July, 1961
THEMEA4sUREMENTO F FILMELASTICITY
Conclusions This work has shown that anion-exchange resins absorb predominantly the ions M02(N03)4- along with some M02(liS03)3from aqueous metal nitrate solutions of the lhexavalent actinides. I t also has shown that the tetranitrato species is a species which does not exist to any appreciable extent in aqueous metal nitrate or nitric acid solutions whereas the trinrtrato complex is detected readily in concentrated nitric acid. The relative amounts of these two complexes in the resin phase were found to be, within experimental error, independent of the aqueous phase nitrate concentration but were dependent on properties of the resin phase (degree of resin loading and total resin capacity). Liquid amines have been found to extract only the trinitrato ions of the hexavalent actinides* despite efforts to extra1.t measurable quantities of the tetranitrato complex by varying both amine concentration in hydrocarbon diluent and aqueous phase metal nitra,te and nitric acid concentration^.^^ This work indicates the fallacy of assuming without direct e\-idenoe, as has been done with erroneous (29) W,E. Keder, Hanford Laboratories private communication.
1107
conclusions,'Q* what complex is present in the resin phase. There is also some danger in assuming that the same species are extracted by liquid amines as are absorbed by anion-exchange resins. However, in most cases the liquid amines probably do extract the same species as those absorbed by the resins. This is certainly the case with the quadrivalent actinide nitrates where the ions M(NOs)6= are extracted by both the liquid amines and the anion-exchange resins.8 The recent use of ( r n ~ o ~ to ~ represent f) ligand anion activity in the calculation of formation coiistants a t high electrolyte concentrations from aiiionexchange data26-28has been rendered highly questionable by the Pu(V1) absorption spectra data presented here. Extension of similar spectrophotometric studies of the actinides to chloride media is planned. Acknowledgment.-The author expresses his appreciation to Robert 31. Wheaton of the Dow Chemical Company for his help in obtaining the low capacity anion-exchange resins. The author also thanks the personnel of the Analytical Laboratories Operation who carried out many of the analyses.
THE RIEASUREMEKT OF FILM ELASTICITY' BY KAROLJ. MYSELS,MICHAEL C. Cox AKD JOHN D. SKEWIS Chemistry Department, Cnicersity o j Southern Calijornia, Los Angela 7 , Calif R e c e i d October 14,1960 The elasticity mot-lulus of soap films as defined by Gibbs has been measured for the first time. The method used involves simultaneous determination of the change in the surface tension acting upon a film under observation and of the motion of the interference fringes which this produces. The force acting upon the film is determined as part of the total force acting upon a vertical frame supporting this film in contact with the solution. The changes in surface tension are produced by rapidly withdrawing another film-forming frame from the solution, thus increasing greatly the total surface. The motion of the fringes is recorded photographically and is then translated into the motion of the surface elements on the assumption that the volume of liquid within the film remains constant. Details and limitations of this procedure are discussed. For a number of mobile fdms the modulus of elasticity is of the order of 10 dynes/cm., while for a rigid film of sodium lauryl sulfate-lauryl alcohol solution it is of the order of 100 dynes/cm. This provides evidence for another factor in the wellknown stabilizing effect of lauryl alcohol upon sodium lauryl sulfate foams.
It is well kna'wn t'hat oiily certain liquids are capable of forming foams, bubbles or films of reasonable stability, soap solutions being the classical example of this behavior. I t seems t'o be well accepted2 that when such liquids are reduced to thin layers, t'hey develop an increasing resist,ance to further extension and further thinning. In other materials, particularly in pure liquids or in gases, there is, on the contrary, an increasing tendency to further thinning due to van der Waals force^.^ There is probably a variety of causes for the increasing resistance to thinning shown by film formers. Among these may he cited bulk viscoelastic effects, which may he operative in some polymer solutioms; iiicreasing viscosity due to (1) Presented in p a r t a t the Atlantic City Meeting of t h e American Chemical Society, September, 1959. This work was supported by t h e Air Force Offire of Scientific Research and Development under Cont r a c t A F 49(638)-300. (2) J. A. Ritchener and C. F. Cooper, Quart. Rei,s. ( L o n d o n ) , 13, 71 (1959).
