Juiic, 1952
CRITICAL
MICELLECONCENTRATIONS
Rate 7 was obtained with 6, X 10-8 gram atom of cobalt and 2 X 10-6 gram atom of iron as hydrous oxide. This rate was not first order but gave a curve when plotted as t,he other rates were. The experimental curve is shown in Fig. 3 along with the curve obtained by subtraction. The latter curve indicates an initial first order rate having a constant of 0.69 and a half-life of one hour. The half-life of the subtracted curve is 5.8 hours. The experimental conditions for rate 7 were thosc for a point on a n isotherm above the region of cobalt ion to adsorbent ratios in which Henry's law holds. Under thcsc conditions, the cobalt adsorbed a t equilibrium is not directly proportional to its concentration in solution: thc unreacted adsorbent is not in large excess but is significantly reduced by the cobalt adsorbed. It seems then that the initial rapid first order ratc is due to the adsorbent, the cobalt ion being in excess. After 5.4 X 10-8 gram atom of cobalt was gram atom in solution, the rate adsorbed, leaving 1 X bccamc expcrimentally first order with respect to cobalt and its half-life was 5.8 hours. Refercncc to Table VI11 shows that this half-life lics bctwcen thosc obtained for 1 and for 0.5 X 10-6 gram atom of iron as hydrous oxide when tho total cobalt uscd was 2.8 X 10-9 gram atom.
BY B U B B L E P R E S S U R E h'fETHO1)
701
m
It is a pleasure to aclinowledge the continued interest of Professor Ed. Mack, Jr., in thiswork. This research \vas supported in part from funds granted
CltI'l'ICRL MICELLE CONCENTRATIONS BY -1 BUBBLE PliESSUltE METHOD BY A . S.BROWN, R. U. ROBINSON, E. H. SIROIS,H. G. THIBAULT, FV. MCNEILLAND A. TOFIAS JIcGregory Hall of Chemislry, Colgale University, Hamilton, N . Y . Received J u l y $0, 1961
The bubblc pressure method of measuring surface tensions has been modified by using it kinetically. The air pressurc needed to maintain a stream of bubbles in a surfactant solution is a complex function of concentration and bubble rate. Plots of bubble pressure against concentration have been obtained for the commercial cationic and anionic materials laurylpyridinium chloride, Santomerse #3 and Tergitol TMN-050. The major discont#inuitieswere confirmed as critical micelle concentrations by conductancc measurements for the L.P.C. and Santomerse. This techni ue shows considerable dctail in thc pressure-concentration plots, possible rcasons for this being considered. The utility of %e method for solutions containing clectrolytes has been examined briefly for Saiitonicrse in 1.84% sulfuric acid.
This Laboratory has recently been interested in the behavior of surfactant systems, particularly under non-equilibrium conditions which resemble practical applications of such agents. This study was initiated in the belief that the pressure required to eject a stream of air bubbles through a given orifice submerged in surfactant solutions would be such a function of both the concentration of the solution and the rate of bubble formation that the dependence of pressure upon concentration would change markedly a t thc critical micelle coiicentration a t some critical bubble rate. During the first experimental work it was noted that a number of reproducible irregularities appeared i n the plots of pressure against concentration and it was believed that these might correspond to the formation of different micelles. To test this interpretation it was decided to measure electrical conductances paralleling the bubble pressure studies since sharp discontinuities in the conductance plots clearly indicate the sudden formation of new species. The correlation between breaks in the two types of plots is encouraging.
