Critical DifferenceTemperahre t
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Correlating Surface Tensions of Liquids
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A NEW NOMOGRAPH
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DONALD F. OTHMER, SAMUEL JOSEFOWITZ, AND ALFRED F. SCHiMUTZLER Polytechnic Institute of Brooklyn, Brooklyn, N . Y . c s i p g techniques developed for many other phJsical properties, surface tensions of a liquid a t various temperatures have been correlated to give straight-line plots on logarithmic paper against the surface tensions of a reference liquid a t constant values of the critical difference temperature. The algebraic expression is: log y = rn log 7' C . This may be shown to be derived simply from the expression log y = n log TO IC, which in turn comes directly from the expression first proposed by E6tvFs in 1886. In these equations n, m, C, and K are constants, y is the surface tension of one liquid, and y' is the surface tension of a reference liquid a t the same critical difference temperature. A nomograph is developed from which the surface tension of any liquid a t any temperature can be read off directly if the surface tension a t two temperatures is known.
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SIMPLE plot has been used (5) to correlate the vapor pressure and latent heat of a substance, on standard logarithmic paper (or the logarithms of the values may be plotted on ordinary graph paper). The Y axis is used in the regular way as the vapor pressure axis. Along the X axis are taken values of the vapor pressures of any convenient referenee substance ; and from a table the corresponding temperature scale is calibrated. Ordinates are erected a t these points, on which are plotted the vapor pressures from the Y axis. These points are connected by a straight line, the slope of which is the ratio of the molar latent heat of the material whose vapor pressures are being plotted t o the molar latent heat of the reference substance at the same temperature. Other articles have shown that this method of correlation may be applied t o numerous other properties of materials, including critical constants (6), gas solubilities (IS), adsorption pressures and heats (12), vapor-liquid equilibrium constants (7), vapor compositions, relative volatilities, and activity coefficients of constituents of solutions (9), viscosities of liquids ( 8 ) )viscosities of gases (IO), and equilibrium constants of chemical reactions (11). By plotting the properties of one substance against the properties of another substance, deviations from the ideal behavior tend t o be compensated because of similar causes for these deviations in most materials. Thus, it may be expected, and has been found, that a better correlation may be obtained by such a reference substance plot than by plotting the property directly versus a temperature scale.
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20 30 40 50 dynes / cm. Surface Tension Of Benzene Figure 1. Logarithmic Plot of Surface Tensions of Various Compounds us. Surface Tensions of Benzene a t Same Critical Difference Temperatures Numbers refer to Compounds i n Table I
All four graphs have same ordinates, which may be either surface tension in dynes per cm. from scale at bottom or critical difference temperature from soale at top
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May 1948
INDUSTRIAL AND ENGINEERING CHEMISTRY
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It was attempted t o apply t o surface tensions the general principles utilized in these correlations of other physical properties. (While surface tensions at 1 atmosphere pressure are considered, in many cases the same correlation can be used for higher pressure and above the boiling point of the liquid.) Following the methods previously used, a logarithmic plot was made of the surface tensions of various liquids versus the surface tensions of a reference substance at the same temperatures. A series of flat curves was obtained instead of the desired straight lines. Other considerations lead t o the use of a temperature scale based on what may be called the critical difference temperature, T,. This is the temperature difference between the experimental temperature, T, and the critical temperature, T,, of the particular compound. The usual temperature scale for expressing data of gases uses absolute zero, -273" C., as the reference point. This point, however, has little meaning for properties of liquids. A more characteristic and meaningful reference point for liquid temperatures has been shown t o be the critical point of the substance (1, 4); and by its use there may be considered the temperature difference or interval between the value,' as usually expressed, T , and the critical temperature, To-i.e., ( T , T ) . This difference of temperature below a fixed point is a more logical means of expressing temperatures of liquids than by absolute temperature or a n y other temperature value above an other fixed point, and hereinafter is referred to as the critical digerence temperature, To.
