Surface Tension and Parachor

Laubengayer, A.W., Ferguson, R.P., Newkirk, A.E., 1941. The densities, surface tensions and parachors of diborane, boron triethyl and boron tribromide. The atomic parachor of boron. J. Am. Chem. Soc. 63, 559-561. 

Parachor is the name (199) of a temperature-independent parameter to be used in calculating physical properties. Parachor is a function of Hquid density, vapor density, and surface tension, and can be estimated from stmctural information. Critical constants for about 100 organic substances have been correlated to a set of equations involving parachors and molar refraction (200). 

The physical properties associated with the parachor, vi2., the liquid surface tension and the density at various temperatures, for benzofuroxan and 5-methylbenzofuroxan are given by Hammick et al. The parachor values were reevaluated by Boyer et al ... 

Sugden J.G.S. cxxv. 1177, 1924 cxxvii. 1525, 1868, 1925) has compared the molecular volumes of substances under conditions such that they possess identical surface tensions and has shown that they are determined by the molecular constitutions of the substances. In obtaining the parachor P Sugden makes use of the approximate relationship between free surface energy and density noted by Macleod Trans. Farad. Soc. xix. 38, 1923) a = c(pi- p y... 

Fowler, R.H. A Tentative Statistical Theory of Macleod s Equation for Surface Tension and the Parachor, Proc., Royal Soc. of London, Series A (1937) 229-246. 

The values for the surface tension and the observed parachor of selenophene are as below ... 

Further information on the structure of phosphorus compounds is given by the parachor, which is a function of surface tension and molar volume, the molar volumes in effect being compared under conditions of equal surface tension.4 For a given liquid the expression... 

Molar volume is not a suitable parameter, for two reasons (i) Molar volumes vary with temperature and must be compared at temperatures and pressures proportional to critical values, (ii) Calculations of molar volumes are highly dependent on molecular structure, due to differences in intermolecular attraction. The parachor, [P], overcomes these difficulties by using surface tension, a property dependent on intermolecular attraction. Parachor is defined by Equation (34). M is molecular weight, y surface tension and D and d are densities of liquid and vapour respectively. SinceD>d, Equation(35)follows. 

Fowler, R.H. A Tentative Statistical Theory of Macleod s Equation for Surface Tension and the Parachor, Proc, Royal Soc. of London, Series A, p. 229,1937. Ghorayt b, K., and Firoozabadi, A. Modeling of Multicomponent Diffusion and Convection in Porous Media." SPE 51932. Proceedings of the 15th SPEReservoir Simulation Symposium, Feb. 14 to 17,1999, Houston.TX. 

The example discussed suggests another more realistic formulation of the equilibrium problem. Under the conditions of the previous problem, instead of P, and Pg, we specify the pressure in one phase, say, Pg. The system of Eqs. (8) and (9) is completed by the Laplace equation in the form of Eqs. (23). In the second equation, (23), the dependence /(/ ) is supposed to be known from the geometry of the porous space. The surface tension and the wetting angle are defined as known functions of the thermodynamic conditions (e.g., the surface is assumed to be wet by the condensate and the surface tension is calculated by the parachor method). The volumetric hquid... 

Over wide ranges of temperatures, parachor values for pure substances are nearly constant, but for solutions they depend on concentration of solutes. Using surface tensions and densities from 10 to 50 °C temperature range, which were determined in the Silesian University, the parachor values for aqueous solutions of citric acid can be expressed by... 

Experimental parachor P calculated from surface tension and density data using (1) Estimated parachor [119, 122]... 

SouckovaM, Klomfar J.Patek J (2015) Surface tension and 0.1 MPa density data for l-Cn-3-methylimidazolium iodides with n = 3, 4, and 6, validated using a parachor and group contribution model. J Chem Thermodyn 83 52-60... 

Numerous other constants are more limited in usefulness (see Table 4-1) as (1) aniline point (D611), (2) Parachor, which involves surface tension and gravity, (3) carbon-hydrogen ratio, (4) characterization gravity, which is used in judging stocks for thermal cracking, (5) Diesel ... 

The surface tension is calculated starting from the parachor and the densities of the phases in equilibrium by the Sugden method (1924) J... 

If reliable values of the liquid and vapour density are available, the surface tension can be estimated from the Sugden parachor which can be estimated by a group contribution method, Sugden (1924). 

Provided, therefore, the additive contributions for different structural components can be quantified, the partition coefficient can be readily computed, A long established and convenient means for such quantification is already available in the form of the parachor, which is equivalent to the molar volume of a substance when its surface tension is unity. Parachor is primarily an additive property and there are extensive tabulations of parachor equivalents for various structural elements, such as that by Quayle (30). Parachor (H) can be related to partition coefficient (P) using the relationship of McGowan (3I) -... 

For pure liquids, an empirical estimation method for surface tension is that of McLeod and Sudgen, based on the parachor (P), which be calculated from the chemical groups of the molecule [13]. 

In this equation, (P) is the parachor and the p values are the liquid- and vapour- molar densities in mol/cm3. Then a is obtained in mJ/m2. For the case of mixtures in the presence of vapour phase, the surface tension of a mixture is calculated in terms of the liquid and vapour composition, as ... 

Ixspcr has compiled the xurlave icnsiun ol ucetaldchsdc. propi waldehydc. and butyraldehyde at various tempera lure. I he surface tension ot formaldehyde wav estimated h the method described in Appendix A This method relate surface tension lo (he parachor. density, and molcculur weight I hr error is less than 50r. 

It appears that for these cyclic polymers the values of the specific refraction and the specific parachor are almost constant, though the refractive index, the density and the surface tension vary notably. The specific refraction and the specific parachor are independent of the degree of polymerization. 

The properties of Ge(OR)4 allow them to be considered more likely to be the esters of an inorganic acid than metal alkoxides these are colorless volatile liquids, containing monomeric tetrahedral molecules. The solid crystalline form is known only for R = Bu, OC6Hnc, and also 2,6-substituted phenoxides. All the members of the Ge(OR)4 homologous series are characterized by thoroughly determined physical characteristics — density, refraction index, surface tension, viscosity (and calculated parachor values), dipole moments in different solvents [222, 857, 1537] (Table 12.9). The results of the investigation of vapor pressure, density, viscosity polytherms, and so on. permitted rectification for the preparation of samples of high purity for sol-gel and MOCVD applications [682, 884]. 

The specific surface energy of a polymer can be estimated by means of an additive quantity, the Parachor. Alternatively, it maybe calculated from the molar cohesive density (which is also additive). Rules are given for the estimation of the interfacial tension and the contact angle of a liquid on a solid. 

Table 8.2 compares the experimental values of the surface tension of polymers (obtained by different methods) and the calculated values, the latter being obtained by means of the parachor. The discrepancies between the different experimental values are reasonably small. The calculated values are, with a few exceptions, in reasonable agreement with the experimental values. 

The Rao function has the same form as the Sugden function or Molar Parachor (Ps = My1/4/p), derived by Sugden in 1924, which correlates the surface tension with the chemical structure. Also the Small function or Molar Attraction Function, which correlates the cohesion energy density, ecoh, and the solubility parameter, 8, with the chemical structure, has this form ... 

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