Experimental The bubble pressure apparatus i s depicted in Fig. 1. The bubblc-forming orifice comprised standard tubing, ther-
mometer tubing or 22 gagc B & D hypodcrmic needles, the tip being immersed to a known dept,h of 3 to 10 mm. in the solution. The needle hub was attached horizontally to glass tubing by De Khotinsky (medjiim) cement, as shown separately on an enlarged scale 111 Fig. l . Air pressure was measured on a simple manorncter such as Cenco #73840 against, atmospheric pressure, the open end being either free (for major adjustments) or restricted by a capillary to minimize pulses during readings. Air was supplied at a rate controlled either by a sensitive long-arm screw clamp on a supply from a Kipp generator opcratcd with water or preferably, aR shown in Fig. 1, by water displacement of the air in a 1or 2-pintswide-mouth vacuum bottle. Tho Iat)t>crtcchniquc pcrniitt,cd inscrtion of a manifold of rcstrictivc capillary tubes abovc the vacuum bottle and in tho water line from thc constant head supply permitting a rapid shift from onc water dropping rate to another wit.h a minimum of delicatc adjustment. The constant head water supply was a Matviakl unit wit,h t,he lower end of the water leg, the dropping tip, adjusted vertically to compensate for changes in the manomet,ric pressure. Rate of water flow could be checked by counting drops. Glass tubing was connected with rubber tubing, and scrcw clamps, markcd "X" in Fig. 1, served as valves. Conductance measurements were made at 1000 cycles with student-grade boxed slide-wires opcrated near mid-point, adequate decade resistance boxes and Wagner grounds. Calls generally comprised Pyrex flasks with small dependent bulbs containing the Pt hlacked electrodes connected to the bridge circuit with mercury fillcd side arms. Water-bath t,hermostats maintained a temperature of 25.00 f 0.02'. (1)
BI. hlatviak, Chemist-Andust, 40, 24 (1951).
II Needle -6$) tip Fig. 1.-Apparatus
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Dewar
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for bubble pressure measurement.
Surfactants were commercial materials. Solutions were prepared from stock solutions whose concentrations were calculated on a dry basis after moisture estimates were obtained on other samples by prolonged drying a t about 60". Conductivity water was obtained by passing distilled water through a Barnstead "Bantam" demineralizer and had a conductivity about 8 X lo-' mho cm.-1. I n conductance work all glass containers were steamed after cleaning. There was no evidence of significant adsorption of surfactant on glass with the possible exception of the very lowest concentrations in the conductance measurements. It may be noted that the accuracy requirement on concentrations is only that demanded for assignment of critical concentrations.
Results (A) Laurylpyridinium Chloride.-Laurylpyridinium
chloride (L.P.C.) was selected as an important, cationic surfactant. The results of bubble pressure measurements on solutions of L.P.C. are plotted in Fig. 2. These data were obtained with a capillary comprising a roughly 3.5-cm. length of thermometer tubing having a bore 0.027 cm. The plots of pressure against surfactant concentration (log scale) show a n initial rapid decrease in pressure to a short plateau, a second drop to a longer plateau and finally a gradual approach to a low pressure. Discontinuities appear a t conI
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[ I I I I
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110-2
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90
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1
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1
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88 86
5
84
U
82
z 5 $ 80
2 78
I I I I I I
1 10-3
centrations 4.4 X 10-8, 5.7 X 10-3 and 8 X 10-3 molar. The second of these is particularly accentuated at higher bubble rates. At an infinitely slow bubble rate this technique becomes a traditional surface tension measurement. The trend of the plots a t slower rates is consistent with the form of equilibrium surface tension curves. Attempts to use higher bubble rates were not satisfactory as results scattered widely, probably because of inadequate rate control chiefly, since a t the time this work was done the rat,e had to be set manually for each measurement and there is an astonishingly sharp upper limit t o counting rate. It is int,eresting to note the overshooting of the pressure drop a t 4.5 X 10-3 M , the system acting as though a slight excess of a presumably simpler solute form must be present before effecting the change t o a second structural form. The conductivity data for L.P.C. are presented in Fig. 3. These results, which were obtained before the pressure data, were initially interpreted as indicating a single break a t a concentration 0.0051 M , with rounding possibly due to a n equilibrium between molecular and colloidal species. The detail shown by the bubble pressure plots now indicates that the conductivity results should beinterpreted as a series of linear segments with breaks a t 1 / M about 0.063 and 0.088, corresponding to molarities 0.0040 and 0.0077. This interpretation, allowing for the difficulty in fixing intersections of lines of only moderately differing slopes, confirms rather well the critical concentrations obtained by the bubble pressure technique. I t will be noted that there is an indication of an intermediate break a t about 5.2 X 10-3 molar but the data hardly warrant such an assignment. While it was not the purpose of these measurements t o fix the conductance a t infinit.e dilution such a n extrapolation gave a limiting mole-', the limiting value between 89 and 90 mhos slope being roughly 25% above theoretical.