(3) (a) A . J. De \-rips, Rec. trao. chim., 7 7 , 383 (19.58); ( b ) J. T h . G. Overheek, ,I. I ' h y s . Chcm., 64, 1178 (1960).
cooling or evaporation, which accounts for the ease of bubble formation by molten glass4; the increase in surface tension due to evaporative cooling which permits sometimes film formation in pure 1icruids5; the repulsion of the two surfaces of the film due to hydration or entropy effects of adsorbed iioii-ionic. surfactants, and especially due to the double layer repulsion of adsorbed ionic surfactants, both of which become operative when the film i5 thin enough to appear black, ie., is belox1 about 500 A very important reason for the iesistance to thinning and one which can operate in films thick enough to show interference colors, in n'ewtonian liquids and in the absence of cooling or evaporation is iurface elasticity. Sur face elasticity is the increase in burface ten(4) C V. Boys "Soap Bubbles Their Colours and the Forces nhich Mould Them," (Second Edition o n l y ) Eoc for Pronioting Christian Knowledge, London. F 6 Graham Ne\? York l ( l l 2 Reprinted Dover, New T o r k 1959, pp 116-117 ( 5 ) G Van der Mensbrugghe Mem dead Roy Si1 Beio 43 (4) (1882), T H Hailehurst and H A Ne\ille, J Phys Chem 41, 1205 (19'37)
K. J. ~ I T S E L31. S , C. Cox AND J. D. SKEWIS
1108
b)
(1 1
face tension higher. Gibbs also has ihon.11 how film elasticity can be calculated in terms of the chemical potential of the surfactant for a pure, two component system. His result is E = 4r2(d,u/dG) (2) nhere r is the surface density of the solute, I.( its chemical potential, and G its total amount present in the film per unit area. illthough the concept of film elasticity is thus quite old and the important role it plays in film stability is well established, little is known about its numerical value. Its theoretical evaluation is difficult because of the uncertainties concerning the chemical potential of surfactants. especially above the critical micelle concentration, and because of the difficulty of realizing a pure, two component system with these materials. Experimentally, no attempt seems to have been made to measure it directly. The present paper describes an experimental approach to measuring film elasticity and presents exploratory results which establish its reality. Our method is based on qualitative observations wported elsewhere8 and consists in simultaneously iecaoiding: the motion of fringes of a film and the force exerted upon this film. Si1ic.e fringes are lines of equal thickness and not fixed with respect to the surface of the film, one has to translate their motion into the motioii of the surface itself as described below. The force exerted on the film is due to changes in surface tension of the solution in contact with it, and this in turn is changed by the mechanized motion of a large rectangular frame pulling a film in and out of the solution and thus effectively changing the total surface of the system by a considerable fraction. Experimental
CI
Fig. t.--C;luss frames used in this study.
Fig. 2 --Schematic front view of the apparatus for measuring film elasticity. The relative position of frames (b) and (c) is shown on the right.
sion of a film when its area is being extended and, therefore, ith thickness decreased. Since the film has two surfaces, this leads to Gibbsj6 definition ot the modulus of film elasticity, E , as E
=
2sdr/ds
1-01. 62
(1)
where s is the surface area and y is the surface tension. A few years before Gibbs, Marangoni’ pointed out in effect that the difference between dynamic and static surface tension provides one reason for surface elasticity. This could be quite effective against sudden disturbances of the film, hiit in view of the thinness of the film, its relaxation time should be a very small fraction of a second and its effects rather transient. The reason for a smaller but less transient surface elasticity was shown ‘by Gibbs to lie in the depletion of surfactant in the intralamellar solution as it is adsorbed upon the more extended surface. The equilibrium surface concentration thus becomes lower and the sur(6) J. W. Gibbs, “On t h e Equilibrium of Heterogeneous Substances,” T m n s . Connecticut Acad., 3, 108, 343 (1876); ”Collected JVorks,” IJonzniaris Green, New York, 1928, 1931, Vol. 1. p. 56. ( 7 ) C. Alarangoni, A-uouo Cimento, (21 6--6, 239 (1872).
