The Ring Method

A method that has been rather widely used involves the determination of the force to detach a ring or loop of wire from the surface of a liquid. It is generally attributed to du Noiiy [42]. As with all detachment methods, one supposes that a first approximation to the detachment force is given by the surface tension multiplied by the periphery of the surface detached. Thus, for a ring, as illustrated in Fig. II-ll, 

Harkins and Jordan [43] found, however, that Eq. 11-26 was generally in serious error and worked out an empirical correction factor in much the same way as was done for the drop weight method. Here, however, there is one additional variable so that the correction factor/ now depends on two dimensionless ratios. Thus 

Experimentally, the method is capable of good precision. Harkins and Jordan used 

A zero or near-zero contact angle is necessary otherwise results will be low. This was found to be the case with surfactant solutions where adsorption on the ring changed its wetting characteristics, and where liquid-liquid interfacial tensions were measured. In such cases a Teflon or polyethylene ring may be used [47]. When used to study monolayers, it may be necessary to know the increase in area at detachment, and some calculations of this are available [48]. Finally, an alternative method obtains y from the slope of the plot of W versus z, the elevation of the ring above the liquid surface [49]. 

Experimentally, the method is capable of good precision. A so-called chainomatic balance has been used to determine the maximum pull, but a popular simplified version of the tensiometer, as it is sometimes called, makes use of a torsion wire and is quite compact. Among experimental details to mention are that the dry weight of the 

---

The CMC of commercial AOS and other surfactants at 40°C has been determined by Gafa and Lattanzi [6] who plotted the surface tension of aqueous surfactant solutions against concentration. The surface tensions were determined with the ring method according to du Nouy. Table 5 gives their CMC values in mmol/L and the surface tension at the CMC in mN/m. Table 5 also contains CMC values of isomerically pure sodium alkyl sulfates, sodium alkylbenzene-sulfonates, sodium hydroxyalkanesulfonate, and sodium alkenesulfonates at 40°C, taken from the literature [39 and references cited therein]. 

For a completely symmetrical curve, the end-point can be easily established as the inflection point through which a tangent can be drawn here for convenience the "rings method (Fig. 2.23) can be used, where the inflection point is obtained by intersection of the titration curve with the line joining centres of fitting circles (marked on a thin sheet of transparant plastic see ref. 61). 

There are numerous other methods for measuring surface tension that we do not discuss here. These include (a) the measurement of the maximum pressure beyond which an inert gas bubble formed at the tip of a capillary immersed in a liquid breaks away from the tip (the so-called maximum bubble-pressure method) (b) the so-called drop-weight method, in which drops of a liquid (in a gas or in another liquid) formed at the tip of a capillary are collected and weighed and (c) the ring method, in which the force required to detach a ring or a loop of wire is measured. In all these cases, the measured quantities can be related to the surface tension of the liquid through simple equations. The basic concepts involved in these methods do not differ significantly from what we cover in this chapter. The experimental details may be obtained from Adamson (1990). 

Sharma, R. R. 1963. Determination of surface tension of milk by the drop method and the ring method. Ind. J. Dairy Sci. 16, 101-108. 

As in Basic Protocol 1, the steps below describe determination of interfacial tension for a liguid/gas interface (i.e., a sample consisting of a single surface-active solution). Although it is very difficult, the ring method can also be used to determine the interfacial tension between two liquid phases (for modifications see Alternate Protocol 1). 

Figure 4.6 Measurement of interfacial tension by the ring method...

FIGURE 4.9 The ring method for the measurement of interfacial tension. 

The ring method (du Nuoy tensiometer) can be used to measure the interfacial tension as shown in Figure 4.9. The method measures the force required to detach a platinum wire ring from the interface by pulling on the ring. The mathematical relationship between the pulling force and interfacial tension is given by ... 

For examination of slow changes in the tension of an exposed surface the ring method is perhaps the best, and the use of du Nouy s tensi-meter, with the corrections of Harkins and Jordan, gives fairly accurate results. 

In some cases the surface tension also was measured by the ring method using a du Noiiy tensiometer. 

The possible dependence of the ring method on a contact angle has been discussed Ferguson stated that it is independent of contact angle, but this has not always been accepted. The basic formula for the method is ... 

IV) Residual background suppression. The residual background has been evaluated with two different methods the Alpha fit and the Ring method. 1) Alpha method the distribution of the Alpha parameter has been fitted with a second order polynomial, without the linear term, between 20 and 80 0 (where only background is present). Then the fit extrapolation to the 0-12.5° region... 

Freud and Freud (1930) and is rather complicated, but the calculated values of/agree with the empirical values within the experimental precision of about 0.25%. The schematic representation of the ring method is shown in Figure 6.14. 

It is possible to perform interfacial tension measurements between two immiscible liquids by the ring method, just like surface tension measurements, by ensuring that the bulk of the ring probe is submerged in the light phase prior to beginning the experiment. 

There are two modifications to the Wilhelmy plate method. In the first modification, the cup carrying the liquid is mobile and is lowered until the previously immersed plate becomes detached from the liquid surface, and the maximum vertical pull, / max on the balance is noted, similarly to the ring method. Then the capillary force, for the zero contact angle, can be given as... 

Okahara and coworkers prepared a number of diaza-crown compounds with substituents on the macroring carbon atoms. They used the reaction of a diazaoligoethylene glycol with a ditosylate to close the ring (method H-4) (Maeda et al., 1983). They used a strong base that favored reaction by the... 

The diisocyanate derivative of ethylenediamine was treated with sulfur-containing diamines or glycols in THF to form macrocycles containing sulfur, nitrogen, and in some cases, oxygen atoms in the ring (method Z-16) (Ishii et al., 1988). No specific details for these reactions were given in the patent. 

The surface tensions were determined by the ring method with appropriate corrections [7,10] and the viscosities were measured in an Ostwald-Cannon capillary viscometer. 

The angular distribution of elastically scattered neutrons of 3-7 Mev have been measured by Whitehead and Snowdon, using the ring method. Their results, which were confined to Al, Fe, and Pb, required very considerable correction for multiple scattering. Recently, the angular distribution of 1.0 Mev neutrons has been measured very accurately for a large number of elements by... 

In order to simplify presentation, in accordance with other authors, this monograph loosely uses the ring method of portra)dng naphthalene and higher con-... 

The rectangular test gap has a length of 12 mm, a width of 10 mm, and a height that is adjustable from 0.1 to 1.0 mm. This geometry has been used for studies with thermoplastics [7] as well as with thermosets [8]. A modification of the flat plate wear tester is the BASF wear tester. This test simulates the wear process in a molding machine. Another test apparatus developed at the DKI is the ring method, shown in Fig. 11.7. 

In practice, the absolute value is in error because of the diameter of the wire, the density of the liquid, as well as other terms, and it is often calibrated by a variety of substances to minimize such errors. The most important application of this method is the determination of interfacial tension between two liquids, where other methods do not apply very readily. The ring method is shown in Fig. C.5. 

---