10-1
Molarity. lpig. 2.-Bubblc preaaurc~for L.I'.C, tinic for 10 ~ u I J I J I ~ s : 0,5 sec.; 0 , 10 acc.; 0 , 16 scc.
76 74 Y
0
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I I I 6 7 8 9 lOO&f. Fig. 3.-Conductance of L.P.C. a t 25".
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(B) Santomerse #3.-Santomerse #3 was selected as :til example of a n alkyl aryl sulfonate available with a low dcgree of inorganic contamination. Its moisture content was 1.5%. For purposes of calculating molarities the molecular weight was taken to be 348.5. A preliminary exploration of this material by the bubble pressure method, covering the concentration range 3.2 X 10-6 to 3.2 X 10-2 M , was obtained with a vertical capillary of 10.75 cm. length, having a bore 0.0316 em. and a n external diameter 0.567 cm. Bubble rates of 4 and 5 seconds for 10 bubbles were used. These results are plotted in Fig. 4 togethcr with data obtained with a horizontal tip comprising :I 0.3-cm. Icngth of 22 gagc stainlcss hypodcrmic ncedlc a t a rato of 1.5 seconds for 10 drops of air displuccnient watcr.
TO3 I
Ill1
1-
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Ill111
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100
90
3 E‘ so
70
a .-C 60
50
40
60
0.161
0.0522 Fig. 4.-Santomerse
0.641 1.61 3.22 6.41 16.1 32.2 Molarity x lo3. bubble pressures a t rates of 10 bubbles in: 0 , 4 sec.; 0, 5 sec.; a,15 sec.
I t again appears that the higher rates of interface forination show greater complexity in such plots and that there are a number of concentration regions requiring more detailed examination. The needle tip also showed greater complexity in these plots a t higher rates and in the lower concentration range but this tip is more difficult to operate under such conditions. Rates set with such widely differing tips are, of course, only roughly comparable. The concentfration range 2.6 X 10-4 t o 8 X Jf vias examined in more detail with the glass tip, the results being plotted in Fig. 5 for rates of 4 and 12 seconds per 10 bubbles. The pressures for distilled water were 109.2 and 98.2 mm. HzO for these rates, respectively, the difference reflecting change in kinetic head and, particularly, changes in the niounting of the capillary which sliows sensitivity to angular I
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deviation from vertical. While this sensitivity affects tlic pressure level and range somewhat it does not seem to affect the critical concentration estimation. These results show a downward break a t about 4.2 X 10-4 M and the formation of a plateau a t about 6.4 X 10-4 M , this plateau being more prominant a t higher rates (as confirmed a t other high rates not plotted) than a t the lowest rate used. The unexpected steeper slope of the low concentration branch of the plot a t the higher bubble rate is confirmed by the drop in these
-oa$
60
50
40
“4-
30
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2.55
Fig. 5.-Santomersc
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6.44 9.06 Rlolarity X IO4. detail ut rates of 10 bubblcs in: 0, 4 see.: a,12 SCC.
10 20 30 40 Molarity X lo4. Fig. 6.-Saiitoniersc detail at rat:, of 10 bubLlcu in: 0, 2.7 sec.; a,4.1 SIX. 6
8
E. H. SIltOIS, H. G. THIBAULT, W. MCNEILLAND A. l 704 A. S.DltOWN, R. U.I~OBIR’SON,
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tion form a t decreasing rate of interface formation. An attempt was made by D. L. Hoyt in this Laboratory to use the dye solubilization technique on this surfactant. While this method has been generally unreliable here it ia interesting that there were indications of a discontinuity in solubilization a t about 0.07y0 and t,hat solubilization was increasing between 0.01 and 0.04%. This feature is confirmed by the bubble pressure results since the pressure in water was 110 mm., a value considerably higher than in 0.03%Tergitol solution.