The apparatus is a modification of the one described elsewhere.9 I t consists essentially of a square bottle 5 X 5 cm. containing the solution and of three frames dipping in the solution and supported from above. The bottle is closed by a heavy brass plate and a foam plastic gasket with connections to the three frames passing through small holes in the plate. One of the frames (a, Fig. 1 ) bears the film under observation and is supported by a dynamometer measuring the forces acting upon the film. Another frame ( b ) serves to extend the surface and is operated by a mechanized rack and pinion device mounted above the brass plate. The third frame (c) merely serves to compensate for the buoyancy effect produced by the motion of the second frame and it is moved synchronously but in opposite direction by the same rack and pinion device. Figures 2 and 3 show schematically the arrangement used. The observation frame (a) was made of very thin glass rod about 1 mm. in diameter and was generally 2 cm. wide, although frames 1 and 2.25 cm. wide were also used. The rod supporting this frame was suspended from the arm of a dynamometer. This suspension was such that the frame could oscillate freely but could not rotate and was fixed at a 45’ angle with respect to the incoming light and the direc tion of observation. The total weight of the frame and suspension was 0.40 g . The dynamometer mas a Statham Instruments, Los Angeles, Calif ., transducer model G 10-0.07-2000, which is essentially a lever whose rigidity is due to four sets of wires connected in a bridge network. The changes of resistance of these wires as they contract or expand with the motion of (8) K. J. Mysels, K. Shinoda and S. Frankel. “Soap Films. Stiidiea of Their Thinning and a Bibliography,” Pergarnon Press, New York, N. Y . , 1959, p. 16. (9) K. J . hlysels and hI. C . Cox, J . CoZZoid Sci.,in i m s s .
July, 1961
THE FASU SURE ME ST
the lever provide the electric signal. The bridge network is activated by approximately 20 volts d.c. and the strength of the signal is 14 mv. per gram. An external network provides means for zeroing this signal a t any desired weight within the range of the instrument, which is f 2 g. The difference signal was am lified and when desired observed directly on a Hewlett-gackard Model 425A micro-voltammeter, whose noise level is of the order of 0.2 pv. The output of this instrument was generally recorded on a Leeds and Northrup 10 nnv. recorder. This arrangement permitted observation of changes of the order of 0.1 dyne acting on the frame which corresponded to about 0.02 dyne/cm. changes in surface tension with a response time of the order of one second. At this sensitivity considerable drift was observed, however, iinless the dynamometer was thermally insulated. The dynamometer was calibrated frequently by means of directly suspended weights. The displacement of the dynamometer arm was about 0.2 p per dyne which is completely negligible. I n early experiments the frame was manually immersed in the solution and then lifted and suspended on the dynamometer; in later experiments the dynamometer bearing the frame was mounted on a dovetail slide manually operated by a rack and pinion. This permitted immersion of the frame and rapid formation of the film without removing the frame from the dynamometer. The dynamometer was, of course, sensitive not only to the surface tension forces exerted upon the film, but also to those exerted on the frame. In addition, even slight changes in level of the liquid exerted considerable buoyant forces upon the frame. After proper adjustment of the compensating frame (c), these effects did not amount to more than 10% of the total force and were taken into account by blank runs in which the observation frame (a) did not bear a film. The expansion and compensating frames (b) and (c) were made of the same 1 mm. glass rod to reduce buoyancy effects and were arranged so that the upper horizontal part of frame (b) would just tourh the top of the solution and thus assure the formation of a film, while the corresponding part of frame (c) would never touch the solution and thus never bear a film. Both frames were connected to brass rods passing through Teflon bearings in the upper plate and attached to two racks operated by the same pinion so that one frame would move lip while the other was moving down The pinion in turn was operated by a synchronous reversible motor through a multiple speed transmission. A microswitch operated by adjustable pins on one of the racks permitted automatic reversal of the motion of these frames at any desired point. The maximum speed at which the frames could be opeirated was 2.15 cm./sec. and this could be reduced by a factor of 2.5,5,10,20, etc. The width of the film on the extending frame (b) was 2 cm and a convenient height for its travel was 5.5 cm. Hence, this system permitted an 80% expansion of the surface of the solution in 2.5 seconds and an equally rapid return to the original value. Recording of Fringes.