We prove that there are solutions u ( ~, z ) of the heat equation ut = uxx such that every continuous function f : [a, b] + R can be uniformly approximated by a subsequence of u ( n , . ), n E IN.
The Estimation of the Molecular Weight of Polytetrafluoroethylene Based on the Heat of Crystallisation. A Comment on Suwa's Equation
✍ Scribed by Uwe Lappan; Uwe Geißler; Liane Häußler; Gisela Pompe; Ulrich Scheler
- Publisher
- John Wiley and Sons
- Year
- 2004
- Tongue
- English
- Weight
- 116 KB
- Volume
- 289
- Category
- Article
- ISSN
- 1438-7492
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✦ Synopsis
Abstract
Summary: The influence of number‐average molecular weight $\overline M _{\rm n}$ ranging from 1.4 · 10^4^ to 1.2 · 10^6^ g/mol on the thermal behaviour of polytetrafluoroethylene (PTFE) has been studied. Samples have been prepared by radiation‐induced degradation of commercial PTFE. The molecular weight $\overline M _{\rm n}$ has been calculated using end‐group concentration determined by infrared (IR) spectroscopy and ^19^F solid‐state nuclear magnetic resonance (NMR) spectroscopy. Melting and crystallisation heats were investigated by differential scanning calorimetry (DSC). The results have been discussed with respect to quantitative relationships between number‐average molecular weight and heat of crystallisation of PTFE described in the literature. The molecular weight calculated from Suwa's equation, which is often used in the literature, has been found to be too low.
Concentration of end‐groups and the molecular weight of PTFE versus the irradiation dose.
imageConcentration of end‐groups and the molecular weight of PTFE versus the irradiation dose.
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