(D) Summary of Results.-For purposes of facilitating comparison of the results obtained by the different experimental methods the concentrations a t G which anomalous behavior was observed. the “critical” concentrations, are collected in Table I. It will be noted that the sevcrul techniques gave results agreeing \vi thin about
L 4 5
100d1M. Vig. 7.-Santomerse
) proaches equilibrium surface tension-concentra-
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conductance a t 25 ’.
prcssurcs from that observed in water. I t may be significant that the high rate plot shows more prominent overshooting in the pressure drop a t 6.4 X 10-4 ill. I n any event it appears that these very dilute solutions are somewhat more effective at higher rates of interface formation, a conclusion also obtainable from Fig. 4. The concentration range 6.5 X 10-4 to 2.9 X 10-3 M was studied in detail with the needle tip a t the high ratcs 2.7 and 4.7 seconds per 10 drops of air displacement watcr. These results, plotted in Fig. 6, show erratic behavior a t concentrations below about 7 X 10-4 M . At higher concentrations they are reasonably consistent and indicate a downward break at about 9 X 10-4 M , a short plateau from ill and a subsequent downward about 1.9 to 2.3 X break. There IS evidence for the existence of addit,ional complexity in these plots. Conductivity measurements on Santomerse #3 were made two years before the bubble pressure results were obtained but the conclusions were not available until afterwards. These data, plotted in Fig. 7, clearly indicate two breaks, one a t about 9.1 X 10-4 M and another a t about 2.0 X hi‘, agreeing quite well with the more prominently critical concentrations estimated by the bubble pressure mrthod. The conductivity data show no break below 9 X lo.-‘ Jl but such measurements become increasiiigly inure difficult a t these dilutions while the need for prccision increases because the slopes are low. At the l o w s t concentrations adsorption becomes troublcsome; the csperimental limiting slope being only 3/4 of the theoretical value. It seems worthy of nohe that mildly erratic hehavior in the conductivity measurements, over the conccntration range studied, is observed a t the same concentrations which exhibit minor uncertainties in bubble pressure plots. These concentrations may well be signifi-
TABLE I SUMMARY O F CRITICAL CONCENTRATIONS BUlJblC
Matcrid
pressurc
L.P.C.
4.4 8.7 8
Santoinorse Y3
Tergitol-TNN
x
10-8
Expcriinental nietliod ConSoluduotance biliaation
nr
x
10-3 Of
I?
7.7
4 . 2 X 10-4 M 6.4 9 2 x io-: M 7.5 X
4.0 (8.2
%
9.1
2.0
x
x
nr
10-4 10-3 M
-7
x
lo-’ %
lo%, this being considered reasonably satisfactory for the present objectives.
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et
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OLtIlli.
A fragmentary study of Santomcrse #3 in solutions .s 60containing 1.84% H2S04was made to test the su,itability i2 of the bubble pressure technique for systems of hlgh elec- 2 t.rolyte cont.ent. Thesc data, taken with a. needle trip, arc % plot,ted in Fig. 8. These results wwc obl#aincdbefore thc k detail in the region 5 X 10-4 to 10-3 Af was appreciat,ed and the dotted portion of the plot is merely speculetivc. Thc rneasurenients are significant in showing the subst.ant,ial effect of the acid in emphasizing a low-conccntratioii drop in bubble pressure and in accentuating changes ncar 1.5 X 10-3 Af that are minor in simple aqueous solutions of this surfactant. ( C ) Tergito1.-A sample of Tergitol marked TMN-650 40 by the manufact,urer2was used in bubble pressure experiment,s with the 0.027 cni. bore capillary, to examine the behavior of a non-ionic surfactant. These data are plotted b I l l l l 1 I A in Fig. 0. The i,csultms show an accentuat,ion of the break 5 7 10 20 30 a t about 7.5 X 1 0 - 2 wt. yo when rate was increased and Molarity X 10‘. possibly the existence of a critical rate of about 10 bubbles in 4 seconds. At high bubble rates and higher surfactant Fig. 8,-santomerse in: 0,~ ~ 0 ,01.84% ; H~SO,at a rate of Concentrations foaming became excessive and pressures 10 bubbles in 8 sec. mere erratic. The region 0.2 t o 0.3 wt. % appears to have interest but was not studied a t this time. Again Discussion it will be noted that the pressure-concentration plot ap~l~~ main objective of the present illvestigatioll
2 -
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(2) Carbide and Carbon Clleiirical Corporation.