-The position of the fringes during expansion and contraction was recorded photographically by the method described elsewheregin which the image of a narrow vertical section of the soap film falls upon a continuously moving photographic film as shown in Fig. 3 . This gives a continuous record of the position of each fringe of the soap film. The record m‘as made either on black and white film with monochromatic light or on color film using white light for illumination. A typical record obtained during oscillation of the expanding frame is shown in Fig. 4. As shown by Fig. 4 there is continuous thinning of the film with time as a result of normal processes such as marginal regeneration. Superimposed on this is the expansion and contraction produced by changes in surface tension. The former must therefore be corrected for and this is done by interpolating, for example, between two crests to get the position that a crest, would have at the time of the mtermediate trough if there had been no expansion. An alternative procedure was to give the extending frame a single stroke instead of oscillation. In this case the rate of thinning before the stroke was extrapolated to the time when the stroke ended. In either case the positions of the fringes then permits construction of a profile of the film before and after expansion from the known thickness corresponding to each fringe. In fact, only relativrs thicknesses are now important. Fig-
OF
FILMELASTICITY FILTER
1109 ,-SQUARE
BOTTLE
t
LLIGHTS
LMOTOR
Fig. 3.-Schematic
top view of apparatus to measure film elasticity.
ure 5a shows schcmatically siich a pair of profiles. The motion of thp fringe, which is a line of equal thickness, is not the same as the motion of the corresponding surface element. The latter can be deduced, however, on the assumption that the amount of liquid in the film from its top to the point of interest remains constant. This amount can be obtained by graphical integration of the profile of Fig. 5a. This integral is shown in Fig. 5b. The difference in height between points of equal volume gives then the expansion of the film a t that height, as shown in Fig. 5c. Finally, the slope of this last curve gives the desired relative extension at any point. -4simplified method of calculation which gives the same results for mobile films within the present over-all accuracy of the experimental procedure, is to assume that the motion of the film element is one-half of that of the corresponding fringe corresponding to its initial position. This is based on the approximation of the film pro!ile to a triangle. In this case it is eitsily seen that the new position of the film element is the harmonic mean of the two positions of the corresponding fringe. For small displacements the harmonic mean may in turn be equated to the arithmetic mean. For rigid films this approximation is too coarse, however. The values reported in Table I were obtairicd using the more exact procedure of Fig. 5. Materials.-High purity lauryl alcohol was obtained from 4pplied Science Laboratories, State College, Pa. Sodium lauryl sulfate was the material prepared by R. J . Otterlo in this Laboratory. The commercial detergent was liquid Luu which is based on sodium alk?l benzene sulfonates with toam-stabilizing and detergency-aiding additives.
Results The results of our measiiremcntq are summarized in Table I. They show that for several systems giving mobile films, whether “piire” sodium dodecyl sulfate or a commercial detergent, the surface elasticity is of the order of 10 dynes/c.m. In contrast, the rigid film of pure sodium dodecyl qiilfate and lauryl alcohol has a film elasticity of the order of 100 dynes/cm. A solution of pure sodium lauryl sulfate containing a quantity of lauryl alcohol insufficient to give a rigid film under the conditions of the experiment gave nevertheless a Pignificant increase in surface elasticity to about 26 dynes/cm. (10)
K.J. Mysels and R. .J. Otter, J. Collozd
Sei , in press.
