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Section: 13 | Second Virial Coefficients of Polymer Solutions |
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John R. Rumble, ed., CRC Handbook of Chemistry and Physics, 103rd Edition (Internet Version 2022), CRC Press/Taylor & Francis, Boca Raton, FL.
If a specific table is cited, use the format: "Physical Constants of Organic Compounds," in CRC Handbook of Chemistry and Physics, 103rd Edition (Internet Version 2022), John R. Rumble, ed., CRC Press/Taylor & Francis, Boca Raton, FL.

SECOND VIRIAL COEFFICIENTS OF POLYMER SOLUTIONS

Christian Wohlfarth

Second virial coefficients characterize the thermodynamic behavior of a dilute polymer solution. They are usually defined via the concentration dependence of the osmotic pressure, π, of a polymer solution:

π/cB = RT[1/Mn + A2cB + A3cB2 + ···]          (1)

where:

A2, A3 second, third osmotic virial coefficient
CB (g cm–3) concentration of polymer (B)
Mn number-average relative molar mass of the polymer
R gas constant
T (measuring) temperature

However, most experimental data are measured by light scattering. Scattering methods enable the determination of A2 via the common relation:

KcB/R(q) = 1/MwPz(q) + 2A2Q(q)cB + ···        (2)

where:

K a constant that summarizes the optical parameters of a scattering experiment
Mw mass-average relative molar mass of the polymer
Pz(q) z-average of the scattering function
q scattering vector q = (4π/λ)sin½θ
Q(q) function for the q-dependence of A2
R(q) excess intensity of the scattered beam at the value q
λ wavelength
θ scattering angle

In the dilute concentration region, the virial equation is usually truncated after the second virial coefficient which leads to a linear relationship. A linearized relation over a wider concentration range can be constructed if the Stockmayer-Casassa relation between A2 and A3 is applied:

A3Mn = (A2Mn/2)2                                           (3)

The values of second virial coefficients depend on the chosen polymer-solvent pair, on temperature and pressure, and on molar mass. In good solvents, a scaling relation can be applied for the molar mass dependence:

A2 = αMw−β                                                     (4)

The constants α and β for a number of polymer-solvent pairs are given in the table below. They were newly fitted to experimental data by a nonlinear least-squares fitting procedure. Experimental data were taken from a recent table of experimental A2 values in Ref. 1. The unit of A2 (used to determine the constants α and β) is cm3 mol g–2. The unit for the molar mass is g mol–1.

Reference

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Mobile-friendly table

Constants to Calculate the Second Virial Coefficients for Polymer Solutions



PolymerSolventT/Kαβ
Continued on next page...
Amylosedimethylsulfoxide298.150.00860.235
Amylose tris(N-phenyl carbamate)2-propanone290.150.01570.417
Cellulose tris(N-phenyl carbamate)2-propanone290.150.00230.177
Cellulose tris(N-phenyl carbamate)tetrahydrofuran298.150.00210.116
Dextranwater298.150.03530.394
Dextran (acid-hydrolyzed)water298.150.05160.361
2-(Diethylamino)ethyl dextranwater293.150.1290.503
Hydroxypropyl celluloseethanol298.150.1080.371
Poly(N-acryloylmorpholine) N,N-dimethylformamide298.150.00840.295
Polybutadienecyclohexane298.150.01120.204
Polybutadienetetrahydrofuran296.150.02350.257
Poly(butyl methacrylate) 2-butanone298.150.00990.285
Poly(4-tert-butylstyrene)cyclohexane298.150.03770.362
Poly(4-tert-butylstyrene)toluene310.150.01290.293
Polycarbonate-bisphenol-A1,2-dichloroethane298.150.03720.319
Polycarbonate-bisphenol-Adichloromethane298.150.01240.205
Polycarbonate-bisphenol-Atetrahydrofuran298.150.04260.333
Polycarbonate-bisphenol-Atrichloromethane298.150.0160.227
Poly(chloroprene)butyl acetate298.150.00410.229


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