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Figure 1 shows that a plot of the surface tension of a Iarge number of compounds against the surface tension of benzene at the same value of the critical difference temperature gives straight lines. Attention is called t o the anomaly of water in this respect (data of Moser from Dorsey, W), which represents a definite break at approximately 35" C. The unusual behavior of the various physical properties of water at that temperature has been observed before and is discussed by Dorsey (2). Timmermans and Bodson (14) showed a n anomaly in'surface tensions of water at 13' C. but did not work above 35" C. t o note this break. It is probably due t o a change in the polymeric structure of liquid water at t h a t temperature. The break of a straightline function is much more noticeable than the corresponding break in a function which gives a curve, where t h e slight change in curvature may be missed. The reduction of plots of data for water t o straight-line functions of a specially devised temperature scale has emphasized this same break for other physical properties (8, 1 1 ) . The numbers in Figures 1 and 2 refer t o the compounds listed in Table I. Because in some cases the range of the critical difference temperature for s o q e of the compounds was greater than that which could be obtained for liquid benzene, the temperature scale of Figure 1 was extrapolated, using a material with a higher critical temperature (phenol) by the same method described for expanding a temperature scale i n the plot of vapor pressures against those of a reference substance (6). The general equation of these straight lines or of the individual sections of the broken line for water is log y = m log y'
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TABLE I. COMPOUNDS TESTED 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
Carbon disulfide Carbon tetrachloride Chlorobenzene Toluene Ethanol Phenol Isoamyl alcohol m-Cresol o-Cresol p-Cresol Methylamine Ethylamine Acetonitrile Benzonitrile
Aniline Dimethylamine Pyridine Dimethyl aniline Methyl propionate 20. E t h y l formate 21. Methyl acetate 22. Acetaldehyde 23. Isovaleric acid 24. n-Butyris acid 25. Propionic acid 26. Acetic acid 27. E t h y l propioflate 28. Propyl formate
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Figure 2. Logarithmic Plot of Surface Tensions of Various Compounds us. Critical Difference Temperatures Number. refer t o Compound. in Table I ,
Vol. 40, No. 5
INDUSTRIAL AND ENGINEERING CHEMISTRY
888 11. x AND Y l T A L U 3 S SURFACE TENSIOK Soiio-
TABLE FOR
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Compound Acetal Acetaldehyde Acetaldoxime Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetophenone Allyl alcohol Anethole Aniline A~ m ~ n~ l P~ . . . ~
Ammonia Isoamyl acetate Isoamyl alcohol Benzene Benzonitrile Benzylamine Bromobensene Isobutyl acetate n-Butyl alcohol Isobutyl alcohol n-Butyric acid Isobutyric acid n-Butyronitrile Carbon disulfide Carbon tetrachloride Chloral Chlorine Chlorobenzene p-Chlorohromobenzene Chloroform p-chlorotoluene a-Cresol m-Cresol p-Cresol Cyclohexane Diethyl ketone Diethyl oxalate Diethyl sulfate Diethyl aniline Dimethyl sulfate Dimethylainine Dimethyl aniline E t h y l acetate E t h y l acetoacetate E t h y l alcohol E t h y l benzoate Ethyl bromide E t h y l n-butyrate E t h y l isobutyrate Ethyl ether E t h y l formate E t h y l iodide E t h y l mercaptan Ethyl propionate E thyla mi ne E t h y l benzene Ethylene chloride Ethylene oxide n-Hexane Hydrogen cyanide Mesitylene Methyl acetate Methyl alcohol Methyl n-butyrate JIethvl isohutyrale lIeth$lchloridc Methyl ether Methyl ethyl ketone Methyl formate Methyl propionate Methyl amine Kaphthalene Nitroethane Nitroinethane Nitrosyl chloride Nitrous oxide n-Octane Paraldehyde Phenetole Phenol Phosphorus oxychloride Piperidine Propionic acid Propionitrile n-Propyl acetate n-Propyl alcohol n-Propyl formate n-Propvlamine p-Isop
