### Abstract

A model is presented that characterizes the temperature dependence of the specific heat of amorphous polymers. The model utilizes a density of vibrational states given by ρ(ω)∝ω^{d̃-1}, where d̃ is the fracton, or spectral, dimension. This density of vibrational states, when introduced into the standard Debye model, leads to a specific heat temperature dependence of the form C(T)∝(T/⊖_{d̃}) ^{d̃}, where ⊖_{d̃} is a characteristic temperature. This model fits the data well for the temperature region ∼4 to ∼40 K. A key feature of the model is the prediction of a crossover of the polymer scaling properties that causes a crossover from T^{2} to T ^{5/3} of the specific heat temperature dependence. In addition, this model allows a simple estimate of the specific heat for a wide range of polymers using only the formula weight.

Original language | English |
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Pages (from-to) | 4680-4683 |

Number of pages | 4 |

Journal | Journal of Chemical Physics |

Volume | 84 |

Issue number | 8 |

Publication status | Published - 1986 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*84*(8), 4680-4683.

**A model for the specific heat of amorphous polymers.** / Allen, James Paul.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 84, no. 8, pp. 4680-4683.

}

TY - JOUR

T1 - A model for the specific heat of amorphous polymers

AU - Allen, James Paul

PY - 1986

Y1 - 1986

N2 - A model is presented that characterizes the temperature dependence of the specific heat of amorphous polymers. The model utilizes a density of vibrational states given by ρ(ω)∝ωd̃-1, where d̃ is the fracton, or spectral, dimension. This density of vibrational states, when introduced into the standard Debye model, leads to a specific heat temperature dependence of the form C(T)∝(T/⊖d̃) d̃, where ⊖d̃ is a characteristic temperature. This model fits the data well for the temperature region ∼4 to ∼40 K. A key feature of the model is the prediction of a crossover of the polymer scaling properties that causes a crossover from T2 to T 5/3 of the specific heat temperature dependence. In addition, this model allows a simple estimate of the specific heat for a wide range of polymers using only the formula weight.

AB - A model is presented that characterizes the temperature dependence of the specific heat of amorphous polymers. The model utilizes a density of vibrational states given by ρ(ω)∝ωd̃-1, where d̃ is the fracton, or spectral, dimension. This density of vibrational states, when introduced into the standard Debye model, leads to a specific heat temperature dependence of the form C(T)∝(T/⊖d̃) d̃, where ⊖d̃ is a characteristic temperature. This model fits the data well for the temperature region ∼4 to ∼40 K. A key feature of the model is the prediction of a crossover of the polymer scaling properties that causes a crossover from T2 to T 5/3 of the specific heat temperature dependence. In addition, this model allows a simple estimate of the specific heat for a wide range of polymers using only the formula weight.

UR - http://www.scopus.com/inward/record.url?scp=0037862983&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037862983&partnerID=8YFLogxK

M3 - Article

VL - 84

SP - 4680

EP - 4683

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 8

ER -