Molecular package density and apparent specific volume of the simulated and actual solutions

The paper discusses the obtained analytical expressions of concentration dependencies of the apparent specific volume on the size ratio k and variations in the molecular packing density of the mixture components Δy for simulated solutions, where 1 < k ≤ 8 and Ay = 0. The apparent specific volume proves to have a linear dependence on a mole fraction if the molecules of the optimal energy wise solution are different only in shapes (k = 1, Δy ≠ 0). It was evaluated how the geometric factor (1 < k ≤ 8, Δy ≠ 0) affects both the apparent specific volume and the packing density coefficient of different types of the real binary solutions. It was found out that the geometric factor is the major one, which affects the apparent specific volume of the mutually conjugate solutions containing nonpolar components. In the case of the solutions containing polar components of different structures (alcohol-acetic acid), the intermolecular interactions arising from the gravity forces are the main affecting factors, which can be comparable to the effect of the geometric factor in the vicinity of alcohol aqueous solutions, if water concentrations are not less than 0.9 of mole fractions.

References

[1] Tager A.A., Adamova L.V. Volumes of Mixing Fluids and Their Importance for the Modern Theory of Solutions. Uspekhi khimii [Russian Chemical Reviews], 1980, vol.XLIX, p. 618 (in Russ.).

[2] Bernal J.D. A geometrical approach to the structure of liquids. Nature, 1959, no. 4655, pp. 141-147.

[3] Balankina E.S. Influence of Size and Packing of the Molecules on the Thermodynamic Properties of Mixtures. Teplofizika vysokikh temperatur [High Temperature], 2009, no. 1, pp. 61-67 (in Russ.).

[4] Gray W.A. The packing of solid particles. London, Chapman and Hall Ltd., 1968.

[5] Haughey D.P., Beveridge G.S.G. Structural properties of packed beds - a review. Can. J. Chem. Eng., 1969, vol. 47, pp. 130-140.

[6] Bek G., Gyunterodt G., eds. Russ. Ed.: Metallicheskie stekla. Vyp. II. Atomnaya struktura i dinamika, elektronnaya struktura i magnitnye svoystva [Metallic Glasses. Vol. II. Atomic Structure and Dynamics, Electronic Structure and Magnetic Properties]. Moscow, Mir Publ., 1986. 456 p.

[7] Smith L.N. Knowledge-based system for powder metallurgy technology. London, Professional Engineering Publishing, 2003, 255 p.

[8] Furnas C.C. Grading aggregates. II. The application of mathematical relations for beds of broken solid of maximum density. Ind. Eng. Chem., 1931, vol. 23, по. 9, p. 1058.

[9] Meng L., Lu P., Li Sh., Zhao J., Li T. Shape and size effects on the packing density of binary spherocylinders. Powder Technology, 2012, vol. 228, p. 284.

[10] Shatalova I.G., Gorbunov N.S., Likhtman V.I. Fiziko-khimicheskie osnovy vibratsionnogo uplotneniya poroshkovykh materialov [Physical and Chemical Foundation of Vibration Compaction of Powder Materials]. Moscow, Nauka Publ., 1965. 221 p.

[11] Clarke A.S., Willey J.D. Numerical simulation of the dense random packing of a binary mixture of a hard spheres. Phys. Rev. B, 1987, vol. 35, p. 7350.

[12] He D., Ekere N.N., Cai L. Computer simulation of random packing of unequal spheres. Phys. Rev. E., 1999, vol. 60, по. 6, p. 7098.

[13] Yu A.B., Zou R.P., Standish N. Packing of ternary mixtures of nonspherical particles. Journal of Am. Ceram. Soc., 1992, vol. 75, по. 10, pp. 2765-2772.

[14] Danish M., Jin Yu., Maske H.A. Model of random packing of different size balls. Phys. Rev. E, 2010, vol. 81, p. 051303.

[15] Balankina E.S., Lyashchenko A.K. Acoustic Properties and Structures of Liquids Materialy XVsessii Rossiyskogo akusticheskogo obshchestva. Moscow, GEOS Publ., 2004, vol. 1, p. 104 (in Russ.).

[16] Adamenko I.I. Vliyanie davleniya na termodinamicheskie svoystva molekulyarnykh zhidkostey i ikh rastvorov [The Effect of Pressure on the Thermodynamic Properties of Molecular Liquids and Their Solutions]. Avtoreferat diss. doct. tekhn. nauk [Dr. eng. sci. diss. abstr.]. Kiev, 1991.

[17] Marcus Y. Ion solvation. N.Y., John Wiley & Sons. 1985. 306 p.

[18] Goates J.R., Ott J.B., Grigg R.B. Excess volumes of n-hexane + n-heptane, + n-octane, + n-nonane, and + n-decane at 283.15, 298.15, and 313.15 K. J. Chem. Thermod., 1981, vol. 13, p. 907.

[19] Benson G.C., Pflug H.D. Molar excess volumes of binary systems of normal alcohols at 25 C. J. Chem. Eng. Data, 1970, vol. 15, по. 3, p. 382.

[20] Zarei H.A. Densities, excess molar volumes and partial molar volumes of binary mixtures of acetic acid+alkanol (C1-C4) at 298.15 K. J. Mol. Liq., 2007, vol. 130, pp. 74-78.

[21] Orge B., Rodriguez A., Canosa J.M., Marino G., Iglesias M. Variation of densities, refractive indices and speeds of sound with temperature of methanol or ethanol with hexane, heptane and octane. J. Chem. Eng. Data, 1999, vol. 44, pp. 1041-1047.

[22] Benson G.C., Kiyohara O. Thermodynamics of aqueous mixtures of nonelectrolytes. I. Excess volume of water-n-alcohol mixtures at several temperatures. J. Solut. Chem., 1980, vol. 9, p. 791.

[23] Huot J.-Y., Battiestel E., Lumry R., Villeneuve G., Lavalle J.-F., Anusiem A., Jolicoeur C. A comprehensive thermodynamic investigation of water-ethylene glycol mixtures at 5, 25 and 45 C. J. Solut. Chem., 1988, vol. 17, по. 7, p. 601.

[24] Xu L., Hu X., Lin R. Volumetric properties of glycerol with N, N-dimethylformamide and with water at 25 C and 35 C. J. Solut. Chem., 2003, vol. 32, по. 4, p. 362.