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# Predicting the density-scaling exponent of a glass-forming liquid from Prigogine–Defay ratio measurements

## Abstract

Understanding the origin of the dramatic temperature and density dependence of the relaxation time of glass-forming liquids is a fundamental challenge in glass science. The recently established ‘density-scaling’ relation quantifies the relative importance of temperature and density for the relaxation time in terms of a material-dependent exponent. We show that this exponent for approximate single-parameter liquids can be calculated from thermoviscoelastic linear-response data at a single state point, for instance an ambient-pressure state point. This prediction is confirmed for the van der Waals liquid tetramethyl-tetraphenyl-trisiloxane. Consistent with this, a compilation of literature data for the Prigogine–Defay ratio shows that van der Waals liquids and polymers are approximate single-parameter systems, whereas associated and network-forming liquids are not.

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## Acknowledgements

The Centre for Viscous Liquid Dynamics ‘Glass and Time’ is sponsored by the Danish National Research Foundation (DNRF). Work at NRL is supported by Office of Naval Research. URP is supported by The Danish Council for Independent Research in Natural Sciences.

## Author information

Authors

### Contributions

U.R.P. and K.N. conceived the project. D.G., U.R.P., B.J., J.C.D. and K.N. wrote the paper with input from C.M.R. D.G., U.R.P., and K.N. did the main data analysis. T.H. measured the shear modulus and compressibility and did the raw data analysis. B.J. and T.C. measured the heat capacity and did the raw data analysis. K.N. measured the expansion coefficient and did the raw data analysis. T.C. and N.B.O. conceived and developed the four thermoviscoelastic measuring techniques used. D.G., D.F. and R.C. measured the high-pressure data and did the scaling data analysis. U.R.P., N.P.B., T.C., T.B.S. and J.C.D. supplied the theoretical background for the project, which was coordinated by K.N.

### Corresponding author

Correspondence to Kristine Niss.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary Information

Supplementary Information (PDF 192 kb)

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Gundermann, D., Pedersen, U., Hecksher, T. et al. Predicting the density-scaling exponent of a glass-forming liquid from Prigogine–Defay ratio measurements. Nature Phys 7, 816–821 (2011). https://doi.org/10.1038/nphys2031

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