound transverse to the molecular axis in a perfectly oriented material.

Cm

The velocity of sound parallel to the molecular axis in a perfectly oriented material.

C

The velocity of sound parallel to the stretch axis in a material under investigation.

E

Young's modulus of a material when measured parallel to the stretch axes in a material under investigation.

Et

Young's modulus of a material measured perpendicular to the molecular axis of a perfectly oriented material.

Em

Young's modulus of a material measured parallel to the molecular axis of a perfectly oriented material.

Ei

Refers to Young's modulus of the i th component measured along the stretch direction.

Eu

Young's modulus of a randomly oriented material.

β

Volume fraction of a component.

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{P}\)1

Refers to the orientation of the polarizer placed before the sample with respect to some reference axis.

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{P}\)2

Refers to the orientation of the polarizer placed after the sample and with respect to the same reference axis as \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{P}\) 1.

\(I_{P_1 P_2 }\)

The intensity seen by the detector when the polarizer and analyzer are oriented in direction \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{P}\) 1 and \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{P}\) 2 respectively.

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Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • G. L. Wilkes
    • 1
  1. 1.Department of Chemical EngineeringPrinceton UniversityPrincetonUSA

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