Fig. 4.-Photographic
3
30 sec.
I-
-.I
record of the motion of fringes of a soap film as surf:w terision is alternately inoreased and decreased.
TABLE I FiLni ELASTICITY MEASUREMENTS Ranee of suriaetant
No. of dctermn.
Commerrinl, 1% Same" Same," 37% glycerol NaLS, 0.29% Same" NaLS, 0.25% LOH, lo-' 70 Same diluted 4:5& Independent mensurrments made
+
21
Strcsaos
d?. dyne cm.
-1
Strains x 10%
ds/s
1 . OF-!). 71 13 2 . 5 -6.4 3 .2& .29 5.8 29 .27-1.3 4.5-18 0.73-14.3 2 ,574.85 12-21 5.8 23 .52-2.8 4.7-20 .73-14.3 13 2 . 2 -5.4 5.2-11 .73-14.3 6 months earlier. Rigid film (all others are mobile). 0.474.51 .21- .43
8.2-1G G.9-13 10-11
Times of elongation. QeD.
F i l m elsstieity, 2
Mcdin", dyne ern.-1
9.8 6.4 5.5 15
8.8 20 100
dr/(ds/a)
Yo Deviation
Au.
Mar.
13 18 3 12 8 14 18
20 52 6 43 8 31 35
may descend as tear drnps to their corresponding level in the bulk of thc film nnlcss t,heyarc prompt.ly resorbed by t,he border. No significant behavior of this type was observed, however, in our normal determinations. As far as the turbulent side borders are concerned, their effect was found to be negligible by comparing the behavior of films of different widths under the same conditions. Our procedure is dependent on the change of surface tension which occurs when the bulk solution surface is extended. I n principle some change Fig. 5 . S c h e m a t i c of the graphical translation of move- would be expected even for a pure two component ment of fringes into extension of film element. system dne to the well known difference between dynamic and static surface tension and the finite Discussion time required to replenish an expanding surface. Our assignment of the extension (strain) of t.he However, we find that in our case the recovery film depends on the assumption that no liquid en- time was of the order of 10 seconds or so which ters the film during the process along the upper makes it very likely that the surface tension edge of the frame or along its sides. The validity changes were largely due to a minor component. of t,his assumpt,ion is supported by the absence of It is t,herefore qnite possible that in a pure two any marked anomalies in the extension curve (Fig. component system the method used would not give 5c) and by visual obscrvations as far as the quies- a sufficient change in surface tension t,o produce a cent upper border is concerned. If very large measurable extension of the film. There are, howforces are applied to t,he film, onc can see visually ever, other methods which can bc used1*to lower that fresh areas are pulled out from t,he upper the surface tension of a solution without affecting border. Being pulled out rapidly, these films are (11) Ref. 8. p. 55; and ref. 9. relatively thick aerording to Frankel's law" and (12) R d . 8 , p. 81. P S,,"
THEMEASUKEMENT OF FILMELASTICITY
July, 1961
1111
replace dL/L by ds/s and F / C by y;6 where 6 is the thickness of the film. Hence for a film of 1 p thickness extending by 20% in one second, which represents rather extreme conditions, the increase in surface tension generated by viscous forces dyne/cm. in m-ater of 1 cp. would amount to viscosity aiid to lo3 times more in pure glyceiol, which would still be negligible in our measurements. That bulk viscosity does not complicate our measurements in other ways either is further indicated by the fact that measurements in a 30% glycerol solution noted in Table I did not show any qignificant effect upon film elasticity. The most significant difference in film elasticity is between the rigid film, 100 dyne cm.-I, and the mobile films which are 4 to 20 times more yielding. That this is not an artifact produced by some undetected effect of surface vixoeity on our determination is shown by the fact that the mobile films themselves display a fivefold range of elasticities despite their relatively minor differences in surface rheology. The marked increase in film elasticity upon addition of lauryl alcohol to sodium lauryl sulfate solution indicates also the possibility of another factor explaining the well known increased stability of these mixed filmslj in addition to the generally accepted effect of surface rigidity and the resulting dower rate of drainage. In the present state of development the precision