Traube rule

The vertical distance between the curves depends on T, but it cimounts to about 2-2.5 kJ per mole of CH2-groups, which at room temperature corresponds to about 1 RT per mole. This is typiCcd and sometimes referred to as the quantitative Traube rule (sec. 1.4.5e)2). 

The partial specific volume, v, (for mudns, normally in the range of 0.60 to 0.65 mL/g) has to be determined separately v is usu y obtained from a plot of solution density versus concentration. The accuracy with which this value can be obtained (compare Section IV,3,a for refractive increment measurements) will largely be affected by errors in concentration measurement, although the final value can be checked by calculation by using the Traube rule (see, for example. Ref. 71), if the amino add and carbohydrate composition of the mucin are known. 

Traube rule, more often referred to as the Traube rule. In agreement with eq. (II. 12), the Ducleaux-Traube rule corresponds to a linear relationship between the surfactant chain length and the p0 - pj,s) value. The latter may be viewed as the work of adsorption performed under standard conditions. Indeed, let us assume that the work of adsorption, p0 - p(0s), is a linear function of the number of carbon atoms in the surfactant hydrocarbon chain, i.e ... 

The value of cpCH2 that corresponds to the Ducleaux-Traube rule is approximately equal to R7Tn (3-3.5)= 3 kJ. 

Fig 11-12. The validity of the Ducleaux- Traube rule for the three surfactants, the neighboring members of the same homologous series... 

When water soluble surfactants adsorb at the interface between a liquid hydrocarbon and water, the trends in adsorption are very similar to those established for the air - solution interface (see Chapter II). The Traube rule remains valid, and the dependence of the surface tension on concentration can be described by Szyszkowski s equation (11.18). Moreover, at identical surfactant concentrations, the absolute values by which the surface tension is lowered at water - air and water - hydrocarbon interfaces are not that different. The surface tension isotherms for these interfaces are parallel to each other (Fig. III-6). That is due to the fact that the work of adsorption per CH2 group, given by eq. (II. 14), is determined mostly by the change in the standard part of the chemical potential of the solution bulk, q0. Similar to the air-water interface, the energy of surfactant adsorption from an aqueous solution at an... 

In the preceding Chapters I to 3 it was demonstrated how surfactants of different nature and structure modify the properties of interfaces due to their adsorption. It was also shown that there is not only one parameter, which allows classifying the action of a surfactant. While some surfactants are called highly surface active when they adsorb and decrease the interfacial tension at extremely low bulk concentrations, others deserve this attribute due to their capability to decrease the interfacial tension to extremely low values. It was also shown that the surfactants properties correlate with each other in a particular way, and the Traube rule is only one of the simple correlations valid for each homologous series. 

The constcint b incretises by a certain factor (essentially between 3 to 3.5) when the hydrophobic chain increases by one CH2 group, which corresponds to the Traube rule. 

It is usually found that the cmc of a homologous series of surfactants decreases by a factor of approximately 2 for every CH2 added to the hydrophobic chain. Traubes rule states that adding a CH2 to the chain changes the surface activity by a factor of 3, in the sense that a concentration one-third as large is required to obtain the same decrease in surface tension. What is the relation—if any—between these two phenomena ... 

For the data in Table 18 the dissociation energies of the primary valence bond, i.e. the heats of combustion had to be used, but now we must consider the energy of overcoming molecular cohesion, which is measured by the heats of sublimation and vaporization or by the van der Waals constant a. For the latter, and for the Sutherland constant closely allied to it, van Laar has already established certain additive relationships. These are expressed even more definitely in the well known Traube rule for the heats of adsorption of homologous series, which, according to Eucken, are closely related to the heats of vaporization. 

The surface activity of the soluble cationic surfactants at the water-air and water-nonpolar oil interfaces is mainly determined by the structure of the hydrocarbon chains. The work of adsorption in the homologous series of alkylammonium salts obeys the Traube rule [24,46,63,76]. Shipunov studied adsorption in the homologous series of tetra-alkylammonium chlorides at the water-heptane interface. He established that the work of adsorption is proportional not to the number of methyl groups in the... 

The fact that a determined from molecular size coincides with that obtained from surface tension fits (Table 4.5) is very nseful for applications. Thus, when fitting experimental data, we can use the value of a from molecular size, and thus to decrease the number of adjustable parameters. This fact is especially helpful when interpreting theoretically data for the surface tension of surfactant mixtures, such as SDS + dodecanol [54] SDS + CAPB [59], and fluorinated + nonionic surfactant [61]. An additional way to decrease the number of adjustable parameters is to employ the Traube rule, which states that increases with. 025kT when a CH2 group is added to the paraffin chain for details see Refs. [54,55,60]. 

The surface tensions for solutions of organic compounds belonging to a homologous series, for example, R(CH2)nX, show certain regularities. Roughly, Traube [145] found that for each additional CH2 group, the concentration required to give a certain surface tension was reduced by a factor of 3. This rule is manifest in Fig. lll-15b the successive curves are displaced by nearly equal intervals of 0.5 on the log C scale. 

Traube s rule accommodates the balance between hydrophobicity and hydro-philicity. It has been extended somewhat and formalized with the development of quantitative methods to estimate the surface area of molecules based on their structures [19, 237]. The molecular surface area approach suggests that the number of water molecules that can be packed around the solute molecule plays an important role in the theoretical calculation of the thermodynamic properties of the solution. Hence, the molecular surface area of the solute is an important parameter in the theory. In compounds other than simple normal alkanes, the functional groups will tend to be more or less polar and thus relatively compatible with the polar water matrix [227,240]. Hence, the total surface area of the molecule can be subdivided into functional group surface area and hydro carbonaceous surface area . These quantities maybe determined for simple compounds as an additive function of constituent groups with subtractions made for the areas where intramolecular contact is made and thus no external surface is presented. 

Traube s rule phys chem In dilute solutions, the concentration of a member of a homologous series at which a given lowering of surface tension is observed decreases threefold for each additional methylene group in a given series. trau-baz, rtil ) tretamlne See triethylenemelamine. tred-3,men ... 

It has been shown 8) that VT, the molar volume calculated from Traube s rule 4), VM, the molar volume of Exner 3), and the parachor,5) P all give significant correlation with the equation... 

Mark and Saito 31) attempted fractionating polymers by means of chromatography as early as 1936. They filtered solutions of cellulose acetate in acetone through a column with a charcoal-like adsorbent made from blood. The eluate contained the fraction of highest molar mass the rest of the sample was trapped in the column. It could be extracted by dioxane from separated portions of the packing. The largest molecules had travelled farthest. This was in contrast to expectation from Traube s rule and indicated size exclusion. 

For organic compounds consisting of hydrocarbon chains, solubility in water decreases with an increase in chain length of the homologous series (i.e., Traube s rule), because the compounds become more hydrophobic and nonpolar. More hydro-phobic adsorbates are expelled from water and thus allow an increasing number of water-water bond to be reformed. A nonpolar adsorbate will be strongly adsorbed from a polar solvent by a nonpolar adsorbent but will not be adsorbed much on a polar adsorbent in a nonpolar solvent. Therefore, an increase in the polarity of an adsorbate decreases its adsorption on activated carbon, which is a relatively polar adsorbent, in water. 

Thus the work of adsorption increases by a constant amount for each CH2 added to the hydrocarbon chain of the molecules. This must mean that each CH2 group is situated in the same relation to the surface as every other such group in the chain, and this can only be the case if the chains lie parallel to the surface. Hence Langmuir concluded that Traube s rule—for this is the name given to the effect of increasing length of chain... 

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