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Calculation of the Density and Activity of Water in ATPS Systems for Separation of Biomolecules

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Abstract

In this study, the perturbed hard sphere chain equation of state is utilized to calculate the activity of water in binary and ternary solutions of polyethylene glycol (PEG), salt and water. The liquid density of the binary and ternary solutions is also predicted. To estimate the water activity in PEG–water binary systems, a linear correlation is obtained for the binary interaction parameter between water and PEG. Then, using this correlation and without introducing any additional binary parameters, the water activities are predicted in ternary solutions of water, salt and PEG with different molecular weights (MW). Our results show that the mean absolute average relative deviation (AARD %) of water activity for binary PEG–water solutions in 298 K is 0.73 %. In addition, the water activity in ternary solutions of water and two PEGs with different MW is predicted within 0.31 % AARD %. Furthermore, the AARD % for prediction of water activities in binary PEG–water solutions over the temperature range 308–338 K is 0.41 %. Also, the water activities of aqueous two-phase systems are predicted with AARD % = 0.64 %. In this regard, no adjustable parameters were correlated between salt and PEG. Finally, liquid densities were predicted in binary solutions of water–PEG and ternary solutions of water–PEG–salt.

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Abbreviations

k ij :

Binary interaction parameter

R:

Number of segments

T :

Temperature (K)

x i :

Mole fraction of component i

Z :

Compressibility factor

EoS:

Equation of state

OF:

Objective function

PHSC:

Perturbed hard sphere chain

SAFT:

Statistical associating fluid theory

Assoc:

Association term

Cal:

Calculated

Expt:

Experimental

Ref:

Reference

Pert:

Perturbation term

i, j :

Component index

ε :

Dispersion energy parameter (J)

εAB:

Energy parameter of the association between sites A and B (J)

ρ :

Number density (number of molecules in unit volume), (Å−3)

σ :

Temperature independent segment diameter (Å)

κ AB :

Volume of interaction between sites A and B

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Authors and Affiliations

  1. Thermodynamics Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, Tehran, 16846-13114, Iran

    Masood Valavi

  2. Department of Chemical Engineering, Iran University of Science and Technology, Tehran, Iran

    Saeed Shirazian

  3. Department of Chemical and Oil Engineering, Sharif University of Technology, Tehran, Iran

    Ali Forouzesh Pour

  4. Department of Chemical Engineering, Amirkabir University of Technology, Tehran, Iran

    Mani Ziary

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  1. Masood Valavi
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  2. Saeed Shirazian
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Correspondence to Masood Valavi.

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Valavi, M., Shirazian, S., Pour, A.F. et al. Calculation of the Density and Activity of Water in ATPS Systems for Separation of Biomolecules. J Solution Chem 42, 1423–1437 (2013). https://doi.org/10.1007/s10953-013-0040-8

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  • DOI: https://doi.org/10.1007/s10953-013-0040-8

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