of the method leaves much to be desired and values reported for a given qystem are significant only to about =+=257,. About 570 of this uncertainty is due to the difficulties of measuring the photographic film, of graphic integration, and in general to the interpretation of data. once obtained. h somewhat larger uncertainty is attached to the obtaining of the data themselves, i.e , their reproducibility when the experiment is repeated immediately under the same condition-. h rnuch larger uncertainty is associated, however, with the application of the same conditions at different times. Clearly, there are significant factors in the history and purity of the surface which we haLe not yet learned to control. This in turn has prevented the study of such factors as the rate of extension or the extent of stretching which seem t o have some effect upon the result. However, this uncertainty of some 2:%, although very disturbing, is small compared to the 20-fold changes in film elasticity which we have found 1,etween the extremes of our systems and we are nom able at least to assign approximate values to a quantity tlL 1 F _ = _ _ whose order of magnitude mas previously unknown. I, dt x c Acknowledgment.-It is a pleasure to acknowlwhere A , the qoefficient of viscous traction, is edge the stimulating discussions with Professor given by X = 3 where 7 is the ordinary coefficient wit!-. Tor oitr purposes we can J. Th. G. Overbeek during the course of this work.
the nature of the observed film, such as dilution or addition of a more active surfactant. Hence, a proper modification of our method could still be iired i n that caye. Furthermore, really pure two romponent systcims of aqueous surfactants are not readily prepared or studied and our procedure ihould be applicable to almost all normally encountered syqtemq. I n fact, our sodium dodecyl d f a t e seems extremely pure as far as bulk criteria :ire concerned. Ais mentioned earlier, film elasticity may be either a dynamic effect-the difference between dynamic and st,itic surface tension-or an equilibrium one, the depletion of the intralamellar solution. I t is likely, though not completely certain, that oiir method nieamrec the latter. This conrlusion is based on three arguments. First, the iame change in surface tension corresponded to almost doubling of the bulk surface but to only .j-2070 changes in film area. Hence a different limiting factor, presumably depletion of the intralamellar liquid. must have been effective in the film. Second, an order of magnitude calculation13 shows that in a film dynamic effects should last millihecontls and thus could not be observed in our qyqt em unless some unsuspected energy barrier is eiicouiitercld. Third, we could not notiae any relaxation of film elasticity either when the bulk surface K I ~ exlended and kept in the extended state so that bulk surface tension was decaying - l o ~ l y or , vhen the bulk surface tension was kept at a constant aiid higher \-slue by continually extending the surface manually. Both of these mperiment5 were, hoTverer, difficult to evaluate and hn arguiio definiteness ('an be claimed for them. ment against this conclusioii is that we have not found any ptrong dependence of film elasticity iipon film thickness aq would be expected from the depletion theory for a two component system. However, the eilfect becomes understandable if attributed to a minor third component which is subqtantially n b w d from the intralamellar solution and present 011ly in the surface. This would make the beha1;ior of the film dependent on the fact that it is thin but not on how thin it is. -4s mentioned earlier, high bulk viscosity as en(miiitered in polymers and glasses, may generate a iignificant force opposing the extension of the film. For liquicls of low viscosity, such as water, and e~ en for glycerol, thi5 effect is, however, negligible, as shown by the following calculation. According to Trouton14 the rate at which the length L of a ciylinder of croscs section C and subject to a force F rhangei TT-ith time t is given by
(17) Rrf 8 11 16 I 141 1 T Tio i t o n t'
or
K o q h o c ( L o n d o n ) A77, -126 (1906).
(15) E o . , A. G Brown. FtT. G Thuman and J. S c i , 8 , 491 (1953).
W.3IcBatn J Collozd