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appears to have been attained in that a kinetic use
~
June, 1952
CRITICAL MICELLECONCENTRATIONS BY BUBBLE PRESSUEE METHOD
705
of the bubble pressure method of measuring surI 1 I I I I l l I I I I I I I I face tension shows the presence of critical surfactant concentrations which correspond fairly +-----4 well with critical micelle concentrations deter06mined by conventional methods. The importance of this lies in the suitability of the bubble pressure technique for systems containing electrolytes, which render conductometric and osmo- 6 80 metric methods inoperative, and systems con9 taining other light scattering particles which E' vitiate nephelometric approaches to this prob- E lem. It is believed that the method has particu- :' 70a, lar merit for evaluating surfactants which are 5 intended for use in processes characterized by the rapid formation of new interfaces. 01 60The bubble pressure technique has shown a more detail than had been anticipated. While 5 this was originally ascribed to experimental uncertainty it has become increasingly evident 50 that at least much of the detail is real. However, an unequivocal explanation of the breaks in the pressure-concentration plots is hardly available a t this time for two reasons. The 40materials studied have been commercial prodI I I I I I II I j I I I I j I ucts which may safely be assumed to have vari0.03 0.1 1.o ants in surfactant structures and some inorganic Weight per cent. The former might account for Fig. S.-Tergitol at rates of 10 bubbles in: 0, 15 sec.; 6,8.1 variations in the central concentration range see.; (3, 5 sec.; 0 , 4 see. of Fig. 6 while sulfate ions might cause thve observed behavior'in Fig. 8 at about 1.5 X 10-3 attainment of some minimum interface concentramolar. This, of course, is pure speculation. tion required for effectiveness. Diffusion of surSecondly, the introduction of kinetic factors gives factant t o the interface and its orientation may be prominence to the rate of Orientation of surfactant expected to lower this minimum concentration as at the air-liquid interface, with several orientations rate of interface formation decreases. At and being possible. Furthermore, the question as to above a critical micelle concentration the supply of the equality of bulk concentration with that in the surfactant to the interface should become less sensineighborhood of the orifice remains unanswered. tive to gross concentration since one micelle provides The bubble stream provides substantial agitation many molecules. The effect of rate of interface and efforts to increase this significantly with added formation then should reflect largely the rate of mechanical stirring resulted in erratic shearing of distribution of molecules from micellar to interface bubbles from the orifice tip. orientation. In the event that micelles are formed A general approac,h to the interpretation of the before the interface attains its minimally effective bubble pressure-concentration plots may be at- concentration the bubble pressure should drop very tempted. At sufficiently lorn gross concentrations sharply at the critical micelle concentration. and at sufficiently high rates of interface formation The existence of several sequences of the presboth concentration and orientation of surfactant sure drop and plateau behavior argues compellingly at the interface will be too small to lower bubble for the recognition of several types of micelle strucpressure from that in water. While these factors tures. The major critical concentrations estimated are not completely separable increase of gross con- by both bubble pressure and conductivity techcentration a t constant bubble rate should affect niques for L.P.C. and Santomerse are in a roughly primarily interface concentration and produce a 2 : l ratio. This might indicate a doubling of the lowering of bubble pressure. Downward breaks micelle, presumably more readily possible for lameliii the plots may be interpreted as marking the lar than for spherical structures. ~
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