Erratum: ``Exchange and Direct Second Virial Coefficients for Hard Spheres''

1967 ◽  
Vol 46 (3) ◽  
pp. 1224-1224 ◽  
Author(s):  
Marjorie E. Boyd ◽  
Sigurd Yves Larsen ◽  
John E. Kilpatrick
Keyword(s):  
Hard Spheres ◽  
Virial Coefficients ◽  
Second Virial Coefficients

Exchange and Direct Second Virial Coefficients for Hard Spheres

1966 ◽  
Vol 45 (2) ◽  
pp. 499-508 ◽  
Author(s):  
Marjorie E. Boyd ◽  
Sigurd Yves Larsen ◽  
John E. Kilpatrick
Keyword(s):  
Hard Spheres ◽  
Virial Coefficients ◽  
Second Virial Coefficients

Second virial coefficients of dipolar hard spheres

2010 ◽  
Vol 22 (32) ◽  
pp. 325104 ◽  
Author(s):  
Albert P Philipse ◽  
Bonny W M Kuipers
Keyword(s):  
Hard Spheres ◽  
Virial Coefficients ◽  
Second Virial Coefficients

scholarly journals Protein aggregation in salt solutions

2015 ◽  
Vol 112 (21) ◽  
pp. 6766-6770 ◽  
Author(s):  
Miha Kastelic ◽  
Yurij V. Kalyuzhnyi ◽  
Barbara Hribar-Lee ◽  
Ken A. Dill ◽  
Vojko Vlachy
Keyword(s):  
Protein Aggregation ◽  
Hard Spheres ◽  
Protein Crystallization ◽  
Virial Coefficients ◽  
Necessary Condition ◽  
Thermodynamic Perturbation Theory ◽  
Salt Solutions ◽  
Biological Drugs ◽  
Second Virial Coefficients ◽  
Square Well

Protein aggregation is broadly important in diseases and in formulations of biological drugs. Here, we develop a theoretical model for reversible protein–protein aggregation in salt solutions. We treat proteins as hard spheres having square-well-energy binding sites, using Wertheim’s thermodynamic perturbation theory. The necessary condition required for such modeling to be realistic is that proteins in solution during the experiment remain in their compact form. Within this limitation our model gives accurate liquid–liquid coexistence curves for lysozyme and γ IIIa-crystallin solutions in respective buffers. It provides good fits to the cloud-point curves of lysozyme in buffer–salt mixtures as a function of the type and concentration of salt. It than predicts full coexistence curves, osmotic compressibilities, and second virial coefficients under such conditions. This treatment may also be relevant to protein crystallization.

Virial Expansions for Low Dimensional Ferrofluids

1991 ◽  
Vol 248 ◽  
Author(s):  
M. Widom ◽  
H. Zhang
Keyword(s):  
Magnetic Susceptibility ◽  
Magnetic Particles ◽  
Particle Density ◽  
Hard Spheres ◽  
Three Dimensional ◽  
Virial Coefficients ◽  
Colloidal Suspensions ◽  
Second Virial Coefficients ◽  
Dilute Gas ◽  
Low Dimensional

AbstractFerrofluids are colloidal suspensions of magnetic particles which we model as a dilute gas of dipolar hard spheres. At low particle density the osmotic pressure and magnetic susceptibility may be expanded in a virial series. We evaluate the second virial coefficients for fluids confined to a line, or to a plane, as well as ordinary three dimensional fluids in ellipsoidal containers. We focus our attention on anisotropy of the magnetic susceptibility and point out the role of particle chaining in determining the magnetic anisotropy of low dimensional ferrofluids.

Critical consolute point in hard-sphere binary mixtures: Effect of the value of the eighth and higher virial coefficients on its location

2010 ◽  
Vol 75 (3) ◽  
pp. 359-369 ◽  
Author(s):  
Mariano López De Haro ◽  
Anatol Malijevský ◽  
Stanislav Labík
Keyword(s):  
Equation Of State ◽  
Binary Mixtures ◽  
Hard Sphere ◽  
Hard Spheres ◽  
Virial Coefficients ◽  
Fluid Mixture ◽  
Binary Fluid ◽  
Virial Series ◽  
Consolute Point ◽  
Critical Constants

Various truncations for the virial series of a binary fluid mixture of additive hard spheres are used to analyze the location of the critical consolute point of this system for different size asymmetries. The effect of uncertainties in the values of the eighth virial coefficients on the resulting critical constants is assessed. It is also shown that a replacement of the exact virial coefficients in lieu of the corresponding coefficients in the virial expansion of the analytical Boublík–Mansoori–Carnahan–Starling–Leland equation of state, which still leads to an analytical equation of state, may lead to a critical consolute point in the system.

The Bender Equation of State and Virial Coefficients

2000 ◽  
Vol 65 (9) ◽  
pp. 1464-1470 ◽  
Author(s):  
Anatol Malijevský ◽  
Tomáš Hujo
Keyword(s):  
Equation Of State ◽  
Virial Coefficient ◽  
Virial Coefficients ◽  
Low Density ◽  
Second Virial Coefficients ◽  
The Third ◽  
Temperature Dependences ◽  
Experimental Values

The second and third virial coefficients calculated from the Bender equation of state (BEOS) are tested against experimental virial coefficient data. It is shown that the temperature dependences of the second and third virial coefficients as predicted by the BEOS are sufficiently accurate. We conclude that experimental second virial coefficients should be used to determine independently five of twenty constants of the Bender equation. This would improve the performance of the equation in a region of low-density gas, and also suppress correlations among the BEOS constants, which is even more important. The third virial coefficients cannot be used for the same purpose because of large uncertainties in their experimental values.

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