Pharmaceutical Research

, Volume 23, Issue 10, pp 2269–2276 | Cite as

A Calorimetric Method to Estimate Molecular Mobility of Amorphous Solids at Relatively Low Temperatures

  • Chen Mao
  • Sai Prasanth Chamarthy
  • Stephen R. Byrn
  • Rodolfo Pinal
Research Paper



To present a calorimetry-based approach for estimating the initial (at the onset of annealing) relaxation time (τ 0) of organic amorphous solids at relatively low temperatures, and to assess the temperature where molecular mobility of the amorphous drug is reduced to a level comparable with the desired shelf-life of the product.

Materials and Methods

Values of τ 0 for six amorphous pharmaceutical compounds were estimated based on the nonlinear Adam–Gibbs equation. Fragility was determined from the scanning rate-dependence of the glass transition temperature (T g). The initial enthalpic and entropic fictive temperatures were obtained from the T g and the heat capacities (C p) of the amorphous and crystalline forms.


At a relatively low temperature (∼40°C or more below T g), τ 0 for the different compounds varies by over an order of magnitude. For some materials, the practical storage temperature at T g − 50 K was found to be still too high to ensure long-term stability. The estimated τ 0 is highly sensitive to the fragility of the material and the C p of the crystalline and amorphous forms. Materials with high fragility or greater C p differences between crystalline and amorphous forms tend to have longer τ 0.


The proposed method can be used to estimate molecular mobility at relatively low temperatures without having to conduct enthalpy recovery experiments. An accurate τ 0 determination from this method relies on faithful fragility measurements.

Key words

amorphous differential scanning calorimetry fictive temperature molecular mobility relaxation stability 



The financial support from the Purdue–Michigan Joint Program on the Chemical and Physical Stability of Pharmaceutical Solids is acknowledged.


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Chen Mao
    • 1
  • Sai Prasanth Chamarthy
    • 1
  • Stephen R. Byrn
    • 1
  • Rodolfo Pinal
    • 1
  1. 1.Department of Industrial and Physical PharmacyPurdue UniversityWest LafayetteUSA

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