### Abstract

A pole inversion formula is derived for textures with an axis of symmetry, for example, planar and fiber orientation obtained by uniaxial and biaxial deformation processes, respectively. The measured pole density distribution function of an (hkl) reflection is expressed as an integral transform of the (required) pole density distribution function (which is usually the chain axis in polymers). Unlike other methods for pole inversion, this formulation does not involve any series expansion of the orientation functions. The integral equation is analytically solved for the special case when the (hkl) reflection is perpendicular to the chain axis, a common feature to most of the semicrystalline and liquid-crystalline polymers.

Original language | English (US) |
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Pages (from-to) | 2382-2387 |

Number of pages | 6 |

Journal | Macromolecules |

Volume | 21 |

Issue number | 8 |

DOIs | |

State | Published - Jan 1 1988 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Organic Chemistry
- Polymers and Plastics
- Inorganic Chemistry
- Materials Chemistry

### Cite this

**An Exact Method To Determine the Complete Orientation Distribution Function of the Chain Axis from an Arbitrary (hkl) Reflection.** / Saraf, Ravi F.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - An Exact Method To Determine the Complete Orientation Distribution Function of the Chain Axis from an Arbitrary (hkl) Reflection

AU - Saraf, Ravi F

PY - 1988/1/1

Y1 - 1988/1/1

N2 - A pole inversion formula is derived for textures with an axis of symmetry, for example, planar and fiber orientation obtained by uniaxial and biaxial deformation processes, respectively. The measured pole density distribution function of an (hkl) reflection is expressed as an integral transform of the (required) pole density distribution function (which is usually the chain axis in polymers). Unlike other methods for pole inversion, this formulation does not involve any series expansion of the orientation functions. The integral equation is analytically solved for the special case when the (hkl) reflection is perpendicular to the chain axis, a common feature to most of the semicrystalline and liquid-crystalline polymers.

AB - A pole inversion formula is derived for textures with an axis of symmetry, for example, planar and fiber orientation obtained by uniaxial and biaxial deformation processes, respectively. The measured pole density distribution function of an (hkl) reflection is expressed as an integral transform of the (required) pole density distribution function (which is usually the chain axis in polymers). Unlike other methods for pole inversion, this formulation does not involve any series expansion of the orientation functions. The integral equation is analytically solved for the special case when the (hkl) reflection is perpendicular to the chain axis, a common feature to most of the semicrystalline and liquid-crystalline polymers.

UR - http://www.scopus.com/inward/record.url?scp=0024054941&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024054941&partnerID=8YFLogxK

U2 - 10.1021/ma00186a014

DO - 10.1021/ma00186a014

M3 - Article

VL - 21

SP - 2382

EP - 2387

JO - Macromolecules

JF - Macromolecules

SN - 0024-9297

IS - 8

ER -