Partial specific volume

The partial specific volume ${\bar {v_{i}}},$ express the variation of the extensive volume of a mixture in respect to composition of the masses. It is the partial derivative of volume with respect to the mass of the component of interest.

V=\sum _{i=1}^{n}m_{i}{\bar {v_{i}}},

where ${\bar {v_{i}}}$ is the partial specific volume of a component $i$ defined as:

{\bar {v_{i}}}=\left({\frac {\partial V}{\partial m_{i}}}\right)_{T,P,m_{j\neq i}}.

The PSV is usually measured in milliLiters (mL) per gram (g), proteins > 30 kDa can be assumed to have a partial specific volume of 0.708 mL/g.^[1] Experimental determination is possible by measuring the natural frequency of a U-shaped tube filled successively with air, buffer and protein solution.^[2]

Properties

The weighted sum of partial specific volumes of a mixture or solution is an inverse of density of the mixture namely the specific volume of the mixture.

v=\sum _{i}w_{i}\cdot {\bar {v_{i}}}={\frac {1}{\rho }}

\sum _{i}\rho _{i}\cdot {\bar {v_{i}}}=1

References

^ Buxbaum, Engelbert (2011). "25: Centrifugation". Biophysical Chemistry of Proteins. New York, Dordrecht, Heidelberg, London: Springer. pp. 237–249. doi:10.1007/978-1-4419-7251-4_25. ISBN 978-1-4419-7250-7.
^ Kratky, O.; Leopold, H.; Stabinger, H. (1973). "5: The determination of the partial specific volume of proteins by the mechanical oscillator technique". In Hirs, C.H.W.; Timasheff, S.N. (eds.). Meth. Enzymol. Vol. 27: Enzyme Structure Part D. pp. 98–110. ISBN 978-0-12-181890-6.